tag:blogger.com,1999:blog-24329768030392595142024-03-14T17:42:04.555+08:00Singapore MathNews and Views about the Good, the Bad, and the Ugly about Singapore MathSingapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.comBlogger77125tag:blogger.com,1999:blog-2432976803039259514.post-52185275645910770072024-02-19T19:56:00.000+08:002024-02-19T19:56:29.489+08:00Thou shalt not use an arrow for an equal sign!<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhICabg_tShXbGHldR46H8V1PHaSUjGfldsuzKD0kvexVpGZiovJbfjloH8zKgYOrLQvuhuSr7TBkDOyMKSzbv_x-TtX6Zyj72fZk16OX6WeIpyZGzbqtdRVFZPcSAEpGOVJimdgfroGH56quUGrUVIFRfA085lboHOA_4f-DnDY63XswQdAP5F2IwGdZw/s2109/IMG_5996.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2109" data-original-width="1284" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhICabg_tShXbGHldR46H8V1PHaSUjGfldsuzKD0kvexVpGZiovJbfjloH8zKgYOrLQvuhuSr7TBkDOyMKSzbv_x-TtX6Zyj72fZk16OX6WeIpyZGzbqtdRVFZPcSAEpGOVJimdgfroGH56quUGrUVIFRfA085lboHOA_4f-DnDY63XswQdAP5F2IwGdZw/w390-h640/IMG_5996.jpeg" width="390" /></a></div><p style="text-align: center;"><small>Shot from Tiesha Sanders/Facebook</small></p><p>The above <a href="http://tinyurl.com/5ebnw7fd " target="_blank">grade one math question</a> from Texas is debatably ill-posed. However, the child answer of “7 ones” is “non-mathematically creative” or “irreverently correct.”</p><p>The teacher’s reply to the mother that “… this is the new math they have us teaching.” would puzzle many math educators outside TrumpLand. Arguably, the correct answer to this routine question has little or nothing to do with “new math” or “new new math” or whatever politically correct mathematical term we want to christen it.</p><p>The child’s “correct” answer that was marked wrong by her teacher defies logic. The use of an equal sign instead of an arrow would have minimized any misunderstanding whatsoever.</p><p>In “fine” Singapore, few teachers and parents would disagree that similar grade one place values questions are deemed routine. The chances of any local school teacher or tutor using arrows rather than equals signs for these drill-and-kill questions are quasi-zero.</p><p>Even for this ill-posed elementary math question, in the first part, if a child has correctly inserted the digit 7 under the ones column, and to expect them to give the same answer for the fill-in-the-blanks for the number of ones, it doesn’t sound too logical or commonsensical. The problem poser is unlikely to ask (or expect) for “7 ones” twice!</p><p><br /></p><p><b>MAGA math: 7 ones ✔️</b></p><p>Insisting that the answer of “7 ones” is equally valid as “27 ones,” or denying that “7 ones” is incorrect, due to the way the question is posed, sounds like the mathematical equivalent of an ex-president insisting that he didn’t lose the election, albeit all the facts or results proved otherwise.</p><p>If the child isn’t wrong (because the parent isn’t wrong), and the teacher, too, isn’t wrong, so who’s right then? <i>Could two conceptual negatives give a concrete positive?</i></p><p><i>Logically & truthfully yours</i></p><p><small>© <a href="http://singaporemathplus.net" target="_blank">Yan Kow Cheong</a>, February 19, 2024.</small></p><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-82495323586578342042023-12-18T14:56:00.000+08:002023-12-18T14:56:52.098+08:00Did You Commit a Prime Murder?<p>More than half a dozen years ago, I coined “Prime Murder” as follows:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxkIzdKGpuuMDfYKZlj4JRZJgf6bAWq6vLHIlh8gHdN2wBRrCxYEhwdqwz7SRKpD9vjWmJNIbLdf3PwKzkTR-p1OPrcNl6fV3gBuXgYdokW8me_56tjYkr6TB-y7ElsBFBvfESW6AkjLPnhGp90qlh4JpC251vMw3rb1GI9ZvBmE70IZGDMmoh6eWA_Zo/s1642/IMG_0705.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="485" data-original-width="1642" height="119" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxkIzdKGpuuMDfYKZlj4JRZJgf6bAWq6vLHIlh8gHdN2wBRrCxYEhwdqwz7SRKpD9vjWmJNIbLdf3PwKzkTR-p1OPrcNl6fV3gBuXgYdokW8me_56tjYkr6TB-y7ElsBFBvfESW6AkjLPnhGp90qlh4JpC251vMw3rb1GI9ZvBmE70IZGDMmoh6eWA_Zo/w400-h119/IMG_0705.jpeg" width="400" /></a></div><p>What proportion of integers are prime? What are the odds that you might commit a prime murder at some point in your mathematical career, be it in teaching, editing, or writing?</p><p>Over the centuries, both professional and amateur mathematicians weren’t spared from it. Think of Pierre de Fermat who erroneously thought that 2^(2⁵) + 1, or 2³² + 1, was a prime.</p><p>So, for the majority of us, whether we’re born or blessed with the “mathematical gene” or not, the chances of being found guilty of a prime murder might not be limited to a single-digit percent. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAjCMWOcakYxImXgC0tpZo67gSZE0s9IrR1djrTyW4lHvIUMJ-avZIX1ByvQfijnCmdRlmjQmhJpNpDolj3KBvBJNWu0lMmVJa0dDLheF5J4kboN76oh9m0MdTn1nGHM8ZGn92pZeqCVm_khh-1cGr-v-VSj-mSQ-TD6O674J3hOp997q4OMXzcaOVQ68/s1631/IMG_5748.jpeg" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="1631" data-original-width="1284" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAjCMWOcakYxImXgC0tpZo67gSZE0s9IrR1djrTyW4lHvIUMJ-avZIX1ByvQfijnCmdRlmjQmhJpNpDolj3KBvBJNWu0lMmVJa0dDLheF5J4kboN76oh9m0MdTn1nGHM8ZGn92pZeqCVm_khh-1cGr-v-VSj-mSQ-TD6O674J3hOp997q4OMXzcaOVQ68/w252-h320/IMG_5748.jpeg" width="252" /></a></div><p style="text-align: left;"><small></small></p><center><small><i>A 2019 graphic novel that explores two most basic mathematical objects: integers and permutations</i></small></center><p style="text-align: left;">Below is a simple exercise that might help reduce the odds of someone being a “prime murderer.”</p><div><p>1. Which of the following numbers are prime?</p><p>a) 919 b) 1,001 c) 1,763 d) 3,221 e) 8,081 f) 123,321</p><p>2. MAGA Math</p><p>a) The Pinocchio-in-Chief faces 91 criminal charges across four indictments, all of which he had pleaded not guilty. What are the chances that he is a <i>prime</i> suspect to these charges?</p><p>b) A “very stable genius” claimed to have an IQ of 211 (base <i>p</i>). Find the value of <i>p</i>.</p><p>c) The “MAGA-in-Chief” wanted a Secretary of State to <i>find</i> 11,780 votes, which would have given him one more than his Democratic opponent. Show that the requested number is not a prime number.</p><p>d) A judge determined that the ex-“Commander in Cheat” had overvalued his Mar-a-Lago property by 2,047% besides claiming that his penthouse in New York was three times its actual size. Is this a “prime percent”?</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSIv_eGXT3ipkMYDfSr20XpdOUW2bKfg4AU3XrvrPs6JYyeWEYOIBSP-MnuAmKrx7Sb8VHmzxfgwUgWZJSPgbepJA6DzMm1BGp8MEW3p70azqajWrqJnoIswCG_qy5fWwVPZ7P8TIb4c3BGNNVM_K-8HiS7TBjuFKvHnulB1V0KwqVoZ9zNgCJiUKynEY/s2757/IMG_5750.jpeg" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="1416" data-original-width="2757" height="205" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSIv_eGXT3ipkMYDfSr20XpdOUW2bKfg4AU3XrvrPs6JYyeWEYOIBSP-MnuAmKrx7Sb8VHmzxfgwUgWZJSPgbepJA6DzMm1BGp8MEW3p70azqajWrqJnoIswCG_qy5fWwVPZ7P8TIb4c3BGNNVM_K-8HiS7TBjuFKvHnulB1V0KwqVoZ9zNgCJiUKynEY/w400-h205/IMG_5750.jpeg" width="400" /></a></div><p></p><p style="text-align: center;"><small>In <i>Prime Suspects, </i>when Prof. Gauss & team looked at the autopsies of the victims of two seemingly unrelated homicides, they discovered the shocking similarity between the structures of each body.</small></p><p>Let’s end with a <i>prime factoid</i>: The writers of <i>The Simpsons</i> and <i>Futurama</i> have been smuggling complex mathematical ideas into prime-time television for over a quarter of a century.</p><p><i>Primely yours</i></p><div class="separator" style="clear: both; text-align: center;"></div><p><small>© <a href="http://www.singaporemathplus.net" target="_blank">Yan Kow Cheong</a>, December 18, 2023.</small></p></div><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-45703401829303806232023-10-16T02:30:00.000+08:002023-10-16T02:30:36.019+08:00A Singapore Grade 4 Geometry Question<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3VNzWB7HG0loMhzpB57_27vipMwUDPl8Fb-HRqBJSXtijtVpcIaEWC9jMCcAzUv_N9xQf0Uqzc-Kb3A95DHdUs51CVCBIYjJ-w55sBfBxDBuyG4D7KG6-vlmAG5_XGHP4Uq3TBU0NVsyzxC4CRGFPVzqN5XpnZuf1lUz81Vc5au0reTC4_iLI0MYCgf0/s1080/IMG_5689.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="858" data-original-width="1080" height="254" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3VNzWB7HG0loMhzpB57_27vipMwUDPl8Fb-HRqBJSXtijtVpcIaEWC9jMCcAzUv_N9xQf0Uqzc-Kb3A95DHdUs51CVCBIYjJ-w55sBfBxDBuyG4D7KG6-vlmAG5_XGHP4Uq3TBU0NVsyzxC4CRGFPVzqN5XpnZuf1lUz81Vc5au0reTC4_iLI0MYCgf0/s320/IMG_5689.jpeg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><p>On Facebook, someone recently posted the above primary 4 (or grade 4) geometry question, asking for help from fellow parents. <i>How would you do it (without calling on ChatGPT)?</i></p><p>If you’re a parent, homeschooler, or tutor, how would you explain it to an eight- or nine-year-old child, who’s struggling with non-drill-and-kill questions on area and perimeter?</p><p><f4><i><b>Give It a Try First!</b></i></f4></p><p>Try figuring out the answer on your own first before peeping at two <i>parents’</i> quick-and-dirty solutions below. Better still, could you present an idiot-proof or peasant-friendly solution that even a smart dog or cat could understand?</p><p><br /></p><p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4rFxjd9T7G40sgEyQHb2ul09yuErMGBEaRLwbKNGep2wnlXRUx9BheA4qt3idAJea3p3VeyySWz38JBVajgWJ7HUqeVZrwgdJiEAwaWbGxrSIcsGWoP-V2Lw3qF4anieMLOPC49JjwEcRw0cDIWnQVucOpw4cXMie8-bznNatyY0g4VLe4ZRaFo2-SXY/s540/IMG_5691.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"> <img alt="Solution by Belinda Sim" border="0" data-original-height="436" data-original-width="540" height="258" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4rFxjd9T7G40sgEyQHb2ul09yuErMGBEaRLwbKNGep2wnlXRUx9BheA4qt3idAJea3p3VeyySWz38JBVajgWJ7HUqeVZrwgdJiEAwaWbGxrSIcsGWoP-V2Lw3qF4anieMLOPC49JjwEcRw0cDIWnQVucOpw4cXMie8-bznNatyY0g4VLe4ZRaFo2-SXY/w320-h258/IMG_5691.jpeg" width="320" /></a></p><p><br /></p><i>Solution</i>:<p></p><p>6 width and 6 long = 3units of the rectangle.</p><p>1 rectangle -> 16cm.</p><p>3 rectangle </p><p>16x3 = 48cm.</p><p><br /></p><p></p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEAHl9qiifUezUzkTWd-YEIlGa5Mxe3-Q-RrEzftQJFqCx9D4PFlqjGb7-CtWcG9fkwdYA2SplyPxWwHmdInJcrTbKcxj3QU_jvJ5mPZ9SS_vj-i0d8NUWlAYRfrsMe59vZAmL2nFnIK0HcXEaJh8eGqejNRXKWJDFZxMdeJj5EOVTzJ1piBnfHHUjd9o/s719/IMG_5690.jpeg" style="margin-left: 1em; margin-right: 1em;"><img alt="Solution by Jesline Ang" border="0" data-original-height="719" data-original-width="697" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEAHl9qiifUezUzkTWd-YEIlGa5Mxe3-Q-RrEzftQJFqCx9D4PFlqjGb7-CtWcG9fkwdYA2SplyPxWwHmdInJcrTbKcxj3QU_jvJ5mPZ9SS_vj-i0d8NUWlAYRfrsMe59vZAmL2nFnIK0HcXEaJh8eGqejNRXKWJDFZxMdeJj5EOVTzJ1piBnfHHUjd9o/w310-h320/IMG_5690.jpeg" width="310" /></a></div><p><f4><b><i>Stretch Your Mind!</i></b></f4></p><p>Many moons ago, I was commissioned to write <i>Mind Stretchers 2*</i>, a grade 5 problem-solving math book, which was popular in a number of local schools and tuition centers—disturbingly, they’re guiltlessly or blatantly photostating entire chapter questions as part of their worksheets.</p><p>And I still recall that on the topic of Perimeter, I’d posed a number of routine and nonroutine questions. What surprised or tickled me then was when the Managing Editor asked me whether or not some of these questions are <i>solvable</i>, because at first glance, they look like there are <i>missing</i> information to solving them.</p><p>These geometry questions can give students (and probably their oft-math-anxious parents and teachers) some goose pimples out of fear or panic if they can’t figure out the answers offhand. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFtrPPrB0VQQXs3UbCXs1NF5nRi359QwMwSlMtiB1m4TMVrzVXXh_N-1e3N7wVQiQJdzMhcrGZ7VduFz0_C66-xjmqg2PGikNuo4cQJsXFgci2Dm1b7lAGcsgnpSi_krgCrCp-tSsRT5p6HZaknG1-w39FutAYSlKMV785AIQiLkaw53tfBkXPdQnigNY/s1404/IMG_0035.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1404" data-original-width="1039" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFtrPPrB0VQQXs3UbCXs1NF5nRi359QwMwSlMtiB1m4TMVrzVXXh_N-1e3N7wVQiQJdzMhcrGZ7VduFz0_C66-xjmqg2PGikNuo4cQJsXFgci2Dm1b7lAGcsgnpSi_krgCrCp-tSsRT5p6HZaknG1-w39FutAYSlKMV785AIQiLkaw53tfBkXPdQnigNY/w237-h320/IMG_0035.jpeg" title="A grade 5 Singapore math title" width="237" /></a></div><p>Understandably, without a cool mind and some patience (or perseverance), even perimeter and area questions at the elementary (or olympiad) level can prove to be a challenge to math educators if they’re not trained to tackling them using the right approach.</p><p>Frustration and fear usually set in, especially for nonroutine questions that don’t normally appear in drill-and-kill school textbooks and workbooks.</p><p><f4><b><i>Premature Testing</i></b></f4></p><p>The danger of setting these types of brain-unfriendly questions too early, or having them prematurely in a class test, especially when most students have yet to fully grasp the concepts of area and perimeter, could be detrimental to the mental health of most average math students.</p><p>Parents who freeze at the sight of these questions would often exhibit a knee-jerk reaction, by getting a tutor for their child, if they’d afford it.</p><p><f4><i><b>Tuition or No Tuition?</b></i></f4></p><p>Most stressed parents often reason that if they couldn’t even solve these grade 4 questions, things would only get worse in later years, as the higher-grade topics get more complicated and the questions become more challenging. They just don’t want to see their child struggle in math, especially when they themselves had had a negative experience of the world’s most disliked school subject.</p><p>Even for math teachers and tutors, there’s nothing to be ashamed of if at first or second reading, they’re clueless how to tackle these nonroutines. Yes, they do appear in mid- or final-year exams arguably as a social filter to separate the nerd from the herd, but once math educators and homeschoolers know how to approach these questions from the right angle, before long, these math problems would become routine to them.</p><p><f4><b><i>The 4F’s of Mathematical Problem Solving</i></b></f4></p><p>Few math teachers and writers would admit that (school or olympiad) math involves lots of fears, false starts, frustrations, and failures. The sooner parents and homeschoolers (and their children and grandchildren) are aware of this oft-unspoken problem-solving process or ritual, the pressure or expectation level for all parties ought to go down significantly in reducing any unnecessary mental or mathematical stress.</p><p>Pain is (always) part of the joy of creative mathematical problem solving—the no-pain-no-gain mantra is axiomatic in math at all levels.</p><p><i>Geometrically & perseveringly yours</i></p><p><small>© Yan Kow Cheong, October 16, 2023.</small></p><p><small>* When the wallet-friendly title was out of print, a senior editorial staff emailed me that he’d pay me a cosmetic S$150 to buy the copyrights. I never bothered to reply to his laughably ridiculous suggestion. I wouldn’t be surprised that they’d since plagiarized the content to be used and reused for other purposes.</small></p><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-78081379583667136722023-09-25T18:16:00.000+08:002023-09-25T18:16:30.908+08:00How to Celebrate Zero Day<div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhudIxePiVABZ2B1lJUE7tWoZ5-9CU5VKW8sF6Gg6_47KY-XhFMhrKX6Lfuc9ftrcw-TuxBkqW_i6v8LMvZTProlo9k9ghZPEe75pGT7TwFBV2IzzEGoNvCvHTMu0w0rkDLtx_3dR_CYeMAy870Hy_ISi9y-TfrK4j_fgsHgS-ks2YJaiPYE3b_OOSDbwE/s3179/IMG_1922.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3179" data-original-width="1989" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhudIxePiVABZ2B1lJUE7tWoZ5-9CU5VKW8sF6Gg6_47KY-XhFMhrKX6Lfuc9ftrcw-TuxBkqW_i6v8LMvZTProlo9k9ghZPEe75pGT7TwFBV2IzzEGoNvCvHTMu0w0rkDLtx_3dR_CYeMAy870Hy_ISi9y-TfrK4j_fgsHgS-ks2YJaiPYE3b_OOSDbwE/s320/IMG_1922.jpeg" width="200" /></a></div><p><br /></p><p>Zero causes so much pain and suffering to tens of millions of students and their parents every day. Indeed, zero is the real troublemaker among the numbers! It's not too late to get even with the Roman Catholic Church’s once-deemed blasphemous <i>infidel number </i>(again).</p><p><br /></p><p>Below are ten idiot-proof activities you’d do to celebrate <i>Zero Day</i>.</p><p><br /></p><p><b>10. Avoid writing the now-redundant zero before a decimal point: .23, .583, .0045, …—move away from dated deception, faux religion, or numerological superstition.</b></p><p><br /></p><p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkCgMvcQpaSE7_G8B3Yy91csetjYRbmc8XoVVYUKdehK3qOifByGRGh6P1-MXiQRMQgosaKqSULHI0nUJXDRltstGO3DW5_czdEMQ3VlTwhLTijlFsXYn-0vH3TbmAvfbvBFC-cuy_46UaYZ_gxwwOUQCiYbD0IbKgIeOb6zRx6v13Vq0hf0geXYdSUpY/s1048/IMG_1092.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="928" data-original-width="1048" height="177" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkCgMvcQpaSE7_G8B3Yy91csetjYRbmc8XoVVYUKdehK3qOifByGRGh6P1-MXiQRMQgosaKqSULHI0nUJXDRltstGO3DW5_czdEMQ3VlTwhLTijlFsXYn-0vH3TbmAvfbvBFC-cuy_46UaYZ_gxwwOUQCiYbD0IbKgIeOb6zRx6v13Vq0hf0geXYdSUpY/w200-h177/IMG_1092.jpeg" width="200" /></a></p><p>9. Use the letter “o” or “O” when you mean the number or numeral “0”—for example, when giving a bank account or ID number to someone requesting it on the phone for verification purposes.</p><p><br /></p><p><b>8. Use “nothing” to half-truthfully convey the idea of zero, even though the number zero is “anything but nothing.”</b></p><p><b><br /></b></p><p></p><p>7. Fight for the <i>Year Zero</i> to be included in the timeline, to avoid confusing billions of people that the year 2023 is conventionally in the 21st century rather than in the 20th century.</p><p><br /></p><p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7tRhVtfT6uuarpJYu6VCIJyjLRPbAMyPUHNHdk7znYzPn60dMW_PvBojc3HX6_CBcaVwbCOlN8guR75PpAVwnzlmbLZ5eXDN25Rx03F2Mz_yACXCXWFVZt_EAyeI6skQDmNVvX_D-MlOYp-d4IJHAcaYv4MjjtL0H7gUkP8Ju7fwGAfushobMLfOVKic/s2605/IMG_1874.jpeg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="2605" data-original-width="2092" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7tRhVtfT6uuarpJYu6VCIJyjLRPbAMyPUHNHdk7znYzPn60dMW_PvBojc3HX6_CBcaVwbCOlN8guR75PpAVwnzlmbLZ5eXDN25Rx03F2Mz_yACXCXWFVZt_EAyeI6skQDmNVvX_D-MlOYp-d4IJHAcaYv4MjjtL0H7gUkP8Ju7fwGAfushobMLfOVKic/w161-h200/IMG_1874.jpeg" width="161" /></a></p><p>6. Canvass for the number zero instead of the number one to be the first number in the set of whole numbers, especially in some puritan or radical circles, where the <i>devil number</i> is excluded.</p><p><br /></p><p>5. Mobilize semi- or quasi-innumerate folks to use a different numeral when zero is used as a place number and as a number itself—strip zero of its double personality. For instance, use Ø in lieu of 0: 3Ø14Ø to emphasize place-value.</p><p><br /></p><p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqVkTPajIqv3MZyVw105c446PW3qxpV6i-bJAiZavpNw0pC_l2IrMfLruUp96WaeN87JxfFqgj-pKXm2mDGwjgfPfOYU6PoplmWW3H61rmOcwJpy_Ut2WbsTr9A1MekAclrMR_LJqWQdSbxQ7kkoa0pQHlR1tg4e0KXaUffjoN3GwWDGc-9g2DvjEvpDE/s712/IMG_2512.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="375" data-original-width="712" height="106" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqVkTPajIqv3MZyVw105c446PW3qxpV6i-bJAiZavpNw0pC_l2IrMfLruUp96WaeN87JxfFqgj-pKXm2mDGwjgfPfOYU6PoplmWW3H61rmOcwJpy_Ut2WbsTr9A1MekAclrMR_LJqWQdSbxQ7kkoa0pQHlR1tg4e0KXaUffjoN3GwWDGc-9g2DvjEvpDE/w200-h106/IMG_2512.jpeg" width="200" /></a></p><p>4. Be a <i>zerobreaker</i>, by defying the eleventh commandment, <i>Thou shalt not divide by zero!</i> without life-threatening consequences—that one has the (civil or political or religious) rights to divide by zero, although the answer may prove insensible or unreasonable.</p><p><br /></p><p></p><p>3. Puncture the egos of haughty geeks who think they know it all, by exposing mathematical loopholes in their reasoning, resulting from illegally (or unknowingly) dividing by zero—humble them with fallacies and paradoxes, such as 1 = 0 or π = 3.</p><p><br /></p><p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKV9oPTkJ63c5wAmP4ZkYTSF54_cY1vs_WaYx1QywptgIqYN94PnvMspy5roi0pvG6UZjmbHEiCu-X4RlWTnmEKDCO9rcvRK_LvYVgA3YeOJCCuYZPBWwZOlGS6pahOvUdmXjCKqW0Ygh1bZJ1agdS4KA6CdPg27Pxylr7AOHz1MIY7rExFwej0aasYE0/s2592/IMG_1881.jpeg" style="clear: left; display: inline !important; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="2592" data-original-width="1936" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKV9oPTkJ63c5wAmP4ZkYTSF54_cY1vs_WaYx1QywptgIqYN94PnvMspy5roi0pvG6UZjmbHEiCu-X4RlWTnmEKDCO9rcvRK_LvYVgA3YeOJCCuYZPBWwZOlGS6pahOvUdmXjCKqW0Ygh1bZJ1agdS4KA6CdPg27Pxylr7AOHz1MIY7rExFwej0aasYE0/w149-h200/IMG_1881.jpeg" width="149" /></a></p><p><br /></p><p><br /></p><p>2. Have a law that fines companies from offering 0% interest rate as a gimmick to lure gullible customers.</p><p><br /></p><p><br /></p><p><br /></p><p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnIsISh1VfmGd_deXNhuvUCtRmsNLMRp3naSAK4JzeC4chjptvPtq7_TgyQObfRkap6PMI9wAvxAmLxFE71huDkmy3-utTjnggE5iOIc4i4SetAxFA_tW8quxxB0HwnWnM15ZUs-2r8b7naolN7A3IUNyy9xYdKL-l7Ma3nxrsU-rZydKgR4LOPpISKzw/s725/IMG_1163.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="433" data-original-width="725" height="119" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnIsISh1VfmGd_deXNhuvUCtRmsNLMRp3naSAK4JzeC4chjptvPtq7_TgyQObfRkap6PMI9wAvxAmLxFE71huDkmy3-utTjnggE5iOIc4i4SetAxFA_tW8quxxB0HwnWnM15ZUs-2r8b7naolN7A3IUNyy9xYdKL-l7Ma3nxrsU-rZydKgR4LOPpISKzw/w200-h119/IMG_1163.jpeg" width="200" /></a></p><p><br /></p><p>1. Warn people to flee from the free—beware of free gifts, free seminars, and free air tickets, which seldom have zero strings attached.</p><p><br /></p><p><br /></p><p>Now is the time to teach Zero who’s in charge here—<i>zero is your servant, not your master</i>.</p><p><br /></p><p><i>Nøtøriøuly yours</i></p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_rNImCLF5YhQnstV4WrZ-DehAT6KGdac2qSYFgx4oDDLDmYhD4Yk2AY0PjVtp3dMVK9rnFmhrIenZ0C5-SCgJH07Tx8CiImB41evwPEr3Xku7Q6y8L2_R9a8dsvRU9B1bvev53nAdnripol7MOyz4bhR-mQrgyGA43vhyLkQ3vpC0E_1KSOCmEuMf6rg/s2369/IMG_2182.jpeg" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="2369" data-original-width="1606" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_rNImCLF5YhQnstV4WrZ-DehAT6KGdac2qSYFgx4oDDLDmYhD4Yk2AY0PjVtp3dMVK9rnFmhrIenZ0C5-SCgJH07Tx8CiImB41evwPEr3Xku7Q6y8L2_R9a8dsvRU9B1bvev53nAdnripol7MOyz4bhR-mQrgyGA43vhyLkQ3vpC0E_1KSOCmEuMf6rg/w218-h320/IMG_2182.jpeg" width="218" /></a></div><p><small><br /></small></p><p><small>© <a href="https://singaporemathplus.net/" target="_blank">Yan Kow Cheong</a>, September 25, 2023.</small></p><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-34724782029663362002023-08-21T19:33:00.001+08:002023-08-21T19:40:42.315+08:00A Numbers Puzzle<p>On X (formerly Twitter), @wiseconnector posed the following question:</p><p><i>How many numbers can you find?</i></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiwEqm79u_HIaJxpSJdGFJbJxv7kxXKAq7inMG994UhejegkG9kUNuTyWOCTou9UFvbFxZgNFt43CHxa3Vrxtx8IcRZKO5VeSDLkMyefXyiV5ExUnmUn05IFAqqgepv0Kf9L3DHkMnFue6WrLFC7WfFj0EF3KDLMZvv1ZOBrhnKH_6PlQ-RfvupX-TXPk/s480/IMG_5471.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="269" data-original-width="480" height="112" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiwEqm79u_HIaJxpSJdGFJbJxv7kxXKAq7inMG994UhejegkG9kUNuTyWOCTou9UFvbFxZgNFt43CHxa3Vrxtx8IcRZKO5VeSDLkMyefXyiV5ExUnmUn05IFAqqgepv0Kf9L3DHkMnFue6WrLFC7WfFj0EF3KDLMZvv1ZOBrhnKH_6PlQ-RfvupX-TXPk/w200-h112/IMG_5471.jpeg" width="200" /></a></div><p>It’s never too late for an eye check-up and also an opportunity to hone your logical and visualization skills.</p><p>This logic or math question can serve as an icebreaker at a birthday party even for those who proudly or unashamedly boast of being “hopeless at math or numbers.” </p><p><i>Try it!</i> <i>The answer is anything but obvious.</i></p><p>Ask a toddler or kindergartener, and also your seniors at home, especially if you’re concerned that they might succumb to dementia or Alzheimer’s in their later years, based on your family health history—a [generational?] curse you can break in the name of Jesus if you don’t want your children and their children to go through this mental illness in their golden years.</p><p>Summarize the answers to this puzzle from different age groups in a statistical diagram, say, a pie or bar chart. The information is likely to surprise you, giving you some insights what is going on in people’s minds when they try solving this kind of trick or tricky math question.</p><p>This little <i><a href="https://www.amazon.com/s?k=Mathematical+Quickies+%26+Trickies&crid=19VMECB11DJDH&sprefix=mathematical+quickies+%26+trickies%2Caps%2C398&ref=nb_sb_noss" target="_blank">mathematical quickie</a></i> has the potential to unite rather than divide people, by bringing them and their loved ones and friends much joy and laughter—never mind if they can’t always agree on the <i>correct</i> answer.</p><p><i>Logically & visually yours</i></p><p><small>© <a href="http://singaporemathplus.net" target="_blank">Yan Kow Cheong</a>, August 21, 2023</small></p><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-7483826879901142142023-08-07T03:44:00.000+08:002023-08-07T03:44:05.264+08:00Racism in Singapore Math Publishing<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg28jbOx9jDDbgpD12Tlu6qy4JFaUqZGcZpSbpwZlvCi0KaNg2deToeGHRYkORwuU0GlRXcqQUcEBeUdIl-DfSyVhK74TPUMdf2Ai5hq511cIeoTRiHiy4VWRU58wrRD0CXmmnYbwb3SlRyi0LjikiscJXr2KzIjx0x8t07DAoErbhzmEB1ADiPYnKKvyw/s1120/IMG_0534.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1120" data-original-width="1026" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg28jbOx9jDDbgpD12Tlu6qy4JFaUqZGcZpSbpwZlvCi0KaNg2deToeGHRYkORwuU0GlRXcqQUcEBeUdIl-DfSyVhK74TPUMdf2Ai5hq511cIeoTRiHiy4VWRU58wrRD0CXmmnYbwb3SlRyi0LjikiscJXr2KzIjx0x8t07DAoErbhzmEB1ADiPYnKKvyw/s320/IMG_0534.jpeg" width="293" /></a></div><p><small></small></p><center><small><a href="https://fb.watch/lTvXKc6VyK/?mibextid=v7YzmG">https://fb.watch/lTvXKc6VyK/?mibextid=v7YzmG</a> </small></center><p></p><p><br /></p><p>Does the comedic rant on “<a href="https://fb.watch/lTvXKc6VyK/?mibextid=v7YzmG" target="_blank">Racism in Maths Problem Sums</a>” serve as a “proof” that inequality or racism is rampant in math and math education?</p><p>Often times, math educators pose and solve these artificial or contrived word problems without giving much thought to them, especially when they’re oblivious that they might trigger mixed or negative feelings among highly sensitive schoolchildren and parents that belong to certain racial or minority or economically disadvantaged groups.</p><p><br /></p><p><f4><b>Math in Multicultural Singapore</b></f4></p><p>It’s no harm nor too late for the Ministry of Education (MOE) to occasionally review their approved textbooks presently used in local schools, which might perceivably promote some form of racial inequality in multiethnic or multicultural Singapore.</p><p>Not too long ago, to promote multiculturalism in math education, there was this unofficial or unwritten directive from the MOE for local math teachers and textbook writers to mindfully or multiculturally use people’s or children’s names from different racial groups in their word problems or problem sums. An educational move that would likely be banned and dubbed “woke math” in some political circles or polarized parts of the globe today.</p><p>Because Singapore has four official languages (English, Mandarin, Malay, Tamil), math educators are encouraged to permute or vary their choice of names in order not to appear racially prejudiced, especially when the majority of textbook authors have traditionally been Chinese.</p><p>In the name of racial or religious harmony, commendable or encouraging as the curricular or political move was then, its implementation wasn’t a walk in the park, because in practice, it’s not a mere change of substituting a Chinese name with a minority or non-Chinese one.</p><p>The present trend appears to revert to generic names in math textbooks and assessment titles for reasons unknown to me. Is it part of a grand marketing scheme to internationalizing (or colonizing?) the Singapore math brand to as many countries as possible?</p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2nZUy6dzaqDXXzbM0NBl8zzC7QS1vIYyfB8Lt8uBha2R1Pn1ESU34M47X5VNuu5v7urxo_ronGSrVSVkGW4pH5MagKuFbMOVutJt_Cq8ahUEj_ZSElX2M9eksEd7N3tm4-TmZIuICG9sbefenCnwk4CbQLxtn3PTLeQWjWuNMQtY0KAEALb_RNxy4VwM/s1637/IMG_0535.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="500" data-original-width="1637" height="122" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2nZUy6dzaqDXXzbM0NBl8zzC7QS1vIYyfB8Lt8uBha2R1Pn1ESU34M47X5VNuu5v7urxo_ronGSrVSVkGW4pH5MagKuFbMOVutJt_Cq8ahUEj_ZSElX2M9eksEd7N3tm4-TmZIuICG9sbefenCnwk4CbQLxtn3PTLeQWjWuNMQtY0KAEALb_RNxy4VwM/w400-h122/IMG_0535.jpeg" width="400" /></a></div><p><b><f4><br /></f4></b></p><p><b><f4>XX, XY, or Others?</f4></b></p><p>Some Chinese first names are used by both males and females; in other instances, it can be tricky to guess the gender by just looking at some Asian or Chinese names—the task doesn’t get any easier if you’re a non-Chinese. In fact, just recently, I needed to Google a Chinese name (in Hanyu Pinyin) to make sure that I don’t mistake one gender for another. Indeed, it’s pretty embarrassing or unacceptable to address a <i>he</i> or <i>she</i> (or <i>he-she</i>) by a <i>Miss</i> or <i>Mr</i>. When in doubt, don’t assume—ask!</p><p>For a long time, I thought the name of one of the original math co-writers of the then MOE’s Curriculum Development Institute of Singapore (CDIS) writing team belongs to a certain gender, when I later found out of my mistaken assumption, because in the olden days, certain names were used by both sexes.</p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRswXpfOmH45wo8Pq58hCKvqyorl89TZ9RKG3HmNJ7Zy61WSQ-2BoEO8FrXeqGQbGeB4HPMCCb-WKcr5TPe-TIpckVbDQ6F2ySYupPHrAjo_ZFQlFOlvZ8aDvDeLYp_S4KRk797zNrHwPeC6b29JbbxES-Yu2O4nZxA_99-LdPhHfWi3PehEGcUm-fgz0/s1285/IMG_5271.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="1227" data-original-width="1285" height="383" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRswXpfOmH45wo8Pq58hCKvqyorl89TZ9RKG3HmNJ7Zy61WSQ-2BoEO8FrXeqGQbGeB4HPMCCb-WKcr5TPe-TIpckVbDQ6F2ySYupPHrAjo_ZFQlFOlvZ8aDvDeLYp_S4KRk797zNrHwPeC6b29JbbxES-Yu2O4nZxA_99-LdPhHfWi3PehEGcUm-fgz0/w400-h383/IMG_5271.jpeg" width="400" /></a></div><p></p><p><br /></p><p></p><p><f4><b>Foreign Editions: Pluses & Pitfalls</b></f4></p><p>A similar situation arises when Singapore math textbooks are adopted or adapted for overseas markets. Changing names of living and nonliving things that have both British and American equivalents, or replacing local names or terms like local food or fruit with foreign substitutes that readers elsewhere are familiar with, is a common practice.</p><p>Of course, local publishers would also caution math writers to avoid using any Chinese or Asian names if their titles are being tailor-made for a Western audience, or if they don’t want to alienate potential “anti-woke” homeschoolers-customers.</p><p>Lesser known or discussed is that math publishers in Singapore have mixed feelings about local authors using their full Asian names, because in their marketing eyes, readers in the US and in the EU would prefer a Western name of the form X Y (with the first name X before the surname Y) rather than an Asian (or traditional Chinese) name of the form Z Y X (where the surname Z precedes the first name Y X) on the cover of a math textbook or supplementary math title.</p><p><br /></p><p><f4><b>Western Names <i>Preferred</i></b></f4></p><p>Many moons ago, I vividly recall a respected experienced publishing manager advising me to use a Western or European name, because my targeted (American) audience might not be receptive to seeing an Asian or Chinese name on the covers of my <a href="https://www.amazon.com/s?k=mathematucal+quickies+%26+trickies&crid=3C14X01QXZCI1&sprefix=mathematucal+quickies+%26+trickies%2Caps%2C392&ref=nb_sb_noss" target="_blank">recreational</a> and <a href="https://www.amazon.com/s?k=mathematucal+quickies+%26+trickies&crid=3C14X01QXZCI1&sprefix=mathematucal+quickies+%26+trickies%2Caps%2C392&ref=nb_sb_noss" target="_blank">problem-solving math</a> titles. </p><p>Just as every (additional) equation in a general or pop math book targeted at the lay public might potentially halve its sales, the odds of an Asian math author, who insists on using their real rather than a [Western] pen name, achieving a decent sale in front of their non-white audience are significantly (or unprovenly) reduced. There is this apparently unspoken bias towards nonwhite authors appearing on covers of math titles.</p><p>Personally, I’m not sure of the extent of this alleged or perceived discrimination vis-à-vis Asian math authors, but I’ve faith to believe that those who’ve taken a risk to order my wallet-friendly, brain-unfriendly books online, or to buy them in a bricks-and-mortar bookstore, have got their money worth, except for a few one-star haters or sour grapes who revel in posting vitriolic book comments on Amazon.</p><div>At the other extreme, it’s also not uncommon for math publishers in Singapore or Asia to conveniently or unethically omit the names of the authors, consultants, or foreign advisors (if they can get away with it), especially if foreign editions exist, or sale of copyrights occur at book fairs, with zero knowledge from the authors (until or unless morally convicted or vindictive editors leaked out the news).</div><div><br /></div><div>Recently, upon requesting my author’s overdue complimentary copies to one of my foreign editions titles, I discovered that both the author’s name and his American Curriculum Advisor of <i><a href="https://www.singaporemath.com/pages/challenging-word-problems-samples" target="_blank">Challenging Word Problems (Grade 6)</a></i> were missing from the title page and imprint page, respectively, which raises serious IP and ethical concerns on the part of the publisher and potential customers and readers.</div><div><br /></div><div>Without a name on the cover or title page, when previous editions had carried them, it just makes one wonder about the rationale of these unconsulted omissions, when the parties involved in the writing or reviewing of the content were kept in the dark. This only opens up the floodgate to unauthorized use, or helps promote plagiarism or piracy, where the party that often benefits is the lawyer.</div><div><br /></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgseOZSCiSDRliNh4sc8gzUddIebLBckmHrDdE8ZCi83cMAyxHfyIwHG6SWa9i_3h-M2-l-urHJuLGA6AzndCbLquc_MOJJhY3EkrZPoiycRYt-4LhLc-2xGpGX_FjOO8-El8GcSqrIfPlB9PvaVJ0h8B_fP6R65YKkVEsgPqvgcbQDxrDn2bk_mg-j_dY/s1485/IMG_5035.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1151" data-original-width="1485" height="310" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgseOZSCiSDRliNh4sc8gzUddIebLBckmHrDdE8ZCi83cMAyxHfyIwHG6SWa9i_3h-M2-l-urHJuLGA6AzndCbLquc_MOJJhY3EkrZPoiycRYt-4LhLc-2xGpGX_FjOO8-El8GcSqrIfPlB9PvaVJ0h8B_fP6R65YKkVEsgPqvgcbQDxrDn2bk_mg-j_dY/w400-h310/IMG_5035.jpeg" width="400" /></a></div><br /><div><br /></div><div><b><f4><i>The Chinese Advantage (in Singapore)</i></f4></b><p>Years ago, a non-Chinese co-author on Singapore’s bar modeling approached me, and wanted me to be his co-author or consultant for one of his upcoming math projects. He’d pay me for being his faux partner, because understandably having a Chinese name associated to a new book or website would add credibility to the project.</p><p>Businesswise, I couldn’t disagree with him, and I was praying that he’d find someone else more qualified than me, who wouldn’t mind being his lifelong business buddy.</p><p>Indeed, the Singapore math publishing industry is an ethical minefield that few have traversed without compromising their character or reputation. This is one of the oft-unspoken reasons why<i> </i>unlike other developing (and developed) countries that pay lip service to copyrights, Singapore is a first-class economy with a third-class educational publishing industry.</p><p><br /></p><p><i>Ethically and multiculturally yours</i></p><p><i><br /></i></p><p><small>© Yan Kow Cheong, August 7, 2023.</small></p></div><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-83419161247030223142023-07-27T20:44:00.000+08:002023-07-27T20:44:03.159+08:00Musk vs. Math<p>In the aftermath of Twitter being rechristened to X, the letter or symbol X can now boast of a new nonmathematical meaning.</p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq9gwcHUHBYHF00gaO9Yxfboe_KkLYeGZpLMt_6IrZvLNnYK5L9XVI21xtNzBXONbwu1FE8R7mzjf8-nBjlrC9BWL1lP49jD0vJ9bYQcsfahiO-9ygDYwE0CDktDnzi18aQnn1YGdlQWLuEV3tUBLcd-N-I33eFXJDuuF7FB-lb_B3yHbXs6l_2fLEqfw/s1551/IMG_0519.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1551" data-original-width="1258" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq9gwcHUHBYHF00gaO9Yxfboe_KkLYeGZpLMt_6IrZvLNnYK5L9XVI21xtNzBXONbwu1FE8R7mzjf8-nBjlrC9BWL1lP49jD0vJ9bYQcsfahiO-9ygDYwE0CDktDnzi18aQnn1YGdlQWLuEV3tUBLcd-N-I33eFXJDuuF7FB-lb_B3yHbXs6l_2fLEqfw/w325-h400/IMG_0519.jpeg" width="325" /></a></div><br /><p><br /></p><p></p><h4>The Lawsuit of the Century</h4><p></p><p>Would the world soon be witnessing the legal case of the year: X vs. Math Educators? Or Musk vs. Math?</p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipZMXCvO9Vx77XHse_eqi9k6QE-DnIR7kpJU9poYnSvBHu7gnSfitn4-VsYZ5R40Q-HlTn3Kqzmn-nfEI50pCHwiMLFqlTKxwXkiy9UG5cIHGOddY0EoNMYd3ZZ28rWswnhybztJjfdbneh-_78PpP4-m5X5V_3Lwr_f0lP_oPiJh5XcXrxI6SMoklyvE/s599/IMG_5470.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="416" data-original-width="599" height="222" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipZMXCvO9Vx77XHse_eqi9k6QE-DnIR7kpJU9poYnSvBHu7gnSfitn4-VsYZ5R40Q-HlTn3Kqzmn-nfEI50pCHwiMLFqlTKxwXkiy9UG5cIHGOddY0EoNMYd3ZZ28rWswnhybztJjfdbneh-_78PpP4-m5X5V_3Lwr_f0lP_oPiJh5XcXrxI6SMoklyvE/w320-h222/IMG_5470.jpeg" title="Meme © Anon." width="320" /></a></div><div><br /></div><small><center>Meme © Anon.</center></small><br /><p>What on earth is behind the choice of the letter or symbol or logo X to rebrand a once-beloved app, whose shelf life now looks shaky, to say the least?</p><p><br /></p><p></p><h4>The X of Singapore Math Publishing</h4><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-z55hQ2dcgS_QsvM-HzJPUSWYm8Yjxh4PWX8GqM43SpwquPRi6WohjGyZEWNwSJVqIPlxxMbeW-XUTG8aXG8vRzd-JfGHS0PZu0xCzpjRv87PiN7N34myRW-V7rnFkdFrkA-JW-1yYWiTV4mT7jo0G991_MUNJE2vW-dj9tLG2LP9usIRYTsdoEy59sQ/s516/IMG_0518.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="401" data-original-width="516" height="156" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-z55hQ2dcgS_QsvM-HzJPUSWYm8Yjxh4PWX8GqM43SpwquPRi6WohjGyZEWNwSJVqIPlxxMbeW-XUTG8aXG8vRzd-JfGHS0PZu0xCzpjRv87PiN7N34myRW-V7rnFkdFrkA-JW-1yYWiTV4mT7jo0G991_MUNJE2vW-dj9tLG2LP9usIRYTsdoEy59sQ/w200-h156/IMG_0518.jpeg" width="200" /></a></div><p>Earlier, I’d x-ed (or “tweeted”) tongue-in-cheek that</p><p>“Changing Twitter’s iconic bird logo to a white “X” hoping to launch a "super app" is like Singapore math editors—who’re responsible for their publishers’ MOE-rejected titles—rationalizing that by joining a competitor, their odds of approval would be higher.”</p><p>Most mediocre math editors are often deluded into thinking that their new higher position or pay in another publishing house would magically make them a better “word doctor,” thus increasing the chances of their manuscripts getting approved by the Ministry of Education.</p><p><br /></p><p></p><h4><i>Twitterdamus: The Fall of Twitter</i></h4><p></p><p>Late last year, when the founder of SpaceX started downsizing Twitter’s workforce, the temptation to coin <i>Twitterdamus</i> was just too strong.</p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_JYkYNhiucHowJ-tGdTsNscNHDeYa5LLpT2zOLbTyzvZlfIQDJ5BKW9MoYMxVT8TKCDAdW1gpW8ye5FL1dh8r-G-ZeurBERukID9-VmANyS2K6FLrc6gnih4j6ooTD7m9_UVnUUjlehe-U7ITBMN7evJYkHw4LSwkLybZi5AbBlpV3KARhd31eRMFRbw/s1235/IMG_0120.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="895" data-original-width="1235" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_JYkYNhiucHowJ-tGdTsNscNHDeYa5LLpT2zOLbTyzvZlfIQDJ5BKW9MoYMxVT8TKCDAdW1gpW8ye5FL1dh8r-G-ZeurBERukID9-VmANyS2K6FLrc6gnih4j6ooTD7m9_UVnUUjlehe-U7ITBMN7evJYkHw4LSwkLybZi5AbBlpV3KARhd31eRMFRbw/w400-h290/IMG_0120.jpeg" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div><br /></div>I tweeted the above definition with this hypothesized question: “Twitter Math: Guesstimate the number of Twitterdamuses who secretly wished to witness the bankruptcy of Twitter in a-not-too-distant future.”<div><br /><div class="separator" style="clear: both; text-align: center;"></div><p></p><h4>Threat from <i>Threads</i></h4><p></p><p></p><p>Below are some tweets I recently posted related to the privacy or security of our personal data. </p><p><i><b>Your metadata has now a choice. Who’s your less trusted or beloved billionaire?</b></i> [Cartoon from FRusty.creates]</p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgohKBuZS6ssnk2UeyQn0xH8O-qPORWkuBv6WJi0buVFT2nnxQsiMFZOOUb16anMdlRg-IO8zllSOS_bl_j6BzS20sv2sbQpFFsB3jTb6tm9oRUIrmYCq_OqxTM0qtVnEpxZS6-HV3ST-D3MVBedYbCenZboHJL1sL8um4xPKneJEa5UNSDXz81Kv33FiI/s1440/IMG_0512.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1440" data-original-width="1440" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgohKBuZS6ssnk2UeyQn0xH8O-qPORWkuBv6WJi0buVFT2nnxQsiMFZOOUb16anMdlRg-IO8zllSOS_bl_j6BzS20sv2sbQpFFsB3jTb6tm9oRUIrmYCq_OqxTM0qtVnEpxZS6-HV3ST-D3MVBedYbCenZboHJL1sL8um4xPKneJEa5UNSDXz81Kv33FiI/s320/IMG_0512.jpeg" width="320" /></a></div><p><i><br /></i></p><p><i>Threads’s Threat: Is the <a href="https://www.bbc.com/news/world-us-canada-66129215" target="_blank">Threads</a> app an Alibaba version of Twitter? Sounds like the social media equivalent of Trump’s frivolous lawsuits against those who expose him! Why isn’t Twitter also suing Weibo—China’s copycat?</i></p><p><b><i>When Free is often costly: If the product or service is free, you are the product. Think of Google, Facebook, Instagram, YouTube, and Twitter, which have sold or resold your personal data multiple times for billions</i>.</b></p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNAqr4dy5J3rPcHh6aCEU4NvWUMBTAFlKdxaSPZ6gH_XDrsMqOgHdCqg7Po2W1YMtUwBVu46G2YdL4sGB7TcjKaM2J-hkJoJM4i_0u5eAD7QnA-9sLJ3Kg3C8Cl_H1jXT9VA0Tt2_9eLrCM2gNwjRVqJcqSZinhy-lKRktyYnRR1VNOhH87xF3TJv3-Qk/s1501/IMG_8275.jpeg" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="1501" data-original-width="1314" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNAqr4dy5J3rPcHh6aCEU4NvWUMBTAFlKdxaSPZ6gH_XDrsMqOgHdCqg7Po2W1YMtUwBVu46G2YdL4sGB7TcjKaM2J-hkJoJM4i_0u5eAD7QnA-9sLJ3Kg3C8Cl_H1jXT9VA0Tt2_9eLrCM2gNwjRVqJcqSZinhy-lKRktyYnRR1VNOhH87xF3TJv3-Qk/w350-h400/IMG_8275.jpeg" width="350" /></a></div><p></p><p><br /></p><p>A prayer for millions of anti-𝕏 followers who sorely miss the little blue bird: <i>Let 𝕏 Be Twitter Again!</i></p><p><i><br /></i></p><p><small>© <a href="http://singaporemathplus.net" target="_blank">Yan Kow Cheong</a>, July 27, 2023.</small></p></div><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-70315993944771056002023-07-16T22:55:00.000+08:002023-07-16T22:55:04.097+08:00Mortal Math<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwRcLJUhi00rBMY3mryEItXag_YAS7dyHxyGnyXVxASoukNUmq8TEFuo2p7Mq2-uyltPt3colNTV8fOQJrbf-JsbiRGNdNaGTKQ2InblHY7Yr7JjyPV7Fts0DPSkRFdKmPllTHvqT211-oq0hszgWlIFUyj1RidW_mtGZcGnTkOMCTJYHOsI9q2jXhUuQ/s500/IMG_5181.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="283" data-original-width="500" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwRcLJUhi00rBMY3mryEItXag_YAS7dyHxyGnyXVxASoukNUmq8TEFuo2p7Mq2-uyltPt3colNTV8fOQJrbf-JsbiRGNdNaGTKQ2InblHY7Yr7JjyPV7Fts0DPSkRFdKmPllTHvqT211-oq0hszgWlIFUyj1RidW_mtGZcGnTkOMCTJYHOsI9q2jXhUuQ/s320/IMG_5181.jpeg" width="320" /></a></div><p style="text-align: center;"><small>Photo © Anon.</small></p><p><br /></p><p>Few would disagree that the above math or science question has now gained deadly relevance or importance in this year’s cruel summer, especially during this week’s abnormally hot weather.</p><p><br /></p><p><b>EcoMath 4 Everyone</b></p><p>Is it apt for math teachers to use this week’s extreme weather condition plaguing some parts of the planet to help some middle-school students brush up their Celsius-Fahrenheit conversion skills, and to challenge them with some real-world problems in the aftermath of climate change? </p><p>A typical grade nine (or secondary three) ecomath question is the following:</p><p><i>On a certain day, the Celsius thermometer and the Fahrenheit thermometer registered the same numerical value for the temperature. Given that 86°F = 30°C and 104°F = 40°C, what was the temperature that day?</i></p><p><br /></p><p><b>Post-Pandemic <i>Holeydays</i> </b></p><p>Guesstimate how many tourists regret flying to some parts of the US and the EU at this time of the year—when popular tourist attractions are closed during the hottest hours to protect visitors from dehydration or to reduce the odds of their visiting an emergency room.</p><p>How much would tourism-related businesses in heat-stricken regions suffer financially this summer?</p><p>What percents of unlucky tourists would need to extend their “holidays” due to prolonged heat-related hospital stay?</p><p><br /></p><p><b>The Polluters Preaching to the Poor </b></p><p>Estimate the number of deaths in the animal kingdom resulting from our hotter planet, which is primarily driven by materialistic consumers in the developed world, who now hypocritically want to lecture the developing world about human-induced climate change and to some extent the naturally-occurring weather pattern known as El Niño.</p><p>Why should China, India, Indonesia, and other emerging economies listen to the West, which are historically responsible for the dire climatic situation we’re in today? Why must much-maligned totalitarian China and undemocratic others donate to international climate funds set up by “guilty” high-GDP big polluters to help poorer nations struggling with climate change?</p><p>With the world paying lip service on cutting down on oil and gas for alternative sources of renewable or clean energy to grow their economies, low yield of crops and the increasing risk of wildfires and floods, not to say, frequent electricity blackouts in poorer or corrupt developing nations, are likely to be the new (new) normal.</p><p><br /></p><p><b>Heat Kills</b></p><p>According to the Centers for Disease Control (CDC), more than 700 people in the US lose their lives to extreme heat each year, with close to 68,000 people being sent to emergency rooms.</p><p>Guesstimate how many locals and foreigners, especially the homeless, the migrant workers, and the refugees, in all the global regions now experiencing a heatwave would find it hard to avoid a heat-related hospital visit this year. How many of them might fail to cheat death simply because of their helplessness or others’ indifference?</p><p><br /></p><p><b>The Dodo Effect</b></p><p>The world has already warmed by about 1.1°C since the industrial era began and scientists forecast temperatures will keep rising unless governments and businesses around the world have the (political or moral) will to cut greenhouse gas emissions.</p><p>How many fish in rivers and canals, or seabirds and whales, would disappear or starve thanks to “global warring”? How many animal and plant species are going the way of the dodo in coming years and decades?</p><p><br /></p><p><b>Singapore’s First Winter</b></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfuGaS54T4OYY8Io2RsA6Cg7W3zh5nK0dSFfnWZg1mWvOSeMfYo1sDfk-NHVmQAWDdhf5l8tfYLFioIQNOkzoX71QU7u0OkJ9pGldR37wx0yHuBlCjPD2NL-iAW0Avn-OSD9-4Clj0leOMmUHXXXLjRqwyCrxmCVjdHeFurzLb4XvB86oK04zMQVDojao/s960/IMG_5454.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Source Photo: © Anonymous" border="0" data-original-height="960" data-original-width="720" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfuGaS54T4OYY8Io2RsA6Cg7W3zh5nK0dSFfnWZg1mWvOSeMfYo1sDfk-NHVmQAWDdhf5l8tfYLFioIQNOkzoX71QU7u0OkJ9pGldR37wx0yHuBlCjPD2NL-iAW0Avn-OSD9-4Clj0leOMmUHXXXLjRqwyCrxmCVjdHeFurzLb4XvB86oK04zMQVDojao/w240-h320/IMG_5454.jpeg" width="240" /></a></div><p>Way back in 2016, I’d tweeted tongue-in-cheek about Singapore’s experiencing her first winter:</p><p><i>Singapore's 1st Winter: Will fine dining up and more folks aspiring to be middle-class cause Singapore to witness its #Singageddon? #climate (1/25/16)</i></p><p><i>Fake News: Singapore experienced its first winter this week—tens of thousands of Singaporeans took no-pay leave when the temperature dropped to zero degrees! #climate #humor #zero #winter Source Photo: © Anonymous (1/14/18)</i></p><p>At the current rate in the global rise (or drop) in temperature, the chances of those of us (who’ll be blessed to live beyond the three-scores-and-ten lifespan) seeing snow in Singapore are anything but zero.</p><p><br /></p><p><i>Environmentally & morally yours</i></p><p><br /></p><p><small>© <a href="http://singaporemathplus.net" target="_blank">Yan Kow Cheong</a>, July 16, 2023.</small></p><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-25354205833029385062023-06-29T22:21:00.000+08:002023-06-29T22:21:15.319+08:00A Grade 3 Singapore Math Question<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrVbKlmN32JP0IJRnAxw-jIIZrCArBQmNF6lH1T9lYQqOgTtjQ01QWo5VAgn2yV7kIi63VPTgUoejASiq6znKAfTRZXwqaV2W9AalPwPSDCCConO4Hu-jLdLmWL16tQacGXgo4AlxsIXADo2fQ0KKrP3tHGZrTaMQWUSNxFvZL8hz4H_Ba-WYxAN7y3mk/s1024/IMG_5378.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="444" data-original-width="1024" height="174" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrVbKlmN32JP0IJRnAxw-jIIZrCArBQmNF6lH1T9lYQqOgTtjQ01QWo5VAgn2yV7kIi63VPTgUoejASiq6znKAfTRZXwqaV2W9AalPwPSDCCConO4Hu-jLdLmWL16tQacGXgo4AlxsIXADo2fQ0KKrP3tHGZrTaMQWUSNxFvZL8hz4H_Ba-WYxAN7y3mk/w400-h174/IMG_5378.jpeg" width="400" /></a></div><br /><p style="text-align: left;"><span style="text-align: left;">Not too long ago, a mother posted the above grade three question on Facebook, and sought help from fellow parents: “Hi all, can anyone advise this P3 qn? Thanks!”</span></p><p>Before you read some of the replies or suggestions below, if you’re a parent or tutor, how would you solve this fraction question (with the mathematical knowledge of an average grade three student)?</p><p>A parent’s reply was: “This is a question that wants u to compare the fraction with half. Whichever fraction is smaller than half is the answer.</p><p>“To compare against half, take the denominator and divide by 2. If the numerator is less than the divided value, it is smaller than half.”</p><p>The mother replied, “蔡锦森 oh ic! Nv thought of that! Gosh, how to explain to a P3 ? 😝”</p><p>Another parent or tutor joined in: “So for such questions, there are 2 types. One type requires the student to compare against half. The other is to compare the difference with 1 whole. E.g. Which fraction is closest to 1? 7/8, 3/4, 6/7 etc”</p><p>Later, another member commented: “Normalize all the denominators and compare.”</p><p><i>Would you use any of the suggested strategies to solve the problem?</i></p><p><br /></p><h4 style="text-align: left;"><i><b>An Apt Question for Grade Three Students? </b></i></h4><p>In the Singapore math curriculum, the guidelines for elementary school students (or primary school pupils) learning fractions at different grades are as follows:</p><p><b>Primary 2 (Grade 2): Add and subtract like fractions whose sum is less than 1.</b></p><p>Primary 3 (Grade 3): Learn equivalent fractions; add and subtract related fractions whose sum is less than 1.</p><p><b>Primary 4 (Grade 4): Along with improper and mixed numbers; add and subtract related fractions whose sum exceeds 1.</b></p><p>As I’ve zero idea about the source of this test question, I leave it to the reader to decide for themselves whether or not this grade three question is in line with the local syllabus.<i> If not, why? Or do you think this question is somewhat ill-posed?</i></p><p><br /></p><h4 style="text-align: left;"><i><b>What If?</b></i></h4><p>Imagine if the same question were to be assigned to a group of grade five students. How would they approach it? </p><p>Would most of them resort to a knee-jerk solution by finding the LCM of the four fractions, before comparing their numerators, rather than thinking whether a less-tedious or shorter method might do the job?</p><p>Or would they conveniently convert the fractions into decimals (with or without a calculator)?</p><p><br /></p><h4 style="text-align: left;"><i>The Art of Problem Posing</i></h4><p>I wonder whether rephrasing the above question might make it mathematically (or fractionally?) more meaningful for students to apply their knowledge of comparing fractions. Say, what if we asked them to compare a set of fractions vis-à-vis a base fraction like 1/2?</p><p><b>Which of the following fractions is greater than 1/2?</b></p><p><b>A. 2/5 B. 3/7 C. 6/10 D. 4/9</b></p><p>Again, here too, the aim is to discourage students from religiously applying the fraction-decimal conversion, or from tediously converting these fractions to a common denominator.</p><p>At higher grades, we’d use larger fractions that would make finding equivalent fractions painfully tedious or time-consuming.</p><p>Meanwhile, may I encourage you to share how you’d tackle this fraction question without adding more pressure on students (who might already be suffering from some form of “fraction trauma” as a result of being subject to premature abstraction and procedural methods)?</p><p><br /></p><p><i>Methodically & meaningfully yours</i>.</p><p><small>© <a href="http://singaporemathplus.net" target="_blank">Yan Kow Cheong</a>, June 29, 2023.</small></p><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-53533242154725222932023-06-04T17:39:00.000+08:002023-06-04T17:39:35.744+08:00Is a Pythagorean Ban or Bill in the Pipeline?<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdlggqaYzrzOu4LANEIyIg2FFTktngwNItoDA-0IrxQwP2XyHXtqW77mS5XMYRa4t_-jUX-7DWf-Jevc_xKjPZkLbCazsnz_v3larsefSW2UgtlbBOG0XfWBHa9roHxuXTWTN6vbrb0zwMku21pFrCa9ZJpKgrKobxIQTWteDo9HHgyPnzJKLTKJKi/s1284/IMG_5353.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1163" data-original-width="1284" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdlggqaYzrzOu4LANEIyIg2FFTktngwNItoDA-0IrxQwP2XyHXtqW77mS5XMYRa4t_-jUX-7DWf-Jevc_xKjPZkLbCazsnz_v3larsefSW2UgtlbBOG0XfWBHa9roHxuXTWTN6vbrb0zwMku21pFrCa9ZJpKgrKobxIQTWteDo9HHgyPnzJKLTKJKi/s320/IMG_5353.jpeg" width="320" /></a></div><p>Is the above geometry question a “trick” question to check whether the “anti-woke” curriculum censors in some red states are awake or not?</p><p>Or just pro-Disney critics trying to poke fun at some pro-DeSantis “math specialists” (or ultra-MAGA patriots and puritan parents), who’re hell-bent to ban any deemed questionable or objectionable math questions that could potentially add unnecessary stress to math-anxious students and their parents?</p><p>If a poem promoting national or racial unity could “cause confusion and indoctrinate students,” a nonroutine math question from an alien or foreign source might also inflict twice as much psychological harm to the self-esteem (or mental health) of students who’re not born or blessed with the “mathematical gene.”</p><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="1810" data-original-width="1276" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKC7d4K21pb91lqtlAZuDClgS6qjnzQWNf0XJ0bpBPbkIsW8_xJ-6NXHZ8hT2IvPfNMp2Gdk4WDS_ibkMeKwVkTnJrOM48YMgB518IxwnYXhF4US1hOllDZJBdGHF3u7hd2FZgrZvGpJeaKLtm9cHbuED3UjRWMKLAFDso6LD2WKHp4rhprYWcytDW/w453-h640/IMG_0468.jpeg" width="453" /></div><p>In the name of <i>mathematical wokeism</i>, what would qualify as a “worst [math] question”? One that could lead to a temporary mental blackout or a three-second-long stroke?</p><p>Or one that would trigger common symptoms like faster heartbeat, sweaty palms, and dry throat, which unspokenly affect all of us to a certain degree, when faced with a time-based brain-unfriendly or fiendish math question?</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitdXEi6RghaRagUKy0pAZ-PjKV9nvG6fKoACbWxkbsrwNPwm07MMsDcfYwKxGKpJuTNwl0iKkDIxWw1xl7Cu-aWjarIRqim6Vcuf0eHYi4cMoNvGJ2wW3g33tb_GKoJf4a04P_dS4qSglhEbT9OXNOR05SMWhR2KYokKcfTADnwvSLVp8RQmdVQ99_/s828/IMG_5361.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="752" data-original-width="828" height="291" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitdXEi6RghaRagUKy0pAZ-PjKV9nvG6fKoACbWxkbsrwNPwm07MMsDcfYwKxGKpJuTNwl0iKkDIxWw1xl7Cu-aWjarIRqim6Vcuf0eHYi4cMoNvGJ2wW3g33tb_GKoJf4a04P_dS4qSglhEbT9OXNOR05SMWhR2KYokKcfTADnwvSLVp8RQmdVQ99_/s320/IMG_5361.jpeg" width="320" /></a></div><p></p><p>Should polarized politics or racial puritanism be allowed to triumph over mathematical problem solving and critical thinking? When “holy votes” from a significant proportion of the population dictate the direction of math education, curricular or educational decisions that would benefit the nation would be rarer than perfect numbers.</p><p><i>Questionably & critically yours</i></p><p><small>© Yan Kow Cheong, June 4, 2023.</small></p><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-65822750013504029432023-05-19T23:52:00.000+08:002023-05-19T23:52:27.751+08:00Creativity or Stupidity?<p></p><div class="separator" style="clear: both; text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiU2ekMcYrrnFXpmbBsBYqACqYGtc9Q7M7gLifg2VMmjDm_w_YHaug7NAZBRKkaVCUKF5Uw2RagfoNPO0iH_pL6MV11JovUbmKI7a9JW_NDriN83WNZeV-xSIvzNgtxz5qGxZrCXEOPMNGx0xPZEKT2cPhJTW0lDDrgxSoKY7-Etu-goViU7fyFeQ6O/s960/IMG_5327.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="960" data-original-width="913" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiU2ekMcYrrnFXpmbBsBYqACqYGtc9Q7M7gLifg2VMmjDm_w_YHaug7NAZBRKkaVCUKF5Uw2RagfoNPO0iH_pL6MV11JovUbmKI7a9JW_NDriN83WNZeV-xSIvzNgtxz5qGxZrCXEOPMNGx0xPZEKT2cPhJTW0lDDrgxSoKY7-Etu-goViU7fyFeQ6O/s320/IMG_5327.jpeg" width="304" /></a></div></div><div class="separator" style="clear: both; text-align: justify;"><span style="text-align: left;"><br /></span></div><div class="separator" style="clear: both; text-align: justify;"><span style="font-family: inherit; text-align: left;">This week, I saw this attached (grade one?) test item or math meme on Facebook, which was initially posted by “The Language Nerds” group.</span></div><p>Based on the multiple comments to this ill-posed math question, it’s amusing, yet also disturbing, to read that most responders are <i>praising</i> the student for his “creative” answer, or criticizing the “uncreative” teacher for penalizing the poor child.</p><p>In this postmodern or polarized world we’re living in, you’d think that maybe only someone who’s a “very stable genius” would rationalize or argue that the student’s response qualifies as one of the equally valid answers. And if the biased teacher insisted on marking the creative child wrong, the parents might consider suing him or her for giving their son an undeserved zero.</p><p><br /></p><p><b><i>Creative or Uncreative Comments</i></b></p><p>Below are some netizens’ replies to the math question from “Maths Jokes Daily,” which range from the hilarious to the ridiculous to the preposterous.</p><p><b>I think because the circles weren't closed properly 🤔</b></p><p>honestly think its possible for most people to understand what you are supposed to do here, so I would definetely argue that this is not a badly formed question :)</p><p><b>Were the correct answers 1.39, 2.17 and 3.96 ?</b></p><p>He got it wrong because he marked 3 numbers, and the question only asked for one, so the right answer is 15</p><p><b>He provided 3 right answers. He identified the smallest number in each row disregarding the periods and commas. LOL !</b></p><p>He circled 3 numbers. Number 1 is the smallest number and therefore should have only selected the 1 single number.</p><p><b>Also, why did the teacher put 3 lowercase "alpha" symbols?🤣</b></p><p>it’s evident smallest number and not smallest numberS so he should have circled only 1</p><p><b>Because he only circles 1 but not 1.39 Same with others</b></p><p>The fault lies entirely with the fool that numbered the questions with Roman Numerals and then used 1, 2, 3 instead of a, b, c</p><p><b>That kid is already smarter than the teacher.</b></p><p>Thats at least .5 for thinking outside the box</p><p>? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! </p><p><br /></p><p>Would you side with the teacher or the student? How would you respond to the “wrong” answer to this ill-posed or improperly posed question?</p><p><i>Creatively or uncritically yours</i></p><p><small>© <a href="http://singaporemathplus.net" target="_blank">Yan Kow Cheong</a>, May 19, 2023.</small></p><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-48963704031724792552023-05-09T18:35:00.000+08:002023-05-09T18:35:04.351+08:00Book-Smart Math vs. Street-Smart Math<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzvRlpmLxMcJImn97CqFzQzWXS_--Kz7btYEZFVFJs_6APdh6t6MHRabB7-6EdEYnzOC2vbXe9oPFj4EEDabxzIRaMkjXOf5ciKAhfk0R5I3QNkk5dpfqMTS9VDJlBADqI5MS6zRtX8jOth5eRPzTIP4KstbU2LVa3jP9IgFZlZJwz6ubR0cfhRClz/s845/IMG_5313.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="845" data-original-width="700" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzvRlpmLxMcJImn97CqFzQzWXS_--Kz7btYEZFVFJs_6APdh6t6MHRabB7-6EdEYnzOC2vbXe9oPFj4EEDabxzIRaMkjXOf5ciKAhfk0R5I3QNkk5dpfqMTS9VDJlBADqI5MS6zRtX8jOth5eRPzTIP4KstbU2LVa3jP9IgFZlZJwz6ubR0cfhRClz/w331-h400/IMG_5313.jpeg" width="331" /></a></div><br /><p></p><p>Based on the picture and text, who do you think got a better deal? Which party ended up happier: Customer or Seller?</p><p>Would you agree that the young exam-smart customer was outfoxed by the old street-smart fruit seller? </p><p>Aren’t we all guilty of this “book- or exam-smart syndrome,” when we’d buy more than what we needed because we thought we’re getting a good deal, or we didn’t want to be taken advantage of?</p><p>In the end, isn’t the supermarket or shop owner or fruit seller who’s having the last laugh, while the customer thinks they’re the “smarter one”?</p><p>Isn’t it a case of “more is less”? When A-students are being outwitted every day by C-students in the marketplace!</p><p>It’s probably no wonder that most exam-smart A-students around the world end up working for street-smart C-students. The former have so much to lose, compared to the latter who’ve far more to gain (if they do make it!).</p><p>If you’re a “math educator” (teacher, tutor, writer, editor, ghostwriter, lecturer, “moonlighter,” …), do you have what it takes to venture into the business of math or math education? </p><p><i>Smartly yours</i></p><p><br /></p><p>Photo © Anon.</p><p>Stole the attached picture from ex-colleague-and-friend WeePing Chun on Facebook.</p><p>© <a href="http://Singaporemathplus.net" target="_blank">Yan Kow Cheong</a>, May 9, 2023.</p><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-18321245591779623322023-03-10T23:57:00.000+08:002023-03-10T23:57:34.223+08:00Math à la Japonaise<p>We need to thank Mrs. Marie Kondo for advocating that tidying up needn’t be obeyed as an eleventh commandment, especially for a significant number of us who can’t afford to live sans a mess, or who just refuse to be <i>Konned</i> by her enviable minimalist lifestyle.</p><p>Since the tidying consultant has been in the limelight recently after her long overdue admission that the art of tidying up could be an optional activity for those who can’t stand the sight of all kinds of oft-dated, sentimental, or hoarded items lying around the house (and in the office), I thought it’s apt to share about “KonMari Math,” which I christened two years ago, to show that even math educators too haven’t been spared by the gospel or philosophy of the organizing goddess.</p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOfXmQ7eJwHNMxkaRj8PfjpH1q5I2RyPckKcPOLsG6WdHZE5U29EWQR-wRyjuwjHVSoC3GLqvt1RrHhgt-_qKufnYBxR-XHudLLVvSodBhnvpoFCT1Ps30YY3th4bLmKlFjrZcFAuco_Z9RXa_9QGgudbozrpLdmnv8CWDDzNxaiuE0cA7B3iAqa_I/s1624/CC1577CA-DD2A-44FB-A1F7-1D250DAAC18A.jpeg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="510" data-original-width="1624" height="125" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOfXmQ7eJwHNMxkaRj8PfjpH1q5I2RyPckKcPOLsG6WdHZE5U29EWQR-wRyjuwjHVSoC3GLqvt1RrHhgt-_qKufnYBxR-XHudLLVvSodBhnvpoFCT1Ps30YY3th4bLmKlFjrZcFAuco_Z9RXa_9QGgudbozrpLdmnv8CWDDzNxaiuE0cA7B3iAqa_I/w400-h125/CC1577CA-DD2A-44FB-A1F7-1D250DAAC18A.jpeg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><small>Math word du jour</small><br /><br /><br /></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGUP-cVma9OuCp3v-UkAo3nkuBuAEDFI0_Jhviq2yM3NLG0VF8QMjuC7hH-cNJzXiqRPTrXPd2VasMzkpGT1Lyh6iHGllwEOhWe-LNTck6Zv-z51Wuw4oVzxeTtMINzoeRcfkbwmohuxQoqYVTFb0vUVNmL7R_o8cc3RQIlwMg5p24T1gIRb1kWugY/s960/1BD7BED9-1E22-41BC-ADED-3A9404006E35.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="500" data-original-width="960" height="209" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGUP-cVma9OuCp3v-UkAo3nkuBuAEDFI0_Jhviq2yM3NLG0VF8QMjuC7hH-cNJzXiqRPTrXPd2VasMzkpGT1Lyh6iHGllwEOhWe-LNTck6Zv-z51Wuw4oVzxeTtMINzoeRcfkbwmohuxQoqYVTFb0vUVNmL7R_o8cc3RQIlwMg5p24T1gIRb1kWugY/w400-h209/1BD7BED9-1E22-41BC-ADED-3A9404006E35.jpeg" title="Photo from math prof @mathematicsprof on 17/2/19" width="400" /></a></div><div><br /></div><div style="text-align: center;"><small>Photo from math prof @mathematicsprof on 17/2/19</small></div><p>Personally, I’m dazzled by most things Japanese: origami, sushi, wasabi, not to say, soroban (Japanese abacus—square-rooting, cube-rooting, differentiating, and integrating), Kumon math, Sakamoto math, Sangaku, and Wasan.</p><p>After being introduced to Mr. Kenji Wakabayashi by my ex-colleague and friend, Mr. O.K. Heng, to learn about the ABCs of the <i>Sakamoto Maths Method</i>, I was later offered the opportunity to attend a months-long series of math talks on the Japanese problem-solving heuristic (or “problem-solving strategy” as it’s known in some parts of the globe).</p><p>To certify that I’d mastered Sakamoto math, I reluctantly had to take an exam with fellow participants who’re much younger than me. I was already around forty then, and needless to say, by then, it’d been a while since I last sat for a math proficiency test or exam.</p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwm1PGUHHDzo96GGCAGrgQ6e53E8l3GMB9GCHXwmZ87ZovQCHVZ8WDHVJQ9crrhHGo_D536EP-MVBxloX3Jg7cCw1Q9-zowiCDFNFcDMfO3KKdpTMT7ofkUH6K-LrNvMZAhT8ACwGR4Ae2bOdk8GSi9LXvj8AAu0FVk3UX1lp9JIYgtw4CZkU3UX-_/s825/42C3D648-D531-4888-8C1F-5CC88B05C5B2.jpeg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="825" data-original-width="600" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwm1PGUHHDzo96GGCAGrgQ6e53E8l3GMB9GCHXwmZ87ZovQCHVZ8WDHVJQ9crrhHGo_D536EP-MVBxloX3Jg7cCw1Q9-zowiCDFNFcDMfO3KKdpTMT7ofkUH6K-LrNvMZAhT8ACwGR4Ae2bOdk8GSi9LXvj8AAu0FVk3UX1lp9JIYgtw4CZkU3UX-_/s320/42C3D648-D531-4888-8C1F-5CC88B05C5B2.jpeg" width="233" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><small>Front cover of the manual</small></td></tr></tbody></table><p>Today, I’m thankful to Mr. Wakabayashi who gave me an opportunity to get a strong foundation on Sakamoto math, which has proved to be a more advantageous or intuitive problem-solving strategy than the bar model method in a number of problem situations.</p><p>What is even more amazing is that I attended all these Japanese math lessons without forking out a penny. Talking about being blessed mathematically (and financially), when other participants or franchise sponsored trainers have to pay hundreds of dollars to attend these twice weekly and weekend classes.</p><p>Indeed, Sakamoto math offers paid, sponsored, or guest attendees another method of solution to solving brain-unfriendly word problems. I think a Singapore math educator-turned-trainer ought to be versed with not only the bar model method, but also with the stack model method and the Sakamoto math method—a trinity of problem-solving strategies.</p><p>Recently, while working on a bar modeling manuscript, I accidentally came across some Wasan (or Japanese math) materials, which further solidifies my knowhow of Nippon math, especially some of the techniques I learned in Sakamoto math moons ago.</p><p>May I encourage all of you to expose yourself to the richness of Wasan, which would help broaden and deepen your appreciation and knowledge of multicultural math, if you’re open to learning different problem-solving strategies (or heuristics) commonly used in countries with a rich mathematical heritage.</p><p>Of course, to learn Sakamoto math effectively, do it preferably under a master-trainer from Japan—never mind their accent—rather than merely reading the notes of your child or nephew who’s signed up for a Sakamoto math course.</p><p>May the learning of Nippon math and multicultural math (Vedic math, bar model method, stack model method, line model method, …) spark mathematical joy in your life.</p><p>Wishing you many blessed joy-sparking or aha! moments.</p><p><i>Mathematically & multiculturally yours</i></p><p><br /></p><p><b><small>References</small></b></p><p><small>Kondo, M. (2022). <a href="https://www.amazon.com/Marie-Kondos-Kurashi-Home-Organize-ebook/dp/B09SKWM3SY/ref=mp_s_a_1_1?crid=FJ1K68SDL1V1&keywords=marie+kondo%27s+kurashi+at+home&qid=1678445439&sprefix=Marie+Kondo%27s+Kurashi%2Caps%2C422&sr=8-1" target="_blank">Marie Kondo’s Kurashi at home</a>. New York: Ten Speed Press.</small></p><p><small>Yan, K.C. (2016). Sangaku — Japanese temple geometry. <a href="https://www.amazon.com/Geometrical-Quickies-Trickies-Mathematical-Trickles/dp/9810973896/ref=mp_s_a_1_1?crid=33H9TWUOU1OL&keywords=Geometrical+Quickies+%26+trickies&qid=1678445341&sprefix=geometrical+quickies+%26+trickies%2Caps%2C337&sr=8-1" target="_blank">Geometrical quickies & trickies</a>. Singapore: MathPlus Publishing.</small></p><p><small>© <a href="http://singaporemathplus.net" target="_blank">Yan Kow Cheong</a>, March 10, 2023.</small></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGuQ3EizLodSd5qiXCVNrYfO38ugwbaYEmha1xnrYY3dh8RqFtzZ_usjaxrBnW_HOf5nulzSzjRXtQYS2tn8OWYt6yzQP1-DZA8ael7oKXxEs6nitaALiNgB4E9eV-4nji_HsRhjT7txqzipjEk43nwTZ1QywAtWTyenW-wgrSXjX0zfS0M1RmZADO/s1122/76F12562-240E-4167-8F77-6A49560273BB.jpeg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1122" data-original-width="1024" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGuQ3EizLodSd5qiXCVNrYfO38ugwbaYEmha1xnrYY3dh8RqFtzZ_usjaxrBnW_HOf5nulzSzjRXtQYS2tn8OWYt6yzQP1-DZA8ael7oKXxEs6nitaALiNgB4E9eV-4nji_HsRhjT7txqzipjEk43nwTZ1QywAtWTyenW-wgrSXjX0zfS0M1RmZADO/w365-h400/76F12562-240E-4167-8F77-6A49560273BB.jpeg" width="365" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="text-align: left;"><small>A New Yorker cartoon by Evan Lian.</small></span></td></tr></tbody></table><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-9082205386142005492023-02-08T16:17:00.000+08:002023-02-08T16:17:02.327+08:00Freedom from Crypto Addiction<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmsd-LrdVG7LYcfqd86GaBqriKA3jzUbIoiuaQ6-8uJi6gO_Jcm8vTixtgBQn5YnNvi14N8inHQkjk0tMGbgsE4kJFcmE9Ko1D9Wjrc4N9GGwhf8WKEi14HtAmB6XkrQDQrB7VbWJvS0wz9HuMv7IxUgaYGfrTDJgY8ZEY7kS8y-mt0DtL4A_ukGUp/s1551/A49F0F54-269D-4951-B313-BEB0419065D6.jpeg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1551" data-original-width="1241" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmsd-LrdVG7LYcfqd86GaBqriKA3jzUbIoiuaQ6-8uJi6gO_Jcm8vTixtgBQn5YnNvi14N8inHQkjk0tMGbgsE4kJFcmE9Ko1D9Wjrc4N9GGwhf8WKEi14HtAmB6XkrQDQrB7VbWJvS0wz9HuMv7IxUgaYGfrTDJgY8ZEY7kS8y-mt0DtL4A_ukGUp/w512-h640/A49F0F54-269D-4951-B313-BEB0419065D6.jpeg" width="512" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><br /><i>Cure from crypto addiction needn’t be costly!</i><br /><br /></td></tr></tbody></table><p>Help is now dearly available for those who’re hard hit by the recent crypto winter.</p><p>For those who can’t afford the <i>nouveau-riche</i> treatment, or who’re thinking of following Anthony Bourdain’s or Jeffrey Epstein’s template, because there seems to be no way out, know that there’s a (better) way to come out of that hell.</p><p>A better and faster (or cheaper) solution for crypto addicts would be to attend a counseling-and-praying session or two so that they’d be delivered once for all from the spirit of gambling.</p><p>Complete deliverance and healing is a mere prayer away if they’d turn to the Deliverer-and-Healer who has the power to free them from their short- or long-term addiction or affliction or persecution.</p><p>The Miracle Worker who turned water into wine, or who used five loaves of bread and two fish to feed five thousand people or families, is waiting and willing to deliver them from their gambling or years-long bad habit or addiction if only they agree or humble themselves to be delivered.</p><p>May their pride (or unbelief or negative faith or ignorance) not be a stumbling block to their being freed from crypto addiction, massive debt, or financial ruin.</p><p><i>Freely yours</i></p><p><small>© Yan Kow Cheong, February 8, 2023.</small></p><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-57141674695095308452023-01-27T17:27:00.000+08:002023-01-27T17:27:10.333+08:00Crime Watch and Crime Math<p></p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp8T4uEXtXnhZeCJdVAQz4fYshEy7hnossVFPhemiCNnrH1H0qieGKE7uaOk42bGckTVzkWNuJN_0osgblIwefGDLnbHR-sClegyi3g-zc_Ezu1b9N0awsMcgqLU2NnRUDTTZuQ5hkhRGHh9pW2z9tOaJC_nAMXOdVVCMt8fvtU6w6T8tfRfEXCsTs/s1289/0ADBDF13-7A7E-40B6-8871-C10830262315.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="967" data-original-width="1289" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp8T4uEXtXnhZeCJdVAQz4fYshEy7hnossVFPhemiCNnrH1H0qieGKE7uaOk42bGckTVzkWNuJN_0osgblIwefGDLnbHR-sClegyi3g-zc_Ezu1b9N0awsMcgqLU2NnRUDTTZuQ5hkhRGHh9pW2z9tOaJC_nAMXOdVVCMt8fvtU6w6T8tfRfEXCsTs/w400-h300/0ADBDF13-7A7E-40B6-8871-C10830262315.jpeg" width="400" /></a></div><p><br /></p><p>Singapore is known for its low crime rate in the developed world, and those who occasionally peek at what’s happening in the island-state might be surprised to read about more local and foreign shoplifters being recently caught in CCTV-equipped supermarkets and <a href="https://www.todayonline.com/singapore/12-month-conditional-warning-3-australian-schoolgirls-arrested-shoplifting-orchard-rd-mall-3-others-get-stern-warning-2054751?cid=internal_sharetool_iphone_27012023_today" target="_blank">shopping centers</a> islandwide.</p><p><br /></p><p><b><i>Dark Data</i></b></p><p>Below is an immoral statistics question that could serve as a “teaching moment” to warn both elementary and middle school (or upper primary and lower secondary) students against shoplifting and crime, especially when inflation around the world is at an all-time high.</p><p>The 2020–2022 estimated losses from the <a href="https://www.todayonline.com/singapore/fairprice-infant-forumala-lock-theft-2092741?cid=internal_sharetool_iphone_26012023_today" target="_blank">thefts of milk powder</a> at retailers in Singapore are as follows:</p><p style="text-align: center;"><b>2020: $18,000 (73 cases)</b></p><p style="text-align: center;">2021: $26,000 (96 cases)</p><p style="text-align: center;"><b>2022: $27,000 (80 cases)</b></p><p style="text-align: center;">2023: $XY,000 (Z cases)</p><p>Based on past <a href="https://www.todayonline.com/singapore/baby-milk-powder-theft-cases-2022-police-2097396?cid=internal_sharetool_iphone_26012023_today" target="_blank">crime statistics</a>, and in the light of a gloomy global economy that could bring about a financial apocalypse if the war in Ukraine dragged on, and should Mother Nature lose her patience with earthlings in spite of frequent natural calamities visiting the planet in recent years, predict the number of milk powder thefts and the accompanying monetary loss that would occur in the “fine” city of Singapore, in 2023.</p><p>How much revenue (or fines) could the authorities generate from these shoplifters-turned-resellers of milk powder (<a href="https://www.cnn.com/2023/01/20/health/abbott-labs-doj-investigation/index.html" target="_blank">contaminated</a> or not) in the coming decade?</p><p>Would there be a (higher) jail sentence for repeated offenders of infant formula? Or is caning in the pipeline for hardcore thieves? Or hundreds of community service hours for those unfit to be behind bars for whatever health or wealth reasons?</p><p><br /></p><p><i><b>A Moral/Social Issue</b></i> </p><p>How many of these shoplifters genuinely couldn’t afford to feed their kids, especially when there is quasi-zero government assistance for the unemployed or underemployed, or for senior citizens with zero pension or savings in their “golden” years?</p><p>Do the shoplifters (and potential rioters) belong to some demographic groups that need the authorities to step in to avoid social disorders like public strikes and hate crimes perpetrated by racists-supremacists-turned-opportunists, which we’re witnessing in some right-wing political circles or red-pilled states?</p><p><br /></p><p><i><b>From Profit to Profiteering</b></i></p><p>Like pharmaceutical companies that are notoriously known to overprice or overcharge their products, milk powder manufacturers don’t seem to be any morally different from them. Unless their dear milk powder came from holy cows or goats that have been <i>anointed</i> by Vatican-approved priests!</p><p><br /></p><p><b><i>A Formula for an Equitable World</i></b></p><p>The social and political chaos plaguing many parts of the globe provides math educators worldwide an opportunity to step up and speak out against rogue politics and profiteering, poverty and inequality, and crime and robbery.</p><p>Some degree of equality or equity could come to pass via creative mathematical problem solving and active moral mindfulness on the part of math educators to help right some of the social ills, political hypocrisies, and business malpractices.</p><p><br /></p><p>Remember: <i>Low crime doesn’t mean no crime</i>.</p><p><br /></p><p><small>© <a href="https://singaporemathplus.net/" target="_blank">Yan Kow Cheong</a>, January 27, 2023.</small></p><div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com2tag:blogger.com,1999:blog-2432976803039259514.post-10515582756939248602019-11-01T02:33:00.000+08:002019-11-01T02:33:12.949+08:00Panda Math<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-family: inherit;">Two-odd years ago, with sporadic news on the low fertility rate of pandas, I cheekily coined “Panda Math”:</span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small;"><b>Panda</b> <b>Math</b> was published on Urban Dictionary before its online presence was cut short.</span></td></tr>
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<span style="font-family: inherit;"><span style="font-family: inherit;">Like the <a href="https://www.singaporemathplus.com/2019/07/rabbit-math.html?m=1" target="_blank">rabbit </a>and the koala, the <a href="https://en.m.wikipedia.org/wiki/Giant_panda" target="_blank">panda</a> is much liked and loved by </span>people<span style="font-family: inherit;"> of all ages and from different parts of the world. It's hard to imagine those who wouldn't like to be around a panda or two if they're given that rare </span>opportunity. <i>What are the odds</i> <i>that someone doesn't</i> <i>like both <span style="font-family: inherit;">math and panda?</span></i></span><br />
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<span style="font-family: inherit;">How could elementary and middle school math teachers leverage on the cute panda bear popular among school children to pose a number of brain-unfriendly math questions to sharpen their problem-solving skills?</span><br />
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<span style="font-family: inherit; font-size: 12pt;"><b>Panda Diplomacy and </b></span><b>Numeracy</b></span><br />
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<span style="font-family: inherit;">To </span>strengthen<span style="font-family: inherit;"> diplomatic ties, China loans pandas to countries around the world—a version of its soft diplomacy, </span>aimed at winning hearts and minds abroad.<br />
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<span style="font-family: inherit;"><span style="font-family: inherit;">The practice existed as far back as the <a href="https://en.m.wikipedia.org/wiki/Tang_dynasty" target="_blank">Tang Dynasty</a>, when Empress <a href="https://en.m.wikipedia.org/wiki/Wu_Zetian" target="_blank">Wu Zetian</a> (625–705) sent a pair of pandas to the Japanese emperor. </span><span style="font-family: inherit;">Giant pandas are very popular among the Japanese, and they symbolize the friendly ties between Japan and China then.</span></span></div>
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<i><span style="font-family: inherit;"><span style="font-family: inherit;">Guesstimate how many more pairs of pandas would be given as diplomatic gifts to other </span>China-friendly<span style="font-family: inherit;"> nations in the next decade, as President Xi and gang expand their political influence worldwide.</span></span></i></div>
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<span style="font-family: inherit;"><span style="font-family: inherit;">Below are a sample of questions that could be used to </span>spice<span style="font-family: inherit;"> the teaching of math, especially among panda-and-math lovers.</span></span><br />
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<tr><td style="text-align: center;"><img border="0" data-original-height="759" data-original-width="1224" height="123" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGvEUGF7tESGXlrhv_m9W_yB6lnNEz-GGHZeg-YW8kgJ4_1HJpCkCNONTqllnspnTRskyobrxTcssy5Q5LU29VtleRcqR7uQcuVZcodYGTsvd8XXSB1hz3GQHxBqpJPlDw_srdAhfx2Gc/s200/C1B69009-0F31-499E-8DEA-E4D67E62F48F.jpeg" style="margin-left: auto; margin-right: auto;" width="200" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Philamath embraces the panda.</td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGvEUGF7tESGXlrhv_m9W_yB6lnNEz-GGHZeg-YW8kgJ4_1HJpCkCNONTqllnspnTRskyobrxTcssy5Q5LU29VtleRcqR7uQcuVZcodYGTsvd8XXSB1hz3GQHxBqpJPlDw_srdAhfx2Gc/s1600/C1B69009-0F31-499E-8DEA-E4D67E62F48F.jpeg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-family: inherit;"></span></a><span style="font-family: inherit; font-size: 12pt;"><span style="font-family: inherit;"><span style="font-size: small;">Sally bought some 50-cent and 65-cent stamps for a total of $5.10. How many 50¢ stamps and how many 65¢ stamps did she buy? </span><span style="font-size: xx-small;">Answer: Five 50¢ and four 65¢ stamps</span></span><span style="font-family: "helvetica"; font-size: xx-small;">.</span></span></div>
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<span style="font-family: inherit;">Chuang Chuang, a 19-year-old giant panda died </span>unexpectedly in a Thai zoo. Assume that giant pandas normally live up to 25 to 30 years in captivity, in human terms, how old would the cute and cuddly bear be? </span></div>
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<span style="font-family: inherit; font-size: 12pt;"><b>Adult Math</b></span></div>
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<span style="font-family: inherit;">Let's bring in some biology to hone students' mathematical problem solving.</span><br />
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<span style="font-family: inherit;"><i>The Mating Game</i></span><br />
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<span style="font-family: inherit;"><span style="font-family: inherit;">On average, a baby panda weighs 100 g, which is only 1/900 of their mother's weight, compared to 1/20 for a human. During the breeding season, when males and females come together for no more than 2 to 4 days, what would be the </span>frequency<span style="font-family: inherit;"> for a male panda to mate with his partner before a baby bear is born?</span></span></div>
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<span style="font-family: inherit; font-size: 12pt;"><span style="font-size: small;">What are the chances of a pair of pandas producing baby giant panda twins*? Or even triplets? Are the odds of a female panda giving birth to triplets lower than those of a human being being hit by lightning, or winning the lottery twice?</span></span><br />
<span style="font-family: inherit; font-size: 12pt;"><span style="font-size: small;"><br /></span></span><span style="font-family: inherit; font-size: 12pt;"><span style="font-family: inherit; font-size: x-small;">* In the wild, half of all pandas give birth to twins; however, it is rare for both cubs to survive as the panda mother is only able to raise one at a time and abandon the second twin—she has insufficient milk or energy to care for the twins.</span></span></div>
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<span style="font-size: 12pt;">Or, what about getting grades 1–2 students to indulge in some <a href="https://www.amazon.com/Mathematical-Quickies-Trickies-Kow-Cheong/dp/9810854129/ref=mp_s_a_1_2?keywords=mathematical+quickies+%26+trickies&qid=1572541447&sr=8-2" target="_blank">mathematical quickies</a> such as the following?</span></span><br />
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<span style="font-family: inherit; font-size: 12pt;"><span style="font-size: small;">The total age of Kai Kai and Lin Lin at an unspecified zoo is 14. Kai Kai is 4 years older </span><span style="font-size: small;">than Lin Lin. How old is each panda bear? </span><span style="font-size: x-small;"><i>Hint</i>: Not 4 and 10</span><span style="font-size: small;">.</span></span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">At a zoo, all bears are pandas except two, all bears are polar bears except two, and all bears are brown bears except two. How many panda bears are there?</span></div>
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<span style="font-family: Times, Times New Roman, serif; font-size: 12pt;"><i>Love at First Sight (or Smell)</i></span><br />
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<span style="font-family: Times, Times New Roman, serif; font-size: 12pt;">Compared to African elephants, which can communicate over distances of one kilometer, or koalas up to 50 meters, pandas can recognize each other within a proximity of 20 meters. However, they can only figure out the gender of a potential mate if they are less than 10 meters away.</span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="font-style: italic;">Guesstimate the </span><i>total</i><span style="font-style: italic;"> distance adult pandas in the wild must travel every year before </span><i>lovemaking can successfully take place.</i></span></div>
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<span style="font-family: inherit; font-size: 12pt;"><i>Bamboo Math</i></span></div>
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<span style="font-family: inherit;">To maintain their energy needs, pandas must consume 12 kg to 38 kg worth of bamboo each day. </span><span style="font-family: inherit;">Estimate how must bamboo forests needs to be allocated to provide enough food to sustain them.</span></span></div>
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<span style="font-family: inherit;"><b><br /></b></span><span style="font-family: "times" , "times new roman" , serif; font-size: 12pt;"><b>Will the Panda Be Dodo 2.0?</b></span><br />
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<span style="font-family: Times, Times New Roman, serif; font-size: 12pt;">Barring extreme climate change, which would make it pretty hot for the bamboo to grow, what are the odds that with mating and breeding challenges, the giant pandas might suffer the fate of the <a href="https://en.m.wikipedia.org/wiki/Dodo" target="_blank">dodo</a>?</span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="font-family: inherit; font-size: 12pt;"><span style="font-family: Times, Times New Roman, serif;">Estimates suggest that there are fewer than 2000 pandas left in the wild. </span><span style="font-family: inherit;">If President Trump and gang are allowed to promote their climate change hoax or "global warring" agenda, are the days of the pandas numbered? How many panda bears would still be around by 2050?</span></span></span><br />
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<b><span style="font-family: inherit;">Singapore (Math) and Panda</span></b><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNT9oY_ZekjXXHZCSCO-KKiyNN8l6zNI09zxDQoj_TJpJ1CQ8iHCfQLgx3X1_zOFKX8gaPhBQtg4CNJKvo0-78nbA41mLM856AgfOZ8JQfcM1SZlWyN5l4gvDCKTX1OQOczJQQkI50fPg/s1600/F769E521-9D75-4303-BDF8-FECEB0A383F7.jpeg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto; text-align: center;"><span style="font-family: inherit;"><img border="0" data-original-height="415" data-original-width="511" height="161" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNT9oY_ZekjXXHZCSCO-KKiyNN8l6zNI09zxDQoj_TJpJ1CQ8iHCfQLgx3X1_zOFKX8gaPhBQtg4CNJKvo0-78nbA41mLM856AgfOZ8JQfcM1SZlWyN5l4gvDCKTX1OQOczJQQkI50fPg/s200/F769E521-9D75-4303-BDF8-FECEB0A383F7.jpeg" width="200" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: inherit; font-size: x-small;">The intersection is not empty.</span></td></tr>
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<span style="font-family: Times, Times New Roman, serif;"><span style="font-family: inherit;"><br /></span><span style="font-family: Times, Times New Roman, serif;"><span style="font-family: inherit;">On the surface, it looks like there is zero correlation between <i>Singapore</i> and <i>Panda.</i> Once we put on our thinking cap, it’s not difficult to come up with a number of parallels between these two </span>items.</span></span><br />
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<span style="font-family: inherit;"><span style="font-family: inherit;">For example,</span></span></span><br />
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<span style="font-size: 12px;"><span style="font-family: "georgia" , "times new roman" , serif;">Singapore’s <a href="https://www.singstat.gov.sg/modules/infographics/total-fertility-rate" target="_blank">fertility rate</a> of 1.14 is presently below replacement level. </span></span><br />
<span style="font-family: "georgia" , "times new roman" , serif; font-size: 12px;"><b>Pandas’ low fertility rate is a warning sign for possible extinction.</b></span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Singapore could have just ended being another Commonwealth developing country in a sea of corrupt, mediocre nations.</span></div>
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<b><span style="font-family: "georgia" , "times new roman" , serif; font-size: 12px;">The panda could have been just another member of the Bear family, </span><span style="font-family: "georgia" , "times new roman" , serif; font-size: 12px;">or a mere zoo attraction with hardly any global </span><span style="font-family: "georgia" , "times new roman" , serif;"><span style="font-size: 12px;">recognition.</span></span></b></div>
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<span style="font-family: "georgia" , "times new roman" , serif;"><span style="font-size: 12px;"><a href="https://www.urbandictionary.com/define.php?term=Singapore%20Math" target="_blank">Singapore math</a> is a "success story" in math education: the island state's top rankings in <a href="https://en.m.wikipedia.org/wiki/Trends_in_International_Mathematics_and_Science_Study" target="_blank">TIMSS</a> and <a href="http://www.oecd.org/pisa/" target="_blank">PISA</a> have attracted a fair bit of attention among math educators worldwide. </span></span></div>
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<span style="font-family: "georgia" , "times new roman" , serif; font-size: 12px;"><b>Breeding panda in captivity is a success story (including a few births in some zoos), and panda diplomacy promotes friendship between China and other countries.</b></span></div>
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<span style="font-family: "georgia" , "times new roman" , serif; font-size: 12px;">Singapore is a "Disneyland with a death penalty"—economic success and political </span><span style="font-family: "georgia" , "times new roman" , serif;"><span style="font-size: 12px;">stability at the expense of political freedom and an aversion to alternative lifestyles.</span></span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;"><span style="font-size: 12px;"><b>Pandas are a favorite attraction at zoos, which could be flown back if China's political system is questioned.</b></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaDG3WPqRWzTc-f4dJehJW34b7nf6LaoldZwiOANXWX3_QZVG7vPc_76W7kxnQQo-WRHTbI10p3bR1wlgLkvYeN_Vz0plmZIa5N43ckqauEbuGIJx0GwRHKOidFb9JZB8FnRQC0SCIpGQ/s1600/B3A2DBAE-16CA-47E7-AA7D-9BCEC5C21B22.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="722" data-original-width="600" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaDG3WPqRWzTc-f4dJehJW34b7nf6LaoldZwiOANXWX3_QZVG7vPc_76W7kxnQQo-WRHTbI10p3bR1wlgLkvYeN_Vz0plmZIa5N43ckqauEbuGIJx0GwRHKOidFb9JZB8FnRQC0SCIpGQ/s200/B3A2DBAE-16CA-47E7-AA7D-9BCEC5C21B22.jpeg" width="165" /></a><span style="font-family: "georgia" , "times new roman" , serif;"><span style="font-size: 12px;">The panda is the logo of the World Wide Fund for Nature (<a href="https://en.m.wikipedia.org/wiki/World_Wide_Fund_for_Nature" target="_blank">WWF</a>), </span></span><span style="font-family: "georgia" , "times new roman" , serif; font-size: 12px;">which originated from a panda named Chi Chi that had been </span><span style="font-family: "georgia" , "times new roman" , serif; font-size: 12px;">transferred from Beijing Zoo to London Zoo in 1958. </span></div>
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<b><span style="font-family: "georgia" , "times new roman" , serif;"><span style="font-size: 12px;">Singapore math is associated with the "bar model method," </span></span><span style="font-family: "georgia" , "times new roman" , serif; font-size: 12px;">a powerful problem-solving visualization heuristic to solve challenging </span><span style="font-family: "georgia" , "times new roman" , serif; font-size: 12px;">word problems.</span></b></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">Products "made in Singapore" are no longer shun away; instead, the Singapore brand is well respected in many parts of the world for quality and honesty.</span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;"><span style="font-size: 12px;"><b>Pandas are beloved zoo animals around the world, although capitalist China pays lip service to the rule of law and copyrights, and is silent on human rights abuses, kidnappings, and torture.</b></span></span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="font-family: inherit;">It's your turn to list another half a dozen similarities </span>between<span style="font-family: inherit;"> Singapore (or Singapore math) and pandas.</span></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoIDb3ZuWBoFK7kitzIVAJ2li04Qgr2Nlrcm8UO4KHKaIAZOonRzgJOFQWDqYZ5nn0Eh2Y1OYU4bd_-l5JMsNNBDlypFtdg7cmPTbzYNmz-KifdIE8boDJ9OoA_adYvc6um4wU8MboAIs/s1600/C518C06F-A11B-4ACE-A1FC-F69B576D8138.jpeg" imageanchor="1" style="font-family: -webkit-standard; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="800" data-original-width="800" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoIDb3ZuWBoFK7kitzIVAJ2li04Qgr2Nlrcm8UO4KHKaIAZOonRzgJOFQWDqYZ5nn0Eh2Y1OYU4bd_-l5JMsNNBDlypFtdg7cmPTbzYNmz-KifdIE8boDJ9OoA_adYvc6um4wU8MboAIs/s200/C518C06F-A11B-4ACE-A1FC-F69B576D8138.jpeg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small;">When the panda refuses to remain silent on illegal occupation.</span></td></tr>
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<span style="font-family: inherit; font-size: x-small;"><b>Bibliography & References</b></span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="font-family: inherit; font-size: x-small;">Third time lucky? Pandas Kai Kai, Jia Jia get down to </span><span style="font-family: inherit; font-size: x-small;">‘serious business’ </span><span style="font-family: inherit; font-size: x-small;"><a href="http://www.todayonline.com/node/2827076">http://www.todayonline.com/node/2827076</a> </span></span></div>
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<span style="font-family: Times, Times New Roman, serif; font-size: x-small;">Giant panda death in Thailand leaves China asking questions <a href="https://www.bbc.co.uk/news/world-asia-49737215">https://www.bbc.co.uk/news/world-asia-49737215</a></span></div>
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<span style="font-family: Times, Times New Roman, serif; font-size: x-small;">Giant pandas can tell a mate from their calls <a href="http://www.bbc.co.uk/news/science-environment-45575604">http://www.bbc.co.uk/news/science-environment-45575604</a></span></div>
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<span style="font-family: Times, Times New Roman, serif; font-size: x-small;">Panda's habitat 'shrinking and becoming more fragmented' <a href="http://www.bbc.co.uk/news/science-environment-41366274">http://www.bbc.co.uk/news/science-environment-41366274</a></span></div>
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<span style="font-family: Times, Times New Roman, serif; font-size: x-small;">How did China save the giant panda? <a href="http://www.bbc.co.uk/news/world-asia-china-37273337">http://www.bbc.co.uk/news/world-asia-china-37273337</a></span><br />
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<span style="font-family: inherit; font-size: xx-small;">ⓒ <a href="https://www.singaporemathplus.net/" target="_blank">Yan Kow Cheong</a>, October 31, 2019.</span></span></span><br />
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<div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com1tag:blogger.com,1999:blog-2432976803039259514.post-81486626688549393022019-07-30T13:33:00.000+08:002019-07-30T13:33:48.979+08:00Rabbit Math<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: inherit;">Looking at the number of math questions that feature animals and birds, not even man’s best friend comes close to the rabbit—the beloved pet of math writers and teachers.</span></div>
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<span style="font-family: inherit;"><span style="font-family: inherit;">Think of the <a href="https://en.m.wikipedia.org/wiki/Fibonacci_number" target="_blank">Fibonacci numbers</a>, published by Leonardo of Pisa </span>in <i><a href="https://en.m.wikipedia.org/wiki/Liber_Abaci" target="_blank">Liber Abaci</a> </i>("Book of the Abacus" or "Book of Calculating") in 1202, in connection with the rabbit population:</span></div>
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<span style="font-family: "times" , "times new roman" , serif;"><b>If every month a pair of rabbits produces one new pair, which begins to bear young two months after its own birth, how many pairs of rabbits will there be after a year?</b></span><br />
<span style="font-family: "times" , "times new roman" , serif;"><b><br /></b></span><span style="font-family: inherit;">Show that at the end of the twelfth month, there will be a dozen dozen pairs from a single pair.</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFWP5ZFwWsY1WjF6OLNuFX2PTOUhBSEOMJXmzNX12VY9D-lEsJu7y4z9KYNzpKbb4gm_KswRhyqDAGeAmSaspcbBR5OHPu7WFyhnZPA2nVFdF6cANNcxB1BmeFAY2PKuneXGBSq04IEKU/s1600/file+12-6-17%252C+9+30+59+am.jpeg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="294" data-original-width="420" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFWP5ZFwWsY1WjF6OLNuFX2PTOUhBSEOMJXmzNX12VY9D-lEsJu7y4z9KYNzpKbb4gm_KswRhyqDAGeAmSaspcbBR5OHPu7WFyhnZPA2nVFdF6cANNcxB1BmeFAY2PKuneXGBSq04IEKU/s320/file+12-6-17%252C+9+30+59+am.jpeg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small;">An e-card I made before someecards banned users from designing their own. </span></td></tr>
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<span style="font-family: inherit; font-size: large;"><b>Why Singapore Math <i>Loves</i> Bunnies</b></span></h3>
<span style="font-family: inherit;"><span style="font-family: inherit;"><a href="https://www.urbandictionary.com/define.php?term=Singapore%20Math" target="_blank">Singapore math</a> wouldn’t quite stand out from other foreign math curriculums, without its unhealthy number of brain-unfriendly math questions on chickens and rabbits (and goats and sheep). </span>Even the smarter and (arguably) cleaner pigs unfairly lose out vis-à-vis the rabbits, simply because it's politically or religiously incorrect to use "infidel" pets or mammals and "haram" items in Singapore math textbooks, which are primarily targeted at a multiracial and multicultural student population. </span><br />
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<span style="font-family: inherit;"><span style="font-family: inherit;">Through my dozen-odd supplementary </span><a href="https://www.urbandictionary.com/define.php?term=Singapore%20Math%20Books" style="font-family: inherit;" target="_blank">Singapore math books</a><span style="font-family: inherit;">, I'm guilty of contributing to the undue stress inflicted on millions of bunnies and their caring (or </span>mathophobic?)<span style="font-family: inherit;"> owners around the globe. Below are two elementary math rabbit questions taken from my unpublished manuscripts:</span></span><br />
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<span style="font-family: "times" , "times new roman" , serif; line-height: 21.600000381469727px;"><b>A farmer has some chickens and rabbits. </b></span></div>
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<span style="font-family: "times" , "times new roman" , serif; line-height: 21.600000381469727px;"><b>There are 60 eyes and 100 legs altogether. </b></span></div>
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<span style="font-family: "times" , "times new roman" , serif; line-height: 21.600000381469727px;"><b>How many chickens and how many rabbits are there?</b></span></div>
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<span style="font-family: "times" , "times new roman" , serif;"><span style="line-height: 21.600000381469727px;">Since both chickens and rabbits each have 2 eyes, the total number of animals is 60 </span><span style="line-height: 21.600000381469727px;">÷</span><span style="line-height: 21.600000381469727px;"> </span>2 = 30.</span></div>
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<span style="font-family: "times" , "times new roman" , serif;"><span style="line-height: 21.600000381469727px;">Suppose all 30 animals were chickens. Then there would be a total of 30 ×</span><span style="line-height: 21.600000381469727px;"> 2 = 60 legs.</span></span></div>
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<span style="font-family: "times" , "times new roman" , serif; line-height: 21.600000381469727px;">So the extra (100 – 60) = 40 legs must have come from the rabbits.</span></div>
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<span style="font-family: "times" , "times new roman" , serif; line-height: 21.600000381469727px;">Each rabbit has (4 – 2) = 2 more legs than a chicken.</span></div>
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<span style="font-family: "times" , "times new roman" , serif;"><span style="line-height: 21.600000381469727px;">So there are 40 ÷</span><span style="line-height: 21.600000381469727px;"> 2 = 20 rabbits and 30 – 20 = 10 chickens.</span></span></div>
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<span style="line-height: 21.600000381469727px;"><span style="caret-color: rgb(16, 16, 15); color: #10100f; font-family: "times" , "times new roman" , serif;"><i>Challenge</i>: Can you solve the above word problem, using a different method, say, the <i><a href="https://www.singaporemathplus.net/stack-modeling-as-mathematical-art/" target="_blank">Stack Model Method</a>,</i> or the <i><a href="http://twitter.com/SakamotoMath" target="_blank">Sakamoto Method</a></i>?</span></span><br />
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<span style="line-height: 21.600000381469727px;"><span style="caret-color: rgb(16, 16, 15); color: #10100f; font-family: inherit;">The next grade five or six question showcases two methods of solution, commonly used in Singapore local schools—students aren't expected to solve it by substitution or elimination methods, as these aren't formally taught in elementary school.</span></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEge0KFZiC6N31CXlnJ5B8Bdf4HIw3C-Yzr8i9XQjm82NlARCC4A1sA8Z9BlYv_ZjTUThBpIgqhinOV_rWwacb6SjqJT7xJAcGDm8lR3HhURmECaqHcfgog0E6G48HqAGL2t4xv9Hy_ClhY/s1600/4D730904-1EC0-4598-9EE7-BCACE4C2245C.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1376" data-original-width="759" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEge0KFZiC6N31CXlnJ5B8Bdf4HIw3C-Yzr8i9XQjm82NlARCC4A1sA8Z9BlYv_ZjTUThBpIgqhinOV_rWwacb6SjqJT7xJAcGDm8lR3HhURmECaqHcfgog0E6G48HqAGL2t4xv9Hy_ClhY/s640/4D730904-1EC0-4598-9EE7-BCACE4C2245C.jpeg" width="352" /></a></div>
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<span style="font-family: inherit; font-size: large; line-height: 21.600000381469727px;">Guess Who's <i>Suing </i>Singapore?</span></h3>
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<span style="font-family: inherit; line-height: 21.600000381469727px;">A few years ago, I produced the bunny meme pictured below and posted it on the Imgur app, together with the accompanying wicked question:</span></div>
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<span style="font-family: "times" , "times new roman" , serif; line-height: 21.600000381469727px;"><b>Farmer Yan has almost twice as many chickens as rabbits. </b></span></div>
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<span style="font-family: "times" , "times new roman" , serif; line-height: 21.600000381469727px;"><b>The total number of legs and heads is 184.</b></span></div>
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<b><span style="font-family: "times" , "times new roman" , serif;">How many rabbits are there?</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuVGnrUWDLTrl1BsbiHhAqUOJAkCxgR-tLQMwUfw10x_lz1rFrFjD9as1UTUv975SqkjFncL-YjRvhL3h-uCBxyxdBbbQPRW0nTTaQJWC2SIldBOesETbIRRgnDGYqM_WoMNktgtXN1F8/s1600/34DB950B-7E20-46F5-BCEA-9F0AACD632F2.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="800" data-original-width="800" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuVGnrUWDLTrl1BsbiHhAqUOJAkCxgR-tLQMwUfw10x_lz1rFrFjD9as1UTUv975SqkjFncL-YjRvhL3h-uCBxyxdBbbQPRW0nTTaQJWC2SIldBOesETbIRRgnDGYqM_WoMNktgtXN1F8/s320/34DB950B-7E20-46F5-BCEA-9F0AACD632F2.jpeg" width="320" /></a></div>
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Now you know why these angry bunnies are "mathematically stressed," compared to the lazy, pampered cats and guinea pigs! Can you show why the answer is 17 rabbits? If as an elementary math student you could solve this, the odds that you might be born or blessed with the "mathematical gene" are pretty high.</div>
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<span style="font-family: inherit; font-size: large;">Murderous Math—Let's <i>Prey</i></span></h3>
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<span style="font-family: "times" , "times new roman" , serif; font-size: 16px;">In the wild, the rabbit is inarguably the most preyed-on animal in the world: from cobras, pythons, eagles, owls, lions, tigers, wolves, and hyenas, just to name a few common predators.</span></div>
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<span style="font-family: inherit;"><span style="font-family: "times" , "times new roman" , serif; font-size: 16px;">Guesstimate how many predators depend on the rabbits for their livelihoods every year. Or, how many rabbits have their lives cut short to feed their predators? Well, see these predators as playing their part in maintaining a healthy ecosystem for mankind—a <i>proof</i> that life isn't fair.</span></span></div>
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<span style="font-family: inherit; font-size: large;">Political Rabbit Math</span></h3>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRPxHkNO_1XE0mxYvQrNMRwYhjO2adl3er6U4tUNaZnbjUTSF4bgoPSSD-45bozrETkHnOO3wVQCCIytnl4VuGkxorUtGne5H1ZhcrllX_ucYuNP7rWwa-gD6sYASmD2tXUAE4yM9iD8I/s1600/C96EC091-7876-4705-8DE0-DC2C8ABB73AD.jpeg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1359" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRPxHkNO_1XE0mxYvQrNMRwYhjO2adl3er6U4tUNaZnbjUTSF4bgoPSSD-45bozrETkHnOO3wVQCCIytnl4VuGkxorUtGne5H1ZhcrllX_ucYuNP7rWwa-gD6sYASmD2tXUAE4yM9iD8I/s200/C96EC091-7876-4705-8DE0-DC2C8ABB73AD.jpeg" width="167" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small;">My childhood made-in-China candies</span></td></tr>
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<span style="font-family: inherit; font-size: small;"><span style="font-weight: normal;">Recently, in the heat of </span><span style="font-weight: normal;">the</span><span style="font-weight: normal;"> trade war between the US and China, </span><span style="font-weight: normal;">as nationalistic mainland Chinese tried to promote their own brands </span><span style="font-weight: normal;">of local products, I coined </span><i style="font-weight: normal;">Rabbit Math</i><span style="font-weight: normal;"> and got it approved on </span><span style="font-weight: normal;"><a href="https://www.urbandictionary.com/" target="_blank">Urban Dictionary</a>, before some mean fellow probably </span><span style="font-weight: normal;">with an axe to grind maniacally tried to continually downvote the phrase</span><span style="font-weight: normal;"> and had it taken down </span><span style="font-weight: normal;">from cyberspace.</span></span></div>
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<span style="font-family: inherit;"><span style="font-family: inherit; font-size: small;"><span style="font-weight: normal;"></span></span><br /><span style="font-family: inherit; font-size: small;"><span style="font-weight: normal;"></span></span><span style="font-weight: normal;"><span style="font-family: inherit;">Beware</span> of "digital terrorists" who just </span><span style="font-weight: normal;">don't</span><span style="font-weight: normal;"> want to see even neutral mathematical </span><span style="font-weight: normal;">terms or words floating </span><span style="font-weight: normal;">on the</span><span style="font-weight: normal;"> internet—indeed, </span><span style="font-weight: normal;">this sounds like the mathematical </span><span style="font-weight: normal;">equivalent of <a href="https://en.m.wikipedia.org/wiki/Boko_Haram" target="_blank">Boko Haram</a>.</span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0QCttWJFEInETcUcGODO-Ly2AdpUrio3o9vEi7yRiZjzu1TuzY4rPmxBXqy4vH8GMTmPNn-WPJNPAPo1ZzF-5ch82RbGoNf1Ks_PiYlJKQ1FVcg_TqtjuJLwSMOzUabEaNirJgrqRVBs/s1600/A2A552EC-D3CE-4E85-84BF-3D3AD39B5E81.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1386" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0QCttWJFEInETcUcGODO-Ly2AdpUrio3o9vEi7yRiZjzu1TuzY4rPmxBXqy4vH8GMTmPNn-WPJNPAPo1ZzF-5ch82RbGoNf1Ks_PiYlJKQ1FVcg_TqtjuJLwSMOzUabEaNirJgrqRVBs/s400/A2A552EC-D3CE-4E85-84BF-3D3AD39B5E81.jpeg" width="345" /></a></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7RV5ucILm3m_PF8nkJbB-aks4YBx8ErHzlZuWyrNP6Rw_4Rj6QiZ-CqGZBhmrCzIQ0bWZx5fwOFwJCaJ9Os0HVhqmwFF97W81NP9BiB0K-4K1HP3RXRVjJ8JOrR2gOBtuPoNw7N3KjNA/s1600/4D0E8FD4-A238-4235-A055-C2D204C1CC8C.jpeg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><span style="font-family: inherit; font-size: medium;"><img border="0" data-original-height="1600" data-original-width="1567" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7RV5ucILm3m_PF8nkJbB-aks4YBx8ErHzlZuWyrNP6Rw_4Rj6QiZ-CqGZBhmrCzIQ0bWZx5fwOFwJCaJ9Os0HVhqmwFF97W81NP9BiB0K-4K1HP3RXRVjJ8JOrR2gOBtuPoNw7N3KjNA/s200/4D0E8FD4-A238-4235-A055-C2D204C1CC8C.jpeg" width="195" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="text-align: left;"><span style="font-family: inherit; font-size: xx-small;">One pair of rabbits can produce 60 babies a year.</span></span></td></tr>
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<span style="font-family: inherit; font-size: large;">Go Forth and Multiply</span></h3>
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<span style="font-family: Times, Times New Roman, serif;"><span style="font-family: inherit;">Before 1788, there were zero rabbits in Australia. That year, rabbits arrived on a boat from England; by 1950, there were </span>600-odd million rabbits in the Land of the Kangaroos.</span></div>
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<span style="font-family: Times, Times New Roman, serif; font-size: 12pt;">If humans had babies at the rate rabbits do, show that our global population would double every three weeks. </span></div>
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<b><span style="font-family: inherit; font-size: large;">The Rabbit Habit</span></b></h3>
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<span style="font-family: "georgia" , "times new roman" , serif;"><span style="font-family: inherit;">Early this year, I christened "5-Day Weeken</span><span style="font-family: inherit;">d" as a working template to promote creativity and productivity among time-poor workers, who always complain that their weekends are too short, and can't hardly get any productive work done on weekdays.</span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaPnAsYquTzoV7LHDnlfA5rhyphenhyphenHbowdgRFCr5vR0LorfOV-h5Vmci_hkz9RCTfGaK3EJYpJexU1faeGI0MKoflPZfeS-Xxc-mt7sCKKYFx833_MZYGL0w2mhz_7WVQru6iEygjXBkbiWGY/s1600/C5219C07-CE0D-4FBA-8744-859AFA51F2D0.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1103" data-original-width="1451" height="302" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaPnAsYquTzoV7LHDnlfA5rhyphenhyphenHbowdgRFCr5vR0LorfOV-h5Vmci_hkz9RCTfGaK3EJYpJexU1faeGI0MKoflPZfeS-Xxc-mt7sCKKYFx833_MZYGL0w2mhz_7WVQru6iEygjXBkbiWGY/s400/C5219C07-CE0D-4FBA-8744-859AFA51F2D0.jpeg" width="400" /></a></div>
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<b><span style="font-family: inherit; font-size: large;"><i>Rabbits by Numbers</i></span></b></h3>
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<span style="font-family: inherit;">Let me end with some tidbits about the </span>idiosyncrasies of our beloved bunnies.</div>
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<span style="font-size: xx-small;">From: Mike Lowery’s “Random Illustrated Facts” (2017)</span></div>
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Those of you, who are bunny lovers, please share with the rest of us your favorite numerical factoids or <a href="https://www.amazon.com/Numeroids-Number-Things-Didnt-Know/dp/1903071186" target="_blank">numeroids</a> about these cute animals.</div>
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<span style="font-family: inherit; font-size: large;"><i>As Productive as Fibonacci</i></span></h3>
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<span style="font-family: inherit;">Amateur-mathematician <a href="https://plus.maths.org/content/life-and-numbers-fibonacci" target="_blank">Fibonacci</a> was </span>a<span style="font-family: inherit;"> math popularizer and writer, who promoted the Hindu numerals during his European travels, besides blessing the mathematical brethren with a number of interesting or story </span>arithmetic<span style="font-family: inherit;"> problems, one of which is the "rabbit problem" for which he's dearly </span>remembered<span style="font-family: inherit;"> today. </span></div>
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<span style="font-family: inherit;">At a time </span>when greying Singapore is historically experiencing its <a href="https://mothership.sg/2019/03/spores-2018-fertility-rate-is-lowest-in-history-even-as-more-sporeans-get-married/" target="_blank">lowest fertility rate</a>—which may lead the island-state to go the way of the dodo, if no disruptive measures are taken, other than conveniently (or simplistically?) depending on <a href="https://babybonus.msf.gov.sg/parent/web/home?_afrLoop=1992030374378303&_afrWindowMode=0&_afrWindowId=null#%40%3F_afrWindowId%3Dnull%26_afrLoop%3D1992030374378303%26_afrWindowMode%3D0%26_adf.ctrl-state%3D63gedbc5t_4" target="_blank">baby bonus</a> incentives and immigration to arrest the population decline—for us, math educators, l<span style="font-family: inherit;">et's not stop being as mentally </span>fertile<span style="font-family: inherit;"> and creative and productive as Dr. Fibonacci, although few of us would dare to promote the kind of productivity rate of his fertile bunnies!</span></div>
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<b><span style="font-family: inherit; font-size: x-small;">Bibliography & References</span></b></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: xx-small;">Adam, F. (2014). <i><a href="https://blackwells.co.uk/bookshop/product/9781619637931?gC=f177369a3b&gclid=EAIaIQobChMIi7PxiIva4wIVw4RwCh2FqgfpEAQYAyABEgLIXPD_BwE" target="_blank">The awesome book of awesomeness</a></i>. London: Bloomsbury.</span><br />
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<span style="font-size: xx-small;"><span style="font-family: inherit; font-size: xx-small;">Fairbrass, M. & Tanguy, D. (2017). <i><a href="https://www.amazon.com/Scale-Things-Mind-blowing-Proportions-Extraordinary/dp/1787130576" target="_blank">The scale of things</a></i>. London: Quadrille Publishing Limited.</span></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif; font-size: xx-small;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif; font-size: xx-small;">Lowery, M. (2017). <a href="https://books.google.com.sg/books/about/Random_Illustrated_Facts.html?id=OWdCDgAAQBAJ&printsec=frontcover&source=kp_read_button&redir_esc=y" target="_blank">Random illustrated facts</a>. New York: Workman Publishing Co, Inc.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: xx-small;">White Rabbit milk tea sells at 2,000% premium as Chinese consumers show support for local brands amid trade war <a href="http://bit.ly/2KPj43h">http://bit.ly/2KPj43h</a></span><br />
<span style="font-family: Arial, Helvetica, sans-serif; font-size: xx-small;"><span style="font-family: inherit; font-size: xx-small;"><br /></span>
<span style="font-family: inherit; font-size: xx-small;">Yan, K. C. (2015). <i><a href="https://www.amazon.com/Stack-Model-Method-Grades-5-6/dp/9810938357/ref=sr_1_1?keywords=The+Stack+Model+Method&qid=1564421430&s=gateway&sr=8-1" target="_blank">The stack model method: An intuitive and creative approach to solving word problems—Grades 5–6</a></i>. Singapore: MathPlus Publishing.</span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif; font-size: xx-small;"><span style="font-family: inherit; font-size: xx-small;"><br /></span>
<span style="font-family: inherit; font-size: xx-small;">Yan, K. C. (2015). <i><a href="https://www.amazon.com/Stack-Model-Method-Grades-3-4/dp/9810938330/ref=sr_1_3?keywords=The+Stack+Model+Method&qid=1564421499&s=gateway&sr=8-3" target="_blank">The stack model method: An intuitive and creative approach to solving word problems—Grades 3–4</a></i>. Singapore: MathPlus Publishing.</span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif; font-size: xx-small;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif; font-size: xx-small;"><span style="font-family: inherit; font-size: xx-small;">Yan. K. C. (2013). The chickens-and-rabbits problem. </span><a href="https://www.singaporemathplus.net/the-chickens-and-rabbits-problem/">https://www.singaporemathplus.net/the-chickens-and-rabbits-problem/</a></span><br />
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<span style="font-family: inherit; font-size: xx-small;">© <a href="https://www.singaporemathplus.net/" target="_blank">Yan Kow Cheong</a>, July 30, 2019.</span></div>
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<div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com1tag:blogger.com,1999:blog-2432976803039259514.post-62864884328904398032019-01-31T13:47:00.000+08:002019-01-31T13:49:53.777+08:00Seven Irreverent Definitions of Singapore Math<div dir="ltr" style="text-align: left;" trbidi="on">
Since I started christening mathematical words on <a href="https://www.urbandictionary.com/" target="_blank">Urban Dictionary</a>, as someone who makes a living evangelizing the gospel of <a href="http://www.singaporemathplus.net/" target="_blank">Singapore Math</a>, it’s too tempting not to attempt defining the <i>love-or-hate</i> term, depending on your personal experience with the alien, hybrid math curriculum. Indeed, your geography or maturity would most likely determine your position or reaction vis-à-vis <i>Singapore Math</i>—for a number of you, not only you love <i>Singapore Math</i>, but <i>Singapore Math</i> loves you, too!<br />
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Since last December, I discovered that out of the hundreds-odd math terms or phrases I had contributed to <a href="https://www.urbandictionary.com/">Urban Dictionary</a>—the "anti-<a href="https://www.wikipedia.org/" target="_blank">Wikipedia</a>"—under different pseudonyms, one “terrorist stalker” has been serially and wickedly downvoting a number of them on a daily basis to the point that the online dictionary had to temporarily suspend and eventually remove the most downvoted entries to prevent further <i>digital abuse</i> or <i>digital persecution</i>—two of those deleted definitions involve <i>Singapore Math</i>.</div>
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The <i>Fear Factor</i> in Singapore Math Education</h4>
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If math teachers, tutors, writers, and editors were given the assurance that they wouldn't be punished, fined, jailed, or even caned for speaking up and speaking out on the good, the bad, and the ugly of Singapore math education, it's inconceivable why Singapore couldn't potentially become a global mathematical hub of choice for those born with the <i>mathematical gene</i> (let’s pretend that there’s such a thing) and a sense of humor or irreverence.</div>
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As a <i>proof</i> that we in <a href="https://www.urbandictionary.com/define.php?term=Singapore">Singapore</a> aren’t the boring, exam-smart math educators that some outside the island-state would like to portray us, below are seven <i>irreverent </i>or light-hearted<i> </i>definitions on <i><a href="https://www.urbandictionary.com/define.php?term=Singapore%20Math">Singapore Math</a></i>, which were approved and published on <a href="https://www.urbandictionary.com/">Urban Dictionary</a>, the World's No. 1 online dictionary.<br />
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<i>Could you figure out which two of the seven definitions were "censored" or deleted?</i> At one point, I thought maybe there is a vigilante math squad, a subset of the small army of moral and political policemen and women, recruited by the Singapore authorities to monitor any citizens or residents who try to publish any mathematical thing, which speaks ill of the government, the police, the army, and the judiciary. </div>
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Who knows that these e-censors might be on the lookout to report any "mathematical black sheep" to the authorities, who might then threaten and sue them, if they refuse to take down any content or comment that allegedly promotes the dark side of math or math education in Singapore?</div>
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<b><i>Singapore Math</i> with a New Twist</b></h4>
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May I encourage you to redefine “Singapore Math” based on your personal experience and interaction with fellow math educators, students, parents, and caregivers (or <i>maids-turned-tutors</i>). Indeed, <i>Singapore Math</i> has many faces, and your unique perception and definition of it would allow us to peek at a hitherto unseen (sexier or darker) side of it. It's never too late to share your definition (or frustration) with fellow math educators.<br />
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In <i>Singapore Math</i>, we trust!</div>
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<span style="font-size: x-small;">© <a href="http://www.singaporemathplus.net/" target="_blank">Yan Kow Cheong</a>, January 31, 2019</span><br />
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<div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com1tag:blogger.com,1999:blog-2432976803039259514.post-25771878603766064552015-10-15T20:54:00.001+08:002015-10-15T20:54:40.115+08:00Gross Singapore Math<div dir="ltr" style="text-align: left;" trbidi="on">
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif; font-size: xx-small; text-align: left;">© S. Mockus, & T. Millard, (2010)</span></td></tr>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Estimation (or <i>guesstimation</i> as it is more commonly known in the U.S.) is a creative mathematical activity that is seldom given enough curriculum attention and time in Singapore. For the lay public, and probably for a disturbingly large proportion of local math teachers, tutors, and parents, estimation is often confused with approximation (or rounding off numbers).</span><br />
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Like swimming, cycling, and driving, estimating ought to be a life skill that is indispensable for all responsible citizens aiming to be numerate in our quantitative world of bloated data.</span><br />
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b>A PSLE <i>Estimation Routine</i></b></span><br />
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br />In this year Singapore's PSLE (grade 6) math paper, a routine guesstimation <a href="https://t.co/cblkO4NQJX" target="_blank">MCQ question</a> has irked some parents, who "blamed" the Ministry of Education for posing an "unfair" question.</span></div>
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<tr><td class="tr-caption" style="text-align: center;"><i>Ghostly Math</i> from @MathPlus</td></tr>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b>How to <i>Fermi-ize</i></b></span><br />
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Current Singapore math textbooks are often too Puritan, not to say, boring, to contain fertile exercises that could hone students' estimation skills. A dose of humor, without insulting or shocking the readers, will go some way in nurturing some <a href="https://en.wikipedia.org/wiki/Fermi_problem" target="_blank">Fermi disciples</a>. Let's look at eleven non-drill-and-kill guesstimation questions, which could be posed to above-average math students bored by school math.</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><b>0. Zero Toilet Paper </b></span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">If all the toilet paper used in Singapore in an entire year were rolled out, how far would it stretch?</span></div>
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<tr><td class="tr-caption" style="text-align: center;"><b style="text-align: left;"><span style="font-family: Georgia, Times New Roman, serif; font-size: xx-small;"><a href="https://www.pinterest.com/pin/A-O9DAAQQFcH7_hlSxwAAAA/">https://www.pinterest.com/pin/A-O9DAAQQFcH7_hlSxwAAAA/</a></span></b></td></tr>
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<b><span style="font-family: Georgia, Times New Roman, serif;">1. The Trillionth Heartbeat</span></b></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Assuming an average human heart of 72 beats per minute, estimate that most folks would breathe their last breath around their billionth heartbeat, or by their near-666 weeks of life on this side of eternity.</span></div>
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<span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0); font-family: Georgia, Times New Roman, serif;"><b>2. Pools of Eyeballs</b></span><br />
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<span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0); font-family: Georgia, Times New Roman, serif;">About how many Olympic-sized swimming pools would all the world's human eyeballs fill?</span></div>
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<span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0); font-family: Georgia, Times New Roman, serif;"><b>3. Death Nailed by Tobacco Sticks</b></span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">© Chua Sin Yew</span></td></tr>
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<span style="-webkit-text-size-adjust: auto; font-family: Georgia, Times New Roman, serif;">A medical association claims that a cigarette smoker shortens the length of his life by 9 minutes for each cigarette smoked. A student smokes three-quarters of a pack of 20 cigarettes every day for 30 years. Excluding leap years, by how many months or years has this student cut short his life to?</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><b>4. To Pee or Not to Pee</b></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">How much urine is in a typical public swimming pool? Or, how much</span><span style="-webkit-tap-highlight-color: rgba(26, 26, 26, 0.294118); color: #262626; font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif; font-size: 16px;"> </span><a href="http://tinyurl.com/n65t64j" style="-webkit-tap-highlight-color: rgba(26, 26, 26, 0.294118); font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif; font-size: 16px;" target="_blank">pee in a pool</a><span style="-webkit-tap-highlight-color: rgba(26, 26, 26, 0.294118); color: #262626; font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif; font-size: 16px;"> </span><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">would kill you?</span></span></div>
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<b><span style="font-family: Georgia, Times New Roman, serif;">5. Length of Intestine</span></b></div>
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<span style="font-family: Georgia, 'Times New Roman', serif;">If you were to pull your small intestine out and laid it in a straight line, how long would that be? Is it shorter than the distance from Earth to Moon?</span></div>
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<b><span style="font-family: Georgia, Times New Roman, serif;">6. <i>A Nation of Vampires</i>—Human Blood Aplenty</span></b></div>
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<span style="font-family: Georgia, Times New Roman, serif;">If you were to take all the human blood from all the living people in Singapore and pour it into the Singapore Indoor Stadium, how deep would it be?</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8fd0RpWKgcWXbh7HXkpgit_EAxwnPJyGKgJGthnITTsAohwloDbv1DBdRHWdRu0QLn5oRM_8TDc7PvwsseMygrpg7Sb7j4T9say1n3BQjSCju00M2d3qhi-Rutp_-JIW1RRXIiFyIg2Y/s640/blogger-image-1883362468.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Georgia, Times New Roman, serif;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8fd0RpWKgcWXbh7HXkpgit_EAxwnPJyGKgJGthnITTsAohwloDbv1DBdRHWdRu0QLn5oRM_8TDc7PvwsseMygrpg7Sb7j4T9say1n3BQjSCju00M2d3qhi-Rutp_-JIW1RRXIiFyIg2Y/s320/blogger-image-1883362468.jpg" width="240" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif; font-size: xx-small;">© Mark Parisi</span></td></tr>
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<b style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><span style="font-family: Georgia, Times New Roman, serif;">7. Zoo Poo</span></b></div>
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<span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0); font-family: Georgia, Times New Roman, serif;">Estimate how much zoo poo is collected every week at the Singapore Zoological Gardens. How much of it could be used as fertilizers?</span></div>
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<b style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><span style="font-family: Georgia, Times New Roman, serif;">8. The Host with the Most</span></b></div>
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<span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><span style="font-family: Georgia, Times New Roman, serif;"><span style="line-height: 24px;">How many (unfriendly and not-s0-friendly) </span></span></span><span style="font-family: Georgia, Times New Roman, serif;"><span style="line-height: 24px;">bacteria are living on and inside you right now?</span></span></div>
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<b style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><span style="font-family: Georgia, Times New Roman, serif;">9. <i>Cash in on the Trash</i></span></b></div>
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<span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0); font-family: Georgia, Times New Roman, serif;">Show that, on average, every square mile of sea on the planet contains 46,000 pieces of rubbish. How much cash could be generated annually by an entrepreneur involved in the trash business? [1 mile is about 8/5 kilometers.]</span></div>
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<b style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);"><span style="font-family: Georgia, Times New Roman, serif;">10. <i>Green Pollution</i></span></b></div>
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<span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0); font-family: Georgia, Times New Roman, serif;">Thanks to Indonesia's mostly incompetent politicians and corrupt businessmen, its neighbors Malaysia, Singapore, and Thailand, have unhealthily been affected by the annual haze visiting them, as a result of illegal forest burning by local farmers to save costs for their bosses.</span></div>
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<span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0); font-family: Georgia, Times New Roman, serif;">Guesstimate the number of people inside and outside Indonesia, who have been affected in the last two decades from this man-made pollution. How many natives, Mohammedans, and "infidels" will die prematurely because of near-zero political will from oft-corrupt Indonesian politicians?</span></div>
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<b><span style="font-family: Georgia, Times New Roman, serif;">Estimation Skills via Gross, Illegal, or Murderous Math</span></b></div>
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<span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0); font-family: Georgia, Times New Roman, serif;">Be it via "Gross Math," "Murderous Math," or "Illicit Math," creative or fertile questions on the "shit," "death," or "illegal" business, could be posed to enhance students' guesstimating skills.</span></div>
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<span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0); font-family: Georgia, Times New Roman, serif;">Indeed, gross Singapore math could serve as a catalyst to imparting real-life estimation skills to students, and to reducing more complaints from <i>kiasu</i> Singapore parents, whose children will be sitting for the PSLE oft-dreaded math paper in coming years.</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0); font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: xx-small;">2. A</span>bout 73 swimming pools.</span></div>
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<span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0); font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: xx-small;">5. About 18 miles long.</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="-webkit-text-size-adjust: auto; font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: xx-small;">8. About </span>2,000,000,000,000,000 bacteria.</span><br />
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<b><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><i><br /></i></span></b></div>
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<b><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><i>BONUS: Some</i> Facebook<i> Estimation Quickies</i></span></b><br />
<b><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><br /></span></b>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">The Boring Talkative Math Teacher</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><a href="https://www.facebook.com/SingaporeMathPlus/posts/264086550381959:0">https://www.facebook.com/SingaporeMathPlus/posts/264086550381959:0</a></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">500 GB of data can store X books. What is X?</span></div>
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<a href="https://www.facebook.com/SingaporeMathPlus/posts/210130295777585"><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">https://www.facebook.com/SingaporeMathPlus/posts/210130295777585</span></a></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Number of people in the picture</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><a href="https://www.facebook.com/SingaporeMathPlus/posts/183777521746196:0">https://www.facebook.com/SingaporeMathPlus/posts/183777521746196:0</a></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Grave Humor</span></div>
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<a href="https://www.facebook.com/AddMaths360/posts/704358079657056:0"><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">https://www.facebook.com/AddMaths360/posts/704358079657056:0</span></a></div>
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<i style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif;"><a href="https://www.facebook.com/AddMaths360/posts/721850734574457:0" target="_blank">How to be a Real Jerk to the nth Degree</a></i><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif;"> </span><br />
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<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">Ballroom Readers' Institute (2011). <i>Uncle John's impossible questions and astounding answers</i>. Ashland, Oregon: Bathroom Readers' Press.</span><br />
<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span>
<span style="font-family: Georgia, 'Times New Roman', serif; font-size: x-small;">Krantz, S. G. (1997). <i>Techniques of problem solving</i>.</span><span style="font-family: Georgia, 'Times New Roman', serif; font-size: x-small;"> American Mathematical Society.</span><br />
<span style="font-family: Georgia, 'Times New Roman', serif; font-size: x-small;"><br /></span></div>
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<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">Mockus, S. & Millard, T. (2010). H<i>ow to speak zombie: A guide for the living</i>. San Francisco, CA: Chronicle Books LLC.</span></div>
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<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">Rimmer, G. (2005). <i>How to make a camel smoothie and other surreal sums</i>. Cambridge: Icon Books.</span></div>
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<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">Teng, A. (2015). An informed estimate is worth its weight in coins. <i>The Straits Times</i>, Oct 9, 2015. <a href="http://tinyurl.com/q7ly7bx" style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;">http://tinyurl.com/q7ly7bx</a></span></div>
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<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span></div>
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<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">The Bathroom Readers' Institute (2011). <i>Uncle John's bathroom reader impossible questions and astounding answers</i>. Ashland, OR: The Bathroom' Readers Innstitute.</span></div>
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<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span></div>
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<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">Yan, K. C. (2012). <i><a href="http://mathpluspublishing.com/mathematical-quickies-trickies-2/" target="_blank">Mathematical quickies and trickies</a></i>. Singapore: MathPlus Publishing.</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: xx-small;">© <a href="http://www.singaporemathplus.net/" target="_blank">Yan Kow Cheong</a>, October 15, 2015.</span></div>
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<div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-24830801801047254642015-03-01T01:18:00.000+08:002015-03-25T01:52:04.342+08:00A Dozen Numerical Deeds for the Chinese New Year<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: Georgia, Times New Roman, serif;">The <i>Lunar New Year</i> is often a time of receiving rather than a time of giving for most youngsters. However, like Christmas, for not-well-to-do donors, it's the worst time of the year, when they're expected to give <i>hong baos</i> or gifts to the younger generation, many of whom think it's their juvenile rights to receive these <i>red packets</i>.</span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjG-NEX2vbewFdUWpNyQSIGhfqe3cz3Y4vhQEQzc_NUQAUCRFjJt26z68Qhg25HroyJb1tHAUMDqXqW1xohdCcFQ8JxpEqqaIloaHbafnEme4QUEg2WxARgnJfjiw9v798mLZ01jyF_QGI/s640/blogger-image-1498931036.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><span style="font-family: Georgia, Times New Roman, serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjG-NEX2vbewFdUWpNyQSIGhfqe3cz3Y4vhQEQzc_NUQAUCRFjJt26z68Qhg25HroyJb1tHAUMDqXqW1xohdCcFQ8JxpEqqaIloaHbafnEme4QUEg2WxARgnJfjiw9v798mLZ01jyF_QGI/s400/blogger-image-1498931036.jpg" width="318" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="text-align: left;"><span style="font-family: Georgia, Times New Roman, serif;"><span style="font-size: small;">An extra zero is always welcomed! </span><br /><span style="font-size: x-small;">From: <i>The Straits Times</i>, Feb. 18, 2015. p. A24.</span></span></span></td></tr>
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<span style="font-family: Georgia, Times New Roman, serif;">In recent years, more shops and supermarkets are open during the Chinese New Year, because foreign workers and non-Chinese Singaporeans are willing to work overtime to serve locals, who would otherwise be inconvenienced when it comes to buying household items; or having a wallet-friendly meal, while they go around visiting friends and relatives. Not to say, foreign-born doctors and nurses who are on stand-by to look after local patients, who are admitted to hospitals during the Chinese New Year public holidays. </span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">There is no better time than the Chinese New Year to show our appreciation to the financially disadvantaged and to tens of thousands of migrants, who help sustain the economy, when most Chinese Singaporeans are having a good time catching up with relatives and friends.</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><b>A Dozen Deeds for Singaporeans of All Sizes, Shapes, and Ages</b></span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">Here are a dozen simple numerical deeds many could afford to do during this festive season, especially after receiving fat <i>hong baos</i> from senior family members and relatives.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkX_jP05C_vYYk_1hxejUTwfDqcLy_BK6DMiCmZZ9MjINEU8hvUPOF8YsCNCpgHpU9x4RS3T6GSY5Jz2n0V4f82wuBwPyNxYVOyBCvXVRJzAF_TIcMeortmcxhZvLldB10gVA3_YXAiF0/s640/blogger-image-195415798.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: Georgia, Times New Roman, serif;"><img border="0" height="122" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkX_jP05C_vYYk_1hxejUTwfDqcLy_BK6DMiCmZZ9MjINEU8hvUPOF8YsCNCpgHpU9x4RS3T6GSY5Jz2n0V4f82wuBwPyNxYVOyBCvXVRJzAF_TIcMeortmcxhZvLldB10gVA3_YXAiF0/s200/blogger-image-195415798.jpg" width="200" /></span></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2pRfuTIfYm7AevLp_45wHjNVe6tkqOjfk0TadRW2TDY0kyzKxX1v6m9fDCJGFRQFL0F7F5YrqmBqgRNxqTWys_tWcy6JOoG9Kx9vu3GJxs2-ZwKhudDeuapm1Tn5-j2ttqv-rhcxCCVk/s640/blogger-image--2061939145.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-family: Georgia, Times New Roman, serif;"><img border="0" height="111" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2pRfuTIfYm7AevLp_45wHjNVe6tkqOjfk0TadRW2TDY0kyzKxX1v6m9fDCJGFRQFL0F7F5YrqmBqgRNxqTWys_tWcy6JOoG9Kx9vu3GJxs2-ZwKhudDeuapm1Tn5-j2ttqv-rhcxCCVk/s200/blogger-image--2061939145.jpg" width="200" /></span></a><b><span style="font-family: Georgia, Times New Roman, serif;"></span></b><br />
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<b><span style="font-family: Georgia, Times New Roman, serif;">12. Give some iTunes or Google play gift cards to children from disadvantaged homes for them to purchase some educational apps or ebooks.</span></b><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXjhWDyBB0FavScR_PQ48Y_IqVZtZj8Sgu0hhdUrgRpSaK6cKJxDt51mRS0qBLzzw0SzkS0-PelmthivVMvmrawnrboxFy2DxFyk1C9gachSLmtF2tX0B4jfAOWIPH2PlOVnBUwfmnHB8/s1600/blogger-image-538130942.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXjhWDyBB0FavScR_PQ48Y_IqVZtZj8Sgu0hhdUrgRpSaK6cKJxDt51mRS0qBLzzw0SzkS0-PelmthivVMvmrawnrboxFy2DxFyk1C9gachSLmtF2tX0B4jfAOWIPH2PlOVnBUwfmnHB8/s200/blogger-image-538130942.jpg" width="200" /></a></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJNLSnE1GOhFrvPAIDUF548chDXpGhW8_lsYeeK8JVjLZqCh1QpZMbKWJGxWiCqM8LToWdLdzjq74qFPWJzG3nitXK6FGGKopn5r8JgVSAQ7gJrdCncYyu3SFjUyNdTF-TiNCYk3Vkirw/s640/blogger-image-339014902.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: Georgia, Times New Roman, serif;"></span></a><span style="font-family: Georgia, Times New Roman, serif;"><span style="-webkit-composition-fill-color: rgba(130, 98, 83, 0.0980392); color: rgba(0, 0, 0, 0.701961); font-family: UICTFontTextStyleBody; font-size: 19px;"><span style="font-family: Georgia, Times New Roman, serif;"><span style="-webkit-composition-fill-color: rgba(130, 98, 83, 0.0980392); color: rgba(0, 0, 0, 0.701961); font-family: UICTFontTextStyleBody; font-size: 19px;"><br /></span></span>
11. Do</span><span style="-webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">nate a <a href="https://play.google.com/store/books/details/Yan_Kow_Cheong_The_Stack_Model_Method_Grades_3_4?id=BP4QBgAAQBAJ&hl=en" target="_blank">math ebook</a>, or offer a <a href="http://mathpluspublishing.com/wp-content/uploads/2014/05/c9_quckiest.pdf" target="_blank">sample chapter</a>, or book voucher to someone whose child might benefit from it.</span></span><br />
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<b><span style="font-family: Georgia, Times New Roman, serif;">10. Overtip a waitress.</span></b></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJNLSnE1GOhFrvPAIDUF548chDXpGhW8_lsYeeK8JVjLZqCh1QpZMbKWJGxWiCqM8LToWdLdzjq74qFPWJzG3nitXK6FGGKopn5r8JgVSAQ7gJrdCncYyu3SFjUyNdTF-TiNCYk3Vkirw/s1600/blogger-image-339014902.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJNLSnE1GOhFrvPAIDUF548chDXpGhW8_lsYeeK8JVjLZqCh1QpZMbKWJGxWiCqM8LToWdLdzjq74qFPWJzG3nitXK6FGGKopn5r8JgVSAQ7gJrdCncYyu3SFjUyNdTF-TiNCYk3Vkirw/s320/blogger-image-339014902.jpg" width="225" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The book may be unsuitable for non-geeks!</td></tr>
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<span style="font-family: Georgia, Times New Roman, serif;">9. Give ten bucks to a street musician or blind person.</span></div>
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<b><span style="font-family: Georgia, Times New Roman, serif;">8. Compliment three strangers every day during this festive season.</span></b></div>
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<span style="font-family: Georgia, Times New Roman, serif;">7. Give a gift certificate or cash voucher to a beggar.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdrPAqMosbI2RfddHr98JrGooSYRw-JKDYBO9aPRFX5uQkbY5qQS3VMM2eHNM0Ez9e5EZSC-n8Ce7Dj6z0WCQNUwoYp24ncCRQz_tTBMqO6OffMEpWBAUjfBApmTJbHWe4tzRBRZaDXrw/s640/blogger-image-1412177918.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: Georgia, Times New Roman, serif;"></span></a></div>
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<b><span style="font-family: Georgia, Times New Roman, serif;">6. Bless a poor child with a Rubik's Cube.</span></b></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdrPAqMosbI2RfddHr98JrGooSYRw-JKDYBO9aPRFX5uQkbY5qQS3VMM2eHNM0Ez9e5EZSC-n8Ce7Dj6z0WCQNUwoYp24ncCRQz_tTBMqO6OffMEpWBAUjfBApmTJbHWe4tzRBRZaDXrw/s1600/blogger-image-1412177918.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="270" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdrPAqMosbI2RfddHr98JrGooSYRw-JKDYBO9aPRFX5uQkbY5qQS3VMM2eHNM0Ez9e5EZSC-n8Ce7Dj6z0WCQNUwoYp24ncCRQz_tTBMqO6OffMEpWBAUjfBApmTJbHWe4tzRBRZaDXrw/s320/blogger-image-1412177918.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Not all Rubik's cubes are made equal!</td></tr>
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<span style="font-family: Georgia, Times New Roman, serif;">5. Offer ten percents of your income to charity, on top of your tithe.</span></div>
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<b><span style="font-family: Georgia, Times New Roman, serif;">4. Surprise an old friend overseas with a phone call.</span></b></div>
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<tr><td style="text-align: center;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXT8LK0E7MzMO1Er_Bol24Jjcn8qwl5zD7LQWBdneypnr1kb2tA0J2RXeiNyZ4A0sWfxJqiJQ9Kh13Wz317VHHJmyqY-MkBKtvQQn2V2cNeQfqaagDjiWPqgk1SWRDjPq7kShmD0rKMl4/s320/blogger-image-942413400.jpg" style="margin-left: auto; margin-right: auto;" width="238" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">A value-for-money grade 3 SG math book</td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXT8LK0E7MzMO1Er_Bol24Jjcn8qwl5zD7LQWBdneypnr1kb2tA0J2RXeiNyZ4A0sWfxJqiJQ9Kh13Wz317VHHJmyqY-MkBKtvQQn2V2cNeQfqaagDjiWPqgk1SWRDjPq7kShmD0rKMl4/s640/blogger-image-942413400.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-family: Georgia, Times New Roman, serif;"></span></a><span style="font-family: Georgia, Times New Roman, serif;">3. Volunteer to teach or tutor someone how to use the model- or <a href="http://www.singaporemathplus.net/stack-modeling-as-mathematical-art/" target="_blank">stack-model method</a> as a problem-solving strategy to solve brain-unfriendly questions.</span></div>
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<b><span style="font-family: Georgia, Times New Roman, serif;">2. Settle the restaurant bill for a family of four strangers while they are enjoying their meal.</span></b></div>
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<span style="font-family: Georgia, Times New Roman, serif;">1. Buy a seasoned train ticket and give it to a poor person.</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">The time to spread happiness and joy is now, especially among foreign and migrant workers and the economically disadvantaged. For the young, it's never too early to be a cheerful giver! Let the spirit of giving be extended far and wide <i>vis-à-vis</i> disadvantaged Singapore citizens and residents!</span></div>
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<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">© <a href="http://www.singaporemathplus.net/" target="_blank">Yan Kow Cheong</a>, March 1, 2015.</span></div>
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<div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-25392095162354465372015-01-20T20:35:00.000+08:002015-01-20T20:35:46.061+08:00Another Math Ban from Singapore<div dir="ltr" style="text-align: left;" trbidi="on">
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<tr><td class="tr-caption" style="text-align: center;"><i>Sorry, U.S. accounts ONLY!</i></td></tr>
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<span style="font-family: Georgia, Times New Roman, serif;">A less-known disturbing fact in local educational publishing is that Singaporeans, Malaysians, and other nationalities can't purchase any Amazon Kindle and iBooks math e-books from their own local bookstore. For example, Singaporeans can't access to any free or paid e-books from Amazon or iTunes, unless they switch from the Singapore store to the U.S. store. This means they have to officially open a U.S. account with the bookseller, which is anything but a simple procedure. Why erect this wall to make it harder for Singaporeans and Malaysians to buy e-books in the U.S.?</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAwV_wmdjxZm5vkM-ReW6o5zWEYbfmA0-f5MzKgPmllwL5Tu7ffKRaIEvRe9Qxmfo9k6pIeHJIGWH-VxgFGo0RPhLRHhPcmrgAOaVE_6TZUHaTaYwuumN8me3ili9QGPVQwasxHBezYI0/s640/blogger-image--1984399644.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><span style="font-family: Georgia, Times New Roman, serif;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAwV_wmdjxZm5vkM-ReW6o5zWEYbfmA0-f5MzKgPmllwL5Tu7ffKRaIEvRe9Qxmfo9k6pIeHJIGWH-VxgFGo0RPhLRHhPcmrgAOaVE_6TZUHaTaYwuumN8me3ili9QGPVQwasxHBezYI0/s200/blogger-image--1984399644.jpg" width="125" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="http://www.amazon.com/Problems-Grades-Students-Singapore-Math-ebook/dp/B00LGRDHW4/ref=sr_1_2?ie=UTF8&qid=1421754785&sr=8-2&keywords=Yan+Kow+Cheong" target="_blank"><span style="font-family: Georgia, Times New Roman, serif;">Suitable for mathletes</span></a></td></tr>
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<span style="font-family: Georgia, Times New Roman, serif;">Last year, I released a Kindle book with Amazon, and I asked them why there is such a restriction on locals to download free, or to purchase paid, Amazon Kindle e-books. The answers were vague and unsatisfactory, to say the least. For instance, you can't even test or preview how your e-book will look like on certain platforms with certain apps, as they're not available in the Singapore store, unless you've a U.S. account, which makes it eligible for you to download them.</span></div>
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<i><b><span style="font-family: Georgia, Times New Roman, serif;">What's the Motive behind the Ban?</span></b></i><br />
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<span style="font-family: Georgia, Times New Roman, serif;">Several reasons have been conjectured online as to why locals can't access e-books from the world's biggest bookstore. <span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;">It looks like some decision-makers in Singapore and Malaysia are behind this ban to protect their vested business interests. If this is truly the case, then this augurs badly for the writing community or local publishing industry, especially for Singaporeans and Malaysians who plan to publish e-books under Amazon or iBooks. Interestingly, such a restriction doesn't apply for apps, though.</span></span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwh6VQL20afxF6l-2mzPXaV6UscVwykerSU3TZm5lxxZd9O8ZCUuoNXYAmGsDw96AZYxalN-BKYqhq2TRkInGgH4kqVcFxiIZ2r9kPvUmRkv3eZGezcxL5_39Jm_bTeCjGMuBppr_WdOw/s640/blogger-image-633536324.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><span style="font-family: Georgia, Times New Roman, serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwh6VQL20afxF6l-2mzPXaV6UscVwykerSU3TZm5lxxZd9O8ZCUuoNXYAmGsDw96AZYxalN-BKYqhq2TRkInGgH4kqVcFxiIZ2r9kPvUmRkv3eZGezcxL5_39Jm_bTeCjGMuBppr_WdOw/s640/blogger-image-633536324.jpg" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">No Singapore!</span></td></tr>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;"></span><span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;"></span>It'd be understandable if such a purchase ban were to apply to, say, North Koreans and Iranians, because Amazon and Apple might not want to deal with countries ruled by dictators who sponsor or promote terrorism and violence<span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;">. But to deprive ordinary citizens from countries whose human rights records are no worse than those in the Middle East and Asia, where women are often treated as second-class citizens, sounds like a business mockery! </span></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><i><b>Few Value-for-Money Apps</b></i></span><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;">With all these restrictions in place, one wonders whether this is the main reason why there have been few decent Singapore math apps (and far fewer math e-books) </span><span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;">on both Amazon and iTunes so far</span><span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;">. Presently, most math apps by locals on App Store are of little value—most just give away a sample chapter, or the Contents page, of their printed textbooks, unlike the paid Singapore math apps produced mainly by non-locals.</span></span></div>
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<i><b>Singapore Math iBooks</b></i></span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">Last week, I released two Singapore math books on iTunes; again, students, teachers, and parents in Singapore are unable to purchase them, because the titles are not available in the Singapore store. They need to have a US account to buy them. </span></div>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><span style="text-align: left;">App Store: <a href="https://itun.es/us/JCU84.l">https://itun.es/us/JCU84.l</a><br />Google play: </span><a href="http://tinyurl.com/pqfeh9s"><span style="background-color: rgba(255, 255, 255, 0);">h</span><span style="background-color: rgba(255, 255, 255, 0);">ttp://tinyurl.com/pqfeh9s</span></a></span></td></tr>
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<span style="font-family: Georgia, Times New Roman, serif;">A few local math educators are willing to review the books to better assess their suitability to audiences that might benefit from these problem-solving books, but they gave up when they couldn't do so from their tablets, which is, by default, connected to the Singapore store. It's already a pain to update apps like Kindle (which isn't available in the local store) much less purchase or review e-books that can only be downloaded with a U.S. account.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">It's an irony that our own local math students and teachers can't purchase Singapore math e-books, when others outside the country can freely and conveniently do so. The<b> </b>last thing we want is another ban that forbids us to assess mathematical knowhow, which <span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;">has zero correlation with politics, democracy, or terrorism.</span></span></div>
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<i><b>Google Play as a Last Resort</b></i></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">However, all isn't lost for those who still wish to access their free or paid Singapore math e-books online. They could download or buy them from Google play, if they are available there.</span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqJKHyZDl4E7ccRqiFAKVGzsUb6JkNmhqow-oDoy9GZSGWvw7sl6gGmVwj31S8EOuuU-OvQcOU8m-3TVnKHD1hZjs7DDgMX7gdD_0vAsAIQMpW8YaByqDqeEqqTBlCkPkkSPdNAepIZGs/s640/blogger-image-1761012269.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Georgia, Times New Roman, serif;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqJKHyZDl4E7ccRqiFAKVGzsUb6JkNmhqow-oDoy9GZSGWvw7sl6gGmVwj31S8EOuuU-OvQcOU8m-3TVnKHD1hZjs7DDgMX7gdD_0vAsAIQMpW8YaByqDqeEqqTBlCkPkkSPdNAepIZGs/s320/blogger-image-1761012269.jpg" width="214" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><span style="text-align: left;">App Store: <a href="https://itun.es/us/fP384.l">https://itun.es/us/fP384.l</a><br />Google play: </span><span style="text-align: left;"><a href="http://tinyurl.com/my8q3dt">http://tinyurl.com/my8q3dt</a></span></span></td></tr>
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<i><b><span style="font-family: Georgia, Times New Roman, serif;">The Future for Singapore Math E-Books</span></b></i></div>
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<i><b><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></b></i></div>
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<span style="font-family: Georgia, Times New Roman, serif;">At a time when the days of <span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;">printed boring math books are numbered, and more students and teachers are switching to smartphones and tablets as a new platform for learning and teaching, </span><span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;">restricting them to buying or downloading math e-books</span><span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;"> online is simply a dozen steps backwards to encouraging local writers—often stifled by politically correct local publishers and <i>faux</i> math editors—in reaching out to a wider local readership and global audience. </span></span><br />
<span style="font-family: Georgia, Times New Roman, serif;"><span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;"><br /></span></span>
<span style="font-family: Georgia, Times New Roman, serif;"><span style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;">Math and math education must be free and be freely available, not to be dictated by some folks with a profit agenda.</span></span></div>
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<span style="font-size: xx-small;"><span style="font-family: Georgia, Times New Roman, serif;">© <a href="http://www.singaporemathplus.net/" target="_blank">Yan Kow Cheong</a>, January 20, 2015.</span></span><br />
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<div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-13236183684894049802014-10-15T22:19:00.000+08:002014-10-15T22:19:21.618+08:00Stamping Up Singapore Math<div dir="ltr" style="text-align: left;" trbidi="on">
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<b style='mso-bidi-font-weight:normal'>20¢<o:p></o:p></b></p>
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mso-bidi-font-size:12.0pt;font-family:"Apple Chancery";mso-bidi-font-family:
"Times New Roman"'>MATH$ <o:p></o:p></span></b></p>
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<b
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mso-bidi-font-size:12.0pt;font-family:"Apple Chancery";mso-bidi-font-family:
"Times New Roman"'>I$ MONEY<o:p></o:p></span></b></p>
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</v:shape></v:group><![endif]--><!--[if !vml]--><span style="height: 107px; margin-left: 328px; margin-top: 4px; mso-ignore: vglayout; position: absolute; width: 87px; z-index: 251660288;"></span><!--[endif]--><span style="color: black; font-family: "Big Caslon"; mso-bidi-font-family: "Times New Roman";"><a href="http://www.singpost.com/" target="_blank">SingPost</a> seems to have somewhat </span><span style="font-family: 'Big Caslon';">cheapened the value of
Singapore stamps, by issuing First Day </span><span style="font-family: 'Big Caslon';">Covers, as if they're selling parking
coupons—Singapore issues, on average, </span><span style="font-family: 'Big Caslon';">a dozen sets of new stamps
every year.</span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLzS8DKvEuq0oi1t0hy-EXE4qJ6K8aYj0aHwZpEXP-SqdWMngTbqFLYqPorUrfK6HO0u3nqSX5CQRGnMXcpAuAN6wOGqwN-j2iFFU7ABOkA04h9HgRNFO_TCM4Rrn8f2TG4CR8fyIkVeA/s640/blogger-image-578257558.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLzS8DKvEuq0oi1t0hy-EXE4qJ6K8aYj0aHwZpEXP-SqdWMngTbqFLYqPorUrfK6HO0u3nqSX5CQRGnMXcpAuAN6wOGqwN-j2iFFU7ABOkA04h9HgRNFO_TCM4Rrn8f2TG4CR8fyIkVeA/s320/blogger-image-578257558.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Semi-circle stamps of yesteryear</td></tr>
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<span style="color: black; font-family: "Big Caslon"; mso-bidi-font-family: "Times New Roman";">In general, most Singapore
stamps have an uninteresting theme or design; SingPost's</span><span style="font-family: 'Big Caslon';"> commemoratives seem
to have been issued more as a means </span><span style="font-family: 'Big Caslon';">to generating extra revenue from stamp collectors, with little </span><span style="font-family: Big Caslon;">attention paid to aesthetics and beauty.</span></div>
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<span style="color: black; font-family: "Big Caslon"; font-size: large; mso-bidi-font-family: "Times New Roman";"><b>Numeracy via <i>Singapore Math</i> Stamps</b></span><br />
<span style="color: black; font-family: "Big Caslon"; mso-bidi-font-family: "Times New Roman";"><br /></span><span style="color: black; font-family: "Big Caslon"; mso-bidi-font-family: "Times New Roman";">In general, although philatelists don't have a positive view of Singapore stamps, however, not all is bleak for our postal department. To promote
mathematics and mathematics education in Singapore, in particular Singapore’s
mathematical achievements locally and internationally, it wouldn’t be a bad
idea if SingPost considers issuing commemoratives with a
mathematical flavor. For instance, it can issue First Day Covers on the following themes:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhddA7JXUsWQO5S3Il14cabpse5i8clORjwGAyoGkthTPHCvM19srtEDrluY06DYEtU2RgVMRxe03kQX72_nx5PpOiZiKt8DTr0liMISJfePDc6GGkTXW01gC1-soykm1YpgQNgRR3vgIc/s1600/StampTIMSS.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhddA7JXUsWQO5S3Il14cabpse5i8clORjwGAyoGkthTPHCvM19srtEDrluY06DYEtU2RgVMRxe03kQX72_nx5PpOiZiKt8DTr0liMISJfePDc6GGkTXW01gC1-soykm1YpgQNgRR3vgIc/s1600/StampTIMSS.jpg" height="320" width="260" /></a><b><span style="font-family: Symbol; font-size: 11pt;">·</span><span style="font-family: 'Big Caslon'; font-size: 11pt;"> A set of three stamps
featuring Singapore’s triple firsts at the Third International Mathematics and
Science Study (TIMSS), which has since put Singapore on the Mathematics Education World Map—an economic by-product of this would be to produce more localized adaptations of Singapore math textbooks, hopefully from some politically unstable, resources-rich developing countries;</span></b></div>
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the concrete-pictorial-abstract model </span><span style="font-size: 11pt;">in primary (or elementary) school mathematics, </span><span style="font-size: 11pt;">which arguably has contributed</span><span style="font-size: 11pt;"> </span><span style="font-size: 11pt;">to
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celebrating special <i>Math Days</i> like the <i style="mso-bidi-font-style: normal;"><a href="http://www.singaporemathplus.net/how-to-cook-up-numbers-on-an-abacus/" target="_blank">AbacusDay</a></i>, <i style="mso-bidi-font-style: normal;">Statistics </i></span></b><b><i><span style="color: black; font-family: "Big Caslon"; font-size: 11.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt;">Month</span></i><span style="color: black; font-family: "Big Caslon"; font-size: 11.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt;">, <i>Metric Week</i>, and <i>Pi Day</i>;</span></b></div>
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Asian superstitions, myths, and legends, related to annual festivals like the <a href="http://www.singaporemathplus.net/hungry-ghosts-dont-do-singapore-math/" target="_blank">Lunar Seventh Month</a> (or Ghost Month); or exposing pseudoscientific </span><span style="font-size: 15px;">beliefs involving so-called</span><span style="font-size: 11pt;"> <i>auspicious</i> and <i>inauspicious</i> (or <i>lucky</i> and <i>unlucky</i>) <i>numbers</i>, </span><i style="font-size: 11pt;">f</i><i style="font-size: 11pt;">eng shui</i><span style="font-size: 11pt;"> <i>numbers</i>, and </span><i style="font-size: 11pt;">I Ching</i><span style="font-size: 11pt;">;</span></span></div>
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<b><span style="font-family: Symbol; font-size: 11pt;">·</span><span style="font-family: 'Big Caslon'; font-size: 11pt;"> A set of stamps on the
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magic squares used by Asians in numerology and astrology;<o:p></o:p></span></div>
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<span style="color: black; font-family: Symbol; font-size: 11.0pt; mso-ascii-font-family: "Big Caslon"; mso-bidi-font-size: 12.0pt; mso-char-type: symbol; mso-hansi-font-family: "Big Caslon"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;"><b>·</b></span></span><span style="color: black; font-family: "Big Caslon"; font-size: 11.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt;"><b> A set of stamps featuring
Asian achievements in mathematics, whether at the International Mathematics
Olympiad (IMO) or in regional contests and competitions;</b><o:p></o:p></span></div>
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<br /></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPX6uwp1O466wyexWvZbM2VG80I6iwdDiW1qezSxQXjIRhHt6q0ib1T4FsOC85uU15U-1eXYr4wcwic4SzUGk4AObAgyTVQ-ErQS5gnbut4BhV3iJuPi2Ephr-CtNPT7SxjEUMgqATLhg/s1600/StampPentagon.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPX6uwp1O466wyexWvZbM2VG80I6iwdDiW1qezSxQXjIRhHt6q0ib1T4FsOC85uU15U-1eXYr4wcwic4SzUGk4AObAgyTVQ-ErQS5gnbut4BhV3iJuPi2Ephr-CtNPT7SxjEUMgqATLhg/s1600/StampPentagon.jpg" height="200" width="166" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The pentagonal framework defining <br />
Singapore's math curriculum</td></tr>
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<b
style='mso-bidi-font-weight:normal'><span style='font-size:10.0pt;
mso-bidi-font-size:9.0pt;font-family:"Century Gothic"'>SINGAPORE</span></b><span
style='font-size:9.0pt'><span style="mso-spacerun:yes"> </span></span><b
style='mso-bidi-font-weight:normal'>50¢</b><span style='font-size:10.0pt'><o:p></o:p></span></p>
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</v:shape></v:group><![endif]--><!--[if !vml]--><span style="height: 121px; margin-left: 339px; margin-top: 1px; mso-ignore: vglayout; position: absolute; width: 103px; z-index: 251657216;"></span><!--[endif]--><span style="color: black; font-family: Symbol; font-size: 11.0pt; mso-ascii-font-family: "Big Caslon"; mso-bidi-font-size: 12.0pt; mso-char-type: symbol; mso-hansi-font-family: "Big Caslon"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">·</span></span><span style="color: black; font-family: "Big Caslon";"><span style="font-size: 11pt;"> A set of stamps featuring
the five </span><span style="font-size: 15px;">components</span><span style="font-size: 11pt;"> of the mathematical </span></span><span style="font-family: 'Big Caslon'; font-size: 11pt;">problem-solving model (</span><i style="font-family: 'Big Caslon'; font-size: 11pt;">attitude</i><span style="font-family: 'Big Caslon'; font-size: 11pt;">,
</span><i style="font-family: 'Big Caslon'; font-size: 11pt;">metacognition</i><span style="font-family: 'Big Caslon'; font-size: 11pt;">, </span><i style="font-family: 'Big Caslon'; font-size: 11pt;">processes</i><span style="font-family: 'Big Caslon'; font-size: 11pt;">, </span><i style="font-family: 'Big Caslon'; font-size: 11pt;">concepts, </i><span style="font-family: 'Big Caslon'; font-size: 11pt;">and </span><i style="font-family: 'Big Caslon'; font-size: 11pt;">skills</i><span style="font-family: 'Big Caslon'; font-size: 11pt;">), </span><span style="font-family: 'Big Caslon'; font-size: 11pt;">which forms the framework of the mathematics curriculum in
Singapore;</span></div>
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<b><span style="color: black; font-family: Symbol; font-size: 11.0pt; mso-ascii-font-family: "Big Caslon"; mso-bidi-font-size: 12.0pt; mso-char-type: symbol; mso-hansi-font-family: "Big Caslon"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">·</span></span><span style="color: black; font-family: "Big Caslon"; font-size: 11.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt;"> A set of stamps featuring
the most commonly used (or misused or </span><span style="font-family: 'Big Caslon'; font-size: 11pt;">abused) heuristics (e.g., </span><i style="font-family: 'Big Caslon'; font-size: 11pt;">draw a
diagram</i><span style="font-family: 'Big Caslon'; font-size: 11pt;">, </span><i style="font-family: 'Big Caslon'; font-size: 11pt;">make a list</i><span style="font-family: 'Big Caslon'; font-size: 11pt;">, </span><i style="font-family: 'Big Caslon'; font-size: 11pt;">guess</i><span style="font-family: 'Big Caslon'; font-size: 11pt;"> </span><i style="font-family: 'Big Caslon'; font-size: 11pt;">and check</i><span style="font-family: 'Big Caslon'; font-size: 11pt;">, </span><i style="font-family: 'Big Caslon'; font-size: 11pt;">look </i><i><span style="font-family: 'Big Caslon'; font-size: 11pt;">for patterns</span></i><span style="font-family: 'Big Caslon'; font-size: 11pt;">, <i>work backwards</i>) and some artificially forced thinking skills </span><span style="font-family: 'Big Caslon'; font-size: 11pt;">(e.g., </span><i style="font-family: 'Big Caslon'; font-size: 11pt;">classifying</i><span style="font-family: 'Big Caslon'; font-size: 11pt;">, </span><i style="font-family: 'Big Caslon'; font-size: 11pt;">comparing</i><span style="font-family: 'Big Caslon'; font-size: 11pt;">, </span><i style="font-family: 'Big Caslon'; font-size: 11pt;">sequencing</i><span style="font-family: 'Big Caslon'; font-size: 11pt;">, </span><i style="font-family: 'Big Caslon'; font-size: 11pt;">identifying
patterns and relationships</i><span style="font-family: 'Big Caslon'; font-size: 11pt;">, </span></b><i><span style="color: black; font-family: "Big Caslon";"><b><span style="font-size: 15px;">analyzing</span><span style="font-size: 11pt;"> parts
and whole</span></b></span></i><span style="color: black; font-family: "Big Caslon"; font-size: 11pt;"><b>, <i>induction</i>, <i>deduction</i>, <i>spatial
visualization</i>);</b></span></div>
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<br /></div>
<div class="MsoNormal" style="margin-right: .5in;">
<span style="color: black; font-family: Symbol; font-size: 11.0pt; mso-ascii-font-family: "Big Caslon"; mso-bidi-font-size: 12.0pt; mso-char-type: symbol; mso-hansi-font-family: "Big Caslon"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">·</span></span><span style="color: black; font-family: "Big Caslon"; font-size: 11.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt;"> A set of stamps
commemorating the Singapore's Ministry of Education (MOE) <i>visions</i>:</span></div>
<div class="MsoNormal" style="margin-right: .5in;">
<div style="text-align: center;">
<span style="font-family: "Big Caslon"; font-size: 11.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt;"><b>1998:
<i style="mso-bidi-font-style: normal;">Thinking Schools, Learning Nation</i></b> <o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="margin-right: .5in;">
<div style="text-align: center;">
<span style="font-family: "Big Caslon"; font-size: 11.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt;"><b>2006:
<i style="mso-bidi-font-style: normal;">Teach Less, Learn More</i></b> <o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="margin-right: .5in;">
<div style="text-align: center;">
<span style="color: black; font-family: "Big Caslon"; font-size: 11.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt;">2014 and beyond: ?!?!</span><br />
<span style="color: black; font-family: "Big Caslon"; font-size: 11.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt;"></span><br />
<span style="color: black; font-family: "Big Caslon"; font-size: 11.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt;"></span></div>
<br />
<span style="font-family: Big Caslon; font-size: large;"><b><i>Glocalizing</i> Singapore Math via Philately</b></span><br />
<span style="font-family: Big Caslon;"><span style="font-size: 15px;"></span></span><br />
<span style="font-family: Big Caslon;"><span style="font-size: 15px;"></span></span></div>
<div class="MsoNormal" style="margin-right: .5in;">
<span style="font-family: 'Big Caslon';">To promote
an interest and appreciation of Singapore's (or Asia's) mathematical </span><span style="font-family: 'Big Caslon';">history and heritage in
philately, traveling exhibitions may be </span><span style="font-family: 'Big Caslon';">held
locally and regionally. For instance, rare philatelic gems</span><span style="font-family: 'Big Caslon';"> </span><span style="font-family: 'Big Caslon';">such
as mistakes, fakes, and forgeries—how mathematics can help </span><span style="font-family: 'Big Caslon';">detect
forgery and fraud in philately—may be showcased.</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "Big Caslon"; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt;">So, issuing Singapore stamps with a mathematical flavor would go a long
way to marketing and <i>glocalizing</i> Singapore math, while recognizing the contribution of local
math educators, on leveraging the
power of mathematics to help alleviate poverty, or lessen the economic
gap between the haves and the have-nots. Let’s stamp mathematics
firmly on Singapore postage stamps—glue is halal. <i>Stamp up, Singapore!</i><o:p></o:p></span></div>
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<br /></div>
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<br /></div>
<div class="MsoNormal">
<span style="font-family: "Big Caslon";"><b><span style="font-size: x-small;">For further
reading</span></b><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-right: .5in;">
<span style="color: black; font-family: "Big Caslon";"><span style="font-size: x-small;">Wilson. Robin J. (2001). <i>Stamping
through mathematics</i>. New York: Springer-Verlag.</span><span style="font-size: 11pt;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin-right: .5in;">
<br /></div>
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<div>
<small>© <a href="http://www.singaporemathplus.net/" target="_blank">Yan Kow Cheong</a>, October 15, 2014.</small></div>
</div>
<div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-63856262233334621822014-07-11T19:02:00.000+08:002015-10-07T16:14:57.632+08:00The Mathematics of 7Eleven®<div dir="ltr" style="text-align: left;" trbidi="on">
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">The chain of <a href="http://corp.7-eleven.com/" target="_blank">7–11</a> convenient stores is so called because these family-friendly outlets used to be open from 7:00 a.m. until midnight, but now they're open all the time in the least expected locations: 24/7/365. </span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Other than munching and gulping at odd hours at 7Eleven stores, these franchise outlets also provide a fertile ground for math educators to come up with some creative math questions to enhance their students' mathematical problem-solving skills. Here are a sample of eleven non-routine elementary and middle-school math questions that may appeal to your students.</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span></div>
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<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="http://media1.picsearch.com/is?4uM-ydK7Zt21LNkWuiG77vWFml3zBuS-D3fQMQ0V_BA&height=240" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="With prizes ranging from games t-shirts Oakley sunglasses figurines autographed posters and..." border="0" class="thumbnail" data-height="240" data-width="240" id="4uM-ydK7Zt21LNkWuiG77vWFml3zBuS-D3fQMQ0V_BA" src="http://media1.picsearch.com/is?4uM-ydK7Zt21LNkWuiG77vWFml3zBuS-D3fQMQ0V_BA&height=240" style="display: inline-block; height: 190.97081971309547px; padding: 0px; width: 190px;"></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">7-eleven.com</td></tr>
</tbody></table>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b>1. Number of Convenient Days </b></span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">In the U.K., 7/11 is abbreviated as 7th November; in the</span><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif;"> U.S., 7/11 is written as July 11. How many days are there from the U.S. date to the U.K. date?</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b>2. The Recurring 711</b></span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">What fraction represents the recurring (or repeating) decimal 0.711711711…?</span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b>3. The Day of the Week in 711 Days </b></span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">If 7/11 (July 11 in the United States) is a Friday, which day of the week was 7/11 in 2011? What day of the week will it be 711 days from now?</span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span></div>
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<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="http://etc.usf.edu/clipart/34000/34025/nclock-07-11_34025_sm.gif" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Clock 7:11" border="0" height="200" itemprop="contentUrl" src="http://etc.usf.edu/clipart/34000/34025/nclock-07-11_34025_sm.gif" width="200"></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Source: Clipart ETC</td></tr>
</tbody></table>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b></b></span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span></b></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><b><br></b></b></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><b>4. The Acute Angle at 7:11</b></b></span><br>
<br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">What is the angle between the minute hand and the hour hand at 7:11?</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span>
<br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b>5. The Likeliest 7/11 Day of the Week</b></span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Which day of the week is 7/11 most likely to fall in a 400-year calendrical cycle?</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b>6. Tangram-izing 7/11</b></span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span></div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgL7S_x0JDxi95czZoNw1i1c0GbtmvI2LcALInHamSIfO6sZcB-MLvjydQs58n5DNa1BH9xOBmrS5OjNIoXGjl-j5nUWxj9cqMyXyfZFtxhZ4Fc2F-4ABi4XV05jGh3Hhc7col5fjQpxFI/s1600/Tangram+7.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgL7S_x0JDxi95czZoNw1i1c0GbtmvI2LcALInHamSIfO6sZcB-MLvjydQs58n5DNa1BH9xOBmrS5OjNIoXGjl-j5nUWxj9cqMyXyfZFtxhZ4Fc2F-4ABi4XV05jGh3Hhc7col5fjQpxFI/s1600/Tangram+7.jpg"></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXLPjsAdwMyRyztVrvXfBmo3dr-rxjCCfl8YyJIcuLdar9TNKpnsZHD5XYdcVcQicbptpErLVHua1xkshKa8xIInoxZT4NB29lQzKoD78aq9RSq2MDBGZ9-DHqJKG-EY9HMp0xRA8xbjg/s1600/Tangram+1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXLPjsAdwMyRyztVrvXfBmo3dr-rxjCCfl8YyJIcuLdar9TNKpnsZHD5XYdcVcQicbptpErLVHua1xkshKa8xIInoxZT4NB29lQzKoD78aq9RSq2MDBGZ9-DHqJKG-EY9HMp0xRA8xbjg/s1600/Tangram+1.jpg"></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghyphenhyphenQCAA-KX51zU7EuQEjjg8hqV_RkXWEF2C_42oflofUFPEt24ehtlp5OKlY7B4KDS22WnwzB8dVyI7SGm_BzWEpVQ6Bhqnhvh9eCLk82AXCSTxEG52KHh_WGJ_K1UjzKL1XiwgiO1PZ0/s1600/Tangram+1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghyphenhyphenQCAA-KX51zU7EuQEjjg8hqV_RkXWEF2C_42oflofUFPEt24ehtlp5OKlY7B4KDS22WnwzB8dVyI7SGm_BzWEpVQ6Bhqnhvh9eCLk82AXCSTxEG52KHh_WGJ_K1UjzKL1XiwgiO1PZ0/s1600/Tangram+1.jpg"></a></div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Use three sets of the seven-piece Tangram to form the numerals 7 and 11.</span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
</div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b>7. Number Freaking 7/11</b></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">(a) Estimate the average revenue generated by all 7Eleven outlets in the United States every day.</span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">(b) </span><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif;">What land or area space is occupied by all 7/11 convenience stores in the world?</span><br>
<span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif;"><br></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b>8. Are There 711 Digits or More?</b></span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">How many digits do these indexed numbers have</span><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif;">? (a) </span><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif;">7<sup>11</sup> (b) </span><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif;">7<sup>711</sup></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b>9. The 711th Digit Is…</b></span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">What is the 711th digit of the decimal expansion in the reciprocal of 711?</span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b>10. 7Eleven Are Closed …</b></span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b><br></b></span></div>
<div>
<span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif;">7Eleven outlets are open 24/7/365. However, on a few occasions some stores had to be closed. Suggest some possible reasons for the closure of these convenient outlets.</span></div>
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<br></div>
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<br></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b>11. What Are the Prices in 7-11?</b></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span></div>
<div>
<a href="http://upload.wikimedia.org/wikipedia/en/thumb/d/d5/Big_gulp6480.JPG/220px-Big_gulp6480.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" class="thumbimage" data-file-height="2048" data-file-width="1536" height="200" src="http://upload.wikimedia.org/wikipedia/en/thumb/e/e7/711IcyDrinkCup.jpg/340px-711IcyDrinkCup.jpg" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e7/711IcyDrinkCup.jpg/255px-711IcyDrinkCup.jpg 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e7/711IcyDrinkCup.jpg/340px-711IcyDrinkCup.jpg 2x" width="149"><img alt="" border="0" class="thumbimage" data-file-height="2233" data-file-width="1181" height="200" src="http://upload.wikimedia.org/wikipedia/en/thumb/d/d5/Big_gulp6480.JPG/220px-Big_gulp6480.JPG" srcset="//upload.wikimedia.org/wikipedia/en/thumb/d/d5/Big_gulp6480.JPG/165px-Big_gulp6480.JPG 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/d/d5/Big_gulp6480.JPG/220px-Big_gulp6480.JPG 2x" width="105"></a><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Mr. Yan went inside a 7–11 store and selected four items. When he reached the counter to pay for the goods, the cashier took his calculator, pressed a few buttons and said: "The total price is $7.11."</span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Mr. Yan replied, "Are you sure? Do I have to pay $7.11 because the name of your shop is 7–11?"</span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">The half-embarrassed cashier answered, "Of course not! I've multiplied the prices of these four items and I've just given you the total."</span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">The puzzled Mr. Yan laughed and said, "Why did yo</span><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif;">u multiply these numbers? You'd have added them to get the total price!"</span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">The cashier said, "I'm sorry; I've pressed the wrong button!"</span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">The cashier then repeated all the calculations, by adding the prices of the four items, and to his surprise, the total was still $7.11.</span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><i>What are the prices of these four items?</i></span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><i><br></i></span></div>
<div>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<img alt="" height="184" src="http://corp.7-eleven.com/Portals/2/Images/lifestyle/Lifestyle_app_sup.jpg" width="400"><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><b><br></b></span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><b><i>Selected Answers</i></b></span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><b>1. </b>120 days</span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><b>2. </b>79/111</span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><b>3.</b> (i) Monday </span><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif; font-size: x-small;">(ii) Tuesday.</span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><br></span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><b>4.</b> 149.5°</span><br>
<br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><b>8. </b>(ii) 601 digits</span>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><br><br><b>9.</b> 9</span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><br></span>
<span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif; font-size: x-small;"><b>10.</b> $3.16, $1.25, $1.20, $1.50.</span><br>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><b>References</b></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Michalewicz, Z. & Fogel, D. B. (2004). <i>How to solve it: Modern heuristics</i>. New York: Springer-Verlag.</span><br>
<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Yan, K. C. (2011). <i><a href="http://mathpluspublishing.com/christmaths-pageemmanuelyan007/" target="_blank">Christmaths—A Singapore math creative problem solving title</a></i>. Singapore: MathPlus Publishing.</span></div>
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<span style="font-family: Times, Times New Roman, serif; font-size: x-small;">© <a href="http://www.singaporemathplus.net/" target="_blank">Yan Kow Cheong</a>, July 11, 2014.</span><br>
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<span style="color: red; font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><i>Postscript</i>: This writer isn't sponsored in any way by the 7Eleven brand to write this blog article. However, he won't turn down any cash donations or vouchers, if his e-article has helped challenge and benefit tens of thousands of 7Eleven math fans around the world.</span><br>
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<span style="font-family: Georgia, Times New Roman, serif;">Here are 13 <i>lucky</i> e-cards (stolen with zero acknowledgements on social media) you may wish to send to triskaidekaphobic or semi-superstitious friends, fiends, or foes on this most unluckiest day of the calendrical year.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">Why not make your own Friday the 13th e-cards, and share them with the mathematical brethren? <i>Happy Friday the thirteenth!</i></span><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><i>Superstitiously yours</i></span><br />
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<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><b>References</b></span><br />
<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;"><br /></span>
<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">Yan, K. C. (2013). <a href="http://www.singaporemathplus.com/2013/12/13-math-tidbits-on-friday-13.html" target="_blank">13 Math Tidbits on Friday 13</a>. <i><a href="http://www.singaporemathplus.com/" target="_blank">Singapore Math</a></i>, Dec. 13, 2013.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">Yan, K. C. (2013). <a href="http://www.singaporemathplus.net/hungry-ghosts-dont-do-singapore-math/" target="_blank">Hungry Ghosts Don't Do Singapore Math</a>. <a href="http://www.singaporemathplus.net/" target="_blank"><i>Yan's One Minute Math Blog</i></a>, Oct. 12, 2013.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">Yan, K. C. (2012). <a href="http://www.singaporemathplus.com/2012/10/halloween-math.html" target="_blank">Halloween Math</a>. <i><a href="http://www.singaporemathplus.com/" target="_blank">Singapore Math</a></i>, Oct. 31, 2012.</span><br />
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<small><span style="font-family: Georgia, Times New Roman, serif;">© <a href="http://www.singaporemathplus.net/" target="_blank">Yan Kow Cheong</a>, June 13, 2014.</span></small></div>
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<div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0tag:blogger.com,1999:blog-2432976803039259514.post-305823361327054532014-04-29T15:03:00.000+08:002014-04-29T15:03:37.409+08:00Creative Statistics<div dir="ltr" style="text-align: left;" trbidi="on">
The fear of elementary statistics among an oft-innumerate public has often provided fertile ideas for artists and humorists to "abuse" and "misuse" the art and science of representing data meaningfully and creatively.<br />
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Among my favorite statistical diagrams are the ones featured by <a href="http://en.wikipedia.org/wiki/Demetri_Martin" target="_blank">Demetri Martin</a>, a lawyer-turned-comedian, who was a writer with <i>Late Night with Conan O'Brien</i> and a performer on <i>The Daily Show with Jon Stewart</i>. </div>
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If only some mathematicians or math educators suffering from mid-life crisis would switch careers to focus on hilarity instead of mere applied numeracy, they could help reduce the trauma and pain experienced by thousands of [sadistic?] statistics students every year, by humanizing a much-disliked mathematical topic in school.</div>
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Below are a sample of the creative use of <a href="http://en.wikipedia.org/wiki/Category:Statistical_charts_and_diagrams" target="_blank">statistical diagrams</a> to convey both useful and useless information.<br />
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<tr><td class="tr-caption" style="text-align: center;">A classic in pop math literature</td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="text-align: left;"><span style="font-size: xx-small;">© Demetri Martin</span></span></td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small; text-align: left;">© Demetri Martin</span></td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small; text-align: left;">© Demetri Martin</span></td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small;">© Richard Benson</span></td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small;">© Richard Benson</span></td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small;">© Richard Benson</span></td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small;">© Richard Benson</span></td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small; text-align: left;">© Demetri Martin</span></td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: xx-small; text-align: left;">© Demetri Martin</span></td></tr>
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In [Creative] Statistics we mistrust! <i>Thou shalt abuse or misuse statistics to tell white lies!</i><br />
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Humorously and Statistically yours<br />
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<b><span style="font-size: x-small;">References</span></b></div>
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<span style="font-size: x-small;">Benson, R. (2012). <i><a href="http://www.amazon.com/F-in-Retakes/dp/184953313X/ref=sr_1_1?s=books&ie=UTF8&qid=1398752894&sr=1-1&keywords=F+in+Retakes" target="_blank">F in Retakes</a></i>. West Sussex, UK: Summerdale Publishers Ltd.</span></div>
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<span style="font-size: x-small;"><br /></span></div>
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<span style="font-size: x-small;">Martin, D. (2013). <i><a href="http://www.amazon.com/Point-Your-Face-This-Drawings/dp/1455512052/ref=sr_1_1?s=books&ie=UTF8&qid=1398752972&sr=1-1&keywords=Point+your+face+at+this" target="_blank">Point your face at this</a></i>. Penguin Books.</span></div>
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<span style="font-size: x-small;"><br /></span></div>
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<span style="font-size: x-small;">Martin, D. (2011). <i><a href="http://www.amazon.com/This-Book-Demetri-Martin/dp/0446539694/ref=sr_1_1?s=books&ie=UTF8&qid=1398753058&sr=1-1&keywords=This+is+a+book+by+Demetri+Martin" target="_blank">This is a book by Demetri Martin</a></i>. New York: Grand Central Publishing.</span></div>
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<span style="font-size: xx-small;"><span style="color: rgba(25, 25, 25, 0.901961); font-family: HelveticaNeue-Light;">© </span><a href="http://www.singaporemathplus.net/" target="_blank">Yan Kow Cheong</a>, April 29, 2014.</span></div>
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<div class="blogger-post-footer">"Fear not math, fear God." K C Yan</div>Singapore Mathhttp://www.blogger.com/profile/17850835958065560265noreply@blogger.com0