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Singapore Math

Thursday, August 1, 2013

To Count or Not to Count

Einstein said, "Not everything that counts can be counted, and not everything that can be counted counts."


One of my favorite childhood games!
Five stones or five bags containing rice
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Here are a dozen math questions that you may pose to your grades 2–3 child to see whether they've graduated from rote-learning, ready to tackle higher-order thinking questions. Don't ignore their answers off-hand, silly as some of them may appear to be. Use them to question the reasonableness of their thinking processes, or to promote sense making in problem solving.

Questions crying to be solved

1. Farmer Jones had 220 goats: 65 he-goats and 155 she-goats. 100 goats died last winter. How many he-goats did he have left?

2. Film A is only 94 minutes long. Film B is 1 hour 40 minutes. Which film is better? Explain.

\3. The largest painting in museum P is 60 centimeters square; the one in museum Q is one and a half times bigger. Which museum is worth visiting? Why?

4. There are 125 sheep and 5 dogs in a flock. How old is the shepherd?

5. If one Mona Lisa painting is worth $12 million, how much will two such paintings be worth?

6. Mr. Smoth has two children: a 9-year-old son and a 12-year-old daughter. How old is the mother?

Creative logic ©1999 The Straits Times & A. Choy 

7. A fake Rolex watch costs $2,500 at a shop in Dubai. How much would four such watches cost a businessman from a developing country, if he were to buy the original ones?

8. There are 26 sheep, 12 pigs, and 14 goats on a ship. How old is the captain?

9. Yesterday 37 boats sailed into port and 49 boats left it. Yesterday at noon there were 43 boats still in the port. How many boats were still in the port yesterday evening?

10. Tom used to have 45 Facebook friends. After some friends unfriended him for forwarding their personal e-mails without their permission, Tom is now left with 51 friends. How many friends left him?

11. On Tuesday, at 4:00 PM, Sherry was overjoyed when she had seven new Twitter followers. However, the next day, three of them unfollowed her. How many Twitter followers does she have now?

12. Ken received 8 new e-mails today. After deleting some of his e-mails, his inbox was left with 21 of them. How many e-mails were in his inbox at first?

0 friends, 3000+ Facebook friends, fiends, and foes
© 2011 Tanya Cooke

Creative problem posing 

Use these "insensible" or "unreasonable" questions to get the children to amend them, before they're deemed "solvable." Let their creative imagination run wild by posing their own versions; and be prepared for some surprises in their responses. You may be astounded how their literacy and numeracy grow by leaps and bounds.

Happy problem posing and problem solving.


References
Cooke, T. (2011). Help! I'm a Facebookaholic. London: John Blake Publishing Ltd.
Schoenfeld, A. H. (2012). A modest proposal. Notices of the AMS, 59(2), 317-319.
Yan, K. C. (2012). Mathematical quickies & trickies. Singapore: MathPlus Publishing.

© Yan Kow Cheong, August 1, 2013.