**In Praise of Models**

**A K-8 Sample of Singapore Math Questions**

Use the [Singapore] model method to show that (a) 2 + 3 = 5, (b) 9 – 4 = 5.

**Grade 1**Use the [Singapore] model method to show that (a) 2 + 3 = 5, (b) 9 – 4 = 5.

Use a model to show that 3 × 6 = 6 × 3.

**Grade 2**Use a model to show that 3 × 6 = 6 × 3.

**Grade 3****Use a model to show that ½ × ⅘ = ⅖.**

Use a model to show that 2 ÷ ⅖ = 5.

**Grade 4**Use a model to show that 2 ÷ ⅖ = 5.

Use the model method to evaluate the value of 3½ × 4⅚.

**Grade 5**Use the model method to evaluate the value of 3½ × 4⅚.

Use a model diagram to show that the infinite series converges to a finite number.

**Grade 6**Use a model diagram to show that the infinite series converges to a finite number.

½ + ¼ + ⅛ + ⅟₁₆ + ... = 1

Use a model to show that (2

**Grade 7**Use a model to show that (2

*x*)² is not equal to 2*x²*.

Use a model method to solve these equations.

(a)

**Grade 8**Use a model method to solve these equations.

(a)

*x²*– 3*x*(b)*x*² + 3*x*+ 5 = 0**Singapore World Records**

Most participants in a ribbon-cutting ceremony (3,238)

**People wearing balloon hats at one time (1,491)**

Most people caught jumping queues at one time (?)

Most people caught jumping queues at one time (?)

**The first (or fastest) one to board a train at a newly open train station (? sec)**

Most number of people solving a word problem using the model method (

Most number of people solving a word problem using the model method (

*n*!?)**The world's gigantic math model cut on grass (?)**

**Wittgenstein’s***Ghost**: Let one unit represent the number of Singapore Math books.*

**Math educator**

*Homeschooler*: But, Dad, suppose one unit doesn’t represent the number of Singapore Math books.

**New math titles in the pipeline**

*1. The Singapore Model Method for Those with Zero Sight*

[By a Singapore-born blind math educator]

2.

*A Bluffer’s Guide to the Singapore Model Method*[Pending approval from the Censorship Board of Adult Education]

3.

*Singapore Math for SENIORS*[A CHRISTmaths gift for grandparents & godparents]

4.

**China Math**vs.**Singapore Math**: Which is Better?[Does this include

*Taiwan Math*?]5.

[

*Singaporeanizing*Math[

*What on earth is that?*]**An Evolution of Grade 5/6 Singapore Math Word Problems**

**Teaching Math in 1970 (Traditional Math)**

Mr. Yan has three cows and eight chickens. How many legs are there altogether? [Ask a next-door neighbor for the answer.]

**Teaching Math in 1980 (Model Method)**

Mr. Yan has twice as many cows as chickens. If there are 64 legs in all, how many cows are there? [Ask a neighborhood school teacher for the answer.]

**Teaching Math in 2000 (Problem Solving)**

Mr. Yan has cows and chickens. If there are altogether 28 legs, how many chickens and how many cows are there? [Ask a full-time tutor for the answer.]

**Teaching Math in 2010 (Challenging)**

Mr. Yan has almost twice as many chickens as cows. The total number of legs and heads is 184. How many cows are there? [Answer a math coach, or a volunteer from the

*Ask Dr. Math*Website.]

*The Core of the Singapore Math Student*

What the most-disliked subject means for the average or above-average Singapore student (in spite of TIMSS):

K1-K2: Math is a lore.

© Yan Kow Cheong, September 25, 2010

**Grades 1-2: Math is a score.**

Grades 3-4: Math is a bore.

**Grades 5-6: Math is a chore.**

Grades 7-10: Math is a sore.

**Grades 11-12: Math is no more.**© Yan Kow Cheong, September 25, 2010