**Elementary Math from an Advanced Standpoint**

**A Grade 4 Question**

**Ken has 69 planks that are of standard size. He would need 5 such planks to make a bookshelf. What is the most number of bookshelves Ken can make?**

**Method 1**

Let *x* be the number of bookshelves Ken can make.

5*x* ≤ 69

5*x*/5 ≤ 69/5

*x* ≤ 13 4/5

So the maximum whole number that satisfies the inequality *x* ≤ 13 4/5 is 13.

Hence the most number of bookshelves is 13.

**Method 2**

Using the floor function, the most number of bookshelves is ⎣69/5⎦ = 13.

**A Grade Two Question**

**Verify that 2 × 2 = 4.**

*Basic hint*: Use the FOIL method.

*Intermediate hint*: Use area.

*Advanced hint*: Use axioms (*à la *Whitehead and Russell)

#### Solution

*Using the FOIL method*

2 × 2

= (1 + 1) × (1 + 1)

= 1 × 1 + 1 × 1 + 1 × 1 + 1 × 1

= 1 + 1 + 1 + 1

= 4 QED

**A Grade Four Question**

**A recta****ngular enclosure is 30 meters wide and 50 meters long. Calculate its area in square meters.**

#### Solution

## The *My Pals Are Here *Math Series

The *My Pals Are Here* series has been rumored to have been edited and ghostwritten by a hundred odd editors and freelancers in the last decade.

Lack of mathematical rigor was initially targeted against Dr. Fong Ho Kheong and his two co-authors by American profs in the first or/and second editions —probably by those who were “ghost advisors or consultants” for *Everyday Math*.

**Deconstructing the Singapore ****Model Method**

**Deconstructing the Singapore**

**Model Method**

1. It’s a problem-solving strategy—a subset of the “Draw a diagram” strategy.

2. It’s a hybrid of China’s line method and Russia’s box (or US’s bar) method.

3. It’s the “Draw a diagram” strategy, which has attained a brand status in mathematics education circles.

4. It’s a problem-solving method that isn’t recommended for visually challenged or impaired learners.

5. It allows questions traditionally set at higher grades (using algebra) to be posed at lower grades (using bars).

## Painless Singapore Math

Perhaps that’s how we’d promote Singapore math to an often-mathophobic audience!

## A Singapore Ex-Minister’s Math Book

Dr. Yeo had the handwriting below depicted in his recreational math book, regarding his two granddaughters, Rebecca and Kathryn.

**References**

Yan, K. C. (2013). *The lighter side of Singapore math (Part 4)*. December 2013. http://www.singaporemathplus.com/2013/12/the-lighter-side-of-singapore-math-part.html

Yeo, A. (2006). *The pleasures of pi, e and other interesting numbers*. Singapore: World Scientific.

© Yan Kow Cheong, December 30, 2013.