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.

5x ≤ 69
5x/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 rectangular 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

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.