# Numeracy

### Chapter 7 - Division

## Division

"I have learned how to explain my "mental math." I hadn't realized how hard it was to explain in words, the steps that I do to solve a problem in my head. It is much easier to understand the numbers when you can 'see' them."

Numeracy Workshop Participant

Division is probably the most difficult operation for most kids.

## Quotative and Partitive Division

Two ways to visualize division: It's a way to connect multiplication and division. 2 times 31 can be seen as either two groups of 31 or 31 groups of 2.

## Partial Quotients

Use the reverse of the distributive property. 108 divided by 9 is the same as 99 divided by 9 plus 99 divided by 9 because 108 is 99 + 9. This is what we call the box method of factoring polynomials.

## Over and Under

Over and under uses ratios and proportions. Finding a constant ratio makes a problem simpler.

## 5 is Half of 10 Strings

This strategies used multiples of 10 and 5, 100 and 50 etc. Then you add or subtract enough to get the quotient needed.

## Constant Ratio Strategy

Makes use of the fact that the same amount is added or subtracted each time.