Chapter 7 - 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.
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.