Reys Chapters 8 & 9

Reys: Chapter 8

“As children develop rounding skills, they should come to realize that rounding rules may vary and are not universal. ”

Reys discusses in the rounding section that many textbooks explain rounding in different ways. Reys gives the example of how one text explains changing the 5 to 0 and increasing the previous digit by 1 and another text says change the 5 to 0 and if the digit preceding the 5 is even, leave it alone and if the digit preceding the 5 is odd, increase it to the even digit. This can be a problem with some numbers like 85 because in one instance it would be 90 and another would be 80. In the class I am observing for rounding I noticed they had a sound and exactly four rules. The song goes over how if the number is more than five you round up and if its four or less you let it rest. I noticed that the third graders really caught on quickly because the song helped and the four rules are simply step by step. One rule include underlining the number to the right of the circled number. You circle the number you will be rounding.

Reys: Chapter 9

Focus Question # 3: What three distinct types of situations lead to subtraction? What four types of structures lead to multiplication?

The three distinct types of situations that lead to subtraction are separation problems, comparison problems, and part-whole problems. The four types of structures that lead to multiplication are equal-groups problems, comparison problems, combinations problems, and area and array problems.  Reys mentions that the separation problems are usually the easiest problems for students because they look at this as take away problems. The comparison problems involve matching the numbers where one will cancel another basically crossing out pairs and seeing what numbers are left.  For part-whole problems nothing is being added or taken away instead you will only have a static situation that involves parts and a whole.