Give an example of how a teacher might use the concept of equivalent representations in instruction. Why is this concept important to consider in helping children understand place value?

Question

What will be an ideal response?

Answer 1

Complete answers will include the following: Equivalent representations refers to the fact that a number can be represented in many different ways, all of which have the same value but may look different. For example, the number 32 can be represented in a variety of ways using groups of 10: as 3 groups of 10 and 2 singles, as 2 groups of 10 and 12 singles, as 1 group of 10 and 22 singles, and as 0 groups of 10 and 32 singles (see Figure 6-7). Children need to understand that each of these representations is equivalent because each represents the number 32. Children who are able to think flexibly and recognize these equivalent groupings will be better able to regroup and rename two-digit numbers, which will assist them later in computation work, such as when they need to regroup to solve a subtraction problem, for example.