here are 65 children st field day. Ms. Haynes put them into three groups with the same number of children in each group. how many children each group?

Question

can not use division and must use three different strategies

Answer 1

Since 65 students cannot be evenly split into 3 groups, let's assume the question states that there are 66 students. We can easily find that, using division, this would result in 3 groups of 22 students each. However, it seems that we cannot use division to solve the problem and must use 3 different strategies. Let's give it a shot:

Strategy 1

Let's imagine that we have 66 blocks, representing the 66 students. We also have 3 separate and empty bins: Bin A, Bin B, and Bin C. We can add one block to Bin A, followed by adding one block to Bin B, followed by adding one block to Bin C. After the first three additions, we will have 63 blocks left and one block in each bin. If we repeat this process again, we now have 2 blocks in each bin and 60 blocks left. We can repeat this process until we do not have any blocks left, at which point we will find that each bin has 22 blocks in it.

Strategy 2

Imagine again that we have 66 blocks, representing each of the 66 students. If we remove one block from the group of 66 and place it on the side, we now have a group of 1 block and a group of 65 blocks. If we repeat this step, we will have a group of 2 blocks and a group of 64 blocks. We can repeat this step until the number of blocks in the original group is double the number of blocks in the new group. This will happen when there are 22 blocks in the new group and 44 blocks in the original group. At this point, we know that the new group of 22 blocks is 1/3 the size of the original group.

Strategy 3

Once more we will work with the example of 66 blocks. We can start by using a modification of strategy 1 to separate the blocks into two groups of 33 blocks each. Next, we can use strategy 1 to separate each of these groups into 3 groups of 11 blocks each. We now have 6 groups of 11 blocks each. In order to go from 6 groups to 3 groups, we can simply combine the groups in pairs to form 3 groups of 22 blocks each.

Hope this helps!