I love using all kinds of manipulatives (beans, counters, fake money, base ten blocks) to help my learners visualize math procedures and concepts.
I have a student who loved to use base ten blocks to solve problems like 345 divided by 8. He would spend days with his pile of blocks. I asked him “Hey, why don’t you come up with a way to divide without using the blocks?” He took on the challenge and eagerly went home to tell his mom about it. She said “That’s easy, let me show you.”
He came back to school, tried to show me and was thoroughly confused and pretty bummed that he couldn’t remember what to do. I said “That’s okay, why don’t you go back to what you remember, look at the blocks and while you move them, write down what you did, and then come explain it to me?”
With a bit more hop in his step, he went back to his table and proceeded. He then showed me his strategy and was able to easily explain it:
1 – First you look at the ones. (This is what most students do anyway, as they are used to adding and subtracting from right to left. And he did because he wants to divide up the little blocks first.) You have eight blocks, so each block can go into one of the eight piles.
2 – Then you look at the five tens or 50. If you divide those up, each pile would get six ones, with two leftover.
3 – Then you look at the two hundreds which is 20 tens. The 16 tens can be divided up with 2 in each of the eight groups. And then you divide up the 4 tens into 40, so that means each of the eight groups would get 5 more ones. (Or two hundred can be divided into 20 groups of 8 and five groups of 8.)
4 – Then you add up all the ones.
5 – And you have your answer!
He was quite excited and so relieved. He went right home to show his mom, and now she is confused, but also glad that he is confident with division. I talked with her about the importance of knowing how to solve problems and developing strategies.
See if you can understand his other example: