This week, Katie’s SchoolPlus homework continued with the topic of division. She had a worksheet with 25 division problems, going up to numbers as high as 30. After some deliberation over how to handle this, I decided that the involvement of dolls was essential. Predictably, Katie became very excited when I suggested that the dolls have another ball. “They haven’t had one in such a long time!” she exclaimed. I told her that while having a ball, the dolls were going to help us solve some math problems; she didn’t object.
Our first problem was 9 divided by 3. I told her to pick out 9 dolls, meanwhile arranging 3 books on the floor to serve as benches. She had to sit the 9 dolls on the three benches so that all the benches had an equal number of dolls sitting on them. The concept posed no problem, but much effort went into deciding which doll would sit on which bench.
The next batch of problems were solved in a similar fashion. After a few divisions by 1, she was able to do those without the help of the dolls. At some point we started encountering problems where the dividend was greater than 20. We didn’t have that many dolls readily available (there are certainly that many in the house but I wasn’t willing to spend time gathering them), but we did have many mancala stones. Also, I thought that it would be a good idea to vary the setting a bit. So now we were dividing stones among the dolls.
After solving many problems in this way, I decided to test out whether she really understood the concept. When we again encountered a problem with fairly small numbers, I suggested that we go back to sitting dolls on benches. The problem was 6 divided by 3. Katie decided that we needed 3 dolls and 6 benches. I tried telling her that now the role of dolls is replaced by benches and the roll of stones is replaced by dolls, but she kept insisting that the number of dolls was always the smaller one before and so it should be the same way this time. Finally, I told her to solve the problem however she thought fit (I really should have done this right away without saying anything, but it’s always easy to spot mistakes in retrospect).
She put out 6 books and was about to pick out the dolls. Suddenly, she stops and says “Wait, I’m confused, how can we put 3 dolls on 6 benches? That won’t work!” And then she proceeds to take away 3 of the books and place 6 dolls on the remaining 3. Victory!
Here are some concluding thoughts. As is often the case with such things, the process rather than getting the answer was what made it fun for Katie. What she enjoyed most was picking out which dolls would participate for each problem, how to arrange them, and which colored stones they would get. However, the goal of understanding division was achieved. The last problem of the worksheet was 4 divided by 2. Upon seeing it Katie exclaimed, “That’s easy!” and proceeded to write down the correct answer. No props were necessary.