In the story, the King wants to know how many commissioners he has. His two Royal Advisors count the commissioners in different ways. One counts by 2s and reports that are twenty three 2s and 1 extra; the other counts by 5s and reports nine 5s and 2 extras. Their methods confuse the King (who doesn't appear to be too bright), because he wants only to know the total number of commissioners. The Princess steps in to help. She has the commissioners line up in rows of 10, counts four rows of 10 with 7 left over, and convinces the King that there are 47 in all. She proceeds to explain why the Royal Advisors' methods were also correct.
After reading and discussing, I asked the children to finish a writing assignment. They had to explain why each counting method in the story made sense. I said they could use words, pictures, tally marks, or a combination.
Writing helps children clarify their mathematical reasoning, and I particularly like it because their written work provides ME with evidence of their thinking and reasoning. In other words, if I had simply read the story and held a discussion, I would think that every child understood the concept. But after reading some of their stories, I can see that several children were not able to sufficiently articulate their reasoning, and seemed unclear on what was happening. This is very useful information for a teacher to have, and I can now plan for support. It was important also for me to remember that the primary goal of a lesson is not to have children write, but to have them think and reason. Writing is a tool for children to explore their thinking and serves as a record of the ideas they've already formulated.
Here are some samples of the work I collected today. It is interesting to note how each child decided to show their thinking. These children all definitely "got it".
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