Nancy and I have been doing a lot of co-teaching in her Grade 5/6 class. All of our co-teaching sessions have been focused around teaching through problem solving in a three part lesson. This past week we had the students work on a problem around conversion of fractions, decimals and percents. (Picture #3)
We used the Assessing for Learning tool(A for L) as a way to document not only what strategies the students used to solve the problem, but also what errors they make. What came to our attention was a rather large error which became the topic of our consolidation or the third part of our lesson. (Pictures # 1 & 2) Nancy has also modified the A for L tool to meet her needs by making the squares a bit bigger, and also including a box for her to level the students work as well. (Not every time that we use the A for L sheet do we give the students a level - it is mainly used to simply assess for learning)
The students were quite easily able to figure out 1/4 of an amount and then find out what 50% of the remaining amount was. We saw several strategies and heard several different explanations as to how they got through steps one and two. However, where the misconception occurred was when the students got to the part of the question where they had to solve for 0.3.
The students were well aware of how to convert the decimal into a fraction - Except that they were trying to convert this particular decimal into 1/3 which then would give them the wrong answer. Many of the students said that they didn't know what to do when it came time to "deal" with the 0.30. For some that were stuck, we prompted them with open ended questions to them to help make sense of what they should do next.
During our consolidation piece we had one pair come up and share their work with the group. We had pre-selected this pair because we knew they had used the same strategy as most of their peers, and had made the same mistake. As they explained their answer I annotated what was missing from their words and their sheet by using a different coloured marker. When we came to the part about the 0.3 we had them share their answer and asked the class if this looked right. Almost everyone agreed. We then led the students into looking back on the first two questions they solved using the fraction and the percent. We put each one of those into a decimal, percent and fraction form on the board beside of us. We then did the same with 0.3, 30% and then 1/3. It was at this point that a few of the students got the "light bulb" look and put up their hands. They said that 1/3 was not equal to 0.3 but it was 0.33 instead. We then used number lines to help us show the difference between 0.3 and 0.33.
One other group - who were the only ones to correctly get the answer in the first place - put up their hands to share (and show us) how they solved for 0.3 and what it would look like in the context of the problem.
Had we not been doing this problem, this issue might never have come up. The three part lesson is a really powerful tool to help us teach our students better - It allows us the chance to take a simple, and easily corrected, mistake and fix it on the spot. Because of the consolidation piece (or congress) we were able to not only show our students different ways to show a number as a decimal, a fraction and a percent, but also stop them from making the same mistake later on.
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