Reasonable Solutions

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My fourth grade students finished up a project involving area last week. Students were asked to find the area of different playing areas for certain sports. They first calculated the areas of the playing field by multiplying fractions and then found the product.

The next step involved creating a visual model on anchor chart paper. Students worked in groups to put together their athletic park involving the field areas. They were given the area of the park and then had to place the fields where they wanted according to the team’s decision. Students also added additional facilities for their athletic field and then presented their projects to the class.

While presenting, students in the audience were required to either 1) ask a question or 2) provide a constructive comment. Most of the questions that were asked related to why certain fields were placed in specific areas on the field. One question stood out more than the others … does the distance make sense?

The locker rooms had to be adjusted (see whiteout) as one student said, “It doesn’t make sense so I changed it to match the 120 yd.”

Students were looking at the length of the fields and observing whether it was reasonable or not compared to the total length. The class then had a conversation about the terms reasonableness and proportions. The discussion involved how a double-number line and a grid could’ve helped visualize how the distances match.

I’m hoping to revisit this idea during the next few weeks as the school year finishes up.

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I believe teaching multiple grade levels within the same day has value. Being able to observe how students think about numbers and the strategies that they use over time gives teachers a different perspective. It also shows some of the linear progression of math skills and strategies. I found this especially evident as I read through Kathy Richardson’s book during July. I currently serve as a math teacher for students in grades 2-5. I get to see how students progress over time and what tends to trip them up. I also see the problems that emerge when students start to rely on tricks and formulas before having a deep understanding of a particular concept. One thing that I also continue to observe is that students sometimes struggle to be reasonable with their estimates. Part of that may be due to an over-reliance on algorithms and the other part may relate to exposure. Students aren’t given (or take the) time to reflect and ask themselves whether the answer truly makes sense or not. This tells me that students are relying on a prescribed process or algorithm and reasonableness comes second.

In an effort to move towards reasoning, I’ve been using Estimation 180 on a daily basis. I feel that the class is become better at estimating and their justification has improved. Making sense with number puzzles also seem to be helping students create reasonable estimates and solutions. Basically, students are given a story that has blanks.

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Students are then are given a number bank. Sometimes too many numbers are in the bank.

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Then students have to justify why they picked each answer. This can be completed in verbal or written form.

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Usually I have students explain their reasoning with a partner. The class has completed a number of these types of making sense with numbers puzzles. I can say that students are now looking more closely at the magnitude of the actual numbers before estimating or finalizing an answer. That’s progress and I’m confident that students are more willing to use that strategy along their math journey in the future.