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I frequently include real-world problems for my students to tackle in the classroom. This makes the material more tangible and interesting to students. Additionally, I frequently use word problems to improve students’ literacy.
For example, in both of the lessons below, each class example was a real-world situation. Some situations, such as the “v-bucks” on Fortnite, are examples that students themselves encounter in their day-to-day-life. Regardless, I frequently give students word problems for them to work with complex real-world situations.
For example, in the examples below, students are working with the real-world situation of comparing two job offers, determining how much money they make on commission, or determining how much something costs after a discount. These are all important real-world situations students may find themselves in.
This student did not write down all of the steps of the math correctly, which tells me that he was copying down the problem without understanding it. Under this math, he has written down “120+1750” then jumps to adding “120+262.50”, without explaining that the $262.50 is 15% of $1,750. When going through higher-level problems, it is important I gauge for the understanding of lower-level students better so that they do not simply write down some steps of a problem without understanding them.
When given the “practice and score” mini-quiz, this student appears to have the correct answer to problem #1 on first glance. It is clear, however, from analyzing his work from problem #1, that the student does not understand that a commission is not paid on top of a starting salary. In problem #2, it is also clear that the student did not understand how to take 20% of something or what they would be taking 20% of. This student required a re-teach of the material the next day.
This student did understand how commissions and discounts work. For example. the student even translated the beginning conceptual problem that a 2% commission is a 2 cent discount into their own words. I had written at the board $0.02, but the student already knew 2 cents made more sense to them. In problem #1, the student correctly shows her work and puts the work back into the context of the problem. However, in problem #2, while the student did the problem correctly, their work could be both shown and explained more precisely.
Based on her “practice and score” mini-quiz data, this student understands the concept mathematically on how to find a tip or a discount. However, in the second problem, despite finding out that the 15% off coupon gave a $45 discount, she still answered that the $40 off coupon is better. This tells me that she was very successful in going through the motions of the math but unsuccessful in pausing to think about what the math meant in the real-world context. This student did not require a reteach of the math the next day, but she did work with my City Year teaching assistant in a small group on how to put answers to word problems back into their real-world context.
Students have varying levels of understanding of real-world problems, as outlined above. This requires differentiated re-teach plans for them. Regardless of their initial level of understanding, it is still a valuable exercise for students to see math in real-world situations. This builds their math fluency and lets them see how math is used in the “real world”.
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