As I began planning for my unit on the Pythagorean Theorem, one important element kept striking me as vitally important–getting my kids up, moving, engaged, and interested. Eight-graders have a hard enough time sitting still and paying attention as it is, even without the added bonus of having to do it while learning math. Since the Pythagorean Theorem can be applied so widely to real-world scenarios, I wanted to utilize this privilege to its full extent.
This activity, found on the website of the National Council of the Teachers of Mathematics, is perfect for my students. The activity allows students to develop the Pythagorean Theorem through discovery of their own learning. It encourages students to test out scenarios, form conjectures, test these conjectures, and, ultimately, form the Pythagorean Theorem. It has the added bonus of students being able to play with candy. I believe that my students will enjoy the activity, and will greatly benefit from discovering the mathematics on their own. The Pythagorean Theorem is a vital concept throughout algebra, so students need a developed understanding of the ideas at hand.
Pythagorean Theorem with Jellybeans also incorporates a lot of the CCSS Standards for Mathematical Practice. Firstly, students must be able to make sense of the problem of finding a relationship between the squares drawn on sides of a right triangle and persevere in solving this problem. Second, students must reason abstractly. They will move between contextualizing variables to decontextualizing information fluently to represent a physical relationships in the form of a rule or conjecture. Third, they will critique the reasoning of others and develop arguments about their conjectures. They will be able to provide input on the conjectures of their group members and be able to make conjectures of their own. Fourthly, students will use the tools given to them to model the relationship mathematically. Fifth, they will use these tools strategically (and not eat the Jellybeans until they’re finished). Sixth, they will attend to precision to ensure that the conjecture they construct is accurate. Seventh, they will find a pattern between the squares on a right triangle and make use of this structure by developing a universal rule. Finally, after testing their conjectures, they will express reasoning in repeated regularity.
Rarely does an activity touch on all of the SMP, but I think this example is a great one. I’m excited to be able to try this in my class and (hopefully) see a change in the level of engagement and excitement in my kids as a result.