Experience First

Today students will work on problems that incorporate all the skills from the previous three days. In this circuit training activity, students start by completing the first box in top left corner (pre-labeled #1). They then look for their answer in the Answer slot of one of the other boxes. This box then becomes their box #2 and they put a 2 in the blank. They then complete this problem, search for the answer and label this new box with a #3. This continues until students have completed all 16 problems. The answer to problem 16 should lead them back to the first box. If students “short-circuit” they know they have made a mistake somewhere. Some answers are intentionally similar to encourage students to attend to precision.

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Formalize Later

It is worth noting that while problems can be solved with the product rule or quotient rule, not all will require one of the rules. Simplifying and rewriting an expression can help students avoid the product rule or quotient rule. Over time, we hope that students make strategic decisions about when to apply the product rule or quotient rule.

 

You may wish to have a discussion about which strategy students used for each question. Pay special attention to problems that students were able to complete in multiple ways. While the product rule and quotient rule will always work, mathematicians make use of structure and look for efficient problem solving strategies.