This lesson is optional. It offers additional opportunities to look at multiple representations (equations, graphs, and tables) of relationships between two quantities in situations that involve constant area, constant volume, and a doubling relationship. Students have an opportunity to look for and make use of the similar structure in the geometric relationships the first two activities (MP7). as well as to connect the reasoning in the activity about mosquitos to prior work with exponents earlier in the unit. Students may use those observations and knowledge to more easily solve the problems in the activities.

Consider offering students a choice about which problem they work on. Then in the Lesson Synthesis, invite students to share their work with the class and compare and contrast the representations of the different contexts.