Unit 6, Lesson 18
More Relationships (Optional)
Grade 6
Preparation
Lesson Narrative
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.
- Coordinate (orally and in writing) graphs, tables, and equations that represent the same relationship.
- Create an equation and a graph to represent the relationship between two variables.
- Describe and interpret (orally and in writing) a graph that represents a nonlinear relationship between independent and dependent variables.
Let’s use graphs and equations to show relationships involving area, volume, and exponents.
Required Preparation
None
Modify the Activity Synthesis of Activity 4, “Multiplying Mosquitoes,” by asking students to consider and discuss the role of mosquitoes in the environment. Explain that mosquitoes have been called “the most dangerous animal on the planet,” and scientists have studied the question of whether to kill all the mosquitoes on Earth. Ask:
- “What do you think is the argument for getting rid of all mosquitoes?” (They spread deadly diseases. The lives of many people could be saved.)
- “What do you think is the argument against getting rid of all mosquitoes?” (Many animals that rely on mosquitoes for food also could die out, resulting in a domino effect that could collapse ecosystems.)
Survey students on the question, and record the results for all to see and discuss.