Lesson plan

7. Charging conundrum: determine and interpret a linear function given two points (A)

teaches Common Core State Standards CCSS.Math.Content.8.EE.B.6 http://corestandards.org/Math/Content/8/EE/B/6
teaches Common Core State Standards CCSS.Math.Content.8.F.B.4 http://corestandards.org/Math/Content/8/F/B/4
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1
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Lesson objective: Solve problems by using the fact that the rate of change of a linear function is constant.

This lesson provides an opportunity for students to apply their knowledge and understanding that the slopes between all pairs of points on a given line are equivalent to a real-life situation. Students are asked to calculate the rate at which various devices charge, and use this information to determine what the charge of each device will be at a certain time.

Key Concept students will use: 

  • The segment created between any two points on a nonvertical line can be thought of as the hypotenuse of a right triangle. All the right triangles created from segments from the same line are similar.

Skills students will use:

  • calculating rate of change given two points
  • finding additional points on a line given the slope and a point
  • solving proportions (Grade 7, Unit 1)

Students engage in Mathematical Practice 1 (Make sense of problems and perservere in solving them) as they interpret the information provided about each device as a linear relationship, and figure out how to use this realization to find missing information. Students must also make sense of answers in terms of context, for example interpreting a device with a charge of "112 percent" as having been completely charged for some amount of time.

Key vocabulary: 

  • constant rate of change
  • slope