Functions

Lesson 12

Objective

Sketch graphs of functions given qualitative descriptions of the relationship.

Common Core Standards

Core Standards

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  • 8.F.B.5 — Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Criteria for Success

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  1. Identify key details from qualitative descriptions of relationships that translate to a graph, such as where the graph is increasing or decreasing, or how steep or shallow a line segment is.
  2. Sketch a graph that shows distance as a function of time.
  3. Sketch a graph that shows speed as a function of time. 
  4. Model or enact scenarios represented by distance or speed graphs. 

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Anchor Problems

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Problem 1

Two graphs representing a student’s movements are shown below. For each graph, 

  • Discuss what each section of the graph tells you about the movement of the student.
  • Have a student model the movements in the classroom. 

Graph 1:

Graph 2:

Guiding Questions

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Problem 2

Two stories are shown below. For each one, draw a graph to represent the functional relationship between the two quantities. 

Story 1: Distance from home vs. Time
You leave home and walk to the corner store. At the store, you spend a few minutes shopping, but then realize that you forgot your wallet at home. You run home, find your wallet immediately, and then run back to the store where you pay for your items. You leave the store and slowly walk away in the opposite direction of your home, toward the basketball court. Once you get to the court, you look for your friend for a few minutes, but when you realize that he’s not there, you walk quickly back home. 

Story 2: Temperature vs. Time
At 8 AM on a summer day, the temperature in Hartford, Connecticut, was 60°F. By 10 AM, the temperature had risen 10°F, where it stayed until 12 PM. From noon to 3 PM, the temperature rose to 85°F, after which it dropped at a steady rate until it hit 65°F at 9 PM. 

               

Guiding Questions

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Problem 3

Nina rides her bike from her home to school, passing by the library on the way and traveling at a constant speed for the entire trip. (See map below.)

  1. Sketch a graph of Nina’s distance from school as a function of time.
  2. Sketch a graph of Nina’s distance from the library as a function of time.

Guiding Questions

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References

Illustrative Mathematics Riding by the Library

Riding by the Library, accessed on Oct. 27, 2017, 11:12 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • In pairs, have each student write a story and then swap stories and draw the associated graph.

Target Task

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A child at a park sees a slide. She runs across the playground to the slide and slowly climbs up the stairs. At the top of the stairs, she pauses for a moment and then slides down to the bottom. 

Sketch two graphs for the situation: one that shows the child’s distance from the stairs of the slide as a function of time, and the other that shows the child’s speed as a function of time. 

Mastery Response

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