Curriculum / Math / 8th Grade / Unit 4: Functions / Lesson 12
Math
Unit 4
8th Grade
Lesson 12 of 12
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Lesson Notes
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Sketch graphs of functions given qualitative descriptions of the relationship.
The core standards covered in this lesson
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Two graphs representing a student’s movements are shown below. For each graph,
a. Graph 1:
b. Graph 2:
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Two stories are shown below. For each one, draw a graph to represent the functional relationship between the two quantities.
a. 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.
b. 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.
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.)
a. Sketch a graph of Nina’s distance from school as a function of time.
b. Sketch a graph of Nina’s distance from the library as a function of time.
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.
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15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
A child at a park sees some monkey bars. He runs across the playground to the monkey bars and then stops to wait in a small line. When it is his turn, he slowly makes his way across the monkey bars.
Sketch two graphs for the situation: one that shows the child’s distance from the beginning of the monkey bars as a function of time, and the other that shows the child’s speed as a function of time.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Topic A: Defining Functions
Define and identify functions.
Standards
8.F.A.1
Use function language to describe functions. Identify function rules.
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Topic B: Representing and Interpreting Functions
Identify properties of functions represented in tables, equations, and verbal descriptions. Evaluate functions.
8.F.A.18.F.A.28.F.B.4
Represent functions with equations.
8.F.A.18.F.B.4
Read inputs and outputs in graphs of functions. Determine if graphs are functions.
Identify properties of functions represented in graphs.
Topic C: Comparing Functions
Define and graph linear and nonlinear functions.
8.F.A.3
Determine if functions are linear or nonlinear when represented as tables, graphs, and equations.
8.F.A.18.F.A.3
Compare functions represented in different ways (Part 1).
8.F.A.2
Compare functions represented in different ways (Part 2).
Topic D: Describing and Drawing Graphs of Functions
Describe functions by analyzing graphs. Identify intervals of increasing, decreasing, linear, or nonlinear activity.
8.F.B.5
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