Curriculum / Math / 8th Grade / Unit 4: Functions / Lesson 6
Math
Unit 4
8th Grade
Lesson 6 of 12
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Lesson Notes
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Identify properties of functions represented in graphs.
The core standards covered in this lesson
8.F.A.1 — Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8.
8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
The foundational standards covered in this lesson
7.RP.A.2.B — Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
7.RP.A.2.D — Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
In this lesson, students further their analysis of a function graph to find rate of change and initial value. In seventh grade, students found the constant of proportionality in proportional graphs. This lesson prepares students to compare functions across multiple representations in upcoming lessons in this unit, and to determine slope of linear functions in Unit 5.Â
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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
The graph below shows the amount of money on a subway card as a function of the number of subway rides taken. Use the graph to answer the questions that follow.
a. After 2 rides, how much money is on the card?
b. After 4 rides, how much money is on the card?
c. Interpret point $$P$$ in context of the situation.
d. At what rate is the money on the card changing for each ride taken?
e. How much money did the card initially have on it?
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Teacher Version: Grade 8 Unit 5 Lesson 4 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Nov. 3, 2017, 11:39 a.m..
In a laboratory, a scientist is tracking the temperature of a substance over time. Each hour, she takes the temperature and records it in the graph shown below.
a. What is the rate of change of the substance’s temperature, in °F per hour, between 12 PM and 3 PM?
b. What is the rate of change of the substance’s temperature, in °F per hour, between 7 PM and 9 PM?
c. What is the starting temperature of the substance?
d. Does it appear that the temperature of the substance is a function of the time of day? Why or why not?
The ordered pairs below are from a graph, which is not shown. Based on the ordered pairs, determine if the graph is a function.
$${(3,4)}$$ $${(2,5)}$$ $${(1,6)}$$ $${(0,7)}$$ $${(1,8)}$$
A set of suggested resources or problem types that teachers can turn into a problem set
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
The graph below shows the population of the United States over time using data from the U.S. Census Buraeu.
a. Approximately what was the population of the United States in 2010, 2012, and 2014?
b. Approximately when did the population of the United States pass 310 million people?
c. Between 2012 and 2014, what was the rate of change of the population in the United States?
d. Describe the relationship as a function.
Annual Estimates of the Residential Population: April 1, 2010 to July 1, 2016 is made available by the U.S. Census Bureau. Accessed Oct. 31, 2017, 3:51 p.m..
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.
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Define and graph linear and nonlinear functions.
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.
Topic C: Comparing 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
Sketch graphs of functions given qualitative descriptions of the relationship.
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