Curriculum / Math / 8th Grade / Unit 4: Functions / Lesson 5
Math
Unit 4
8th Grade
Lesson 5 of 12
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Lesson Notes
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Read inputs and outputs in graphs of functions. Determine if graphs are functions.
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.
The foundational standards covered in this lesson
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
Lessons 5 and 6 introduce the graphical representation of functions. In Lesson 5, students analyze graphs to identify inputs and outputs and then determine if one variable is a function of the other. In Lesson 6, students will investigate properties of functions as seen in graphs, including rate of change and initial value.
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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
Which graph doesn’t belong? Why?
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Grade 8 Unit 5 Lesson 5 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 Oct. 26, 2017, 8:58 p.m..
A Fitbit is a device that can track your heart rate in beats per minute. The graph below shows Ernest’s heart rate for part of the day, with the number of beats per minute on the $$y$$-axis and the time of day on the $$x$$-axis. Use the graph to answer the questions that follow.
a. Estimate Ernest’s heart rate at 3 AM and at 9 AM. Explain how you find your answers.
b. At what time(s) in the day was Ernest’s heart rate around 75 beats per minute? Explain how you found your answer(s).
c. What time do you think Ernest woke up this morning?
d. Based on the graph, does heart rate seem to be a function of time of day? Why or why not?
e. Based on this graph, does time of day seem to be a function of heart rate? Why or why not?
Detailed heart rate graph by FerdinandFitbit (Fitbit Community) by FerdinandFitbit is made available by Fitbit Community. © Fitbit Inc. All rights reserved. Accessed Oct. 26, 2017, 9:04 p.m..
For each graph, create a table of values that includes some of the inputs and outputs. Then use the graph and the table to determine if the relationship is a function.
a. Graph A
b. Graph B
Grade 8 Unit 5 Lesson 5 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 Oct. 26, 2017, 9:09 p.m..
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 average amount of sunlight per day at the Arctic Circle in the Northern Hemisphere.
a. What is the average number of hours of sunlight in October?
b. Which months average less than 6 hours of sunlight per day?
c. Is hours of sunlight a function of month? Explain why or why not.
d. Is month a function of hours of daylight? Explain why or why not.
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.
Next
Identify properties of functions represented in graphs.
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
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
Sketch graphs of functions given qualitative descriptions of the relationship.
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