Curriculum / Math / 8th Grade / Unit 5: Linear Relationships / Lesson 15
Math
Unit 5
8th Grade
Lesson 15 of 15
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Model real-world situations with linear relationships.
The core standards covered in this lesson
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.EE.B.4 — Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
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 bring several concepts and skills together to be able to model and interpret real-world linear situations. The Problem Set Guidance includes several resources that can be used in connection to this lesson or as part of a review for the unit.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
A student has had a collection of baseball cards for several years. Suppose that $$B$$, the number of cards in the collection, can be described as a function of $$t$$, which is time in years since the collection was started.
Explain what each of the following equations would tell us about the number of cards in the collection over time.
a. $$B=200+100t$$
b. $$B=100+200t$$
c. $$B=2000-100t$$
d. $$B=100-200t$$
Baseball Cards, accessed on Dec. 6, 2016, 3:22 p.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.
You have $100 to spend on a barbeque where you want to serve chicken and steak. Chicken costs $1.30 per pound and steak costs $3.50 per pound. You want to know how many pounds of chicken and steak you can afford to buy.
a. Write an equation that relates the amount of chicken and the amount of steak you can buy. Use your equation to sketch a graph.
b. What is the meaning of each intercept in this context?
c. What is the meaning of the slope of the line in this context?
d. Discuss what your options are for the amounts of chicken and steak you can buy for the barbeque.
Chicken and Steak, Variation 1, accessed on Feb. 26, 2018, 11:31 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.
A set of suggested resources or problem types that teachers can turn into a problem set
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
A parking garage is located in the downtown area of a city. The table below shows the cost for parking in the garage for different amounts of time.
a. What equation represents the cost of parking in the garage, $$y$$, for $$x$$ hours?
b. Sketch a graph to represent the cost of parking over time.
c. What does the slope of your line represent in context of this situation?
d. What does the $$y$$-intercept of your line represent in context of this situation?
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.
Lesson 14
Topic A: Comparing Proportional Relationships
Review representations of proportional relationships.
8.EE.B.5
Graph proportional relationships and interpret slope as the unit rate.
Compare proportional relationships represented as graphs.
Compare proportional relationships represented in different ways.
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Topic B: Slope and Graphing Linear Equations
Graph a linear equation using a table of values.
8.F.B.4
Define slope and determine slope from graphs.
8.EE.B.6
Determine slope from coordinate points. Find slope of horizontal and vertical lines.
8.EE.B.6 8.F.B.4
Graph linear equations using slope-intercept form $${y = mx + b}$$.
8.EE.B.6 8.F.A.3
Write equations into slope-intercept form in order to graph. Graph vertical and horizontal lines.
Topic C: Writing Linear Equations
Write linear equations from graphs in the coordinate plane.
Write linear equations using slope and a given point on the line.
Write linear equations using two given points on the line.
Write linear equations for parallel and perpendicular lines.
Compare linear functions represented in different ways.
8.F.A.2 8.F.B.4
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