Curriculum / Math / 8th Grade / Unit 5: Linear Relationships / Lesson 1
Math
Unit 5
8th Grade
Lesson 1 of 15
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Review representations of proportional relationships.
The core standards covered in this lesson
8.EE.B.5 — Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
The foundational standards covered in this lesson
7.RP.A.2 — Recognize and represent proportional relationships between quantities.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Asia is training for a 10K road race that will take place in October. She starts her training in July and runs every weekend. On her first run, she ran at a constant pace and covered 5.5 miles in 60 minutes. On her last run before the race, she ran at a constant pace and covered 10.2 miles in 1$$\frac{1}{2}$$ hours.
a. What were Asia's speeds, in miles per hour, on her first and last runs?
b. Write an equation to represent Asia's distance ran as a function of time for her first run and for her last run.
c. A 10K road race is approximately 6.2 miles. If Asia ran at her beginning pace, how long would it take her to finish the road race? How long would it take her if she ran at her end pace?
d. Determine which graph below represents Asia’s first run and her last run. Explain your reasoning.
The graph below shows the relationship between the distance an airplane has covered and the amount of time it has been flying.
a. What is the speed of the airplane in miles per hour?
b. What is the rate of change in the relationship?
c. What is the slope of the graph?
d. What equation represents the relationship?
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
Four representations are shown below. Three of the four representations match.
Which one does not belong? Explain your reasoning.
Graph:
Equation:
$${y=2x}$$
Table:
Description:
A caterpillar moves at a constant speed of $$\frac{1}{2}$$ inch per second. Let $$x$$ represent the time in seconds and $$y$$ represent the distance traveled in inches.
An example response to the Target Task at the level of detail expected of the students.
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 2
Topic A: Comparing 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
Model real-world situations with linear relationships.
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