Unit 3
Introduction to Linear Relationships
Linear Relationships
Lesson 5
Expressions and Equations
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Number Talk: Fraction Division
Unit 3 ● Lesson 5
1 min individual - 1 min team share - 3 mins class share
Page 236
21/8 ⦁ 2 = 42/8 = 21/4 = 5¼ = 5.25
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Let’s explore some relationships between two variables.
Unit 3 ● Lesson 5
We will be able to find the rate of change of a linear relationship by figuring out the slope of the line representing the relationship so that we can write the equation of the line.
Learning
Goal
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Where were we? Where are we? Where are we going?
Unit 3 ● Lesson 5
Agenda Review
You are successful today when...,
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
5.2 Activity: Stacking Cups
I can find the rate of change of a linear relationship by figuring out the slope of the line representing the relationship.
10 mins total
2 min individual - 4 mins Group - 4 min class share
pg 236
Seat ___, write your group’s answer on your wall whiteboard
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
5.2 Activity: Stacking Cups
Unit 3 ● Lesson 5
10 mins total
How many cups are needed for a stack with a height of 50 cm?
33 cups
32.25 cups get us to 50 cm height
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
5.3 Activity: Connecting Slope to Rate of Change
Unit 3 ● Lesson 2
15 mins total
8 min group share - 5 mins class share
pg 237
Since the line does not pass through the origin, the relationship is not proportional.
(0,7). If we have 0 cups, the height shows at 7 cm. This does not make sense if we think about the number of cups in the stack. If however, we notice that each cup has a rim, then 7 cm is the height from the bottom of the first cup to its rim.
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
5.3 Activity: Connecting Slope to Rate of Change
Unit 3 ● Lesson 2
15 mins total
Since the line does not pass through the origin, the relationship is not proportional.
Slope triangle or Coach9’s super cool way to find slope between 2 points.
It tells us the distance from the bottom to the rim of the first cup.
4/3 = 1.333… which means this value is how much each cup adds to the height of the stack, and it is called the “rate of change.”
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Introduction to Linear Relationships
Unit 3 ● Lesson 5
How can we tell if a linear relationship is proportional or not…
From the context?
From the equation?
From a table?
From the graph?
Check to see if the y value is zero when x is zero. If the value is NOT (0,0), the relationship is NOT proportional.
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Lesson Synthesis
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Glossary
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Stacking More Cups
Unit 3 ● Lesson 5
½cm. Since 5 cups add 2.5 cm to the height of the stack, each cup adds 0.5 cm.
y = ½x + 4
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Cool-down
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 3 ● Lesson 5
Learning
Targets
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Linear Equation in Slope-Intercept Form
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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.
All curriculum excerpts are under the following licenses:
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.
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