Unit 4
Systems of Equations
Linear Equations and Linear Systems
Lesson 12
8.EE.C.8: Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. Solve real-world and mathematical problems leading to two linear equations in two variables.
8.EE.C.8.a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
8.EE.C.8.b: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.
Expressions and Equations
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Milkshakes
Unit 4 ● Lesson 12
1 min individual - 1 min team share - 3 mins class share
Page 73
Lin will take 48 seconds and Diego will take 30 seconds.
y = -¼x + 12
y = -⅔x + 20
0 = -¼x + 12
-12 = -¼x
12 = ¼x (multiply both side by -4)
48 = x
0 = -⅔x + 20
-20 = -⅔x
20 = ⅔x (multiply both side by -3/2)
30 = x
Amt. Remaining (ounces)
Time (seconds)
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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 learn what a system of equations is.
Unit 4 ● Lesson 12
We will be able to make graphs to find an ordered pair so that we can explain the solution to a system of equations in a real-world context.
Learning
Goal
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Where were we? Where are we? Where are we going?
Unit 4 ● Lesson 12
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.
12.3 Activity: Stacks of Cups
I can make graphs to find an ordered pair that two real-world situations have in common
10 mins total
3 mins individual - 2 minutes group - 5 mins class share
pg 75
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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.
12.2 Activity: Passing on the Trail
I can make graphs to find an ordered pair that two real-world situations have in common
3 mins total
3 mins CLASS
pg 73-4
Han is 4.8 miles away from the parking lot. Jada is 0.6 miles away from the parking lot.
Han’s distance is decreasing because he is walking towards the parking lot. Jada’s time is increasing because she is hiking away from the parking lot (towards the lake).
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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.
12.2 Activity: Passing on the Trail
I can make graphs to find an ordered pair that two real-world situations have in common
d = 3.2t + 0.6
5 mins total
4 mins group - 1 min Class (Q1-2)
pg 73-4
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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.
12.2 Activity: Passing on the Trail
I can make graphs to find an ordered pair that two real-world situations have in common
12 mins total
7 minutes group - 5 mins class share
d = 3.2t + 0.6
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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.
12.2 Activity: Passing on the Trail
I can make graphs to find an ordered pair that two real-world situations have in common
3&4. Find the point where the two graphs intersect each other. What are the coordinates of this point? What do the coordinates mean in this situation?
5. What has to be true about the relationship between these coordinates and Jada’s equation?
6. What has to be true about the relationship between these coordinates and Han’s equation?
0.75 hours or 45 minutes after Han left the lake, he passed Jada on the trail. This happened at a distance of 3 miles from the parking lot.
These values of t and d make Jada’s equation true
These values of t and d also make Han’s equation true
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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.
Glossary
Unit 4 ● Lesson 12
Solved by elimination (adding vertically):
x + y = -2
x - y = 12
2x = 10
x = 5
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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.
Systems of Equations
I can make graphs to find an ordered pair that two real-world situations have in common
3 ines all passing through the same intersecting point.
something about the speed of the third person or their distance from the parking lot at another point in time
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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.
Systems of Equations
I can make graphs to find an ordered pair that two real-world situations have in common
Two or more equations for which you want to find values for all of the variables so that all of the equations are true.
The values for all of the variables that make all of the equations true.
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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.
Milkshakes, Revisited
I can make graphs to find an ordered pair that two real-world situations have in common
There is one solution at (24,4) meaning that after 24 seconds both of them had 4 ounces of milkshake left. Diego still finishes his milkshake first.
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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 4 ● Lesson 12
Learning
Targets
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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.
Glossary
Unit 4 ● Lesson 5
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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.
Glossary
Unit 4 ● Lesson 12
Solved by elimination (adding vertically):
x + y = -2
x - y = 12
2x = 10
x = 5
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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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