Unit 4
All, Some, or No Solutions
Linear Equations and Linear Systems
Lesson 7
8.EE.C.7.a: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form 𝘹 = 𝘢, 𝘢 = 𝘢, or 𝘢 = 𝘣 results (where 𝘢 and 𝘣 are different numbers).
Expressions and Equations
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Equations
Unit 4 ● Lesson 7
1 min individual - 1 min team share - 3 mins class share
Page 40
How is each equation unique from the others?
Only addition
Only multiplication
Only equation with a “2” or just one number on one side
Only equation that is not 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.
Let's think about how many solutions an equation can have.
Unit 4 ● Lesson 7
We will be able to determine whether an equation has no solutions, one solution, or infinitely many solutions so that we can better solve equations.
Learning
Goal
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Where were we? Where are we? Where are we going?
Unit 4 ● Lesson 7
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.
7.2 Activity: Thinking About Solutions
I can determine whether an equation has no solutions, one solution, or infinitely many solutions
Students who pause to think about the structure of a complex equation before taking steps to solve it can find the most efficient solution paths.
Infinitely many solutions—it is true for all values of t.
NO solutions—it is NOT true for any values of n.
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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 7
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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.
7.2 Activity: Thinking About Solutions
I can determine whether an equation has no solutions, one solution, or infinitely many solutions
15 mins total
(Q1 only) 4 mins Group - 3 mins class share
pg 40
(I) Infinite Solutions
(N) NO Solutions
or
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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.
7.2 Activity: Thinking About Solutions
I can determine whether an equation has no solutions, one solution, or infinitely many solutions
Infinite Solutions
Infinite Solutions
Infinite Solutions
Infinite Solutions
NO Solutions
NO Solutions
NO Solutions
NO Solutions
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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.
7.2 Activity: Thinking About Solutions
I can determine whether an equation has no solutions, one solution, or infinitely many solutions
15 mins total
(Q2-3 only) 4 mins Group - 3 mins class share
pg 40
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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.
7.2 Activity: Thinking About Solutions
I can determine whether an equation has no solutions, one solution, or infinitely many solutions
Infinite Solutions
NO Solutions
6u + -10
6u + __
the blank represents any number other than −10.
15 mins total
3 mins Group - 3 mins class share
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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.
7.3 Activity: What's the Equation?
I can determine whether an equation has no solutions, one solution, or infinitely many solutions
15 mins total
7 mins Group - 5 mins class share
pg 41
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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.
7.3 Activity: What's the Equation?
I can determine whether an equation has no solutions, one solution, or infinitely many solutions
2
2
3x
SAME slope, SAME y-intercept (SAME lines)
Infinite Solutions
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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.
7.3 Activity: What's the Equation?
I can determine whether an equation has no solutions, one solution, or infinitely many solutions
not 2
(3x+not 0)
not 2
Equations which are always true for any value of x (infinite solutions), have equivalent expressions on each side.
Equations which have no solution for any value of x simplify to a statement of two unequal numbers being equal, which is always false.
SAME slope, DIFFERENT y-intercept (parallel lines)
NO Solutions
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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.
All, Some, or No Solutions
I can determine whether an equation has no solutions, one solution, or infinitely many solutions
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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.
Choose Your Own Solution
I can determine whether an equation has no solutions, one solution, or infinitely many solutions
Any value other than 8; No solutions (parallel)
Only 8; Infinite Solutions (same line)
Only another variable term, such as -2x;
One Solution (2 lines that intersect at one point only)
Different slope, different y-intercept
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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.
Choose Your Own Solution
I can determine whether an equation has no solutions, one solution, or infinitely many solutions
Solution = (-4,-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 4 ● Lesson 7
Learning
Targets
8
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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.
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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