Unit 4 - Lesson 8 - Grade 8: Illustrative Mathematics
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26 Questions
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Grade 8 Unit 4
Lesson 8: How Many Solutions?
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 4
Lesson 8: How Many Solutions?
CC BY 2021 Illustrative Mathematics®
Lesson: How Many Solutions?
Matching Solutions (Warm Up)
Consider the unfinished equation
12(x - 3) + 18 = _________.
Match the following expressions with the number of solutions the equation would have with that expression.
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1
Question 1
1.
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1
Question 2
2.
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Question 3
3.
Thinking About Solutions Some More
Your teacher will give you some cards.
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1
Question 4
4.
Card #1: Solve the equation with your partner
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1
Question 5
5.
Card #2: Solve the equation with your partner
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1
Question 6
6.
Card #3: Solve the equation with your partner
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1
Question 7
7.
Card #4: Solve the equation with your partner
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Question 8
8.
Sort your cards into categories.
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Question 9
9.
Describe the defining characteristics of those categories and be prepared to share your reasoning with the class.
Make Use of Structure (Optional)
For each equation, determine whether it has no solutions, exactly one solution, or is true for all values of x (and has infinitely many solutions). If an equation has one solution, solve to find the value of x that makes the statement true.
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1
Question 10
10.
If the equation has one solution, solve to find the value of x that makes the statement true.
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1
Question 11
11.
If the equation has one solution, solve to find the value of x that makes the statement true.
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1
Question 12
12.
If the equation has one solution, solve to find the value of x that makes the statement true.
1 point
1
Question 13
13.
If the equation has one solution, solve to find the value of x that makes the statement true.
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1
Question 14
14.
If the equation has one solution, solve to find the value of x that makes the statement true.
1 point
1
Question 15
15.
If the equation has one solution, solve to find the value of x that makes the statement true.
1 point
1
Question 16
16.
If the equation has one solution, solve to find the value of x that makes the statement true.
1 point
1
Question 17
17.
If the equation has one solution, solve to find the value of x that makes the statement true.
1 point
1
Question 18
18.
If the equation has one solution, solve to find the value of x that makes the statement true.
1 point
1
Question 19
19.
If the equation has one solution, solve to find the value of x that makes the statement true.
1 point
1
Question 20
20.
If the equation has one solution, solve to find the value of x that makes the statement true.
1 point
1
Question 21
21.
If the equation has one solution, solve to find the value of x that makes the statement true.
1 point
1
Question 22
22.
If the equation has one solution, solve to find the value of x that makes the statement true.
1 point
1
Question 23
23.
If the equation has one solution, solve to find the value of x that makes the statement true.
1 point
1
Question 24
24.
If the equation has one solution, solve to find the value of x that makes the statement true.
1 point
1
Question 25
25.
What do you notice about equations with one solution? How is this different from equations with no solutions and equations that are true for every x?
Cool Down: How Does She Know?
How Does She Know?
Elena began to solve this equation:
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Question 26
26.
When she got to the last line she stopped and said the equation is true for all values of x. How could Elena tell?