G8

Input/Model

(Teacher Presents)

Directions: Identify an inverse operation to use. Solve and check your solution.

1. x + 3 = 10

Solution:
• Identify operation in the equation: ADDITION
• Identify inverse operation needed to solve: SUBTRACTION

+ 3 = 10
−3 − 3
= 7

Answer: = 7
Check. 7 + 3 = 10

10 = 10 ✓

2. ─3m = 15

Solution:
• Apply the multiplicative inverse of –3: divide by –3 or multiply by − 31.

−3 15
−3 = −3

= −5

Answer: m = −5

Check: −3 • −5 = 15
15 = 15 ✓

3. = −9
3

Solution: 13:

• Apply the multiplicative inverse of multiply by 3.

= −9 • 3 → 13 • = −9 • 3
3•3 31

= −9 • 3

Answer: = −27

Check: −27 = −9
3
−9 = −9 ✓

Copyright © Swun Math 296Grade 8 Unit 4 Lesson 2 P TE

Structured Guided Practice

(A/B Partners Practice)

Directions: Identify an inverse operation to use. Solve and check your solution.
1. r ─ 12 = 40

Solution:
Answer: = 52
Check: 52 — 12 = 40

40 = 40 ✓

2. 20 = 5d

Solution:
Answer: = 4
Check: 20 = 5 • 4

20 = 20 ✓

3. = 12
4

Solution:
Answer: = 48

Check: 48 = 12
4

12 = 12 ✓

297 Copyright © Swun Math Grade 8 Unit 4 Lesson 2 P TE

Final Check for Understanding

(Teacher Checks Work)

Directions: Identify an inverse operation to use. Solve and check your solution.
1. ─12 + x = 20

Solution:
Answer: x=32
Check: 32 — 12 = 20

20 = 20 ✓

2. 3v = 39

Solution:
Answer: v=13
Check: 3(13) = 39

39 = 39 ✓

3. = 10
5

Solution:
Answer: x = 50

Check: 50 = 10
5

10 = 10 ✓

Copyright © Swun Math 298Grade 8 Unit 4 Lesson 2 P TE

Student Practice Name: ___________________________
Date: ___________________________
Unit 4 · Lesson 2: One-Step Equations

Directions: Identify an inverse operation to use. Solve and check your solution.

1. − 5 = 12 2. 6 = −24

Solution: − 5 = 12 Addition Solution: 6 = −24 Division
+5 + 5 6 6
= 17
= −4

Check: 6 ∙ −4 = −24
−24 = −24 ✓
Check: 17 − 5 = 12
12 = 12 ✓

3. 3 = −30 4. = 9
3

Solution: 3 = −30 Division Solution: = 9 Multiplication
3 3 3

= −10 3 ∙ =9 ∙3
3

= 27

Check: 3 ∙ −10 = −30 Check: 27 = 9
−30 = −30 ✓ 3

9 = 9✓

5. + 4 = 19 6. = −20
10

Solution: + 4 = 19 Subtraction Solution: = −20 Multiplication
−4 − 4 10
= 15
10 ∙ = −20 ∙ 10
10

= −200

Check: 15 + 4 = 19 Check: −200 = −20
19 = 19 ✓ 10

−20 = −20 ✓

299 Copyright © Swun Math Grade 8 Unit 4 Lesson 2 P TE

Challenge Problems

Directions: Identify the error, make the correction, and explain your thinking.

1. Bobby’s work: 3 = 12 2. Cindy’s work:
= 36 5 = 15
= 3

Solution: Solution:
Bobby multiplied the 3 and 12, but he should have Cindy divided 15 by 5, but she should have multiplied.
divided. The original equation had multiplication and The original equation had division and the inverse
the inverse operation of multiplication is division. operation of division is multiplication.

3 12 5 ∙ = 15 ∙5
3= 3 5
= 4
= 75

Extension Activity

* MP1: Make sense of the problem and persevere in solving it.
* MP4: Apply mathematics in everyday life.

Write four equations, one with each operation, so that each has a solution of ─4.

Copyright © Swun Math 300Grade 8 Unit 4 Lesson 2 P TE

Closure

Reaching Consensus
*MP3: Do you agree or disagree with your classmate? Why or why not?

Student Presentations
*MP1: What steps in the process are you most confident about?
*MP6: Explain how you might show that your solution answers the problem.

Closure

Recap today’s lesson with one or more of the following questions:
MP1: What inverse operation is needed to solve ____?
MP7: What patterns do you find when solving one-step equations?

301 Copyright © Swun Math Grade 8 Unit 4 Lesson 2 P TE

Homework Name: ___________________________
Date: ___________________________
Unit 4 · Lesson 2: One-Step Equations

Objective: I will solve one-step equations by applying the inverse operations.

Vocabulary Steps

Inverse Operations: operations that undo each 1. Work on the side with the variable.
other 2. Apply the Additive Inverse
3. Apply the Multiplicative Inverse
Addition Subtraction 4. Check the solution by substituting.
Multiplication Division

Additive Inverse: a number and its opposite
whose sum is 0; also called a zero pair

Multiplicative Inverse: a number and its
reciprocal; when these numbers are multiplied,
the product is 1.

Copyright © Swun Math 302Grade 8 Unit 4 Lesson 2 P TE

Homework

Unit 4 · Lesson 2: One-Step Equations

Example # 1 Example # 2

Directions: Identify an inverse operation to use. Solve and check your solution.

+ 3 = 10 −3 = 15

Solution: Solution:
• Identify operation in the equation: ADDITION • Identify operation in equation: MULTIPLICATION
• Identify inverse operation needed to solve:
• Identify inverse operation needed to solve: DIVISION
SUBTRACTION
+ 3 = 10 • Apply the multiplicative inverse of –3: divide by –3 or
−3 − 3 multiply by − 31.
= 7 −3 15
−3 = −3
Answer: = 7 = −5
Check. 7 + 3 = 10
Answer: = −5
10 = 10 ✓
Check: −3 • −5 = 15
Example # 3 15 = 15 ✓

= −9
3

Solution:

• Identify operation in equation: DIVISION

• Identify inverse operation needed to solve: MULTIPLICATION

• Apply the multiplicative inverse of 13: multiply by 3.
−9 • 3
= −9 • 3 →• =
3•3

= −9 • 3

Answer: = −27

Check: −27 = −9
3
−9 = −9 ✓

303 Copyright © Swun Math Grade 8 Unit 4 Lesson 2 P TE

Homework

Unit 4 · Lesson 2: One-Step Equations

Directions: Identify an inverse operation to use. Solve and check your solution

1. −2 = −10 2. = −8
4

3. 12 = − 4 4. + 4 = −7

5. = −9 6. 4 = 48
5

Explain the steps you used to solve problem number _______.

______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________

Copyright © Swun Math 304Grade 8 Unit 4 Lesson 2 P TE

Answer Key

Extension Activity

Answers may vary. Sample responses:

+ 8 = 4 – 1 = −5 = −2 2 = −8
2
2. multiplication; = −32
Homework 4. subtraction; = −11
6. division; = 12
1. division; = 5

3. addition; = 16

5. multiplication; = −45

305 Copyright © Swun Math Grade 8 Unit 4 Lesson 2 P TE

Notes

Copyright © Swun Math 306Grade 8 Unit 4 Lesson 2 P TE

Collect Like Terms MPs Applied MP 8

Conceptual Lesson * Embedded MP *

Grade 8 · Unit 4 · Lesson 3 1234567

MC: 8.EE.7b * 

Problem of the Day Student Journal Pages

Objective: I will collect like terms to simplify expressions. 168-171

Vocabulary Teacher Resources

Term: a constant, variable, or a number and Considerations:
variable, multiplied in an expression and
separated by + or ─ It is helpful to color code like terms using highlighters or
colored pencils. Remember terms are separated by + and –
Like Terms: terms that have the same signs. Signs are always attached to the front of a term.
variable, power, or constant Remind students to keep the sign of the term when
rewriting. Students should be able to identify that they are
4a + 5 + 2a – 3 using the commutative property to “rewrite” the algebraic
5b2 – 6b + 3b2 expressions. Students that are struggling should practice
expanding their expressions.
Algebraic Expression: an expression
using variables, integers and operations; 3x + 2b + 4x + b x + x + x + b + b + x + x + x + x + b
does not have an equal sign
Which simplifies to 7x + b. This can help to understand why
we don’t collect 7x + 10b into 10xb (common mistake).

Coefficient: a number used to multiply a Steps:
variable
1. Expand the expression (if needed).
Constant: a number on its own in an 2. Identify like terms.
expression or equation 3. Reorder the terms.
4. Collect like terms.
Expression Equation Variable 5. Simplify.

− + = +

Term Coefficient Constant Application of MPs:

Collecting Like Terms  MP1: Describe in your own words what you are trying to
do.
4a + 5 + 2a – 3
(a + a + a + a + 5 + a + a – 3) I am trying to .

6a + 2  MP6: How did you know your solution is reasonable?

Collecting Like Terms: My answer is reasonable since I can prove that
Distributive Property .

3(n + 4) + 4(n + 2)
3n + 12 + 4n + 8

7n + 20

307 Copyright © Swun Math Grade 8 Unit 4 Lesson 3 C TE

Input/Model

(Teacher Presents)

Directions: Collect like terms to simplify each expression.
1. 5x + 2 + 3x + 7

Solution:
5x + 2 + 3x + 7
5x + 3x + 2 + 7
8x + 9

Answer: 8x + 9

2. ─11x + 5 ─ 3x ─ 12

Solution: Grade 8 Unit 4 Lesson 3 C TE 308
—11x + 5 — 3x — 12
—11x — 3x + 5 — 12
–14x — 7

Answer: –14x – 7

Copyright © Swun Math

Structured Guided Practice

(A/B Partners Practice)

Directions: Collect like terms to simplify each expression.
1. 2y + 4 + 5y + 8

Solution:
2y + 4 + 5y + 8
2y + 5y + 4 + 8
7y + 12

Answer: 7y + 12

2. ─3y + 9 + 8y ─ 15

Solution:
—3y + 9 + 8y — 15
—3y + 8y + 9 — 15
5y — 6

Answer: 5y – 6

309 Copyright © Swun Math Grade 8 Unit 4 Lesson 3 C TE

Final Check for Understanding

(Teacher Checks Work)
Directions: Collect like terms to simplify each expression.

1. 3r + 5 ─ 12 ─ 6r

Solution:

–3r – 7
2. ─17 + 5x ─10 ─ 10x

Solution:
–27 – 5x; descending order – 5x – 27

Closure

Recap today’s lesson with one or more of the following questions:

MP1: Describe in your own words what you are trying to do.
MP6: How did you know your solution is reasonable?

Copyright © Swun Math Grade 8 Unit 4 Lesson 3 C TE 310

Homework Name: ___________________________
Date: ___________________________
Unit 4 · Lesson 3: Collect Like Terms

Objective: I will collect like terms to simplify expressions.

Vocabulary Steps

Term: a constant, variable, or a number and 1. Expand the expression (if needed).
variable, multiplied in an expression and 2. Identify like terms.
separated by + or ─ 3. Reorder the terms.
4. Combine like terms.
Like Terms: terms that have the same variable, 5. Simplify.
power or constant

4a + 5 + 2a – 3
5b2 – 6b + 3b2

Coefficient: a number used to multiply a variable

Constant: a number on its own in an
expression or equation

Expression Equation Variable

− + = +

Term Coefficient Constant

Collecting Like Terms

4a + 5 + 2a – 3
(a + a + a + a + 5 + a + a – 3)

6a + 2

Collecting Like Terms:
Distributive Property

3(n + 4) + 4(n + 2)

3n + 12 + 4n + 8

7n + 20

Example # 1 Example # 2

Directions: Collect like terms to simplify each expression.

5 + 2 + 3 + 7 — 11 + 5 — 3 — 12

Solution: Solution:

5x + 2 + 3x + 7 —11x + 5 — 3x — 12

5x + 3x + 2 + 7 —11x — 3x + 5 — 12 Answer: ─14x ─ 7

8x + 9 Answer: 8x + 9

311 Copyright © Swun Math Grade 8 Unit 4 Lesson 3 C TE

Homework

Unit 4 · Lesson 3: Collect Like Terms

Directions: Collect like terms to simplify. 2. 10 + 3x ─ 7 + 5x
1. 4r + 7 + 6r + 10

3. ─6x ─ 3 + 9x ─ 6 4. 7y + 9 ─ 10y + 3

5. ─8m ─3 ─ 4m ─ 7 6. 12 ─ 5c ─ 20 ─ 10c

Copyright © Swun Math Grade 8 Unit 4 Lesson 3 C TE 312

Answer Key 2. 8x + 3
4. ─3y + 12
Homework 5. ─15c ─ 8

1. 10r + 17
3. 3x ─ 9
4. ─12m ─ 10

313 Copyright © Swun Math Grade 8 Unit 4 Lesson 3 C TE

Notes

Copyright © Swun Math Grade 8 Unit 4 Lesson 3 C TE 314

Two-Step Equations MPs Applied MP

Procedural Lesson * Embedded MP
Grade 8 · Unit 4 · Lesson 4
12345678
MC: 8.EE.7b
* ** *  *

Problem of the Day Student Journal Pages

172-177

Objective: I will solve two-step equations by collecting like terms and using inverse operations.

Vocabulary Teacher Resources

Expression Equation Variable Considerations:
It is important that students understand what “isolate
− + = + the variable” means. Sometimes it takes multiple
steps to isolate the variable. The last step in solving
Term Coefficient Constant one-step equations is ALWAYS EITHER to multiply or
divide when there is a coefficient attached to the
Inverse Operations: operations that undo each variable.
other A great strategy to implement when moving variables
from one side of the equal sign to the other is to move
Addition Subtraction variable terms to keep the coefficient positive.
Multiplication Division
*If needed, model and teach I/M #3 and all
Additive Inverse: a number and its opposite corresponding problems on the next day of
whose sum is 0; also called a zero pair instruction.

Steps:
1. Collect like terms, if necessary.
2. Move all terms with variables to one side.

(Use Additive Inverse)
3. Move all constants to the other side.

(Use Additive Inverse)
4. Solve for the variable.

(Use Multiplicative Inverse)

Multiplicative Inverse: a number and its Application of MPs:
reciprocal whose product is 1
MP6: What mathematical language can you use to
describe the process of solving for a variable?

I need to use operations to

isolate the variable to identify its value.

MP7: How does solving multi-step equations relate
to solving one-step equations?

When solving for one-step equation I had to

use the operations in isolation.

A multi-step equation requires me to use .

315 Copyright © Swun Math Grade 8 Unit 4 Lesson 4 P TE

Input/Model 2. 11x ─ 9x + 2 ─2 =10

(Teacher Presents)

Directions: Solve and check.
1. 3x + 5 = 38

Solution: 3 + 5 = 38 Solution:

−5 − 5 Collect like terms: 11x ─ 9x + 2 ─2 =10
2x + 2 ─ 2 =10
3x = 33
Simplify: 2─2 = 0, so 2x = 10
3 = 33 Divide each side by 2: x = 5
3 3
Answer: x = 5
x = 11
Check: 11(5) ─ 9(5) + 2 ─2 =10
Answer: x = 11 55 ─ 45 + 2 – 2 =10
10=10 ✓
Check: 3 · 11 + 5 = 38

33 + 5 = 38

38 = 38 ✓

3. 6 = − 3
7

Solution: Grade 8 Unit 4 Lesson 4 P TE
Add 3 to each side to isolate the variable: 3 + 6 = ( 7 ) ─3 + 3
316
9= ( 7 )
Multiply each side by 7: 9(7)= ( 7 )7
Answer: 63=m
Check: 6 =(673 )─3

6 =9─3
6=6 ✓

Copyright © Swun Math

Structured Guided Practice

(A/B Partners Practice)

Directions: Solve and check. 2. 2p ─ (─6p) ─ (─7p) = 15
1. ─17 = 2x + 9

Solution: Solution:
x= ─13 p= 1

3. −1 = −2
4

Solution:
m= ─7

317 Copyright © Swun Math Grade 8 Unit 4 Lesson 4 P TE

Final Check for Understanding

(Teacher Checks Work)

Directions: Solve and check. 2. 16n─3n─10n ─2n =18
1. 15─2m = 13

Solution: Solution:
m= 1 n= 18

3. −7 = −12
3

Solution: Grade 8 Unit 4 Lesson 4 P TE 318
p= ─29

Copyright © Swun Math

Student Practice Name: ___________________________
Date: ___________________________
Unit 4 · Lesson 4: Two-Step Equations
2. 8 ─ 3y = 2
Directions: Solve and check.
1. ─12 + 4n = ─28

Solution: Solution:
n= ─4 y= 2

3. ─19b + 13b + b ─ b = ─18 4. ─14c + 16c = 8

Solution: Solution:
b=3 c=4

5. −n + (−16) = −15 6. − 7 = −5
−4 3

Solution: Solution:
─4 6

319 Copyright © Swun Math Grade 8 Unit 4 Lesson 4 P TE

Challenge Problems 2. 3x + 9 = 6x ─ 12

Directions: Solve.
1. 2x + 6 = 4x + 8

Solution: Solution:
x= ─1 x=7

Extension Activity

* MP1: Make sense of the problem and persevere in solving it.
* MP4: Apply mathematics in everyday life.

Prove that the following equation has infinitely many solutions. Do this by giving the
variable m three different values and solving the equations three times using each value
at one time.

7m + 3 = 4m + 3 + 3m

Copyright © Swun Math Grade 8 Unit 4 Lesson 4 P TE

320

Closure

Reaching Consensus
*MP3: Do you agree or disagree with your classmate? Why or why not?

Student Presentations
*MP1: What steps in the process are you most confident about?
*MP6: Explain how you might show that your solution answers the problem.

Closure

Recap today’s lesson with one or more of the following questions:
MP6: What mathematical language can you use to describe the process of solving

for a variable?
MP7: How does solving multi-step equations relate to solving one-step equations?

321 Copyright © Swun Math Grade 8 Unit 4 Lesson 4 P TE

Homework Name: ___________________________
Date: ___________________________
Unit 4 · Lesson 4: Two-Step Equations

Objective: I will solve two-step equations by collecting like terms and using inverse operations.

Vocabulary Steps:

Expression Equation Variable 1. Collect like terms, if necessary.
2. Move all terms with variables to one side.
− + = + 3. Move all constants to the other side.
4. Solve for the variable using inverse
Term Coefficient Constant
operations.

Inverse Operations: operations that undo each

other

Addition Subtraction

Multiplication Division

Additive Inverse: a number and its opposite
whose sum is 0; also called a zero pair

Multiplicative Inverse: a number and its
reciprocal whose product is 1

−5 ⋅ 1 = 1
−5

Number Multiplicative Inverse

4n = 12
4 12
4 =4

n=3

Copyright © Swun Math Grade 8 Unit 4 Lesson 4 P TE

322

Homework

Unit 4 · Lesson 4: Two-Step Equations

Example # 1 Example # 2
Directions: Solve and check.
11x ─ 9x + 2 ─2 =10
3x + 5 = 38

Solution: 3 + 5 = 38 Solution:
Combine like terms: 11x ─ 9x + 2 ─2 =10
−5 − 5
2x + 2 ─ 2 =10
3 = 33 Simplify: 2-2 = 0, so 2x = 10
Divide each side by 2: x = 5
3 = 33 Answer: x = 5
3 3 Check: 11(10) ─ 9(10) + 2 ─2 =10

= 11 110─90 + 2 – 2 =10
10=10 ✓
Answer: = 11

Check: 3 ∙ 11 + 5 = 38

33 + 5 = 38

38 = 38 ✓

Example # 3

6 = − 3
7

Solution:
Add 3 to each side to isolate the variable: 3 + 6 = ( 7 ) ─3 + 3

9= ( 7 )
Multiply each side by 7: 9(7)= ( 7 )7

Answer: 63=m

Check: 6 =(673 )─3
6 =9─3
6=6 ✓

323 Copyright © Swun Math Grade 8 Unit 4 Lesson 4 P TE

Homework 2. 14 = 4a + 6

Unit 4 · Lesson 4: Two-Step Equations

Directions: Solve and check.
1. ─15 + 5b = ─30

3. 15y ─13y ─2y + 3y = 9 4. 2k ─ (─20k) + 16k ─ 13k ─5k = ─20

5. 1 d + 17 = 28 6. 14+ = 22
4 −8

Explain the steps you used to solve problem number _______.

______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________

Copyright © Swun Math Grade 8 Unit 4 Lesson 4 P TE

324

Answer Key 2. a= 2
4. k = ─1
Extension Activity 6. n = ─190

Answers will vary. Sample responses:

If = 2
7 + 3 = 4 + 3 + 3
7(2) + 3 = 7(2) + 3
14 + 3 = 14 + 3
17 = 17

If = 5
7 + 3 = 4 + 3 + 3
7(5) + 3 = 7(5) + 3
35 + 3 = 35 + 3
38 = 38

If = 10
7 + 3 = 4 + 3 + 3

7(10) + 3 = 7(10) + 3
70 + 3 = 70 + 3
73 = 73

Homework

1. b =─3
3. y = 3
5. d = 44

325 Copyright © Swun Math Grade 8 Unit 4 Lesson 4 P TE

Notes

Copyright © Swun Math Grade 8 Unit 4 Lesson 4 P TE

326

Simplify Expressions: MPs Applied MP
Distributive Property
* Embedded MP
Conceptual Lesson
Grade 8 · Unit 4 · Lesson 5 12345678

MC: 8.EE.7b *  *

Problem of the Day Student Journal Pages

178-181

Objective: I will simplify expressions by expanding the distributive property.

Vocabulary Teacher Resources

Expression Equation Variable Considerations:
This lesson starts with expanding expressions. It is
− + = + helpful for students to understand the integer outside
the parentheses tells how many times the expression
Term Coefficient Constant is repeatedly being added.

Expand Expressions: Steps:
Distributive Property
1. Expand the expression.
3(n + 4) + 4(n + 2) (Use the distributive property)
* Read as: 3 groups of (n+4) and 4 groups of (n +2)
(n + 4) +(n + 4)+ (n + 4) + (n + 2)+ (n + 2) +(n + 2) +(n + 2) 2. Collect like terms.
3. Simplify the expression.
7n + 20
(Variable term first, then constant)

Collecting Like Terms: Application of MPs:
Distributive Property

3(n + 4) + 4(n + 2)
3n + 12 + 4n + 8

7n + 20

MP7: How is the product found when using the
distributive property?

The product is found by the number on

the outside the parentheses by .

MP8: Is there a mathematical rule for the
distributive property?

the number on the outside of
the parentheses to all terms inside the
parentheses.

327 Copyright © Swun Math Grade 8 Unit 4 Lesson 5 C TE

Input/Model

(Teacher Presents)

Directions: Expand the expression and simplify.
1. 2(x + 4)

Solution: Grade 8 Unit 4 Lesson 5 C TE 328

2( + 4) 2 ( + 4)
( + 4) + ( + 4)

+ + 4 + 4
2 + 8

2. 3(y – 3)

Solution:
3( − 3)means 3 groups of ( − 3)

( − 3) + ( − 3) + ( − 3)
+ + − 3 − 3 − 3
3 − 9

Copyright © Swun Math

Structured Guided Practice

(A/B Partners Practice)

Directions: Expand the expression and simplify.
1. 3(2x + 4)

Solution:
(2 + 4) + (2 + 4) + (2 + 4)
2 + 2 + 2 + 4 + 4 + 4

6 + 12

2. 4(─2x – 3)

Solution:
(−2 − 3) + (− 2 − 3) + (− 2 − 3) + (− 2 − 3)

−2 − 2 − 2 − 2 − 3 − 3 − 3 − 3
− 8 − 12

329 Copyright © Swun Math Grade 8 Unit 4 Lesson 5 C TE

Final Check for Understanding

(Teacher Checks Work)

Directions: Expand the expression and simplify.
1. 3(x + 5)

Solution:
+ 5 + + 5 + + 5
+ + + 5 + 5 + 5
3 + 15

2. 4(─3x + 1)

Solution:
(−3 + 1) + (− 3 + 1) + (− 3 + 1) + (− 3 + 1)
−3 − 3 − 3 − 3 + 1 + 1 + 1 + 1
−12 + 4

Closure

Recap today’s lesson with one or more of the following questions:

MP7: How is the product found when using the distributive property?
MP8: Is there a mathematical rule for the distributive property?

Copyright © Swun Math Grade 8 Unit 4 Lesson 5 C TE 330

Homework Name: ___________________________
Date: ___________________________
Unit 4 · Lesson 5: Simplify Expressions:
Distributive Property

Objective: I will simplify expressions by expanding the distributive property.

Vocabulary Steps:

Expression Equation Variable 1. Expand the expression.
(Use the distributive property)
− + = +
2. Collect like terms.
Term Coefficient Constant 3. Simplify the expression.

(Variable term first, then constant)

Expand Expressions:
Distributive Property

3(n + 4) + 4(n + 2)
* Read as: 3 groups of (n+4) and 4 groups of (n +2)
(n + 4) +(n + 4)+ (n + 4) + (n + 2)+ (n + 2) +(n + 2) +(n + 2)

7n + 20

Collecting Like Terms:
Distributive Property

3(n + 4) + 4(n + 2)
3n + 12 + 4n + 8

7n + 20

Example # 1 Example # 2
Directions: Rewrite as a sum and simplify.
3( − 3)
2( + 4)
Solution:
Solution: ( − 3) + ( − 3) + ( − 3)
( + 4) + ( + 4) + + − 3 − 3 − 3
+ + 4 + 4 3 − 9
2 + 8

331 Copyright © Swun Math Grade 8 Unit 4 Lesson 5 C TE

Homework 2. 3(─2x + 1)

Unit 4 · Lesson 5: Simplify Expressions:
Distributive Property

Directions: Rewrite as a sum and simplify.

1. 2(x – 2)

3. 4(3x – 4) 4. 2(─x +1)

5. 3(─3x +3) 6. 5(x ─ 4)

Copyright © Swun Math Grade 8 Unit 4 Lesson 5 C TE 332

Answer Key

Homework 2. (−2 + 1) + (−2 + 1) + (−2 + 1) = −6 + 3

1. ( − 2) + ( − 2) = 2 − 4

3. (3 − 4) + (3 − 4) + (3 − 4) + (3 − 4) = 12 − 16 4. (− + 1) + (− + 1) = −2 + 2

5. (−3 + 3) + (−3 + 3) + (−3 + 3) = −9 + 9 6. ( − 4) + ( − 4) + ( − 4) + ( − 4) + ( − 4) = 5 −
20

333 Copyright © Swun Math Grade 8 Unit 4 Lesson 5 C TE

Notes

Copyright © Swun Math Grade 8 Unit 4 Lesson 5 C TE 334

Solve Equations: Distributive MPs Applied MP
Property
* Embedded MP
Procedural Lesson
Grade 8 · Unit 4 · Lesson 6 12345678

MC: 8.EE.7b ** * **

Problem of the Day Student Journal Pages

Objective: I will solve for a variable by using the distributive property. 182-187

Vocabulary Teacher Resources

Collecting Like Terms: Considerations:
Distributive Property
It is helpful to talk about factors when using the
3(n + 4) + 4(n + 2) distributive property. The integer outside the
3n + 12 + 4n + 8 parentheses tells how many times to use the
factor inside the parentheses.
7n + 20 Remind students to ALWAYS check their
solution by substituting the value for the
Multiplying Integers: variable in the original equation.
 different signs = negative answer
 same sign = positive answer Steps:
1. Identify the parts of the equation.
3 × ─4 = ─12 2. Simplify using the distributive
3 groups of (─4) is ─12 property.
3. Collect like terms, if necessary.
The negative sign means : 4. Use inverse operation of
flip to the opposite side of the number line addition/subtraction.
• Move terms w/variables to one
side.
• Move constants to the other side.
5. Use inverse operation of
multiplication/division.
• Solve for the variable.
6. Check.

Application of MPs:

MP2: What is the relationship between the
quantities?

2(x + 2) equals 2x + 4 because .

MP7: What did you notice when you used the
distributive property?

I noticed that the second expression is

related to the first because .

335 Copyright © Swun Math Grade 8 Unit 4 Lesson 6 P TE

Input/Model

(Teacher Presents)

Directions: Solve and check.
1. ─2(x + 4) = 16

Solution: −2 − 8 = 16

+8 + 8

−2 = 24
−2 −2

= −12

Answer: = −12

Check: −2(−12 + 4) = 16

−2 ∙ −8 = 16

16 = 16 ✓

2. 14 – 2(x + 3) = ─22

Solution: 14 − 2 − 6 = −22

8 − 2 = −22

−8 − 8

−2 = −30
−2 −2

= 15

Answer: = 15

Check: 14 − 2(15 + 3) = −22
14 − 2(18) = −22
14 − 36 = −22
−22 = −22 ✓

Copyright © Swun Math Grade 8 Unit 4 Lesson 6 P TE 336

Structured Guided Practice

(A/B Partners Practice)

Directions: Solve and check.
1. ─3(x – 7) = 21

Solution:
x=0

2. ─5(─2x – 4) + 5x = 50

Solution:
x=2

337 Copyright © Swun Math Grade 8 Unit 4 Lesson 6 P TE

Final Check for Understanding

(Teacher Checks Work)

Directions: Solve and check.
1. ─18 = ─3(x – 2)

Solution: Grade 8 Unit 4 Lesson 6 P TE 338
x=8

2. ─52 = ─7x ─3(x + 4)

Solution:
x=4

Copyright © Swun Math

Student Practice Name: ___________________________
Date: ___________________________
Unit 4 · Lesson 6: Solve Equations:
Distributive Property 2. 3x – 5(x + 2) = ─20

Directions: Solve and check.

1. ─4(x + 4) = ─48

Solution: Solution:
x=8 x=5

3. 14 – 3(x + 7) = 8 4. ─36 = ─6(x ─ 3)

Solution: Solution:
x= ─5 x=9

5. 5x – 2(x ─ 4) = ─16 6. ─5(x ─ 7) ─ 10 = 70

Solution: Solution:
x= ─8 x= ─9

339 Copyright © Swun Math Grade 8 Unit 4 Lesson 6 P TE

Challenge Problems

Directions: Describe and correct the error in the following equations.

1. ─2(x – 4) = 10 2. 14 – 3(x + 1) = 22

Step 1: ─2x – 4 = 10 Step 1: 11(x + 1) = 22
Step 2: ─2x = 14 Step 2: 11x + 11 = 22
Step 3: x = ─7 Step 3:
Step 4: 11x =11
x=1

Solution: In Step 1, when the ─2 is distributed, it Solution: In Step 1, the 3 must be distributed to (x + 1)
should be −2 + 8 = 10. The correct solution:
before it is subtracted from 11. The correct solution:
−2( − 4) = 10 14 − 3 − 3 = 22
−2 + 8 = 10 11 − 3 = 22
−2 = 2 −3 = 11
= −1 −11 2
= 3 − 3 3

Extension Activity

* MP1: Make sense of the problem and persevere in solving it.
* MP4: Apply mathematics in everyday life.

Write an equation that meets the following criteria:
1) Uses the distributive property
2) Has negative coefficients
3) Must collect like terms
4) Has a solution of −2

Copyright © Swun Math Grade 8 Unit 4 Lesson 6 P TE 340

Closure

Reaching Consensus
*MP3: Do you agree or disagree with your classmate? Why or why not?

Student Presentations
*MP1: What steps in the process are you most confident about?
*MP6: Explain how you might show that your solution answers the problem.

Closure

Recap today’s lesson with one or more of the following questions:
MP2: What is the relationship between the quantities?
MP7: What did you notice when you used the distributive property?

341 Copyright © Swun Math Grade 8 Unit 4 Lesson 6 P TE

Homework Name: ___________________________
Date: ___________________________
Unit 4 · Lesson 6: Solve Equations:
Distributive Property

Objective: I will solve for a variable by using the distributive property.

Vocabulary Steps:

Collecting Like Terms: 1. Identify the parts of the equation.
Distributive Property
2. Simplify using the distributive property.
3(n + 4) + 4(n + 2) 3. Collect like terms, if necessary.
3n + 12 + 4n + 8 4. Use inverse operation of

7n + 20 addition/subtraction.
• Move terms w/variables to one
Multiplying Integers: side.
 different signs = negative answer • Move constants to the other side.
 same sign = positive answer
5. Use inverse operation of
3 × ─4 = ─12 multiplication/division.
3 groups of (─4) is ─12 • Solve for the variable.

The negative sign means : 6. Check.
flip to the opposite side of the number line

Example # 1 Example # 2
Directions: Solve and check.
14 − 2( + 3) = −22
−2( + 4) = 16

Solution: −2 − 8 = 16 Solution: 14 − 2 − 6 = −22

+8 + 8 8 − 2 = −22

−2 = 24 −8 − 8
−2 −2
= −12
−2 = −30
−2 −2
= 15
Answer: = −12
Answer: x = 15
Check: −2(−12 + 4) = 16
−2 ∙ −8 = 16 Check: 14 − 2(15 + 3) = −22
14 − 2(18) = −22
16 = 16 ✓ 14 − 36 = −22

−22 = −22 ✓

Copyright © Swun Math Grade 8 Unit 4 Lesson 6 P TE 342

Homework 2. 12 – 3(x + 1) = 30

Unit 4 · Lesson 6: Solve Equations:
Distributive Property

Directions: Solve and check

1. ─4(x – 7) = ─12

3. 8x – 4(x – 6) = ─64 4. ─10(2x – 4) = 100

5. 5 = 4 – (x + 7) 6. 80 = 9x – 5(x ─4)

Explain the steps you used to solve problem number _______.

______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________

343 Copyright © Swun Math Grade 8 Unit 4 Lesson 6 P TE

Answer Key

Extension Activity

Answers will vary. Check equations. Sample response: 2 = ─7x ─ 4(x + 5)

Homework 2. x = ─7
4. x = ─3
1. x = 10 6. x = 15
3. x = ─22
5. x = ─8

Copyright © Swun Math Grade 8 Unit 4 Lesson 6 P TE 344

Equations with Variables MPs Applied MP
On Both Sides * Embedded MP

Conceptual Lesson 12345678
Grade 8 · Unit 4 · Lesson 7
*  *
MC: 8.EE.7b

Problem of the Day Student Journal Pages

Objective: I will learn to solve equations with variables on both sides. 188-191

Vocabulary Teacher Resources

Properties of Equality: two equations that have Considerations:
the same solution are called equivalent; the The use of algebra tiles or colored chips should be
inverse operation can be performed on each side used to model the equations and build conceptual
without changing the equality; additive inverse understanding.
and multiplicative inverse are both examples
Remind students that what is done to one side of the
Algebra Tiles: a visual model used for algebraic equation MUST be done to the other side of the
expressions and equations equation. When getting variables to one side of the
equation, moving the smallest variable will avoid
-x x +1 0 dividing by a negative.
─1
Steps:
1. Collect like terms.
2. Move variables to one side (additive inverse).
3. Move integers to one side (additive inverse).
4. Isolate the variable (multiplicative inverse).
5. Solve and check.

345 Copyright © Swun Math Application of MPs:
MP7: Why is it helpful to understand the properties

of equality?
If I understand the properties of equality, I can
___________________.
MP8: Explain how this strategy made it easier to
identify the solution.
I made the equation easier to solve by
___________.

Grade 8 Unit 4 Lesson 7 C TE