What are we going to do? CFU Students, you already know how to identify variable terms and constant terms in an expression. Now, we will identify like

What are we going to do?

CFU

Students, you already know how to identify variable terms and constant terms in an expression. Now, we will identify like terms in an expression to add and subtract expressions.

Make Connection

We will add and subtract expressions.

Learning Objective

Activate Prior Knowledge

Identify variable terms (underline) and constant terms (circle) in the expressions.

1. (3x + 6) + (-5x - 11)

2. (4d + 10) - (6d - 5)

CCSS 7th Grade Expressions and Equations 1.1Add and subtract expressions.

Lesson to be used by EDI-trained teachers only. ©2013 All rights reserved.

Which terms will be added together when adding the expressions (3y + 9) + (5y - 11)?How do you know?

A 3y + 5y

B 3y + 9

C 9 + (-11)

D 5y + (-11)

CFU

1 put together2 makes3 equal value

Vocabulary

Concept Development

Adding and Subtracting Expressions

Like terms are terms with the same variables raised to the same power.Adding and subtracting expressions is to combine1 like terms.

• Adding and subtracting expressions produces2 equivalent3 expressions.

(3x + 6) + (-5x - 11) and -2x - 5 are equivalent expressions.

(4d + 10) - (6d + 5) and -2d + 5 are equivalent expressions.

(3x + 6) + (-5x - 11)

-2x - 5

(4d + 10) - (6d + 5)

-2d + 5

Animated

3x and -5x are like terms. 6 and -11 are like terms.

3x and -5x are like terms. 6 and -11 are like terms.

4d and 6d are like terms. 10 and -5 are like terms. 4d and 6d are like terms. 10 and -5 are like terms.



Rewrite the addition or subtraction problem vertically. Hint: Line up like terms.

Combine like terms. Hint: Add or subtract each like term.

Interpret4 equivalent expressions. “____ is equivalent to ____”

Add and subtract expressions.1

23

4 explain

Vocabulary

How did I/you rewrite the expressions?How did I/you combine like terms?

CFU

1

2

Skill Development/Guided PracticeAdding and subtracting expressions is to combine like terms.

• Adding and subtracting expressions creates equivalent expressions.

1. (3a - 9) + (7a + 8) 2. (2y + 4) + (5y - 10)

3. (5d + 7) + (11d - 5) 4. (4p - 9) + (9p + 6)

10a - 1

“(3a – 9) + (7a + 8) is equivalent to 10a – 1”

“(2y + 4) + (5y – 10) is equivalent to 7y – 6”

“(5d + 7) + (11d – 5) is equivalent to 16d + 2”

“(4p – 9) + (9p + 6) is equivalent to 13p – 3”

+ 7a + 83a - 9

7y - 6+ 5y - 10

2y + 4

16d + 2+ (11d - 5)

5d + 7

13p - 3+ (9p + 6)

4p - 9

Like Terms

3x and -5x6 and -11



Skill Development/Guided Practice (continued)

Rewrite the expressions as the sum of all terms.Identify like terms in the expressions. (underline and circle)Combine like terms. Hint: Add each like term.

Interpret equivalent expressions. “____ is equivalent to ____”


How did I/you rewrite the expressions?How did I/you identify like terms?How did I/you combine like terms?

CFU

1

2

3

Adding and subtracting expressions is to combine like terms.• Adding and subtracting expressions creates equivalent expressions.

5. (8k - 2) - (4k + 6) 6. (5m + 6) - (10m - 7)

7. (11b + 5) + (-12b - 2) - (4b + 3) 8. (4q + 5) - (9q - 1) + (-12q + 13)

8k + (-2) + (-4k) + (-6)

4k + (-8)

4k - 8

“(8k – 2) – (4k + 6) is equivalent to 4k – 8”

5m + 6 + (-10m) + 7

-5m + 13

“(5m + 6) – (10m – 7) is equivalent to -5m + 13”

11b + 5 + (-12b) + (-2) + (-4b) + (-3)

-5b+ 0

-5b

“(11b + 5) + (-12b – 2) – (4b + 3)is equivalent to -5b”

4q + 5 + (-9q) + 1 + (-12q) + 13

-17q + 19

“(4q + 5) – (9q – 1) + (-12q + 13)is equivalent to -17q + 19”

Like Terms

3x and -5x6 and -11



Skill Development/Guided Practice (continued)

9. What is the perimeter5 of the trapezoid?

__________________________________________________________________

10. What is the perimeter of the triangle?

__________________________________________________________________

4m - 2

4m + 5

3m 7

4m + (-2) + 7 + 4m + 5 + 3m

5n - 5

4n + 16n + 3

The perimeter of the trapezoid is

11m + 10.

6n + 3 + 4n + 1 + 5n + (-5)

The perimeter of the triangle is

15n - 1.


(4m - 2) + (7) + (4m + 5) + (3m)

11m + 10

(6n + 3) + (4n + 1) + (5n - 5)

15n - 1


Interpret equivalent expressions. Hint: Answer the question.


How did I/you rewrite the expressions?How did I/you identify like terms?How did I/you combine like terms?

CFU

1

2

3

Like Terms

3x and -5x6 and -11

5 distance around

Vocabulary



Adding and subtracting expressions will help you solve real-world problems.

Adding and subtracting expressions will help you do well on tests.

1

Does anyone else have another reason why it is relevant to add and subtract expressions? (Pair-Share) Why is it relevant to add and subtract expressions? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why?

CFU

2

Relevance

Sample Test Question:

64. Choose Yes or No to indicate whether each expression is equivalent to 5x - 7 - (3x - 9).

A 2x + 2 B 2x - 16 C 2(x + 1) D x + x + 1 + 1

O Yes O NoO Yes O NoO Yes O NoO Yes O No


Beverly’s fence is in the shape of an isosceles trapezoid. One base is 6 yards shorter than each leg. The other base is 4 yards short of being twice as long as each leg. If the perimeter of the trapezoid is 58 yards, what is the length of each side of the trapezoid?

y - 6

2y - 4

y y

y - 6 + y + y + (2y - 4) = 58

5y - 10 = 58




Interpret equivalent expressions. “____ is equivalent to ____”


What did you learn today about adding and subtracting expressions? (Pair-Share)Use words from the word bank.

Access Common Core

Summary Closure

Word Bank

combinelike terms

equivalent expressions

1. (-3z - 1) + (7z + 6) 2. (11u + 7) - (9u - 1)

Skill Closure

“-3z – 1 + (7z + 6) is equivalent to 4z + 5”

“11u + 7 – (9u – 1) is equivalent to 2u + 8”

Jasmine made an error in adding the expressions below. Describe and correct the error she made.

3m + 1 – (4m + 2)

-2m


-3z + (-1) + (7z) + 6

4z + 5

11u + 7 + (-9u) + 1

2u + 8

Like Terms

3x and -5x6 and -11



Independent Practice

1. (12k - 9) + (2k + 5) 2. (10h + 12) - (7h - 3)

3. (8d + 1) - (13d + 3) 4. (9b + 5) + (-7b - 1)

5. What is the perimeter of the triangle?

__________________________________________________ 3n - 2

2n - 10n + 13

“12k – 9 + (2k + 5) is equivalent to 14k – 4”

“10h + 12 – (7h – 3) is equivalent to 3h + 15”

“8d + 1 – (13d + 3) is equivalent to -5d – 2”

“9b + 5 + (-7b – 1) is equivalent to 2b + 4”

The perimeter of the triangle is 6n + 1.



Interpret equivalent expressions. Hint: “____ is equivalent to ____” or Answer the question.


12k + (-9) + 2k + 514k + (-4)14k - 4

10h + 12 + (-7h) + 3

3h + 15

8d + 1 + (-13d) + (-3)

-5d + (-2)-5d - 2

9b + 5 + (-7b) + (-1) 2b + 4

n + 13 + 2n + (-10) + 3n + (-2)

(n + 13) + (2n - 10) + (3n - 2)

6n + 1

Like Terms

3x and -5x6 and -11



Periodic Review 1

1. 7b - 5 + (6b + 3) 2. 6c + 10 + (-4c - 7) - (-9c + 3)

3. (9f + 8) - (5f - 12) 4. (9q - 3) - (6q + 11)

5. 2k + 8 + (13k - 2) 6. (8y + 11) - (y - 11) + (-7y + 8)

13b - 2 11c

4f + 20 3q - 14

15k + 6 30



Periodic Review 2

Access Common Core

1. (9z - 10) + (5z + 11) 2. -7x + 12 + (9x - 4) - (10x - 6)

3. 5h + 5 - (7h - 1) 4. 8y - 8 + (-y - 8)

14z + 1 -8x + 14

-2h + 6 7y - 16

Describe and correct each error made in adding and subtracting expressions below.

1. A (-5x + 20) - (4x + 3) B (8a - 2) - (6a - 1)

-9x – 23 2a – 3

3. A (7m - 7) + (8m - 4) B (-4y - 9) - (2y + 6)

4m -6y – 3

2. A (-10h + 5) + (8h + 1) B (3k + 8) + (4k - 10)

4h 5k



Periodic Review 3

Access Common Core

1. What is the perimeter of the quadrilateral?

__________________________________________________

2m - 1

2m + 5

3m 5

The perimeter of the quadrilateral is 7m + 9.

1. Choose Yes or No to indicate whether each expression is equivalent to 20h + 12.

A (18h + 12) + 2h B (25h + 7) - (5h - 5) C (13h - 3) + (7h + 15) D (17h + 6) - (-3h + 6)


2. Choose Yes or No to indicate whether each expression is equivalent to -18p + 9.

A (-21p + 5) - (-3p - 4)B (-14p + 9) + 2p C (-7p - 1) + (-11p + 10) D (-13p + 5) - (5p + 4)


3. Choose Yes or No to indicate whether each expression is equivalent to 5d - 11.

A (-2d + 5) - (-7d - 6)B (13d - 3) - (8d + 8) C (-6d - 4) + (11d - 7) D (8d - 11) - 3d


Documents

What are we going to do? CFU Students, you already know how to identify variable terms and constant terms in an expression. Now, we will identify like