Transcript Add and subtract expressions.

Learning Objective
We will add and subtract expressions.
CFU
What are we going to do?
Activate Prior Knowledge
Identify variable terms (underline) and constant terms (circle) in the expressions.
1.
(3x + 6) + (-5x - 11)
2.
(4d + 10) - (6d - 5)
Make Connection
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.
Concept Development
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.
Adding and Subtracting Expressions
Animated
(3x + 6) + (-5x - 11)
3x and -5x are like terms.
6 and -11 are like terms.
-2x - 5
(3x + 6) + (-5x - 11) and -2x - 5 are
equivalent expressions.
(4d + 10) - (6d + 5)
4d and 6d are like terms.
10 and -5 are like terms.
-2d + 5
(4d + 10) - (6d + 5) and -2d + 5 are
equivalent expressions.
©2013 All rights reserved.
CFU
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)
Vocabulary
1
put together
makes
3 equal value
2
CCSS 7th Grade Expressions and Equations 1.1
Add and subtract expressions.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice
Adding and subtracting expressions is to combine like terms.
• Adding and subtracting expressions creates equivalent expressions.
CFU
Add and subtract expressions.
1 Rewrite the addition or subtraction problem vertically. Hint: Line up like terms.
2 Combine like terms. Hint: Add or subtract each like term.
3 Interpret4 equivalent expressions. “____ is equivalent to ____”
1. (3a - 9) + (7a + 8)
3a - 9
+ 7a + 8
10a - 1
“(3a – 9) + (7a + 8) is equivalent to 10a – 1”
3. (5d + 7) + (11d - 5)
5d + 7
+ (11d - 5)
16d + 2
“(5d + 7) + (11d – 5) is equivalent to 16d + 2”
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2. (2y + 4) + (5y - 10)
1 How did I/you rewrite the
expressions?
2 How did I/you combine like
terms?
2y + 4
+ 5y - 10
7y - 6
Like Terms
3x and -5x
6 and -11
“(2y + 4) + (5y – 10) is equivalent to 7y – 6”
4. (4p - 9) + (9p + 6)
4p - 9
+ (9p + 6)
13p - 3
“(4p – 9) + (9p + 6) is equivalent to 13p – 3”
Vocabulary
4
explain
CCSS 7th Grade Expressions and Equations 1.1
Add and subtract expressions.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice (continued)
Adding and subtracting expressions is to combine like terms.
• Adding and subtracting expressions creates equivalent expressions.
Add and subtract expressions.
1 Rewrite the expressions as the sum of all terms.
2 Identify like terms in the expressions. (underline and circle)
3 Combine like terms. Hint: Add each like term.
4 Interpret equivalent expressions. “____ is equivalent to ____”
5. (8k - 2) - (4k + 6)
CFU
1 How did I/you rewrite the
expressions?
2 How did I/you identify like
terms?
3 How did I/you combine like
terms?
6. (5m + 6) - (10m - 7)
8k + (-2) + (-4k) + (-6)
5m + 6 + (-10m) + 7
4k + (-8)
-5m + 13
Like Terms
3x and -5x
6 and -11
4k - 8
“(8k – 2) – (4k + 6) is equivalent to 4k – 8”
“(5m + 6) – (10m – 7) is equivalent to -5m + 13”
7. (11b + 5) + (-12b - 2) - (4b + 3)
8. (4q + 5) - (9q - 1) + (-12q + 13)
11b + 5 + (-12b) + (-2) + (-4b) + (-3)
-5b + 0
4q + 5 + (-9q) + 1 + (-12q) + 13
-17q + 19
-5b
“(11b + 5) + (-12b – 2) – (4b + 3)
is equivalent to -5b”
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“(4q + 5) – (9q – 1) + (-12q + 13)
is equivalent to -17q + 19”
CCSS 7th Grade Expressions and Equations 1.1
Add and subtract expressions.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice (continued)
Adding and subtracting expressions is to combine like terms.
• Adding and subtracting expressions creates equivalent expressions.
CFU
Add and subtract expressions.
1 Rewrite the expressions as the sum of all terms.
2 Identify like terms in the expressions. (underline and circle)
3 Combine like terms. Hint: Add each like term.
4 Interpret equivalent expressions. Hint: Answer the question.
9. What
is the perimeter5 of the trapezoid?
10. What is
1 How did I/you rewrite the
expressions?
2 How did I/you identify like
terms?
3 How did I/you combine like
terms?
the perimeter of the triangle?
Like Terms
4m - 2
3m
7
4m + 5
(4m - 2) + (7) + (4m + 5) + (3m)
4m + (-2) + 7 + 4m + 5 + 3m
11m + 10
6n + 3
4n + 1
5n - 5
(6n + 3) + (4n + 1) + (5n - 5)
6n + 3 + 4n + 1 + 5n + (-5)
15n - 1
_________________________________
The perimeter of the trapezoid is
_________________________________
The perimeter of the triangle is
_________________________________
11m + 10.
_________________________________
15n - 1.
©2013 All rights reserved.
3x and -5x
6 and -11
Vocabulary
5
distance around
CCSS 7th Grade Expressions and Equations 1.1
Add and subtract expressions.
Lesson to be used by EDI-trained teachers only.
Relevance
Adding and subtracting expressions is to combine like terms.
• Adding and subtracting expressions creates equivalent expressions.
1 Adding and subtracting expressions will help you solve real-world problems.
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
y
y - 6 + y + y + (2y - 4) = 58
5y - 10 = 58
2 Adding and subtracting expressions will help you do well on tests.
Sample Test Question:
CFU
64. Choose Yes or No to indicate whether each
expression is equivalent to 5x - 7 - (3x - 9).
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?
A
B
C
D
©2013 All rights reserved.
2x + 2
2x - 16
2(x + 1)
x+x+1+1
O Yes
O Yes
O Yes
O Yes
O No
O No
O No
O No
CCSS 7th Grade Expressions and Equations 1.1
Add and subtract expressions.
Lesson to be used by EDI-trained teachers only.
Adding and subtracting expressions is to combine like terms.
• Adding and subtracting expressions creates equivalent expressions.
Skill Closure
Add and subtract expressions.
1 Rewrite the expressions as the sum of all terms.
2 Identify like terms in the expressions. (underline and circle)
3 Combine like terms. Hint: Add each like term.
4 Interpret equivalent expressions. “____ is equivalent to ____”
1. (-3z - 1) + (7z + 6)
-3z + (-1) + (7z) + 6
2. (11u + 7) - (9u - 1)
11u + 7 + (-9u) + 1
4z + 5
2u + 8
“-3z – 1 + (7z + 6) is equivalent to 4z + 5”
Like Terms
3x and -5x
6 and -11
“11u + 7 – (9u – 1) is equivalent to 2u + 8”
Access Common Core
Jasmine made an error in adding the expressions below.
Describe and correct the error she made.
3m + 1 – (4m + 2)
-2m
Summary Closure
Word Bank
combine
like terms
equivalent
expressions
What did you learn today about adding and subtracting expressions? (Pair-Share)
Use words from the word bank.
©2013 All rights reserved.
CCSS 7th Grade Expressions and Equations 1.1
Add and subtract expressions.
Lesson to be used by EDI-trained teachers only.
Independent Practice
Adding and subtracting expressions is to combine like terms.
• Adding and subtracting expressions creates equivalent expressions.
Add and subtract expressions.
1 Rewrite the expressions as the sum of all terms.
2 Identify like terms in the expressions. (underline and circle)
3 Combine like terms. Hint: Add each like term.
4 Interpret equivalent expressions. Hint: “____ is equivalent to ____” or Answer the question.
1. (12k - 9) + (2k + 5)
12k + (-9) + 2k + 5
14k + (-4)
14k - 4
“12k – 9 + (2k + 5) is equivalent to 14k – 4”
3. (8d + 1) - (13d + 3)
8d + 1 + (-13d) + (-3)
-5d + (-2)
-5d - 2
“8d + 1 – (13d + 3) is equivalent to -5d – 2”
Like Terms
3x and -5x
6 and -11
2. (10h + 12) - (7h - 3)
10h + 12 + (-7h) + 3
3h + 15
“10h + 12 – (7h – 3) is equivalent to 3h + 15”
4. (9b + 5) + (-7b - 1)
9b + 5 + (-7b) + (-1)
2b + 4
“9b + 5 + (-7b – 1) is equivalent to 2b + 4”
5. What is the perimeter of the triangle?
(n + 13) + (2n - 10) + (3n - 2)
n + 13 + 2n + (-10) + 3n + (-2)
n + 13
2n - 10
6n + 1
The perimeter of the triangle is 6n + 1.
__________________________________________________
©2013 All rights reserved.
3n - 2
CCSS 7th Grade Expressions and Equations 1.1
Add and subtract expressions.
Lesson to be used by EDI-trained teachers only.
Periodic Review 1
1. 7b - 5 + (6b + 3)
13b - 2
3. (9f + 8) - (5f - 12)
4f + 20
5. 2k + 8 + (13k - 2)
15k + 6
©2013 All rights reserved.
2. 6c + 10 + (-4c - 7) - (-9c + 3)
11c
4. (9q - 3) - (6q + 11)
3q - 14
6. (8y + 11) - (y - 11) + (-7y + 8)
30
CCSS 7th Grade Expressions and Equations 1.1
Add and subtract expressions.
Lesson to be used by EDI-trained teachers only.
Periodic Review 2
1. (9z - 10) + (5z + 11)
2. -7x + 12 + (9x - 4) - (10x - 6)
14z + 1
-8x + 14
3. 5h + 5 - (7h - 1)
4. 8y - 8 + (-y - 8)
7y - 16
-2h + 6
Access Common Core
Describe and correct each error made in adding and subtracting expressions below.
1.
A (-5x + 20) - (4x + 3)
-9x – 23
2.
A (-10h + 5) + (8h + 1)
4h
3.
B (8a - 2) - (6a - 1)
2a – 3
B (3k + 8) + (4k - 10)
5k
A (7m - 7) + (8m - 4)
B (-4y - 9) - (2y + 6)
4m
-6y – 3
©2013 All rights reserved.
CCSS 7th Grade Expressions and Equations 1.1
Add and subtract expressions.
Lesson to be used by EDI-trained teachers only.
Periodic Review 3
2m - 1
1. What is the perimeter of the quadrilateral?
5
3m
The
perimeter of the quadrilateral is 7m + 9.
__________________________________________________
2m + 5
Access Common Core
1. Choose Yes or No to indicate whether each expression is equivalent to 20h + 12.
A
B
C
D
(18h + 12) + 2h
(25h + 7) - (5h - 5)
(13h - 3) + (7h + 15)
(17h + 6) - (-3h + 6)
O Yes
O Yes
O Yes
O Yes
O No
O No
O No
O No
2. Choose Yes or No to indicate whether each expression is equivalent to -18p + 9.
A
B
C
D
(-21p + 5) - (-3p - 4)
(-14p + 9) + 2p
(-7p - 1) + (-11p + 10)
(-13p + 5) - (5p + 4)
O Yes
O Yes
O Yes
O Yes
O No
O No
O No
O No
3. Choose Yes or No to indicate whether each expression is equivalent to 5d - 11.
A
B
C
D
(-2d + 5) - (-7d - 6)
(13d - 3) - (8d + 8)
(-6d - 4) + (11d - 7)
(8d - 11) - 3d
©2013 All rights reserved.
O Yes
O Yes
O Yes
O Yes
O No
O No
O No
O No
CCSS 7th Grade Expressions and Equations 1.1
Add and subtract expressions.
Lesson to be used by EDI-trained teachers only.