Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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Warm Up Find the GCF of each set of numbers. 1.
12 and 50 3. 30, 45 and 30 2. 18 and 30 4.
16, 24 and 30 5. 72, 80 and 96
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15
6
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8
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Problem of the Day Erin takes half of the
cherries from a bowl. Then her brother takes half
of the remaining cherries. Finally, Diego takes 3
of the remaining cherries. This leaves 4 cherries
in the bowl. How many cherries were in the bowl
to start?
28 cherries
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I can factor numerical and algebraic expressions
and write equivalent numerical and algebraic
expression.
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Vocabulary
term coefficient equivalent expressions
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The terms of an expression are the parts of the
expression that are added or subtracted. The
terms of the expressions 1404x are 140 and 4x.
In the term 4x, 4 is called the coefficient. A
coefficient is the number that is multiplied by a
variable in a algebraic expression.
You can use the greatest common factor (GCF) and
the Distributive Property to factor numerical
expressions.
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Equivalent expressions are expressions that have
the same value for all the values of the
variables. The expressions 15x18 and 3(5x6) are
equivalent expressions since 15x183(5x6) for
every value of x.
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Additional Example 1 Factoring Numerical
Expressions Factor the sum of terms as a product
of the GCF and a sum.
2739
2739
The terms are 27 and 39
3.3.33.13
The GCF of the terms is 3
Rewrite each term as a product with GCF
3.93.13
3(913)
Apply the distributive law
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Check It Out Example 1 Factor the sum of terms
as a product of the GCF and a sum.
1545
2739
The terms are 15 and 45
3.53.3.5
The GCF of the terms is 15
Rewrite each term as a product with GCF
1.153.15
15(13)
Apply the Distributive property
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Additional Example 2 Factoring Algebraic
Expressions Factor the sum of terms as a product
of the GCF and a sum.
12b 28
12b 28
The terms are 12b and 28
2.2.3.b2.2.7
The GCF of the terms is 2.2
Rewrite each term as a product with GCF
4.3b 4.7
4(3b7)
Apply the Distributive law
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Check It Out Example 2 Factor the sum of terms
as a product of the GCF and a sum.
16b32
16b32
The terms are 16b and 32
2.2.2.2.b2.2.2.2.2
The GCF of the terms is 2.2.2.2
Rewrite each term as a product with GCF
16.b16.2
16(b2)
Apply the distributive property
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Additional Example 3 Writing Equivalent
Expressions Write four equivalent expressions for
each given expression.
A. 915
915
The terms are 9 and 15
Rewrite each term as a product with GCF
3.33.5
3(35)
Apply the Distributive property
3(53)
Apply the Commutative property
3(8)
Add
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Continued Example 3
B. 25m-5m
25m-5m
The terms are 25m and 1m
Rewrite each term as a product with common factor
5m
5.5m-1.5m
(5-1)5m
Apply the Distributive property
4.5m
Subtract
20m
Multiply
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Continued Example 3
C. 2(4p2)
2(4p2)
Apply the Distributive property
2.4p2.2
8p4
Multiply
48p
Apply the Commutative property
423p
Write the coefficient of 8 as 23
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• Check It Out Example 3
• Write four equivalent expressions for each given
  expression.

3(9p3)
3(9p3)
Apply the Distributive property
3.9p3.3
27p9
Multiply
927p
Apply the Commutative property
933p
Write the coefficient of 27 as 33
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Lesson Quiz
Factor the sum of terms as a product of the
GCF and a sum
15(31)
1. 45 15
8(35)
2. 24 40
4(4y9)
3. 16y 36
30(32s)
4. 90 60s
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Continued Lesson Quiz
Write four equivalent expressions for each given
expression.
5. 20 - 8
2(10-4) 4(5-2) 4.3 12
6. 9z 12
3(3z4) 3(43z) 32z12 129z
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Lesson Quizzes
Lesson Quiz for Student Response Systems 1.
Factor the sum of terms as a product of the
GCF and a sum 6030
A. 60(12) B. 90 C. 30(2) D.
30(21)
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Continued Lesson Quiz for Student Response
Systems 2. Factor the sum of terms as a
product of the GCF and a sum 1339r
A. 13(13r) B. 13(13) C. 13(3r)
D. 42r
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Continued Lesson Quiz for Student Response
Systems 3. Which expression is not equivalent to
12-3?
A. 3(4-1) B. 3(22-1) C. 3.4-3 D.
3(1-3)
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Continued Lesson Quiz for Student Response
Systems 4. Which expression is not equivalent to
8z12?
A. 8z4.3 B. 4(2z3) C. 4(2z12)
D. 4(32z)