2. Content Standard and Learning
Expectations
7.EE.1 - Apply properties of operations as strategies to add, subtract,
factor, and expand linear expressions with rational coefficients.
7.EE.2 - Understand that rewriting an expression in different forms in a
problem context can shed light on the problem and how the quantities in
it are related.
Students will learn how to apply the distributive property to factor out the
greatest common factor from an algebraic expression, such as 2 + 4x.
3. If you don’t know the rules you can’t play the game
What’s the game? Solving math problems
What are the rules? Properties of operations
In this lesson we will apply properties of operations as strategies to:
add, subtract, and factor expressions
4. The Properties of Operations
are the Foundation of
Arithmetic
We will use these properties when performing
computations in this lesson:
Addition property of operations
Subtraction property of operations
Commutative property
Distributive property
5. Combine like Terms Review
STOP! Simplify these expressions on your
guided notes before moving on
1. 9y + 3 – 4x – 2y – 3x – 5
2. 4c – 1a + 7b – 2c + 8b
3. c – 3 + 4ax – 7a + 2a – 6ax – 5
8. Answer #3
c – 3 + 4ax – 7a + 2a – 6ax – 5
Step 1: Commutative Property
4ax – 6ax – 7a + 2a + c – 3 – 5
Step 2: Addition and Subtraction Properties of Operations
– 2ax – 5a + c – 8
9. Distributive Property
Use the Distributive Property to simplify the product of a
number and a sum and difference.
Let a, b, and c be real numbers
Fill out this chart on your guided notes
Algebra Examples
a(b + c) = ab + ac 4(50 + 7) = 4(50) + 4(7)
(b + c)a = ba + ca (50 + 7)4 = 50(4) + (7)4
a(b – c) = ab + ac 6(40 – 9) = 6(40) - 6(9)
(b - c)a = ba - ca (40 – 9)6 = 40(6) - 9(6)
10. Practice the Distributive Property
STOP! Simplify these expressions on your guided notes before
moving on. Show your work
1. 5(x + 15)
2. (x + 27)4
3. 8(x – 19)
4. (x – 12)6
15. How can we use the distributive
property to factor expressions?
Students learn to apply the distributive property when an
expression can be factored. Start with finding the greatest
common factor (GCF).
30b + 45
5 * 6 * b + 5 * 9
Factor out the GCF 5 to rewrite the expression
5(6b + 9)
16. Video on Distributive Property
Factor algebraic expressions using the distributive property
Learn how to apply the distributive property to factor out the
greatest common factor from an algebraic expression.
Khan Academy
17. Your Turn
Factor out the GCF of each term and apply the distributive
property to determine an equivalent expression
1. 24 + 48x
2. 35x + 49
3. 200x – 150
18. Answer #1
24 + 48x
Step 1: Factor out the GCF
24
Step 2: Apply the Distributive property
24(1 + 3x)
19. Answer #2
35x + 49
Step 1: Factor out the GCF
7
Step 2: Apply the Distributive property
7(5x + 7)
20. Answer #3
200x - 150
Step 1: Factor out the GCF
50
Step 2: Apply the Distributive property
50(4x - 3)
21. Show me what you know
Part 1
Explain the
distributive property in your own
words on your notes.
22. Show me what you know
Part 2
Write four problems involving the
distributive property
Solve the problems
Show your work
Check your answer