1. The Distributive Property 6.EE.A.2b, 6.EE.A.3, and 6.EE.A.4

2. Bellwork Simplify 1. -7a(-8t) 2. -6j(3)(5k) 3. -2xy if x = -8 and y = 5

3. Objective Students will use the distributive property to re-write numerical and algebraic equations.

4. The Distributive Property The distributive property states: To multiply a number by a sum, multiply each number inside the parentheses by the number outside the parentheses The distributive property can be used with multiplication and addition or multiplication and subtraction Let ’ s see what it looks like…

5. Example 1 5(3 + 2) 15 + 10 = 25 Proof: 5(3+2) = 5(5) = 25

6. Algebraic Expressions The distributive property can be used to re-write algebraic expressions. Use the same process…multiply what ’ s on the outside of the parenthesis by each term within the parenthesis Let ’ s see what that looks like…

7. Example 2 3(x + 1) 3x + 3 Note: In this instance 3x and 3 are not like terms. Therefore, you cannot combine them…so the expression is simplified to just 3x + 3

8. Distributive Property There are 2 ways that you can see the distributive property With the multiplier on the left of the parenthesis With the multiplier on the right of the parenthesis Example 5(2 + 3)OR(b + 3)5 In either event you multiply what ’ s on the out side of the parenthesis with EACH term inside the parenthesis

9. Comments The distributive property is a key algebraic concept…make no mistake about it…you are REQUIRED to be able to recognize and work with the distributive property if you are to pass Algebra.

10. Common Errors The most common error that students make when working the distributive property is that they only multiply what on the outside of the parenthesis with the first term within the parenthesis The other common error is that students get the signs wrong…I do not give partial credit for incorrect signs!

11. Example - Common Error 3(x - 1) 3x - 1 THIS IS INCORRECT!

12. Your turn Use the distributive property to rewrite the expression 1. 8(5 + 7) 2. (b + 9)6 3. (6 – z)5 4. 3(x+2)+9 5. 2 -3(x+7)

13. Another Example Write two expressions that are equivalent to 4(2x + 7y).

14. Summary summarize the key concepts covered in today ’ s lesson Today we discussed The distributive property How will you recognize it? How does it work?

15. Homework Worksheet: Reminder This assignment is due tomorrow Make sure you write the problem Draw the arrows like we did in the examples Display your answer below the problem