Factoring and Equivalence in Expressions

1. Exploratory Social Studies English Science Math

2. 2/11/16 Activator • Take out packet. • Use Greatest Common Factor and the distributive property to write equivalent expressions in factored form. • Copy this onto pg. 47 and solve: • 13ab +15ab 13ab+ 15ab ab(13+15)

3. OBJECTIVE(S): 2/11/16 • I will be able to: • Model and write equivalent expressions using the distributive property to move from an expanded form to a factored form of an expression, and to move from factored form to expanded form of an expression. • I will know I got it when: • I can successfully complete exercise 1 independently or with my partner with at least 80% accuracy 6.EE.A.2 6.EE.A.3 6.EE.A.4

4. ‪Lesson 11: page 48 example 1 2 2 The sumof two groups of five and two groups of three 2(5) + 2(3)

5. Example 1: pg. 48 2 2 Two groups of the sum of five and three -(-5) (5+3) + (5+3) or 2(5+3)

6. Page 49 Yes. Both expressions have two 5s and two 3s. 2(5) +2(3) = 2(5+3) 2(5) +2(3) =2(5+3) 2 is multiplied by 5 and then by 3 before adding the products together 5 and 3 are added first and then multiplied by 2 Distributive Property

8. How do you feel? topic.

9. Pg. 50 3(f+g) Rewrite in factored form. GCF will go outside the parentheses. 3  f + 3 g GCF = 3 3f+3g 3 outside and f+g inside the parentheses 3(f+g)

10. Pg. 51 3(2x+3y) + Rewrite in factored form. The number outside the parentheses is the GCF. 23x +33y • “factor out” the 3 from both terms • put 3 outside parentheses • What is left in the terms goes inside the parentheses. 3 (2x+3y) 3

11. Pg. 51 c(3+11) Yes. Expand each term. 3c+ 11c c (3+11)

12. 4. Pg. 51 8(3b+1) 24b= 2223b 8 = 222 GCF = 8 8goes outside the parentheses and 3b+1 goes inside the parentheses. 24b + 8 2223b + 222 3b + ____ 1 In this case when I factor out an 8 from 8, I am left with a 1 because 81=8 Think “groups”. • 8 groups of 3b and 8 groups of 1 8(3b) + 8(1) • or as 8 groups of the sum of 3b+1 8(3b+1)

13. With your partner, complete Exercises 1 on pages 52 7x+ 7y 18h+13 h 35g+45h 511m+11 1 36m+67 n 71+78 y 310a+313 b 11f+15 f

14. With your partner, complete Exercises 2a. on pages 52

15. With your partner, complete Exercises 2b. on pages 52

16. With your partner, complete Exercises 2c. on pages 53

17. With your partner, complete Exercises 2d.-2e. on pages 53 Both problems had the the same answer when substituted with the same value. The two expression will still be equivalent, no matter the value of the variable.

18. Page 53 I use GCF and the distributive property to change the expressions from standard form to factored form. Find the missing value that makes the two expressions equivalent. 4 4x+43 y 5 57x+510 y 9 29x+91 y 8 48x+8y 100 100x+7100y

19. Pg. 58 three groups of (x+y) Sumof three groups of x 3x and three groups of y 3y Sum of four groups of 2hand four groups g. Four groups of (2h+g) 2h + 2h + 2h +2h + g + g + g + g 4 (2h +g) 8h +4g

20. Pg. 59 8h+ 24 6h+ 21 15x+ 54y 44h+ 12g 7jk+ 12mj 9ab+ 13a

21. a ( b +c ) “a” groups of the quantity “b” plus “c” ab + ac To write an equivalent expression, I would multiply “a” times “b” and “a” times “c”. Then, I would add the two products together. ab + ac Means “a” groups of size “b” plus “a” groups of size “c”.

22. Page 54 Page 59-60

23. Feb. 11, 2016 Ticket-To-Go: • Answer in agenda (or notebook) • Use the distributive property to write equivalent expressions in expanded form. 5(7h+3m) = 35h+ 15m -(-43) or 43 -(-5) or 5

24. Feb. 11, 2016 Accommodations • Read or reread presentation or activity directions, as needed or after prompting • Use examples to model and act as a guide for emerging learners