1. Chapter 2 Unit Question How do we use the basic operations in Algebra?

2. Open Learning Logs Date on Left…Section 2 – 6 on right

3. Warm Up A pack of NBA basketball cards costs $2.19. Ellen bought four packs of cards last week, three packs yesterday, and two packs today. 1.How much did she spend on basketball cards? 2.Explain TWO ways in which you can find the answer.

4. Section 6 How can we use the distributive property to add like terms and simplify expressions/equations?

5. Homework Check

6. Distributive Property Definition To add like terms For all real numbers a, b, c ac + bc = (a + b)c ac – bc = (a – b)c

7. EXAMPLES: -4n + -3n Let’s call combining like terms… MATCH THE MATES (-4 + -3)n (3 + 8)p 11p 3p + 8p -7n ac + bc = (a + b)c Definition

8. Simplify by MATCHING THE MATES 2t + 3 + 6t + 9 8t + 12 6 + a + 5b + -a + -b + 2a + 7 A way to keep organized is to use… The CHAIN LINK Use shapes around variables that look the same (MATES) 2a+ 4b+ 13 (7y)(3y) + 7(4y 2 ) 21y 2 + 28y 2 49y 2 If we can, we must PEMDAS before Matching the Mates

9. Turn your Guided Notes over! Create an expression in 15 seconds that must use the distributive property to combine like terms to simplify. Give it to your partner to simplify! Check your partner’s work!

10. Distributive Property Definition To remove parenthesis For all real numbers a, b, c c(a + b) = ac + bc c(a – b) = ac – bc What do you notice about the two Distributive Property definitions?

11. EXAMPLES: -3(5b + 3) Let’s call removing parenthesis… Deal the Deck -15b 4a 4(a + 2) c(a + b) = ac + bc Definition -4x( -3x – 5) 12x 2 + 8 + (-9)= -15b – 9 + 20x It’s like a card game: The card being dealt is the term touching the table, the table is the parenthesis, the players are the terms inside the parenthesis 6x 6(x – 2) – 12

12. Turn your Guided Notes over! Create an expression in 15 seconds that must use the distributive property to remove parentheses to simplify. Give it to your partner to simplify! Check your partner’s work!

13. Calculate mentally… Stereo components sell for $199 each at Best Buy. How much do 3 cost? 3 Components will cost $597 In my head? Don’t think so…Let’s use the Distributive Property instead

14. “OPPOSITE OF” A SUM PROPERTY -( a + b ) - a + -b -a – b Now…Deal the Deck! Now…Use the Definition of Subtraction! There’s proof that all 3 are THE SAME!

15. “OPPOSITE OF” A DIFFERENCE PROPERTY -( a – b ) - a – -b -a + b Now…Deal the Deck! Now…Use the Definition of Subtraction! There’s proof that all 3 are THE SAME!

16. TRY THESE -( k + 23 ) Look and flip! -k – 23 - (6c – 5) -6c + 5 (3y + 8) – (2y – 7) 3y + 8– 2y + 7 y + 15 2z – 4(z + 3) 2z – 4z – 12 -2z - 12

17. Homework Do HoffmaSheet 2 – 6

18. To solve problems, we now have the following steps… Find the variable(s)… Match the Mates Drop the Op Reciprocate Get ‘er Done

19. A $225,000 estate is split among 4 kids and 2 nieces. The kids will receive the same amount…the nieces receive ¼ as much. How much does each kid receive? Each kid will receive $50,000 Each niece will receive $12,500 Let x = amount 1 kids receives

20. WAVE Hardware had 16 cans of paint on the shelf. Those were sold along with 3 cases containing paint. If a total of 112 cans were sold…how many cans of paint were in each case? There are 32 cans per case Let x = number of cans per case