POD 7 12g + (6 + 4g) − 10 + (-2g) 12g + (6 + 4g) +(-10) + (-2g) Simplify the expression. 12g + (6 + 4g) − 10 + (-2g) 12g + (6 + 4g) +(-10) + (-2g) 12g + 4g + (-2g) + 6 + (-10) 14g+ (-4)

Let’s take a look back at what we’ve learned so far in this unit…

Properties of Operations Commutative: order Associative: grouping Distributive: sharing

terms -4x + 12 + x constant coefficient like terms

An algebraic expression is in simplest form if it has no like terms and no parenthesis. Follow these steps to simplify: Change subtraction to adding the opposite Look for like terms that can be moved closer to each other (commutative property) Combine like terms and constants

Let’s take a closer look at the distributive property and how we can use it to simplify equations and do mental math:

The Distributive Property states that to multiply a sum or difference by a number, multiply each term inside the parenthesis by the number outside the parenthesis. a( b + c ) = ab + ac a( b – c ) = ab − ac 8( 2 + 7 ) = 8(2) + 8(7) = 16 + 56 = 72

Example: 1 2 ( y + 2) Share the number outside the parentheses with both terms inside = 2(y) +2(2) = 2y + 4

5(-3x + 7y) 5(-3x) + 5(7y) -15x + 35y Example 2: You are allowed to multiply these 5(-3x) + 5(7y) -15x + 35y

Use mental math to solve. Example 3: Use mental math to solve. 6 × 15 6(10) + 6(5) 60+ 30 90

Whiteboard time 3(-4 + 12) 3(-4) + 3(12) -12 + 36 24

Whiteboard time 4(x + 7) 4(x) + 4(7) 4x + 28

Whiteboard time 12( 2x − 3) 12(2x) − 12(3) 24x − 36

Whiteboard time -2g( 4y + 2) -2g(4y) + -2g(2) -8gy + -4g

Use mental math to solve. Whiteboard time Use mental math to solve. 5 × 35 5(30) + 5(5) 150+ 25 175

Use mental math to solve. Whiteboard time Use mental math to solve. 3 × 124 3(100) + 3(20) + 3(4) 300 + 60 + 12 372

Let’s keep practicing: Pg. 379-380 worksheet

POD #8 basic advanced 12m + 12 + 3m − (-6) 5(3v + 2) + 2(-2v + 6v)

Take out last nights HW: Pg. 379-380 worksheet

(12 − 8)9 9(12) − 9(8) 108 − 72 36 Whiteboard time This is just like all the other problems. The only difference is that the 9 is on the other side. (12 − 8)9 9(12) − 9(8) 108 − 72 36

Whiteboard time -5( -2 – 18) -5(-2) − (-5)(18) 10 − (-90) 100

Whiteboard time 10x(4x − 2) 10x(4x) − 10x(2) 40x2 − 20x

Whiteboard time 1 2 (10g + 28) 1 2 (10g) + 1 2 (28) 5g + 14

Use mental math to solve. Whiteboard time Use mental math to solve. 7 × 14 7(10) + 7(4) 70+ 28 98

5 × 123 5(100) + 5(20) + 5(3) 500 + 100 + 15 615 Whiteboard time Use mental math. 5 × 123 5(100) + 5(20) + 5(3) 500 + 100 + 15 615

Use mental math to solve. Whiteboard time Use mental math to solve. 9 × 22 9(20) + 9(2) 180+ 18 198

How can the distributive property help us solve complicated problems?

Rename $19.95 as $20.00−$0.05 9(20 − 0.05) 9(20) − 9(0.05) Mr. Ito needs to buy batting helmets for the baseball team. The helmets he plans to buy are $19.95 each. Find the total cost if Mr. Ito needs to buy 9 batting helmets for the team. Rename $19.95 as $20.00−$0.05 9(20 − 0.05) 9(20) − 9(0.05) $180 − $0.45 $179.55

Let’s keep practicing: BIM pg. 84-85 #2-26 evens

POD basic advanced 8 × 34 7 × 231 8(30) + 8(4) 7(200) + 7(30) + 7(1) Use mental math to solve: basic advanced 8 × 34 7 × 231 8(30) + 8(4) 7(200) + 7(30) + 7(1) 240 + 32 1400 + 210 + 7 272 1617