Unit 3. Day 3.

Please get out paper for today’s lesson Name Date Period -------------------------------------------------------- Topic: Practice with Equivalent Expressions Use properties of operations to generate equivalent expressions

Today’s Lesson 1) Practice with Expressions 2) Legality of Math Equations 3) 6th Grade Solving 4) 7th Grade Solving

Commercial Break #1 2 2𝑥 ∙ 𝑥 3𝑥 4 3 4 3 4 𝑥 3 4𝑥 1 ∙ 𝑥 1 7 1 1 1 7 𝑥 𝑥 7 𝑥 7 ∙ 𝑥

Commercial Break #1 5𝑛 6 5 6 𝑛 − 7𝑚 8 − 7 8 𝑚 1𝑎 2 1 2 𝑎 𝑎 2

Example A: Rewrite the expressions by collecting like terms 2 3 𝑥 2 3 𝑥− 3 4 𝑦+4𝑥− 𝑦 5 + 5𝑥 6 − 3 4 𝑦 + 5𝑥 6 − 𝑦 5 + 4𝑥 11 2 𝑥 − 19 20 𝑦 2 3 𝑥 + 4 1 𝑥 + 5 6 𝑥 − 3 4 𝑦 − 1 5 𝑦 15 6 𝑥 + 6 𝑥 + 6 𝑥 4 24 5 33 11 2 𝑥 − 20 𝑦− 20 𝑦 4 − 19 20 𝑦 = 6 𝑥 = =

Example B*: Rewrite the expressions by collecting like terms 5 8 − 𝑛 6 +3𝑛−1 3 4 − 3 2 𝑛 5 8 − 1 3 4 − 𝑛 6 − 3 2 𝑛 + 3𝑛 − 9 8 − 9 8 4 3 𝑛 4 3 𝑛 + + 5 8 − 7 4 − 1 6 𝑛 + 3 1 𝑛 − 3 2 𝑛 8 8 − 8 5 14 − 6 𝑛 + 6 𝑛 − 6 𝑛 1 18 6 𝑛 −9 9 = 8 =

Commercial Break #2 2𝑥 3 2𝑥+5 3 5 3 + 8 11 − 5𝑦 11 8−5𝑦 11

Commercial Break #2 8𝑥 − 6 8𝑥−6 12 8𝑥 12 −6 12 12 12 8 12 𝑥 − 6 12 2 3 𝑥 − 1 2

Example C: Rewrite the following expression in standard form 2 3𝑥−4 6 − 5𝑥+2 8 4 6 − 5𝑥+2 8 6𝑥 − 8 3 4 3 24𝑥−32 24𝑥 −32 15𝑥+6 15𝑥 + 6 24 − 24 − 24 −15𝑥 −6 9𝑥 −38 9𝑥 24 38 24 3 8 𝑥 − 19 12 24𝑥 −32 24 = 24 = − =

Example D*: Rewrite the following expression in standard form 2 5𝑔−1 4 − 2𝑔+3 6 3 2 4 − 2𝑔+3 6 10𝑔 − 2 3 2 30𝑔−6 30𝑔 −6 4𝑔+6 4𝑔 + 6 12 − 12 − 12 −4𝑔 −6 26𝑔 −12 26𝑔 12 −6 12 12 13 6 𝑔 30𝑔 = 12 = − 12 = −1

Today’s Lesson 1) Practice with Expressions 2) Legality of Math Equations 3) 6th Grade Solving 4) 7th Grade Solving

Q: What is an equation? A: A math “sentence” with an equal sign 3𝑥 + 4 = 78 3 5−𝑥 =6−3𝑥 5=2+3 6 𝑥+5 =7−9𝑚 𝑥+4=2−13.9

4 = 4 6 = 6 3 = 3 15 = 15 5 = 5 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑡𝑟𝑢𝑒? 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒? Legality of Math Equations 4 = 4 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑡𝑟𝑢𝑒? +2 +2 6 = 6 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒? −3 −3 5 5 3 = 3 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒? 15 = 15 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒? 3 3 5 = 5 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒?

8 = 8 4 = 4 2 = 2 7 = 7 49 = 49 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑡𝑟𝑢𝑒? 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒? Legality of Math Equations 8 = 8 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑡𝑟𝑢𝑒? 2 2 4 = 4 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒? 2 = 2 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒? +5 +5 7 = 7 2 2 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒? 49 = 49 𝐼𝑠 𝑡ℎ𝑖𝑠 𝑠𝑡𝑖𝑙𝑙 𝑡𝑟𝑢𝑒?

Today’s Lesson 1) Practice with Expressions 2) Legality of Math Equations 3) 6th Grade Solving 4) 7th Grade Solving

CCSS.MATH.CONTENT.6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 𝑥+𝑝 =𝑞 𝑝𝑥=𝑞 𝑥+4 =7 3𝑥 =12 𝑥+ 3 4 = 7 8 1 2 𝑥 = 6 5

𝑝𝑥+𝑞 =𝑟 𝑝𝑥=𝑞 1 𝑥−4 =7 3𝑥 =−12 3 𝑥+0 =−12 −2 𝑥−7 =5 3𝑥+4 =−8 CCSS.MATH.CONTENT.7.EE.B.4.A Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. 𝑝𝑥+𝑞 =𝑟 𝑝𝑥=𝑞 1 𝑥−4 =7 3𝑥 =−12 3 𝑥+0 =−12 −2 𝑥−7 =5 3𝑥+4 =−8 1 2 𝑥− 3 7 =− 1 5 − 5 6 𝑥+ 1 2 =− 1 4

𝑥+4 = 7 𝑥+4 = 7 𝑥 = 3 𝑥 𝑥+4 = 7 = + −4 −4 Example 6th: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑥. + Check: +4=7 3 𝑥+4 = 7 𝑥+4 = 7 𝑥 = + 3 7=7 −4 −4 𝑥 𝑥+4 = 7 = + + + + + + + + + + + − − − − − − − −

Example 6th: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑦. 𝑦 + 1 8 = 3 8 2 8 𝑦 = − 1 8 − 1 8 1 4

Example 6th: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 w. 1 4𝑤=24 𝑤 = 6 ∙ 4 4 Check 4 =24 6 24=24

Example 6th: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑛 . 3 4 𝑛= 9 10 𝑛 = ∙ 3 4 3 4 9 10 ÷ 3 4 𝑛= 15 4 9 10 4 3 36 30 6 5 ∙ = =

Today’s Lesson 1) Practice with Expressions 2) Legality of Math Equations 3) 6th Grade Solving 4) 7th Grade Solving

𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒. 𝑎 + 2 5 =− 1 5 Example E*: 𝑛 − 2 9 = 1 3 Example F*:

Example E*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑎. 𝑎 + 2 5 =− 1 5 − 3 5 𝑎 = − 2 5 − 2 5

Example F*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑛. 𝑛 − 2 9 = 1 3 5 9 𝑛 = + 2 9 + 2 9

𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 −15+𝑏=−4 Example G*: −31=𝑑−6 Example H*:

−15+𝑏=−4 𝑏 = 11 +15 +15 Example G*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑏. Check: −15+ =−4 11 −15+ =−4 11 −15+𝑏=−4 +15 −4=−4 +15 𝑏 = 11

−31=𝑑−6 −25 = 𝑑 +6 +6 Example H*: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑑. Check: −31= −6 −25 −31= −6 −25 −31=𝑑−6 +6 −31=−31 +6 −25 = 𝑑

Example I: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝑝. −2𝑚=−16 𝑚 = 8 −2 −2 Check −2 =−16 8 −16=−16

2 7 𝑥 = 5 ∙ 𝑥 = 5 ÷ 2 7 𝑥 = 1 ∙ 𝑥 = 5 ∙ 1 𝑥 = = Example J: 2 7 2 7 2 7 35 2 5 1 7 2 35 2 𝑥 = ∙ =

− 1 3 𝑚 =8 − 2 3 𝑛 =8 −𝑝 =−7 Example K*: Example L*: Example M*: Solve for the variable − 1 3 𝑚 =8 Example K*: − 2 3 𝑛 =8 Example L*: Example M*: −𝑝 =−7

− 1 3 𝑚 =8 ∙ 𝑚 = 8 1 − 3 𝑚 =8 ÷ 1 𝑚 = = −3 −3 − 1 3 − 1 3 − 1 3 𝑚 = Example K*: ∙ 𝑚 = 8 −3 1 −3 − 3 𝑚 =8 ÷ − 1 3 − 1 3 − 1 3 𝑚 = −24 1 8 1 − 3 1 − 24 1 𝑚 = ∙ =

− 2 3 𝑛 =8 ∙ 𝑛 = 8 ÷ − 2 3 𝑥 = 1 ∙ 𝑥 = 8 ∙ 1 𝑛 = = Example L*: − 2 3 − 3 2 − 3 2 ∙ 𝑥 = 8 ∙ − 24 2 1 8 1 − 3 2 − 24 2 𝑛 = ∙ = = −12

Example M*: − 𝑝 =−7 1𝑝 1 = 7 −1 −1 𝑝

Example N: 𝑆𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 x. 3 1 𝑥 3 𝑥 3 = 9 27 𝑥÷3=9 = Or 1 3 𝑥 = 9 1𝑥 3 = 9 𝑥 3 = 9 ∙ 1 3 1 3 9 1 1 3 3 1 27 1 𝑥 = ÷ ∙ = 27