Unit 3. Day 2.

Please get out paper for today’s lesson Name Date Period -------------------------------------------------------- Topic: Distributive Property & Adding/Subtracting expressions Use properties of operations to generate equivalent expressions

Today’s Lesson (1) 7th Grade distributing (2) Adding & Subtracting expressions

𝑥+ = So far all the previous examples were from 6th grade. 7th Grade: CCSS.MATH.CONTENT.6.EE.A.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x 7th Grade: 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.  p(x + q) = r 2 3   𝑥+ = 3 4 − 4 5

Example A: Simplify 2 3 𝑥− 1 2 +5 + 5 − 2 6 +5 2 3 𝑥 − 2 6 +5 2 6 − − 1 3 + 5 1 2 3 𝑥 + 14 3 − 3 + 3 1 15

Example B*: Simplify 1 4 3 5 𝑦− 1 3 − 2𝑦+4 1 − 1 12 3 20 −4 −2 3 20 𝑦 3 20 𝑦 − 1 12 1 12 − −2𝑦 −2𝑦 −4 −4 − 1 12 3 20 − 4 1 − 2 1 − 37 20 𝑦 − 49 12 − 12 − 12 20 − 20 1 3 48 40

Today’s Lesson (1) 7th Grade distributing (2) Adding & Subtracting expressions

Today’s Lesson (1) 7th Grade distributing (2) Adding & Subtracting and Multiplying (a little) expressions

Q: What is an equation? A: A math sentence WITH an equal sign 4=7−3 2𝑥+4=7 5𝑥−6𝑦=8 3 𝑥 2 −7𝑥+13=0 Q: What is an expression? A: A math sentence WITHOUT an equal sign 4+7−3 2𝑥+5 5𝑥−6𝑦−8 3 𝑥 2 −7𝑥+13

7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Expressions Linear Non-Linear 4𝑥+6 4𝑥+ 6 2 2𝑦+3 𝑥 2 −4 2𝑦+3𝑥−4 4𝑚 4 𝑚 2 −7 5 −7

1 + 1 −3𝑎 + 2 + 5𝑎 −3 2𝑎 −1 Example C: Find the sum of −3𝑎+2 and 5𝑎−3

Example D*: Find the sum of 2x−10+𝑦 and 8−3y−11x Example E*: Find the sum of 3 4 𝑏+ 5 8 and − 1 2 𝑏− 1 4

1 + 1 + − 9𝑥 −9𝑥 − 2 − 2 − 2𝑦 − 2𝑦 Example D*: Find the sum of 2x−10+𝑦 and 8−3y−11x 2𝑥−10+𝑦 8−3y−11x 1 2𝑥−10+𝑦 2𝑥−10+𝑦 + 1 8−3y−11x 8−3𝑦−11𝑥 2𝑥 −10 + 𝑦 + − 9𝑥 −9𝑥 − 2 − 2 − 2𝑦 − 2𝑦

3 4 𝑏+ 5 8 − 1 2 𝑏− 1 4 Example E*: Find the sum of 3 4 𝑏+ 5 8 and − 1 2 𝑏− 1 4 3 4 𝑏 + 5 8 3 4 5 8 − 1 2 − 1 2 𝑏 − 1 4 − 1 4 1 + 1 1 4 𝑏 3 8 + 4 − 4 3 2 1 4 8 − 8 5 2 3 8 = = = =

4𝑥+11 3𝑥+5𝑦−4 1 3𝑥+5𝑦−4 − 1 3𝑥 + 5𝑦 − 4 −4𝑥 −11 − 𝑥 1 + 5𝑦 − 15 Example F: “Find the difference when 4𝑥+11 is subtracted from 3𝑥+5𝑦−4 “ 4𝑥+11 3𝑥+5𝑦−4 1 3𝑥+5𝑦−4 − 1 3𝑥 + 5𝑦 − 4 −4𝑥 −11 − 𝑥 1 + 5𝑦 − 15

𝑡+3𝑚 − −20𝑚+17+12𝑡 Example G*: −𝑎+ 1 3 𝑏+2 − 5 6 𝑏− 7 8 𝑎+ 2 3 𝑡+3𝑚 − −20𝑚+17+12𝑡 −𝑎+ 1 3 𝑏+2 − 5 6 𝑏− 7 8 𝑎+ 2 3 Example H*:

1 𝑡+3𝑚 − −20𝑚+17+12𝑡 𝑡+3𝑚 1 1𝑡 + 3𝑚 +20𝑚 −17 −12𝑡 −11𝑡 + 23𝑚 − 17 Example G*: 1 𝑡+3𝑚 − −20𝑚+17+12𝑡 𝑡+3𝑚 1 1𝑡 + 3𝑚 +20𝑚 −17 −12𝑡 −11𝑡 + 23𝑚 − 17

−𝑎+ 1 3 𝑏+2 − 5 6 𝑏− 7 8 𝑎+ 2 3 −𝑎+ 1 3 𝑏+2 1 1 − 5 6 𝑏 + 7 8 𝑎 − 2 3 Example H*: −𝑎+ 1 3 𝑏+2 − 5 6 𝑏− 7 8 𝑎+ 2 3 −𝑎+ 1 3 𝑏+2 1 1 1 3 2 1 − 5 6 𝑏 + 7 8 𝑎 − 2 3 − 5 6 + 7 8 − 2 3 −1 − 1 8 𝑎 − 1 2 𝑏 4 3 + − 1 1 6 − 6 − 8 + 8 2 8 7 6 5 − 3 6 − 1 8 3 − 3 2 4 3 = = = = = =

What mistake did we make? Example I: Find the product of 4 and 2𝑥−6𝑦 4 2𝑥−6𝑦 ∙ 2𝑥−6𝑦 8𝑥 8𝑥 −24𝑦 −6𝑦 What mistake did we make?

−𝑥− 1 3 𝑦+ 5 8 Example J: Find the product of −2 and −𝑥− 1 3 𝑦+ 5 8 −2 −𝑥− 1 3 𝑦+ 5 8 ∙ + 2 3 𝑦 − 5 4 2𝑥 −2 ∙− 1 3 1 2 3 − 2 1 ∙ 5 8 − 10 8 − 5 4 = = =