Common Core Standard 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Student Objective: Use the distributive property to simplify variable expressions. Distributive Property a(b + c) = ab + ac Order of Operations Distributive Property 6(3 + 5) 6(3 + 5) 6(8) 6(3) + 6(5) 48 18 + 30 48

Use the distributive property to simplify. 1) 3(x + 7) 6) x(a + m) ax + mx 3x + 21 2) 2(a + 4) 7) 4(3 + r) 2a + 8 12 + 4r 3) 7(8 + m) 8) 2(x + 8) 2x + 16 56 + 7m 4) 3(4 + a) 9) 7(2m + 3y + 4) 12 + 3a 14m + 21y + 28 5) (3 + k)5 10) (6 + 2y + a)3 15 + 5k 18 + 6y + 3a

Use the distributive property to simplify. 6) a(c + d) 4y + 28 ac + ad 2) 3(b + 6) 7) 8(3 + r) 3b + 18 24 + 8r 3) 5(9 + m) 8) 4(x + y + 1) 45 + 5m 4x + 4y + 4 4) 5(4 + a) 9) 5(2m + 3 + t) 20 + 5a 10m + 15 + 5t 5) (7 + k)6 10) (11 + 2y)+3y 42 + 6k 11 + 5y

4(3 + 7) Geometric Model for Distributive Property 3 7 4 3 7 4 Two ways to find the total area. Width by total length Sum of smaller rectangles 4(3 + 7)

= 4(3 + 7) 4(3) + 4(7) Geometric Model for Distributive Property 3 7 4 3 7 4 4(3) 4(7) Two ways to find the total area. Width by total length Sum of smaller rectangles = 4(3 + 7) 4(3) + 4(7) 4(10) 12 + 28 40 40

= 9(4 + x) 9(4) + 9(x) Geometric Model for Distributive Property 4 x 9 Two ways to find the total area. Width by total length Sum of smaller rectangles = 9(4 + x) 9(4) + 9(x)

Does Order of Operations Geometric Model for Distributive Property 4 x 9 9(4) 9(x) Two ways to find the total area. Width by total length Sum of smaller rectangles = 9(4 + x) 9(4) + 9(x) 36 + 9x Does Order of Operations help to simplify here?

Factoring Find the missing factor. 1) 2) 3) 4) 5)

GCF: GCF: GCF: GCF: Factoring GCF - Greatest Common Factor Find the GCF of the following mentally. 1) 2) 3) 4) GCF: GCF: GCF: GCF:

GCF: ___ 2 GCF: ___ 5 GCF: ___ 7 GCF: ___ 4 Factoring One type involves the Distributive Property in reverse. Factor the following expression. FIND GCF first: 1) 2) 3) 4) GCF: ___ 2 GCF: ___ 5 GCF: ___ 7 GCF: ___ 4

Factoring One type involves the Distributive Property in reverse. Factor the following expression. 5) 7) 6) 8)

Like Terms Like Terms Unlike Terms 7x 3x 7x 3y 5y y 5y 10xy 2yx 2a 3ab Variable terms that differ only in their coefficients. Variables must be same letters and powers (exponents). Ex) x can only combine with other x terms. x can only combine with other x terms. 2 2 Like Terms Unlike Terms 7x 3x 7x 3y 5y y 5y 10xy 2yx 2a 3ab

Simplify by combining like terms. 1) 7x + 4y + 2x + y 5) 4k + (2j) + 6k + j 9x + 5y 10k + 3j 2) 3m + 10n + 4m + 1 6) 10 + 4x + 3y + 17x 7m + 10n + 1 21x + 3y + 10 3) 7x + 3y 7) 7x + 3y 4) 6x + (5x) + 2x + 3 8) 13x + 3

Simplify the expression using the Distributive Property and then combining like terms. 1) 3) 2) 4)

Simplify each variable expression. 5) 7(x + 4) + 2x 8) 3(b + 2) + 6b 7x + 28 + 2x 3b + 6 + 6b 9x + 28 9b + 6 6) 5x + 3(x + 1) 9) 2(3m + 1) + 4m 5x + 3x + 3 6m + 2 + 4m 8x + 3 10m + 2 7) a + 2(4 + a ) + 1 10) 3(k + m) + 5(k + 2m) a + 8 + 2a + 1 3k + 3m + 5k + 10m 3a + 9 8k + 13m