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Mastering Geometry: Perimeter and the Distributive Property Homework Guide

This homework guide covers key concepts related to geometry, focusing on finding perimeter and simplifying expressions using the distributive property. Students are required to complete various problems from the textbook, including exercises on pages 81 and 74. Additionally, a quiz on sections 2.1-2.3 will take place on Thursday. The guide emphasizes the importance of understanding area calculations, simplified expressions, and using variables effectively. Students will enhance their problem-solving skills through guided practice and journal activities.

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Mastering Geometry: Perimeter and the Distributive Property Homework Guide

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  1. Do Now 10/2/09 • Take out HW from last night. • Text p.81, #10-21 all, #33-35 all • Copy HW in your planner. • Text p.74, #12-48 evens • Quiz sections 2.1-2.3 Thursday • In your journal, find the perimeter of the figure. (Hint: The answer will be a variable expression). 3x x + 2 x + 2 5x

  2. Simplifying Expressions in Geometry • What is the perimeter of the trapezoid? Perimeter is the distance around a figure. 3x Add together each of the sides. 1x + 2 1x + 2 1x + 2 + 3x + 1x + 2 + 5x (reorder terms) 1x + 3x + 1x + 5x + 2 + 2 (combine like terms) 5x 10x + 4

  3. 10) terms: 10x, 7, 3x; like terms: 10x & 3x; coefficients: 10 & 3; constant terms: 7; simplified: 13x +7 11) terms: 4y, 23, -1y, -6; like terms: 4y & -1y; 23 & -6; coefficients: 4 & -1; constant terms: 23 & -6; simplified: 3y + 17 12) terms: -19, -11a, 1a, 16; like terms: -11a & 1a, -19 & 16; coefficients: -11 & 1; constant terms: -19 & 16; simplified: -10a – 3 13) terms: 2b, -8, 4b, -6b; like terms: 2b, 4b, & -6b; coefficients: 2, 4, & -6; constant terms: -8; simplified: -8 14) terms: 9, 1n, -1, -7n; like terms: 1n & -7n, 9 & -1; coefficients: 1 & -7; constant terms: 9 & -1; simplified: -6n +8 15) terms: 8p, -5p, 5, -1p, -2; like terms: 8p, -5p & -1p; 5 & -2; coefficients: 8, -5, & -1; constant terms: 5 & -2; simplified: 2p + 3 Homework Text p.81, #10-21 all, #33-35 all

  4. Homework Text p.81, #10-21 all, #33-35 all • 16) 6x • 17) 7a • 18) -8b • 19) 6x • 20) 7c² • 21) 21y • 33) x + x + 5 + 2x + 1; 4x + 6 • 34) a + 2a + (10 – 3a); 10 • 35) 7y – 5 + 2y + 7y – 5 + 2y; 18y – 10

  5. Objective • SWBAT apply the distributive property to solve problems

  6. Evaluate. 5(11 + 2) 5(11) + 5(2) 65 This means to multiply 65

  7. Section 2.2, “The Distributive Property” DISTRIBUTIVE PROPERTY- a(b + c) = ab + ac a(b - c) = ab - ac Both of these expressions are EQUIVALENT EXPRESSIONS- meaning they have the same value.

  8. The Distributive PropertyOrder doesn’t matter… DISTRIBUTIVE PROPERTY- (b + c)a = ba + ca (b - c)a = ba - ca Both of these expressions are EQUIVALENT EXPRESSIONS- meaning they have the same value.

  9. Distributive Property Multiply across Parentheses 3(2 + 4) = 3(2) + 3(4) 3(6) = 6 + 12 18 = 18 Think of it as looking to DISTRIBUTE something

  10. 3(x + 7) -2(a + b) (8 – 7)(-9) 10(x + 2y - z) A). 3(x) + 3(7) 3x + 21 Evaluate B). -2(a) + -2(b) -2a + (-2b) or -2a – 2b C). (8)(-9) + (-7)(-9) -72 + 63 = -9 D). 10(x) + 10(2y) - 10(z) 10x + 20y - 10z

  11. Find the Area of the Figures 8 – 12w 8 – 3y 9 12 Area = length x width Area = (½)bh Area = (9)(8 – 12w) Area = (½)(12)(8 – 3y) Area = 72 – 108w units² Area = 6(8 – 3y) Area = 48 – 18y units²

  12. 3x – (x + 7) 3x + (-1)(x + 7) 3x + (-1x) + (-7) 2x + (-7) Challenge

  13. Homework Guided Practice Text p. 81, #22-30 evens -Text p.74, #12-48 evens

  14. Distributive Property Using Algebra Tiles Write an expression for the area model. =x Use the distributive property to simplify =1 = (x+2) 2x+4 2 =

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