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Course 2

Lesson Presentation. Course 2. Sunshine State Standards. MA.7.G.4.1 Determine how changes in dimensions affect the perimeter [and] area…of common geometric figures and apply these relationships to solve problems. Additional Example 1: Comparing Perimeters and Areas

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Course 2

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  1. Lesson Presentation Course 2

  2. Sunshine State Standards MA.7.G.4.1 Determine how changes in dimensions affect the perimeter [and] area…of common geometric figures and apply these relationships to solve problems.

  3. Additional Example 1: Comparing Perimeters and Areas Find how the perimeter and the area of the figure change when its dimensions change. = 1 inch Draw a model of the two figures on graph paper. Label the dimensions. The original figure is a 4  2 in. rectangle. The smaller figure is a 2  1 in. rectangle.

  4. P = 2(l + w) P = 2(l + w). Additional Example 1 Continued Find how the perimeter and the area of the figure change when its dimensions change. Use the formula for perimeter of a rectangle. Substitute for l and w. = 2(4 + 2) = 2(2 + 1) Simplify. = 2(6) = 12 = 2(3) = 6 The perimeter is 6 in. The perimeter is 12 in.

  5. A = lw = 4 x 2 = 2 x 1 Additional Example 1 Continued Find how the perimeter and the area of the figure change when its dimensions change. Use the formula for area of a rectangle. A = lw Substitute for l and w. Simplify. = 2 = 8 The area is 8 in2. The area is 2 in2. The perimeter is divided by 2, and the area is divided by 4.

  6. Check It Out: Example 1 Find how the perimeter and the area of the figure change when its dimensions change. = 1 inch Draw a model of the two figures on graph paper. Label the dimensions. The original figure is 2 x 2 in. square. The larger figure is a 4 x 4 in. square.

  7. P = 4s P = 4s Check It Out: Example 1 Continued Find how the perimeter and the area of the figure change when its dimensions change. Use the formula for perimeter of a square. Substitute for l and w. = 4(2) = 4(4) Simplify. = 8 = 16 The perimeter is 16 in. The perimeter is 8 in.

  8. A = s2 = 22 = 42 Check It Out: Example 1 Continued Find how the perimeter and the area of the figure change when its dimensions change. Use the formula for area of a square. A = s2 Substitute for l and w. Simplify. = 16 = 4 The area is 4 in2. The area is 16 in2. The perimeter is multiplied by 2, and the area is multiplied by 4.

  9. Multiply each dimension by 4. P = 10 cm P = 40 cm A = 6 cm2 A = 96 cm2 When the dimensions of the rectangle are multiplied by 4, the perimeter is multiplied by 4, and the area is multiplied by 16, or 42. Additional Example 2: Application Draw a rectangle whose dimensions are 4 times as large as the given rectangle. How do the perimeter and area change? 12 cm 3 cm 8 cm 2 cm

  10. Multiply each dimension by 2. P = 16 cm P = 32 cm A = 15 cm2 A = 60 cm2 When the dimensions of the rectangle are multiplied by 2, the perimeter is multiplied by 2, and the area is multiplied by 4, or 22. Check It Out: Example 2 Draw a rectangle whose dimensions are 2 times as large as the given rectangle. How do the perimeter and area change? 10 cm 5 cm 6 cm 3 cm

  11. Additional Example 3: Application Mei works at a local diner whose speciality is making pancakes. She makes silver dollar pancakes with a diameter of 2 inches as well as regular pancakes with a diameter double that of the silver dollar pancakes. Does a regular pancake have twice the area of a silver dollar pancake? Explain. Use 3.14 for . Find the area of each pancake and compare. Silver: A = r2 Use the formula. Regular: A = r2 A(1)2 Substitute for r. A(2)2 A  1 Evaluate the power. A  4 A3.14 Multiply. A12.56

  12. Additional Example 3 Continued Mei works at a local diner whose speciality is making pancakes. She makes silver dollar pancakes with a diameter of 2 inches as well as regular pancakes with a diameter double that of the silver dollar pancakes. Does a regular pancake have twice the area of a silver dollar pancake? Explain. Use 3.14 for . The area of the silver dollar pancake is 3.14 in2, and the area of the regular pancake is 12.56 in2. When the diameter is doubled, the area is 22, or 4, times as great.

  13. Check It Out: Example 3 Sadie is making two sizes of cookies. She makes medium cookies with a diameter of 4 inches as well as large cookies with a diameter double that of the regular cookie. Does a large cookie have twice the area of a medium cookie? Explain. Use 3.14 for . Find the area of each pancake and compare. Medium: A = r2 Use the formula. Large: A = r2 A(2)2 Substitute for r. A(4)2 A  4 Evaluate the power. A  16 A12.56 Multiply. A50.24

  14. Check It Out: Example 3 Continued Sadie is making two sizes of cookies. She makes medium cookies with a diameter of 4 inches as well as large cookies with a diameter double that of the regular cookie. Does a large cookie have twice the area of a medium cookie? Explain. Use 3.14 for . The area of the medium cookie is 12.56 in2, and the area of the large cookie is 50.24 in2. When the diameter is doubled, the area is 22, or 4, times as great.

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