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Scale Factors. Models & Maps. Learning Goal 2 (HS.N-Q.A.1 , 2, 3): The student will be able to use units to solve multi-step contextual problems. Scale Factor.

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## Scale Factors

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**Scale Factors**Models & Maps**Learning Goal 2(HS.N-Q.A.1, 2, 3):**The student will be able to use units to solve multi-step contextual problems.**Scale Factor**• A scale factor is a number by which all the dimensions of an original figure are multiplied by to produce the dimensions of a new figure. • For example: • If you were designing a house, you would draw it out on paper. Your paper wouldn’t be the actual size of the house. • The paper design of the house is called a blueprint.**What is the Actual Height of the House?**Blueprint Actual House • Look at the information you are given: • The height of the house on the drawing is 8.5 inches. • The scale says that 2 inches on the blueprint is equal to 5 feet on the actual house. • Scale Factor: This is the number that you multiply by or divide by to increase or decrease the size of the figure. • The scale factor can’t have units. Write the scale as a fraction and then multiply by a conversion factor to get rid of the units. 8.5 in Scale: 2 in = 5 ft**What is the Actual Height of the House?**• Remove the units for the scale factor continued: • 2 in • 1 ft = 5 ft 12 in • The scale factor is 1/30. This means that the length of the blueprint is 1/30 of the house or the house is 30 times larger than the blueprint. 2 = 1 60 30 The units of feet and inches both canceled out.**What is the Actual Height of the House?**• Actual Height: • Multiply the height of the blueprint by 30. • 8.5 inches (30) = 255 inches. • The actual height of the house is 255 inches tall. • Convert to feet for a more realistic measurement. • 255 inches • 1 foot = 12 in. • The height of the house is 21.25 feet tall. 21.25 feet**AZ Map Activity**• You will be working with a partner to find actual distances of various places in the great state of Arizona. • You will need a ruler. You and your partner will need to determine if you will be using inches or centimeters. • It is important to measure as accurately as possible.

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