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SCALE FACTORS MODELS & MAPS

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43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will be able to use units to solve multi-step contextual problems. - choose, convert, interpret and justify appropriate units in the context of a problem -interpret and create graphical representations of scenarios. The student will be able to choose and convert units to solve multi-step contextual problems. -interpret graphical representations of scenarios. With help from the teacher, the student has partial success with using units to solve multi- step contextual situations. Even with help, the student has no success with using units to solve multi- step contextual situations. Learning Goal 2 (HS.N-Q.A.1, 2, 3): The student will be able to use units to solve multi-step contextual problems.

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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.

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WHAT IS THE ACTUAL HEIGHT OF THE HOUSE? 1.Look at the information you are given: 1.The height of the house on the drawing is 8.5 inches. 2.The scale says that 2 inches on the blueprint is equal to 5 feet on the actual house. 2.Scale Factor: This is the number that you multiply by or divide by to increase or decrease the size of the figure. 1.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. Blueprint 8.5 in Scale: 2 in = 5 ft Actual House

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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.

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WHAT IS THE ACTUAL HEIGHT OF THE HOUSE? 3.Actual Height: 1.Multiply the height of the blueprint by 30. 2.8.5 inches (30) = 255 inches. 3.The actual height of the house is 255 inches tall. 4.Convert to feet for a more realistic measurement. 5.255 inches 1 foot = 12 in. 6.The height of the house is 21.25 feet tall. 21.25 feet

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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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