Today’s Lesson: Scale proportions What: Why: . . . so I can use proportions to solve problems involving scale drawings.

What is the method we practiced for setting up proportions involving scale drawings?

Vocabulary: scale drawing/model — represents something that is too ______________ or too _______________ to be drawn at actual size. scale factor-- gives the ratio of the paper measurement to the________________ measurement (If the scale is 3 cm = 9 mi., then the scale factor is 1 3 ) small LARGE real-life

real-life 0.5 𝑖𝑛 20 𝑚𝑖 = unknown 𝒙 𝟓𝟎 𝒎𝒊 How to solve a scale drawing problem using a proportion: Step One: Set up given map/ blueprint scale as a ratio with paper measurement on top and ____________________ measurement on the bottom. Step Two: Set up other side of proportion by placing what you know (as given in problem) in the correct position (paper on top and real-life on the bottom). “x” goes in the remaining spot (represents the __________________________). Example: A certain map has a scale of ½ inch = 20 miles. If two towns are 50 miles apart, how far apart are they on the map? 0.5 𝑖𝑛 20 𝑚𝑖 = x = 1.25 in Note: The following is not the only way to set up a scale proportion, but it is the way we will use in order to be consistent! real-life unknown 𝒙 𝟓𝟎 𝒎𝒊 Start with the SCALE– given in the problem! What else does the problem already tell us?? 25 = 20x 20 20

x = 50 ft Blueprint Examples: Scale: 2 cm = 5ft Together: If a room is 20 cm in length on the blueprint, what is its actual length? x = 50 ft

Blueprint Examples: On your own: Scale: 𝟏 𝟒 in = 2 ft If a room is 20 ft long in real-life, what is its length on the blueprint? x = 2.5 in

Map scenarios: Together: Scale: 2cm = 9 km If two towns are 56 km apart in real-life, how far apart are they on the map? x ≈ 12.4 cm

Map scenarios: On your own: Scale: 0.75 in = 20 mi If the distance between two towns on the map is 2 in, how far apart are they in real life? x ≈ 53.3 miles

What is the scale? Together: The distance from Pleasantville to Jefferson is 25 miles, but measures 2.5 cm on the map. What is the map’s scale? 1cm = 10 miles

What is the scale? On your own: The kitchen is 3 cm in length on the blueprint, but measures 15 ft in actual length. What is the blueprint’s scale? 1 cm = 5 ft

Wrap-it-up/summary: What is the method we practiced for setting up proportions involving scale drawings? Write the given scale as a ratio– paper on top, real-life on bottom. Set up the “known” in the correct spot on other side– show the labels!!

END OF LESSON