Question

unit 1 lesson 1.1
cool down
scaled courtyard drawings
andre drew a plan of a courtyard at a scale of 1 to 60. on his drawing, one side of the courtyard is 2.75 inches.
a. what is the actual measurement of that side of the courtyard?
express your answer in inches, and then in feet.
__ inches, __ feet
b. if andre made another courtyard scale drawing at a scale of 1 to 12, would this drawing be smaller or larger than the first drawing? explain your reasoning.

unit 1 lesson 1.2
cool down
drawing the backyard
lin and her brother each created a scale drawing of their backyard, but at different scales. lin used a scale of 1 inch to 1 foot. her brother used a scale of 1 inch to 1 yard.
a. express the scales for the drawings without units.
table: lin | lin’s brother
b. whose drawing is larger? how many times as large is it? explain or show your reasoning.

Explanation:

Part a (Scaled Courtyard Drawings)

Step1: Find actual inches

The scale is 1 to 60, meaning 1 inch on drawing = 60 inches actual. The drawing length is 2.75 inches. So actual inches = \( 2.75 \times 60 \)
\( 2.75 \times 60 = 165 \) inches.

Step2: Convert inches to feet

Since 1 foot = 12 inches, divide actual inches by 12. \( \frac{165}{12} = 13.75 \) feet.

The first scale is 1 to 60 (1 unit drawing = 60 units actual). The new scale is 1 to 12 (1 unit drawing = 12 units actual). A smaller scale factor (12 < 60) means that for the same actual length, the drawing length will be larger. For example, if actual length is 60 units, first drawing: \( \frac{60}{60} = 1 \) unit, new drawing: \( \frac{60}{12} = 5 \) units. So the new drawing (scale 1 to 12) is larger.

Lin's scale: 1 inch to 1 foot. 1 foot = 12 inches, so scale is 1 inch : 12 inches → 1:12.

Lin’s Brother’s scale: 1 inch to 1 yard. 1 yard = 36 inches, so scale is 1 inch : 36 inches → 1:36.

Answer:

165 inches, 13.75 feet

Part b (Scaled Courtyard Drawings)