11/16 Scale Drawings and Scale Factor Essential Question: Do architects use the same scale factor for each room when designing a house? Why or why not? NOTE TO TEACHERS: This slide includes the title for the notes, and the instructions regarding note-taking style. On subsequent pages, the slide title indicates the topic for the left-hand side of their Cornell Notes.

Scale Drawing/Scale Models Scale Drawings & Models are used to represent objects that are too large or too small to be drawn or built at actual size Examples: RC Cars, Atlas, Insects… others?

Scale Gives the ratio that compares the measurements of the drawing or model to the measurements of the real object. They are proportional. ex. – map scale

You try it… Find the actual distance if the map scale is 4 inches = 30 miles 2 inches = x = 15 miles Use CMAD (cross multiply and divide) to solve this proportion. First, multiply 2 inches and 30 miles for a product of 60. Then, divide 60 by 4 for a quotient of 15. Note: students will get the same answer if they first simplify 4 inches : 30 miles to 2 inches : 15 miles before they CMAD.

How can you use this? A scale drawing of a rectangular room has a length of 6 inches and a width of 4 inches. 1. How many feet is the length of the room? 2. How many feet is the width of the room? 3. How many square feet is the room? 4. How much will it cost to carpet the room if carpeting costs $5.50 per square foot? The drawing uses a scale of two inch to six feet. There are two methods for solving problem #1. Students could either convert the measurements from the scale drawing into the actual dimensions of a length of 18 feet and a width of 12 feet, then use the formula for finding the area of a rectangle (A=lw) to find the area, or they could square the scale and find that the scale of the area of the rectangle is 1 sq in : 9 sq ft, then set the scale equal to the ratio of the area of the scale drawing (6 inches x 4 inches = 24 sq in). Either process will give the answer as 216 square feet. Using the price of $5.50 per square foot, the answer to #2 is $1,188.

Scale Factor a scale having the same units in simplest form. You may have to convert units to find the scale factor!!! * a replica (an exact copy of the original) has a scale factor of 1:1 * a reduction (from original to smaller) has a scale factor less than 1 * an enlargement (from original to larger) has a scale factor greater than 1

What do they look like? REPLICA (an exact copy of the original) REDUCTION (from original to smaller) ENLARGEMENT (from original to larger)

What’s the difference? SCALE SCALE FACTOR Gives a ratio that compares measurements Does not have to be in the same units EX 1 inch : 5 feet It’s a scale, but it must have the same units, and is in simplest form You might have to convert the units EX 1 inch : 5 feet (scale) CONVERT both to inches ; 1 inch : 60 inches = 1:60 scale factor SCALE SCALE FACTOR

You try it… Find the scale factor 1 inch = 6 feet convert to inches … 12 inches in 1 foot… 1:72 is the scale factor 6 inches = 2 feet convert to inches … 6 inches = 24 inches … SIMPLIFY … 1:4 is the scale factor