7.G.1 Scale Drawings and Scale Models Created By: Melissa Forsyth
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1 Bell Ringers 1. 15% of is what percent of is 20% of what number 4. What is the percent increase from 10 to What is the percent decrease from 30 to 24
2 7.G.1 Scale Drawings and Scale Models
3 Vocabulary scale drawing: proportional two-dimensional drawing of an object (smaller or larger). It is used to represent an object that is too large or too small to be drawn at actual sizes scale model: proportional three-dimensional model of an object (smaller or larger). It is used to represent an object that is too large or too small to be built at actual sizes scale factor: a ratio of the model/drawing s dimensions to the actual object s dimensions in simplest form. scale: ratio between two sets of measurements. It gives the relationship between the measurements on the drawing or model and the measurements of the real object.
4 Examples of Scale Drawings blueprints maps
5 Examples of Scale Models toy car model of a house toy airplane
6 Scale Example: 1 inch = 3 feet (One inch represents an actual distance of 3 feet) 1:24 (1 unit represents an actual distance of 24 units)
7 All scale drawings must have a scale written on them. Scales are usually expressed as ratios. Normally for maps and buildings the ratio is: Drawing length: Actual length For maps the ratio is normally in the ratio: Map distance: Actual Distance Example: 1cm : 100cm The ratio 1cm:100cm means that for every 1cm on the scale drawing the length will be 100cm in real life Example: 1:10000 The ratio 1:10000 means that the real distance is times the length of one unit on the map or drawing.
8 Scale Factor
9 Finding Scale Factor: To find the scale factor you set up the following ratio model s dimensions actual object s dimensions
10 Caution!!! A scale factor is ALWAYS the ratio of the model s dimensions to the actual object s dimensions. It must also be in the same units.
11 Caution!!! It s alright to have a scale factor greater than 1. If the scale factor is greater than 1, this means that the new figure is bigger than the original (think about cells). If the scale factor is less than 1, then the new figure is smaller than the original (think about model airplanes).
12 Finding a Scale Factor You can use the lengths or heights to find the scale factor. MODEL LENGTH 20 Airplane Model AIRPLANE LENGTH 1,800 Length (in.) Height (in.) 1, THEN SIMPLIFY! = 1, SCALE FACTOR!
13 Finding a Scale Factor You can use the lengths or heights to find the scale factor. MODEL HEIGHT 8.4 Airplane Model AIRPLANE HEIGHT 756 Length (in.) Height (in.) 1, THEN SIMPLIFY! = SCALE FACTOR!
14 Finding a Scale Factor Height (in.) Great Dane Model MODEL HEIGHT GREAT DANE HEIGHT THEN SIMPLIFY! = 2 7 SCALE FACTOR!
15 Using Scale On a road map with a scale of 1 cm: 120 mi., the distance between two cities measures 3.5 cm. What is the actual distance between these two cities? MODEL ACTUAL 1 cm 120 mi = 3.5 cm x mi 1x = 420 The actual distance between these two cities is 420 miles.
16 Using Scale Jeffery is making a model of a car. He uses the scale 1 in:12 in. If the length of the actual car is 132 in., what is the length of his model car? MODEL ACTUAL 1 in 12 in = x in 132 in 1x = 132 The length of his model car is 11 in.
17 Example 1: Find Actual Measurements A set of landscape plans shows a flower bed that is 6.5 inches wide. The scale on the plans is 1 inch = 4 feet. What is the width of the actual flower bed? Let x represent the actual width of the flower bed. Write and solve a proportion. Plan width----> 1 inch = 6.5 inches<---plan width Actual width--> 4 feet x feet <-----actual width 1 x = cross multiply x= 26 The actual flower bed width is 26 feet.
18
19 Example 2: Determine the Scale In a scale model of a roller coaster, the highest hill has a height of 6 inches. If the actual height of the hill is 210 feet, what is the scale of the model? Model height---> 6 inches = 1 inch <--model height Actual height--->210 feet x feet <--actual height 6 x = 210 6x = 210 x= So, the scale is 1 = 35 feet
20 Example 3: Construct a Scale Drawing Step 1: Find the measure of the garden s length on the drawing. Let x represent the length. drawing length--> 1/4in = x in <--drawing length actual length--> 2 ft 16ft <---actual length 1/4 16 =2 x 4 = 2x 2 = x On the drawing, the length is 2 inches
21 Step 2: Find the measure of the garden s width on the drawing. Let w represent the width. drawing width-->.25 in = w inches <--drawing width actual width ---> 2 feet 8 feet <---actual width.25 8 = 2 w 2 = 2w 1 = w On the drawing the width is 1 inch.
22 Step 3: Make the scale drawing. Use 1/4 grid paper. Since 2 = 8 squares and 1 inch = 4 squares, draw a rectangle that is 8 squares by 4 squares. < ft > 8 ft
23 Your Turn! On a set of architectural drawings for an office building, the scale is 1/2 = 3 feet. Find the actual length of each room. Lobby: 2 inches Cafeteria: 8.25 inches.5 = 2 3ft x ft.5x = 6 The actual length x = 12 of the lobby is 12 ft.5 = 8,25 3ft x ft The actual length of the.5x = cafeteria is 49.5 feet x = 49.5
24 Your Turn, Again! In an illustration of a honey bee, the length of the bee is 4.8 cm. The actual size of the honeybee is 1.2 cm. What is the scale of the drawing? 4.8 cm = 1cm 1.2 cm x cm 4.8x = 1.2 x =.25 The scale of the drawing is 1 cm =.25cm
25 Using Scale Factor Kelly enlarged her favorite photograph into a poster. The poster is 22 inches by 38 inches. The scale factor is 6/1. Find the size of the original photograph. Round to the nearest tenth. x inches 22 inches x inches 38 inches
26 Using Scale Factor Kelly enlarged her favorite photograph into a poster. The poster is 22 inches by 38 inches. The scale factor is 6/1. Find the size of the original photograph. Round to the nearest tenth. Let s find length first! MODEL ACTUAL 6 in 1 in = 38 in x in
27 Using Scale Factor Kelly enlarged her favorite photograph into a poster. The poster is 22 inches by 38 inches. The scale factor is 6/1. Find the size of the original photograph. Round to the nearest tenth. x inches 22 inches 6.3 inches 38 inches
28 Using Scale Factor Kelly enlarged her favorite photograph into a poster. The poster is 22 inches by 38 inches. The scale factor is 6/1. Find the size of the original photograph. Round to the nearest tenth. Now let s find the width! MODEL ACTUAL 6 in 1 in = 22 in x in
29 Using Scale Factor Kelly enlarged her favorite photograph into a poster. The poster is 22 inches by 38 inches. The scale factor is 6/1. Find the size of the original photograph. Round to the nearest tenth. 3.6 inches 22 inches 6.3 inches 38 inches
30 Now we know... The original size of the photograph is 3.6 inches by 6.3 inches. In this case, the scale factor was larger than one. This means, that the model is larger than the original.
31 Try This: On a scale drawing of a horse, the scale is 1 mm: 10 mm. If the real horse is 1,500 mm tall, how tall is the horse on the scale drawing?
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