2Scale DrawingA drawing that shows a real object with accurate sizes except they have all been reduced or enlarged by a certain amount (called the scale).The scale is shown as the length in the drawing, then a colon (":"), then the matching length on the real thing.
3Example: this drawing has a scale of "1:10", so anything drawn with the size of "1" would have a size of "10" in the real world, so a measurement of 150mm on the drawing would be 1500mm on the real horse.
7A scale of 1:1 implies that the drawing of the grasshopper is the same as the actual object. The scale 1:2 implies that the drawing is smaller (half the size) than the actual object (in other words, the dimensions are multiplied by a scale factor of 0.5).
8The scale 2:1 suggests that the drawing is larger than the actual grasshopper -- twice as long and twice as high (we say the dimensions are multiplied by a scale factor of 2).If no units are listed in the scale, then you can assume that the drawing and the object are measured using the same units. For example, the scale 1:2 might represent 1 cm:2 cm or 1 in.:2 in.
9Teacher’s Domain videos Island of the Little (48 s)Island of the Giants (3min 33s)
10VocabularyScale drawing/scale model: is used to represent an object that is too large or too small to be drawn or built at actual sizesScale: gives the relationship between the measurements on the drawing or model and the measurements of the real objectScale factor: the ratio of a length on a scale drawing or model to the corresponding length on the real object
11Ratios Rates are often written with a slash rather than the word per: such as mi/h for miles per hour$2/dozen for $2 per dozena car traveling 30 miles per hourmaking a long-distance telephone call that costs 20¢ per minuteskating at an ice rink that costs $10 for 2 hours
12Proportions A statement that shows two ratios are equivalent. A proportion is often used when one ratio is known and only part of a second ratio is known, such as:
13Example“The ratio of girls to boys in a class is 6:8 and there are 12 boys in the class.” A proportion can be set up and solved to find how many girls there are in the class.Set up the proportion.
14Solving Proportions_6_ = _X_ 8 12 cross multiply: 6 x 12 = 8 x X 72 = 8x isolate the variable: 8 8 X = 9 girls
15By using proportions, you can find lengths needed to make a scale drawing or can find the actual lengths of an object based on a given scale drawing.
16map scalesIf 1 cm on a map represents a distance of 250 km, what is the approximate distance of a length represented by 2.7 cm? We can set up a proportion to show:1 cm = 2.7cm250 km XSolving the equation for x, we getx = 250 • 2.7 = 675 km.
173 ways scale can be expressed 1 cm = 1 km2. ______ = 1 km3. 1: 50,000
18Practice ProblemA student has a map on which the scale is 2 cm = 5 km. Having measured the distance between two points on the map to be 7.5 cm how do you calculate the real world distance from this measurement?
19Scale FactorExample: Suppose a scale model has a scale of 2 inches = 16 inches. The scale factor is2 orThe lengths and widths of objects of a scale drawing or model are proportional to the lengths and widths of the actual object.
20Your 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 = 1cm1.2 cm x cm4.8x = 1.2x = .25The scale of the drawing is 1 cm = .25cm
21Example 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 widthActual width--> 4 feet x feet <-----actual width1x = 4 cross productsx= 26 The actual flower bed width is feet.
22From the last example, what is the scale factor? To find the scale factor, write the ratio of 1 inch to 4 feet in simplest form.1inch = 1 inch Convert 4 feet4 feet inches to inchesThe scale factor is That is , eachmeasurement on the plan is 1 the actual measurement
23Example 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 heightActual height--->210 feet x feet <--actual height6x = 2106x = x= 35So, the scale is 1” =35 feet
24Your 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 inchesCafeteria: 8.25 inches.5” = 2”3ft x ft.5x = The actual lengthx = of the lobby is 12 ft.5” = 8,25”3ft x ft The actual length of the.5x = cafeteria is 49.5 feetx = 49.5
25Practice Problem A mural of a dog was painted on a wall. The enlarged dog was 45 ft. tall. If the average height for this breed of dog is 3 ft., what is the scale factor of this enlargement? Can you express this scale in more than one way?The scale factor is 45:3. This can be simplified to 15:1 or expressed in other ways, such as 7.5:0.5
26Make a scale map of your desk Place three or four objects on their desk.Orient the objects parallel to the edges of the desk.Use a 1:10 scale, with 1 cm on the map representing 10 cm of the desk top.To help students appreciate what the scale is doing and how the numbers are used in calculating, the teacher may give students a 10 cm × 25 cm rectangle of paper to be one of the objects on the desk. This gives students one object for which it is easy to work out what the scaled version is; they may be able to generalize this to their other objects with more awkward dimensions. A second map using a different scale could then be produced, perhaps 2 cm = 5 cm (which is 1:2.5).Graph paper may help students in drawing their maps.