Presentation on theme: "Lesson 6.5 Scale Drawings Students will be able to understand ratios and proportions in scale drawings."— Presentation transcript:
1 Lesson 6.5 Scale DrawingsStudents will be able to understand ratios and proportions in scale drawings.
2 Write each fraction in the simplest form. Warm UpWrite each fraction in the simplest form.4481121.9135115Convert the following measurements:192 inches = ________ feet18.5 feet = ________ inchesinches = ________ feet1622227
3 This HO gauge model train is a scale model of a historic train This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HOgauge model train is187187This means that each dimension of the model is of the corresponding dimension of the actual train.(1 inch on the model is 87 inches on the actual train.)
4 A scale is the ratio between two sets of measurements A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph shows a scale drawing of the model train.A scale drawing is a proportional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.
5 Write a ratio using one of the dimensions Identify the scale factor.RoomBlueprintLength12 ft.18 in.Width9 ft.13.5 in.Write a ratio using one of the dimensionsBlueprint LengthRoom Length18 in.12 ft.=Units are like quantities (length to length). They must be converted to common units!Which unit will you convert?FEET to INCHES12 ft x _____121in.=144 in.Now replace 12ft with 144 in.1ft.1818Simplify. (Scale factor ratios must be written as a single unit rate)18 in.144 in.=Remember from lesson 6.1 when common units (in.) are used the ratio will NOT have units!18The scale factor is:
6 First: Write a ratio using one of the dimensions Identify Scale Factor: Your Turn!RoomBlueprintLength8 ft.1 in.Width18 ft.2.25 in.First: Write a ratio using one of the dimensionsBlueprint widthRoom widthor2.25 in.18 ft.Blueprint lengthRoom lengthUnits are like quantities (length to length). They must be converted to common units!Which unit will you convert?orRoom widthBlueprint widthFEET to INCHES18 ft. x _________121in.ft.=216 in.1Simplify. (Scale factor ratios must be written as a single unit rate)2.25 in.216 in.2.25196=196The scale factor is:
7 : : = = 300 = x Measurement Application On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles?Write a proportionPittsburgh to Philadelphia (map)Pittsburgh to Philadelphia (actual)=Scale (map)Scale (actual)Substitute Values7.5 in.X miles=1.5 in.60 milesCross Products7.5 x 60 = 1.5x::Divide Both sides by 1.5450 = 1.5x300 = xThe distance between the cities is 300 miles.
8 = = 2.5in. 3 in. 1 in. = 2 ft. = 1in scale 2ft scale Use the scale on the drawing to find the scale factor and the perimeter of the tree house.124Convert to same units for scale factor.1 in.2ft.In.The scale is:=1242 ft. x 12 in.ft.=24 inScale factor =Perimeter ofDrawingActual object1in scale2ft scaleWrite a proportion to find the perimeter of the actual object.=2.5in.3 in.11 in.x ft.1 in.2 ft.Substitute.=1 in. = 2 ft.Use cross products.11 x 2 = 1x22 = xThe actual perimeter of the tree house is 22 ft.