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- 1. Understanding Size Models and Scale
- 2. Enlargement scale factor Reduction Scale Proportions Scale Diagram/Model
- 3. Model • Representation of something else • Usually too big or too small to analyze easily
- 4. Enlargement To make something bigger so that one can analyze/observe the details.
- 5. Reduction To make an object small so that one can observe/analyze the details.
- 6. map distance ground distance • In math, scale shows the relationship between two things as well. • With maps, it is usually between a distance measured on the map and the actual distance on the ground. map scale
- 7. I Can Solve Problems Using Scale Drawings! • We know about scales at the supermarket. They measure weight. • They show the relationship between how much you are buying and how much you have to pay.
- 8. I Can Solve Problems Using Scale Drawings! • We also know about the scales we stand on. They measure our weight. • They help to show the relationship between our health and Grandma’s potato salad last week!
- 9. • A scale drawing represents something that is too large or too small to be drawn at its actual size. • Maps and blueprints are examples of scale drawings.
- 10. All scale drawings must have a scale written on them. Scales are usually expressed as ratios. Normally for maps and buildings the ratio: 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 10000 times the length of one unit on the map or drawing.
- 11. • Scale factor is the ratio of change • The number you multiply by to relate the first shape to the second is the scale factor.
- 12. Scale factor = new measurement old measurement Old measurement x SF = new measurement new SF old - Scale factor more than 1 => shape gets bigger (Enlargement) - Scale factor less than 1 => shape gets smaller (Reduction) - Congruent shapes are similar shapes with SF = 1
- 13. • The scale can be written as a scale factor, which is the ratio of the length or size of the drawing or model to the length of the corresponding side or part on the actual object. • Scale Factor needs to be the SAME UNITS!
- 14. 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 HO 1 gauge model train is 87 . 1 This means that each dimension of the model is 87 of the corresponding dimension of the actual train.
- 15. 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.
- 16. If you have ever seen Jurassic Park, you saw how big the dinosaurs were compared to the people. Pretend that they made a large Human to watch over the animals. What would be the scale factor if a 64 inch person was made to be 160 feet?
- 17. The scale factor tells you how many times bigger than “normal” that person really is. You must make all units of measure the same…. 64 inches 64 inches 64 inches = = 160 feet 160 x 12 1920 inches
- 18. Now take the: 64 inches 1920 inches And simplify 1/30 inches This means that the person was created 30 times his normal size.
- 19.
- 20. Keep like units in the same fraction. Inches = yards Inches yards
- 21. • There is more than one way to set up a proportion correctly! • Cross Multiply! • Use common sense!
- 22. • Tom is drawing a blueprint for a rectangular shed he wants to build. The scale factor is 1 ft. to ¼ inch. If the dimensions of the blueprint are 1 ¼ in. by 2 inches, what are the actual dimensions of the shed going to be?
- 23. • If the length in inches is 2 ¼ inch, what would the actual length be in feet ? ¾ inch to 1 foot
- 24. Scale Drawings On Maps Vehicle design Footprints of houses
- 25. 6cm Scale 1 cm = 1 m Length of units = 6 m 5
- 26. Scale 1 : 1 000 000
- 27. • The blueprint of the pool shows each square has a side length of ¼ inch. • If the scale is written as ¼ in = 2 ft, what is actual width of the pool? – (To figure this out, what else do you need to know?)
- 28. decking pool path Scale 2 cm = 1 m 7
- 29. When objects are too small or too large to be drawn or constructed at actual size, people use a scale drawing or a model. The scale drawing of this tree is 1:500 If the height of the tree on paper is 20 inches, what is the height of the tree in real life?
- 30. The scale is the relationship between the measurements of the drawing or model to the measurements of the object. In real-life, the length of this van may measure 240 inches. However, the length of a copy or print paper that you could use to draw this van is a little bit less than 12 inches
- 31. • Map Scales (Legends) are used to find distances on a map. • For example, if your map legend tells you that ½ of an inch represents 50 miles, how could you find the mileage for a 2 inch distance on the map?
- 32. Ratios and proportions can be used to find distances using a scale. Example: 1 inch = 15 miles The distance from Jacksonville to Smithtown on a map is 4 inches. How many miles are between these cities? 1 in. = 4 in 15 mi. n The distance between 1n = 60 n = 60 the two cities is 60 miles.
- 33. • Suppose the distance between Coral Springs and Fort Lauderdale is about 4.1 centimeters on the map. • What is the actual distance on the ground if the scale is 1 cm = 4.5 km? map distance map scale ground distance
- 34. • Use the scale as a fraction. • Use cross-products to calculate. 1 centimeter 4.5 kilometers Distance Distance 4.1 cm ? km 1x ? 4.5 x 4.1 18.45 km
- 35. I Can Solve Problems Using Scale Drawings! • Width of the pool on the blueprint = 1.75 inches. • How can you use cross products to figure out how wide the pool really is?
- 36. I Can Solve Problems Using Scale Drawings! 1/4 inch 2 feet 1 3/4 inches ? feet 1/4 x ? 2 x 1 3/4 1/4 x ? 14/4 Width of pool 14 feet
- 37. I Can Solve Problems Using Scale Drawings! (SOL 7.6) • You can convert the units in a scale to simplify it. • When you do that, you end up with a scale factor. • It is a ratio written in its simplest form. 1/4 inch 2 feet 1/4 inch 24 inches 4 1/4 inch x 4 24 inches Scale factor 1 96 1 or 1 : 96 96
- 38. I Can Solve Problems Using Scale Drawings! • 1) Find the scale factor of the blueprint of a school bus parking lot if the scale is written as “1 inch = 8 feet”. • 2) On a scale drawing of a new classroom, the scale is 1 centimeter = 2.5 meters. What is the scale factor?
- 39. I Can Solve Problems Using Scale Drawings! • 1) Scale factor = 1/96. That means that each measurement on the blueprint is 1/96th of the actual measurement of the parking lot. • 2) 1 centimeter / 2.5 meters: = 1 cm / (2.5 m x 100) cm = 1 cm / 250 cm = 1/250
- 40. I Can Solve Problems Using Scale Drawings! • If you know the actual length of an object and you know the scale, you can build a scale model. • Scale models are used to represent things that are too large or too small for an actual-size model. • Examples are cars, planes, trains, rockets, computer chips, heart cells, bacteria.
- 41. I Can Solve Problems Using Scale Drawings! • Designers are creating a larger model of a computer memory board to use in design work. The board measures 5 ¼ inches in length. • If they use a scale of 20 inches = 1 inch, what is the length of the model? 20 inches ? inches 1 20 5 1 ? 1 inch 5 1/4 inches 4 Model length 105 inches
- 42. I Can Solve Problems Using Scale Drawings! • Things to remember: – When solving proportions, give your answer in the correct unit of measurement. – Scale factors do not have units. – Equivalent scales have the same scale factor. • For example 1 inch = 8 feet and ¼ inch = 2 feet both equal 1/96 (or 1:96) – Scale is the ratio between the drawing/model measurement to the actual measurement. • Not always the ratio of smaller to larger!

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