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Scale Factor & Scale Drawings

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Understanding Scales 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 times the length of one unit on the map or drawing.

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Scale Factor

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**How to find Scale Factor**

When a figure is dilated, its size is changed by multiplying the length of each side by a scale factor. All angles remain the same and so the new shape (or image) is similar to the original. Can be found by dividing a new side length by the original side length. 𝑁𝑒𝑤 𝑂𝑙𝑑 𝐼𝑚𝑎𝑔𝑒 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑇𝑜 𝐹𝑟𝑜𝑚 When going from a small shape to a larger shape the scale factor is greater than 1. (Enlargement) 𝐵𝑖𝑔 𝐿𝑖𝑡𝑡𝑙𝑒 When going from a large shape to a smaller shape the scale factor is less than 1. (Reduction) 𝐿𝑖𝑡𝑡𝑙𝑒 𝐵𝑖𝑔 Determine the corresponding side lengths. Determine if you are making a larger shape or a smaller shape. Determine if the scale factor is greater than or less than 1. Write the correct ratio.

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**Scale Factor Scale factor = new measurement old measurement**

SF new old Old measurement x SF = new measurement 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

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Vocabulary scale model scale factor scale scale drawing

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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!

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**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 HO gauge model train is 1 87 This means that each dimension of the model is of the corresponding dimension of the actual train. 1 87

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**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.

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**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?

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**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 1920 inches 160 x 12

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Now take the: 64 inches And simplify 1920 inches 1/30 inches This means that the person was created 30 times his normal size.

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**BAIP Instructional Support Version 2**

4/5/2017 Scale Factor The scale factor of the pool is 1” to 20 yards. Or 𝑖𝑛𝑐ℎ𝑒𝑠 𝑦𝑎𝑟𝑑𝑠 = 1 20 What is a Scale Factor?(PowerPoint #1) Teacher prompt: Show students a picture of a competition swimming pool. (See Teacher’s Guide) Teacher prompt: Tell students that the dimensions of this the picture of the pool have a scale factor of 1 in. to 20 yards. Teacher prompt: Explain to students that the scale factor will help us find the actual dimensions of the diagram of the pool. A scale factor is a ratio of measurements in a scale drawing to the actual measurement of the real-world object. Teacher prompt: Ask students, “If 1 in. = 20 yards and the pool’s length is 100 yards, what is the length of the picture of the pool? Student response: If 1 inch equals 20 yards, then 100 ÷ 20 equals 5 inches. The length of the diagram will be 5 inches. Teacher prompt: Yes that is correct. Teacher prompt: Using the same scale factor, find the width of the diagram if the pool’s width is 75 yards. Student response: Using the scale factor of 1 inch to 20 yards I divided the 75 yards by 20 yards. The width of the picture is 3 ¾ inches because 75 ÷ 20 = 3.75 or 3 ¾ inches. Teacher prompt: Using the dimensions you just found, make a diagram of the swimming pool. Student response: The diagram should be a 5” by 3 ¾” rectangle.

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**BAIP Instructional Support Version 2**

4/5/2017 Setting up Proportions Keep like units in the same fraction. Inches = yards Inches yards (3.) Teaching Concept 2: Use a Scale Factor to Set up Proportions to Solve Real-World Problems (PowerPoint #2) Teacher prompt: Another way to solve the competition pool problem is to set up a proportion. Teacher prompt: When setting up a proportion, make sure you keep like units in the same fraction. Teacher prompt: Let us set up a proportion using the previous dimensions. Teacher prompt: Start with the length first. Set up the proportion with the inches in the first fraction and the yards in the second fraction. Once your proportion is set up, solve for the missing length. Student response: Length: 1inch = 20 yards x inch yards 20x = 100 Length: x = 5 inches Width: inch = 20 yards x inches 75 yards 20x = 75 Width: x = 3 3/4 inches Teacher prompt: Good job.

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**Remember… There is more than one way to set up a proportion correctly!**

Cross Multiply! Use common sense!

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**BAIP Instructional Support Version 2**

4/5/2017 Write a Proportion Using Scale Factor 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? Application (PowerPoint #4) 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? Teacher prompt: Have students help you translate what the problem is asking and tell how he/she will solve this problem. Student response: The problem is asking to use the scale factor of 1 ft. to ¼ in. to find the actual dimensions of the shed. The first step is to set up a proportion for one of the sides, length or width. The proportion for the length is: 1/4 inch = 1 foot 2 inches x (4/1)1/4x = 2 Multiply ¼ in. by its reciprocal of 4/1 to get 1x. Then multiply the right side by that same 4/1. 1x = (4/1) 2/1 1x = 8/1 or 8 1x = 8 feet The length of the shed is 8 feet. Next, find the width of he shed. 1 1/4 inches x (4/1)1/4 x = 1 ¼ Multiply 1/4 by its reciprocal of 4/1 to get 1x. Then multiply the right side by the reciprocal, 4/1. 1x = 5/4(4/1) 1x = 20/4 or 5 1x = 5 feet The width of the room is 5 feet.

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**BAIP Instructional Support Version 2**

4/5/2017 Write a Proportion Using a Scale Factor ¾ inch to 1 foot If the length in inches is 2 ¼ inch, what would the actual length be in feet ? (PowerPoint #5) Teacher Prompt: Write the following scale factor on the board. ¾ inch to 1 foot Teacher Prompt: Ask the students, “If the length in inches is 2 ¼ inch, what would the actual length be in feet using the scale factor written on the board?” Student Response: 3/4 inch = 1 foot 2 1/4 inch x 3/4 x = 2 1/4 Multiply 3/4 by its reciprocal of 4/3 to get 1x. Multiply the right side by the same reciprocal of 4/3. 1x = 9/4 ● 4/3 1x = 36/12 or 3 feet 1x = 3 feet Teacher prompt: Good job.

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Scale Drawings

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**What are scale drawings? Scale drawings are everywhere!**

On Maps Footprints of houses Vehicle design Can you think of any more?

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**Scale in everyday life: kitchen design**

Purpose: To share Move On with you and outline what the Project can offer, to you and to learners To give you a brief taste of the National Tests To give you an opportunity to action plan how you will adopt the Move On approach and adapt it to your setting Workshop outline: Presentation covering these aspects of Move On and the National Tests Questions Quiz using National Test questions that you can take away and copy to use with teachers and students in your own organisation Table-talk to explore action you will take and what support you would like from the Move On Project team Action Planning Is there anything else you would like me to include? Scale 1 cm = 1 m 6cm Length of units = 6 m 5

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**Scale in everyday life: maps**

Purpose: To share Move On with you and outline what the Project can offer, to you and to learners To give you a brief taste of the National Tests To give you an opportunity to action plan how you will adopt the Move On approach and adapt it to your setting Workshop outline: Presentation covering these aspects of Move On and the National Tests Questions Quiz using National Test questions that you can take away and copy to use with teachers and students in your own organisation Table-talk to explore action you will take and what support you would like from the Move On Project team Action Planning Is there anything else you would like me to include? Scale 1 :

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**Scale in everyday life: plans**

decking path pool Purpose: To share Move On with you and outline what the Project can offer, to you and to learners To give you a brief taste of the National Tests To give you an opportunity to action plan how you will adopt the Move On approach and adapt it to your setting Workshop outline: Presentation covering these aspects of Move On and the National Tests Questions Quiz using National Test questions that you can take away and copy to use with teachers and students in your own organisation Table-talk to explore action you will take and what support you would like from the Move On Project team Action Planning Is there anything else you would like me to include? Scale 2 cm = 1 m 7

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**BAIP Instructional Support Version 2**

4/5/2017 Using A Scale Drawing Use a Scale Drawing to Find the Actual Dimensions of the Object (PowerPoint #3) Teacher prompt: Look at the following drawing of a Science lab. The blueprint has a scale factor of ½ in. to 1 yard. (See Teacher’s Guide) Teacher prompt: Let x = width of the room in yards. Set up a proportion to find the width of the room and simplify if necessary. Student response: The width is 1½ inches and the scale factor is ½ inch to 1 yard. The proportion is set up as follows: ½ inch = 1 yard 1½ inch x ½ x = 1½ Multiply ½ by its reciprocal of 2/1 to get 1x. Then multiply the right side by that same 2/1. 1x = 3/2 ● 2/1 1x = 6/2 or 3 1x = 3 yards The width of the room is 3 yards. Teacher prompt: Excellent. Now find the length of the science lab. Student prompt: 5 inches x ½ x = 5 1x = 5 ● 2/1 1x = 10/1 or 10 1x = 10 yards The length of the room is 10 yards.

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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?

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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

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**Map Scales 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?

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**The distance between the two cities is 60 miles.**

Map Scales 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. 15 mi. 4 in n = The distance between the two cities is miles. 1n = 60 n = 60

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