Mrs. Fickle showed her class the scale drawing she made for this week s arrangement.

Using Scale SUGGESTED LEARNING STRATEGIES: Summarize/Paraphrase/ Retell, Vocabulary Organizer Mrs. Fickle likes to rearrange her classroom often, even though her students complain about how often she moves them. She is running out of ideas, so she has asked the students to work in groups to create new classroom arrangements. She has decided to change the arrangement of the classroom once each week using a different group s plan. Mrs. Fickle tells the class that the most efficient way to create a floor plan is to make a scale drawing. 1. What do you know about scale drawings? ACTIVITY 3.7 Mrs. Fickle showed her class the scale drawing she made for this week s arrangement. Teacher Desk Table Door 1 cm: 3 ft 2. A scale shows the relationship between the dimensions of the objects in the drawing to the dimensions of the actual objects. This relationship is written as a scale factor. a. What is the scale factor on the drawing, and what does it indicate? When writing scale factors, the scale model is usually listed first, and the actual object listed second. b. In what form is the scale factor written? Unit 3 Two-Dimensional Geometry and Similarity 199

ACTIVITY 3.7 Using Scale SUGGESTED LEARNING STRATEGIES: Think Aloud, Use Manipulatives, Group Presentation, Quickwrite, Think/ Pair/Share, Create Representations, Discussion Group Sometimes scales are written without units. This means that the units are the same, and are given in the context of the problem or by using the grid on the drawing. The scale factor 1 in.:4 ft may be written as 1:48 if 4 feet is converted to 48 inches. Then the unit inches is not needed and is dropped from the scale factor. 3. Write the scale factor from Mrs. Fickle s drawing without units. 4. Where else have you seen or used a scale? 5. To determine the length of Mrs. Fickle s classroom, you can make and use a scale ruler. To do this, use a strip of paper. Start at a corner of the strip and mark every centimeter along one edge of the strip. The corner is 0 ft.; label the first mark 3 ft, the next 6 ft, the next 9 ft, and so on, counting by 3 s because the scale factor is 1 cm:3 ft. The strip is now a scale ruler. Use the scale ruler to measure the length of the room on the drawing. 6. How could you use a regular ruler to find the actual length of the room? 7. Mrs. Fickle forgot to draw the space where the whiteboard goes. If the whiteboard is 8 ft long, how long should it be in the drawing? Explain how you found your answer. 8. How does using scales involve proportional reasoning? 200 SpringBoard Mathematics with Meaning TM Level 2

Using Scale ACTIVITY 3.7 SUGGESTED LEARNING STRATEGIES: Create Representations, Identify a Subtask, Use Manipulatives For Question 9 you will work in a group to plan a new arrangement for your classroom. First you will work together to make a group floor plan of your classroom showing doors, shelves, and other things that cannot be moved on one piece of grid paper. All of you will then make your own copies of the floor plan. Next you will work together to measure any classroom furniture that can be moved. The group will draw and cut out top views of the classroom furniture and use these pieces to try out new arrangements for your classroom. When your group decides on a plan, you will make a group copy and each member of the group will also make a copy of the arrangement. 9. Follow each step. Show how to write and solve any proportions needed to make your floor plan. Group members should work together, but everyone must make a drawing. a. Start with the scale drawing for the floor plan of the room. Step 1: Measure the length and width of the room. Length: Width: Step 2: Create a scale factor. How did you determine the scale factor? Step 3: Step 4: Use grid paper to draw the dimensions of the floor. Be sure to include the scale on the drawing. Plan so that the floor plan takes up most of the paper. Show your conversions below. Measure and label items such as doors, closets, bulletin boards, and whiteboards that may affect placement of furniture. Show your conversions below. Unit 3 Two-Dimensional Geometry and Similarity 201

ACTIVITY 3.7 Using Scale SUGGESTED LEARNING STRATEGIES: Create Representations, Identify a Subtask, Use Manipulatives b. Make scale drawings of the classroom furniture on a second sheet of grid paper. Step 5: Measure furniture. Objects you might include are student desks, teacher desk, tables, bookcases, and so on. You do not need to include every object in the room. List the items you measure and their measurements below. Step 6: Convert each measurement using your scale factor and draw these dimensions on a separate piece of grid paper. Show your conversions below. As a group, cut out only one shape for each piece of classroom furniture. If your classroom has 25 desks and there are 5 people in your group, you should each cut out 5 student desks. Step 7: In your group, cut out and arrange the classroom objects on the group floor plan of the room. When everyone is happy with the arrangement, draw the furniture on the floor plan. Then create your own scale drawing of your group s furniture arrangement. 202 SpringBoard Mathematics with Meaning TM Level 2

Using Scale ACTIVITY 3.7 SUGGESTED LEARNING STRATEGIES: Create Representations, Identify a Subtask, Use Manipulatives, Vocabulary Organizer, Quickwrite The floor plan you made is a scale drawing. It is a model of your classroom in two-dimensions. To make a scale model of your classroom, you need to add the third dimension of height. 10. Now that you have each created a floor plan, work together to measure things on the walls of your classroom. Divide the work among the members of your group to create each wall. Continue to use the same scale factor as you used for the scale drawing of the floor plan. Be sure to include all large items such as whiteboards, doors, windows, bulletin boards, pictures, and so on. Record your work in this table. Objects Measurements Conversions 11. The students working on a wall should make a scale drawing of their wall on another sheet of grid paper. Then the group members cut out and tape the drawings of the four walls together and cut out and lay your group floor plan into the center of the four walls. 12. What your group has just created is called a scale model. Explain this term. Remember that you have already measured the length of each wall when drawing the floor plan. Unit 3 Two-Dimensional Geometry and Similarity 203

ACTIVITY 3.7 Using Scale SUGGESTED LEARNING STRATEGIES: Create Representations, Summarize/Paraphrase/Retell, Think/ Pair/Share, Quickwrite After creating their scale models, each group of Mrs. Fickle s students designs a logo to attach to their group model instead of listing their names on it. When a group s floor plan is chosen for the week, a larger version of their logo gets hung in the classroom. Look below at some of the logos that they have made. 13. Choose one of the logos and create a scale drawing that is an enlargement of it on this grid. 14. Describe your strategy for enlarging the logo. 204 SpringBoard Mathematics with Meaning TM Level 2

Using Scale ACTIVITY 3.7 SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Self/Peer Revision, Discussion Group, Quickwrite 15. Is your enlargement proportional to the original logo? Explain. 16. What is the drawing s scale? Explain. 17. How could you enlarge this picture of a frog? 18. You have now learned two different strategies for making scale drawings. a. Compare the strategy you used for enlarging the frog to the one you used to make the scale drawings of the floor and wall plans. b. Could you have used the strategy used for drawing the floor plan in order to enlarge the logo? Explain. 19. Why is using scale drawings and scale models an effective method for deciding the arrangement of the classroom? Unit 3 Two-Dimensional Geometry and Similarity 205

ACTIVITY 3.7 Using Scale CHECK YOUR UNDERSTANDING Write your answers on notebook paper or grid paper. Show your work. 1. On a map the distance between San Diego and San Francisco is about 5 cm. The map scale is 1 cm:110 mi. About how far is San Diego from San Francisco? 2. Write an equivalent scale factor that does not use units for 1 in.:5 ft. 3. A playground is 100 feet long by 150 feet wide. You want to make a scale drawing of the playground on an 8.5 11 paper. What scale could you use? Explain. 4. A scale model of the Statue of Liberty was built for a class project. The actual height of the Statue of Liberty is about 151 feet. What is the height of the model if its scale factor is 1:30? 5. A tarantula is being enlarged for a movie. Its actual leg span is 8 inches. The movie model of this tarantula has a leg span of 32 feet. What is the scale of the model? 6. Determine whether each scale represents a scale model that is smaller or larger than the actual object. Explain your thinking. a. 3:1 b. 1:0.5 c. 1:9 7. Use this picture of a ladybug on a grid. a. Draw a reduction of the ladybug on grid paper. b. Approximately what scale did you use? 8. MATHEMATICAL REFLECTION How and why are scale drawings and scale models used in the real world? 206 SpringBoard Mathematics with Meaning TM Level 2