Activity 1: Proportions, Ratios, and Scale Drawings Objective Students will learn about proportions, ratios and scale and apply that knowledge to create a scale drawing of an actual room. Questions What is the appropriate scale to map the object(s) being drawn given the size of paper being used? Is the scale appropriate in relationship with other items in the drawing? Is the scale consistent throughout the drawing? Explorations 1. Supplement 1: Proportions Worksheet 2. Map scales and Supplements 2-3. 3. Students will complete a home assignment (Supplement 4: Scale Drawing of a Room) They should choose a room in their home. All large furniture/appliances should be measured and recorded. Using graph paper, students will decide on an appropriate scale and transfer their dimensions. Similar to a map, students will identify their scale. All representations should be drawn to scale. 4. Extended Activity: Students work in groups of three to develop a scale map drawing of the classroom/school. Analyze Results Students will exchange room drawings and work on labeling the dimensions of items in the drawing. Students will use the designated scale to do so. Assessment Students will complete Supplement 5: Reflection Worksheet about the challenges of creating a scale room map. Activity 1 Page 1
Supplement 1: Proportions Worksheet Create a proportion from each set of numbers. This will help students learn proportional reasoning. Miles 45 Hours 1 2 3 4 5 Dollars 3.30 Pounds 1 2 3 4 5 Dollars 45 Hours 1 2 3 4 5 Dollars 42 Hours 1 2 3 4 5 Dollars 15.50 Meters 0.10 0.20 0.30 0.40 0.50 Utilizing the information from the tables above: 1. How many miles will someone travel in 11 hours? 2. If you are working for 9 dollars per hour, how much would you make for an 8 hour shift minus a one hour lunch period? 3. How much would 1 meter of fabric cost? Supplement 1 Page 1
Supplement 2: Map Scale In a scale drawing or a scale model, all the dimensions of the actual object are reduced or enlarged proportionally. A map is a scale drawing in which actual distance is reduced. The towns of Ardon and Bacton are on a map with a scale 1 cm = 15km. If the map distance between Ardon and Bacton is 4.5 cm, what is the actual distance? Actual Distance Actual Distance = Map Distance Map Distance 15 km X km = 1 cm 4.5 cm 1 (x) = 15 (4.5) X = 67.5 km Actual distance between Ardon and Bacton Supplement 2 Page 1
Complete to find each unknown measurement. 1. A map scale is 1 in. = 75 mi. The map distance between Lewiston and Portage is 3.5 in. Find the actual distance x between the towns. Actual Distance Actual Distance = Map Distance Map Distance 2. The actual distance between two towns is 175 km. If the distance between them on a map is 7 cm, what is the map scale? 3. An archway in a ½ in. scale drawing is 4.5 in. tall. Find the actual height x. 4. Under a 7:1 magnification, this letter F appears to be 84 points high. Find the actual height x. Supplement 2 Page 2
Supplement 3: Exercises in Scale The scale of a drawing is ¼ in. = 15 ft. Find the actual measurement. 1. 9 in. 2. 12 in. 3. 14 in. 4. 15 in. The scale is 2 cm = 25 m. Find the length each measurement would be on a scale drawing. 5. 150 m. 6. 475 m. 7. 350 m. 8. 500 m. Tell whether each scale reduces, enlarges, or preserves the size of an actual object. 9. 1 m : 25 cm 10. 8 in : 1 ft 11. 12 in : 1 ft 12. On a map the distance between Atlanta, Georgia, and Nashville, Tennessee, is 12.5 in. The actual distance between cities is 250 miles. What is the scale? 13. Blueprints of a house are drawn to the scale of ¼ in. 1 ft. A kitchen measures 3.5 in. by 5 in. on the blueprints. What is the actual size of the kitchen? 14. A scale model of a house is 1 ft long. The actual house is 50 ft long. In the model, the window is 1 1/5 in. high. How many feet height is the actual window? 15. A model of a skyscraper is 1.6 in. long, 2.8 in. wide, and 11.2 in. high. The scale factor is 8 in. :250 ft. What the actual dimensions of the skyscraper? Supplement 3 Page 1
Supplement 4: Scale Drawing of a Room Create a list of large items/furniture in your chosen room. This activity will involve horizontal scaling to create a room blueprint. Items should be measured by width as well as length. Dimensions of each item should be labeled on the table below, not on the actual drawing. Remember to include the actual wall dimensions minus any doors. ITEM LENGTH WIDTH Example: Dresser 42 in. 18 in. Supplement 4 Page 1
1. Using the graph paper, decide how much area 1 square will represent. Example: 1 = 6 inches 2. Once the scale has been determined, map the layout of your room on the graph paper. Make sure dimensions and scale are appropriate. ROOM SCALE: 1 unit/square = inches Supplement 4 Page 2
Supplement 5: Reflection Worksheet Utilizing your experiences with ratios/scale and proportions, answer the following prompts below: What are some examples of how scale and/or proportions are used in everyday life? In what careers would the understanding of ratios and scale be the most helpful? What was the most challenging part of mapping out your room to scale? In what other ways could you practice understanding scale and proportions? Why is scale important? Supplement 5 Page 1