Unit 1 Scale Drawings — Unit Plan

Title	Takeaways	Assessment
Lesson 1 What Are Scaled Copies?	—	Scaling L (1 problem) Are any of the figures B, C, or D scaled copies of figure A? Explain how you know. Show Solution Only figure C is a scaled copy of figure A. Sample reasoning: In figure C, the length of each segment of the letter L is twice the length of the matching segment in A. Figures B and D are not enlarged evenly. In B, some segments increase and some stay the same. In D, some segments are double in length and some are not.
Lesson 2 Corresponding Parts and Scale Factors	—	Comparing Polygons $ABCD$ and $PQRS$ (1 problem) Polygon $PQRS$ is a scaled copy of polygon $ABCD$ . Segment lengths are given in units. A, B is vertical 1 down. B, C is a diagonal down 1, right 1. C, D is a diagonal right 1, up 2. D, C is horizontal left 2. P, Q is vertical 1.5 down. Q, R is a diagonal down 1.5, right 1.5. R, S is a diagonal right 1.5, up 3. S, P is horizontal left 3. Name the angle in the scaled copy that corresponds to angle $ABC$ . Name the segment in the scaled copy that corresponds to segment $AD$ . What is the scale factor from polygon $ABCD$ to polygon $PQRS$ ? Show Solution Angle $PQR$ corresponds to angle $ABC$ . Segment $PS$ corresponds to segment $AD$ . The scale factor is $\frac{3}{2}$ because $PS = 3$ and $AD = 2$ .
Lesson 3 Making Scaled Copies	—	More Scaled Copies (1 problem) Create a scaled copy of $ABCD$ using a scale factor of 4. Triangle Z is a scaled copy of Triangle M. M Select all the sets of values that could be the side lengths of Triangle Z. 8, 11, and 14. 10, 17.5, and 25. 6, 9, and 11. 6, 10.5, and 15. 8, 14, and 20. Show Solution B, D, E
Lesson 4 Scaled Relationships	—	Corresponding Polygons (1 problem) Here are two polygons on a grid. Two five-sided polygons on a grid. The polygon on the left is labeled ABCDE. The vertices from A going counterclockwise are as follows. Vertex B is 1 unit to the left and 3 units down. Vertex C is 1 unit down. Vertex D is 2 units to the right. Vertex E is 1 unit up. The polygon on the right is labeled PQRTS. The vertices from P going counterclockwise are as follows. Vertex Q is 2 units to the left and 5 units down. Vertex R is 1 unit down. Vertex S is 4 units right. Vertex T is 1 unit up. 1 unit=1 square on the grid. Is $PQRST$ a scaled copy of $ABCDE$ ? Explain your reasoning. Show Solution No. Sample reasoning: $PQRST$ is not a scaled copy of $ABCDE$ because we need to use different scale factors when comparing corresponding lengths (1 for corresponding segments $BC$ and $QR$ and 2 for corresponding segments $CD$ and $RS$ ). Also, not all of their corresponding angles are the same size. Angle $A$ and angle $P$ are not the same size.
Lesson 5 The Size of the Scale Factor	—	Scaling a Rectangle (1 problem) A rectangle that is 2 inches by 3 inches will be scaled by a factor of 7. What will the side lengths of the scaled copy be? Suppose you want to scale the copy back to its original size. What scale factor should you use? Show Solution 14 inches by 21 inches, because $2 \boldcdot 7 = 14$ and $3 \boldcdot 7 = 21$ . $\frac 17$ , because it is the reciprocal of 7.
Lesson 6 Scaling and Area	—	Enlarged Areas (1 problem) Lin has a drawing with an area of 20 in². If she increases all the sides by a scale factor of 4, what will the new area be? Noah enlarged a photograph by a scale factor of 6. The area of the enlarged photo is how many times as large as the area of the original? Show Solution 320 in², Sample responses: $20 \boldcdot 4^2 = 320$ If the rectangle is 4 inches by 5 inches, the scaled copy will be $4 \boldcdot 4$ inches by $4\boldcdot 5$ inches and $(4 \boldcdot 4) \boldcdot (4\boldcdot 5) = 16 \boldcdot 20 = 320$ . If the rectangle is 2 inches by 10 inches, the scaled copy will be $4 \boldcdot 2$ inches by $4 \boldcdot 10$ inches and $(4\boldcdot 2) \boldcdot (4\boldcdot 10) = 8 \boldcdot 40 = 320$ . 36 times as large, because $6^2 = 36$ .
Section A Check Section A Checkpoint		Problem 1 Select all the pairs of figures that are scaled copies of each other. (Note: All measurements are rounded to the nearest whole number.) Show Solution D, E Problem 2 Create a scaled copy of the triangle using a scale factor of 2. Show Solution

Lesson 7 Scale Drawings	—	Length of a Bus and Width of a Lake (1 problem) A scale drawing of a school bus has a scale of $\frac12$ inch to 5 feet. If the length of the school bus is $4\frac12$ inches on the scale drawing, what is the actual length of the bus? Explain or show your reasoning. A scale drawing of a lake has a scale of 1 cm to 80 m. If the actual width of the lake is 1,000 m, what is the width of the lake on the scale drawing? Show Solution 45 ft. Sample reasoning: There are 9 groups of $\frac12$ in $4\frac12$ . If $\frac12$ inch represents 5 feet, then $4\frac12$ inches represents $9 \boldcdot 5$ or 45 feet. 12.5 cm. Sample reasoning: Since every 80 m is represented by 1 cm, 1,000 m is represented by $1, 000 \div 80$ or 12.5 cm.
Lesson 8 Scale Drawings and Maps	—	Walking Around the Botanical Garden (1 problem) Here is a map of the Missouri Botanical Garden. Clare walked all the way around the garden. What is the actual distance around the garden? Show your reasoning. It took Clare 30 minutes to walk around the garden at a constant speed. At what speed was she walking? Show your reasoning. Show Solution It takes about 14 segments of the scale to measure the perimeter of the garden, and $14 \boldcdot 600=8,400$ . So the distance around is about 8,400 feet. If she walks for 30 minutes, that means she was traveling at about 280 feet per minute ( $8,400 \div 30 = 280$ ), or about 16,800 feet per hour ( $280 \boldcdot 60 \approx 16,800$ ).
Lesson 9 Creating Scale Drawings	—	Drawing a Pool (1 problem) A rectangular swimming pool measures 50 meters in length and 25 meters in width. Make a scale drawing of the swimming pool where 1 centimeter represents 5 meters. What are the length and width of your scale drawing? Show Solution
Lesson 10 Changing Scales in Scale Drawings	—	Window Frame (1 problem) Here is a scale drawing of a window frame that uses a scale of 1 cm to 6 inches. Create another scale drawing of the window frame that uses a scale of 1 cm to 12 inches. Show Solution Scaled copy of the drawing where each length is half as long as in the original.
Lesson 11 Scales without Units	—	Scaled Courtyard Drawings (1 problem) Andre drew a plan of a courtyard at a scale of 1 to 60. On his drawing, one side of the courtyard is 2.75 inches. What is the actual measurement of that side of the courtyard? Express your answer in inches and then in feet. If Andre made another courtyard scale drawing at a scale of 1 to 12, would this drawing be smaller or larger than the first drawing? Explain your reasoning. Show Solution 165 in, which is 13.75 ft. Sample reasoning: $2.75 \boldcdot 60=165$ . $165 \div 12 = 13.75$ . It would be larger. Sample reasoning: A scale of 1 to 12 means the length on paper is $\frac{1}{12}$ of the original length, so the drawing would be larger than one drawn at $\frac{1}{60}$ the original length.
Lesson 12 Units in Scale Drawings	—	Drawing the Backyard (1 problem) Lin and her brother each created a scale drawing of their backyard, but at different scales. Lin used a scale of 1 inch to 1 foot. Her brother used a scale of 1 inch to 1 yard. Express the scales for the drawings without units. Whose drawing is larger? How many times as large is it? Explain or show your reasoning. Show Solution Lin’s scale of 1 inch to 1 foot can be written as 1 to 12. Her brother’s scale of 1 inch to 1 yard can be written as 1 to 36. Lin’s drawing is larger. Sample reasonings: The lengths on Lin's plan are 3 times the corresponding lengths on her brother's drawing. The area of Lin's drawing is 9 times the area of her brother's drawing. Since 1 yard equals 3 feet, the scale of Lin’s brother’s drawing is equivalent to 1 inch to 3 feet. Each inch on his drawing represents a longer distance than on Lin’s drawing, so his drawing will require less space on paper. At 1 inch to 1 foot, Lin’s drawing will show $\frac{1}{12}$ of the actual the distances. At 1 inch to 1 yard, or 1 inch to 3 feet, her brother’s drawing will show $\frac{1}{36}$ of the actual distances. Since $\frac{1}{12}$ is larger than $\frac{1}{36}$ , Lin's drawing will be larger.
Section B Check Section B Checkpoint		Problem 1 Here is a map of Yellowstone National Park. Use the map to answer the questions. About how long is the south border of the actual park? Estimate the actual area of the park. Explain your reasoning. A different map of Yellowstone National Park uses the scale 1 inch to 4 miles. How long is the south border of the park on that map? Show Solution about 50 mi about 3,000 sq mi. Sample reasoning: The park is roughly a rectangle. The height of the park is about 60 mi and the width is about 50 mi. $50 \boldcdot 60 = 3,000$ Sample response: 12.5 inches (if 50 mi is used as the actual length) Note: The answer here should be $\frac14$ of whatever value students have for the actual length of the south border of the park.

Lesson 13 Draw It to Scale	—	No cool-down
Unit 1 Assessment End-of-Unit Assessment