Day 1 p.2-3 SS 3.1/3.2: Rep-Tile Quadrilaterals & Triangles
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1 Stretching and Shrinking Unit: Understanding Similarity Name: Per: Investigation 3: Scaling Perimeter and Area and Investigation 4: Similarity and Ratios Date Learning Target/s Classwork (Check Off Completed/ Corrected Items) Tuesday, Nov. 15 Wednesday, Nov. 16 Thursday, Nov. 17 Friday, Nov. 18 Monday, Nov. 21 Tuesday, Nov. 22 Wednesday, Nov. 23 Monday, Nov. 28 Tuesday, Nov. 29 Wed, Nov 30 Thur, Dec 1 I can use rep-tiles to see the effect of scale factor on side lengths, angles, perimeter, and area. I can use scale factors to make scale drawings. I can use scale factors to find missing values in similar figures. I can use scale factors to find missing values in similar figures. I can use equivalent ratios to compare corresponding sides of similar rectangles. I can use equivalent ratios to compare corresponding sides of similar triangles. I can keep calm in class the day before Thanksgiving! I can use proportions to find missing values in similar figures. If needed, I can do EXTRA PRACTICE I can review unit concepts in preparation for the Unit Test. I can prepare for the Unit Test tomorrow. Day 1 p.2-3 SS 3.1/3.2: Rep-Tile Quadrilaterals & Triangles Day 2 p.5-6 SS 3.3: Scale Factors and Similar Shapes Entrance Ticket Day 3 p.8-9 SS 3.4: Additional Practice with Similar Figures Day 4 Check Up Quiz Day 5 p. 12 SS 4.1: Ratios in Similar Rectangles Day 6 p. 14 SS 4.2: Ratios in Similar Triangles Homework (Check Off Completed/ Corrected Items) P. 4 SS Inv 3-4 Day 1 Complete and correct with the EDpuzzle Pg. 7 SS Inv 3-4 Day 2 Edpuzzle: Take notes for 3.4 Pg 10 SS Inv 3-4: Day 3 Complete and Correct with the EDpuzzle Pg. 11 SS Inv 3-4 Day 4 Edpzzule Take notes for 4.1 Pg. 13 SS Inv 3-4 Day 5 EdPuzzle Take notes for 4.2 I have reviewed with a parent/guardian and I am satisfied with the work produced in this packet. Pg. 15 Puzzle: Correct with the KEY Self-Assess Your Understanding of the Learning Target/s Day 7 Activity None (Don t eat too much tomorrow!) Day 8 p : Finding Missing Parts Pg. 18 Puzzle: Correct with the KEY Pg. 19 optional EXTRA PRACTICE Day 9 Unit Review 1 Unit Review #1 Correct with KEY Day 10 Review Day 2 Online Unit Review #2 Day11 Unit Test Comparing & Scaling Unit Readiness WS: Correct with the KEY I can show my understanding concepts relating to Scale Factor. Standards 7.RP.A: Recognize and represent proportional relationships between quantities. o Proportional relationships have a scale factor. 7.G.A.1: Solve problems involving scale drawings of geometric figures. 7.G.B.6: Solve problems involving area of triangles and quadrilaterals. Work Habits: Completed and corrected packet, watched EdPuzzles: 1( Rarely) 2( Sometimes) 3(Most of the time) Initiative: Took advantage of all retake options, completed packet without prompting, asked questions corrected packets online 1( Rarely) 2( Sometimes) 3(Most of the time) Citizenship: Completed and corrected all warm-ups with class, came to class on time and prepared, followed classroom rules, did not talk while teacher was talking. 1( Rarely) 2( Sometimes) 3(Most of the time) Collaboration: On task when group work was assigned, followed along with class as review occurred, did not move ahead of group. 1( Rarely) 2( Sometimes) 3(Most of the time) Student signature: Parent/Guardian Signature: 1
2 DAY 1 SS : Rep-Tile Quadrilaterals and Triangles 1. Look for rep-tile patterns in the design below. For each design, Decide whether the small quadrilaterals within each figure are similar to the large quadrilateral that makes up the whole figure. Explain. If the quadrilaterals are similar, give the scale factor from each small quadrilateral to the large quadrilateral. 2. Suppose you put together nine copies of a rectangle to make a larger, similar rectangle. a. Make a sketch of the large rectangle with the smaller rectangles inside: b. How is the area of the larger rectangle related to the area of the smaller rectangle? c. What is the scale factor from the smaller rectangle to the larger rectangle? d. Challenge: If the area of the large rectangle is 81 in 2, what is the area of one of the small rectangles? e. Challenge: If the area of one of the small rectangles is 15 in 2, what is the area of the large rectangle? 2
3 3. Suppose you divide a rectangle into 25 smaller rectangles such that each rectangle is similar to the original rectangle. a. Make a sketch of the large rectangle with the smaller rectangles inside: b. How is the area of each of the smaller rectangles related to the area of the original rectangle? c. What is the scale factor from the original rectangle to each of the smaller rectangles? d. Challenge: If the area of one of the small rectangles is 4 cm 2, what is the area of the large rectangle? e. Challenge: If the area of the large rectangle is 225 cm 2, what is the area of one of the small rectangles? 4. Look for rep-tile patterns in the figures below. Tell whether the small triangles are similar to the large triangles. Explain. If the triangles are similar, give the scale factor from each small triangle to the large triangle. 3
4 Day 1 HOMEWORK: Similar Rectangles: Complete and Correct with the EDpuzzle Look at the diagram of Rectangles F and G. a. Identify the length, width, perimeter, and area of Rectangle F: Length: Width: Perimeter: Area: i. Give the length and width of a different, similar rectangle H (you get to make it up, but rectangle H must be similar to rectangle F): Length: Width: ii. How do you know rectangle H is similar to Rectangle F? iii. What is the scale factor from Rectangle F to rectangle H? iv. What is the perimeter of rectangle H? v. What is the area of rectangle H? b. Identify the length, width, perimeter, and area of Rectangle G: Length: Width: Perimeter: Area: i. Give the length and width of a different, similar rectangle J (you get to make it up, but rectangle J must be similar to rectangle G): Length: Width: ii. How do you know that your new rectangle J is similar to Rectangle G? iii. What is the scale factor from Rectangle G to rectangle J? iv. What is the perimeter of rectangle J? v. What is the area of rectangle J? 4
5 DAY 2 SS 3.3: Designing Under Constraints Scale Factors and Similar Shapes Use the lab sheet to see Rectangle A and Triangle B and to draw and label the additional similar figures. A. For each part, find a rectangle similar to Rectangle A that fits the given description. 1. The scale factor from Rectangle A to Rectangle C is 2.5. a. What are the side lengths of Rectangle A? b. What is the scale factor from Rectangle A to Rectangle C? i. (Circle one): The rectangle is getting bigger / smaller. c. What are the side lengths of the Rectangle C? Show how you use the scale factor. Length of Rectangle C = Width of Rectangle C = d. Draw and label Rectangle C on the grid. 2. The area of Rectangle D is ¼ the area of Rectangle A. a. What is the area of Rectangle A? b. What is the scale factor from Rectangle A to Rectangle D? i. (Circle one): The rectangle is getting bigger / smaller. c. What is the area of Rectangle D? Show how you use the scale factor. Area of Rectangle D = d. Draw and label Rectangle D on the grid. e. Challenge: How many copies (rep-tiles) of Rectangle D fit inside Rectangle A? 3. The perimeter of Rectangle E is 3 times the perimeter of Rectangle A. a. What is the perimeter of Rectangle A? b. What is the scale factor from Rectangle A to Rectangle E? i. (Circle one): The rectangle is getting bigger / smaller. c. What is the perimeter of Rectangle E? Show how you use the scale factor. Perimeter of Rectangle E = d. Draw and label Rectangle E on the grid. 5
6 B. For each part, find a triangle similar to Triangle B that fits the given description. 1. The area of Triangle F is 16 times the area of Triangle B. a. What is the area of Triangle B? b. What is the area of Triangle F? Area of Triangle F = c. How many copies (rep-tiles) of Triangle B fit inside Triangle F? d. Think about the relationship between rep-tiles and area, as well as the relationship between scale factor and area. What is the scale factor from Triangle B to Triangle F? e. Draw and label Triangle F on the grid. 2. The scale factor from Triangle B to Triangle G is ½. a. What are the base & height of Triangle B? b. What is the scale factor from Triangle B to Triangle G? i. (Circle one): The triangle is getting bigger / smaller. e. What are the base & height of the Triangle G? Show how you use the scale factor. Base = Height = c. Draw and label Triangle G on the grid. C. Rectangles ABCD and EFGH are similar. Find the length of side AD. Explain how you found the length. 6
7 Day 2 HOMEWORK: Complete the notes from the EDpuzzle for SS Triangles ABC and DEF are similar. Find the missing side lengths and angle measures. Explain how you found the missing measures. Angle B: Angle E: Angle F: Side DF: Side FE: 2. What is the relationship between scale factor and corresponding angles? 3. What is the relationship between scale factor and corresponding sides? 4. What is the relationship between scale factor and perimeter? 5. What is the relationship between scale factor and area? 6. What are nested triangles? Match up corresponding and. Look for a. 7
8 DAY 3 SS 3.4: Additional Practice with Similar Figures A. Triangle ABC is similar to triangle PQR. 1. What is the scale factor from triangle ABC to triangle PQR? 2. What is the scale factor from triangle PQR to triangle ABC? 5. What is the measure of angle P? 3. What is the measure of angle A? 6. What is the length of side AB? 4. What is the measure of angle Q? 7. What is the length of side AC? B. Parallelograms ABCD and RSPQ are similar. 1. What is the scale factor from parallelogram ABCD to parallelogram RSPQ? 2. What is the scale factor from parallelogram RSPQ to parallelogram ABCD? 4. What is the measure of angle R? 5. What is the measure of side AD? 3. What is the measure of angle D? C. Judy lies on the ground 45 feet from her tent. Both the top of the tent and the top of a tall cliff are in her line of sight. Her tent is 10 feet tall. About how high is the cliff? Assume the two triangles are similar. (If you need help, look at your homework notes on nested triangles). 8
9 D. Find each missing side length in the nested triangles. E. The right triangles are similar. 1. Find the length of side RS. 2. Find the length of side RQ. 3. The measure of angle x is 40 degrees. 7. What is the measure of angle R? 4. What is the angle relationship between angle x and angle y? 8. What is the angle relationship between angle z and the 80 degree angle? 5. What is the measure of angle y? 9. What is the measure of angle z? 6. What do the angles in a triangle add up to? 10. What is the measure of angle Q? 9
10 Day 3 HOMEWORK: Complete and Correct with the EDpuzzle #1 a. Outline the two different triangles. b. Set up a proportion: 14 x c. Solve for x: #2 a. Outline the two different triangles in different colors. b. Set up a proportion c. Solve for x: x #3 x 5 a. Outline the two different triangles in different colors. b. Set up a proportion c. Solve for x: 10
11 Day 4 HOMEWORK: Complete the notes from the EDpuzzle for SS 4.1 You can use to describe and compare shapes. A ratio is a of two quantities, such as two lengths. The rectangle around the original figure is about 10 centimeters tall and 8 centimeters wide. You can say, The ratio of height to width is 10 to 8. You can also write a ratio as a. You can enlarge or reduce the size of the original and produce these images. The table gives the ratios of height to width for the images: The comparisons 10 to 8 and 5 to 4 are ratios. Equivalent ratios are like equivalent. When you create equivalent ratios (or equivalent fractions), you multiply the numerator (top number) and denominator (bottom number) by the same number. You can think of this as a. You can express equivalent ratios with equations (be sure to match up corresponding sides). A is an equation stating that two ratios are. What if you want to draw a new figure that is similar to the original (10 cm high by 8 cm wide), though you want the image to b 15 centimeters high. How wide should the image be? 1. Set up a proportion (two ratios) comparing corresponding sides and label the unknown value (x) = 2. Find the scale factor to create equivalent ratios 3. Find the unknown value 11
12 DAY 5 SS 4.1 Ratios within Similar Rectangles A. Which rectangles are similar? Explain your reasoning. 1. For each rectangle, find the ratio of the length of a short side to the length of a long side. Rectangle A Ratio of Length of Short Side to Length of Long Side Fraction (Simplify, if possible) This rectangle is similar to B C D 2. What do you notice about the ratios for similar rectangles? 3. What do you notice about the ratios for non-similar rectangles? 4. Choose two similar rectangles. Find the scale factor from the smaller to the larger rectangle. What does the scale factor tell you? 5. Compare the information given by the scale factor to the information given by the ratios of side lengths. 12
13 Day 5 HOMEWORK: Complete the notes from the EDpuzzle for SS 4.2 A. The rectangles at right are similar. 1. What is the scale factor from Rectangle A to Rectangle B? 2. Complete the following sentence in two different ways. Use the side lengths of Rectangles A and B. The ratio of to is equivalent to the ratio of to. The ratio of to is equivalent to the ratio of to. 3. What is the value of x? Explain your reasoning. 4. What is the ratio of the area of Rectangle A to the area of Rectangle B? B. Which pairs of rectangles are similar? 1. For each pair of similar rectangles, find the scale factor from the larger rectangle to the smaller rectangle. 2. For each pair of similar rectangles, find the scale factor from the smaller rectangle to the larger rectangle. 3. For each similar pair of rectangles, find the ratio of the area of the larger rectangle to the area of the smaller rectangle. 13
14 DAY 6 SS 4.2: Ratios within Similar Triangles A. Look at triangles A-D below. Which triangles are similar? Explain your reasoning. 1. For each triangle, find the ratio of shortest side to longest side, and the ratio of shortest side to middle side. Triangle A Ratio (Short: Long) Ratio (Short: Middle) This triangle is similar to B C D 2. What do you notice about the ratios for similar triangles? 3. What do you notice about the ratios for non-similar triangles? 4. Choose two similar triangles. Find the scale factor from the smaller to the larger triangle. What does the scale factor give? 5. Compare the information given by the ratios of the side lengths and the information given by the scale factor. 14
15 Day 6 HOMEWORK: Correct with the KEY Use scale factors and/or proportions to find the missing value in each pair of similar figures. 15
16 DAY 8 SS 4.3: Finding Missing Parts Using Similarity to Find Measurements When two figures are similar, you can find missing lengths in two ways: 1. Use the scale factor from one figure to the other. 2. Use the ratios of the side lengths within each figure to make a proportion. A. Find the missing side lengths in the similar figures. Explain how you know your answer is correct. Similar Triangles: Similar Rectangles: B. The figures at right are similar. 1. Find the value of x. Explain how you found it. 2. Find the value of y. Explain how you found it. 3. Find the area and perimeter of the smaller figure. 4. Use the area and perimeter of the smaller figure and the scale factor to find the area and perimeter of the larger figure. 16
17 C. Find the missing values in the similar figures: The Washington Monument is the tallest structure in Washington, DC. At a certain time, the monument casts a shadow that is about 500 feet long. At the same time, a 40-foot flagpole nearby casts a shawdow that is about 36 feet long. About how tall is the monument? Sketch a diagram and then find the missing value. Deacon uses the shadow method to estimate the height of a flagpole. He finds that a 5-foot stick casts a 4-foot shadow. What is the height of the flagpole? Sketch a diagram and then find the missing value. 17
18 Day 8 HOMEWORK: Correct with the KEY: Find the missing value in each equivalent fraction. 18
19 Extra Practice: Solve each proportion (equivalent ratios). You may find it helps to simplify ratios, if possible, before finding a scale factor (see example). 19
20 20
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