Algebra / Geometry II: Unit 7- Similar Figures
SUCCESS CRITERIA:
1. Use units of measure to to solve ratios and proportions
2. Use proportions to solve real world problems.
INSTRUCTOR: Craig Sherman Hidden Lake High School
Westminster Public Schools
EMPOWER Recorded TARGET SCALE THEME
MA.10.G.02.04 Similarity Transformations
MA.10.G.03.04 Theorems Involving Similarity
PROFICIENCY SCALE:
SCORE REQUIREMENTS
4.0 In addition to exhibiting Score 3.0 performance, in-depth inferences and applications that go BEYOND what was taught in class.
Score 4.0 does not equate to more work but rather a higher level of performance.
3.5 In addition to Score 3.0 performance, in-depth inferences and applications with partial success.
3.0 The learner exhibits no major errors or omissions regarding any of the information and processes (simple or complex) that were explicitly taught.
oSimplify a ratio, AND
o Solve a proportion, AND
o Use proportions to solve real world problems, AND
o Solve real word problems using similarity.
2.0 Can do one or more of the following skills / concepts:
There are no major errors or omissions regarding the simpler details and processes as the learner…
oSimplify a ratio, OR
o Solve a proportion, OR
o Use proportions to solve real world problems, OR
o Solve real word problems using similarity.
1.0 Know and use the vocabulary
- Identify the Basic Elements
- With help, a partial understanding of some of the simpler details and process
Ratios and Proportions
WORD or CONCEPT / DEFINITION or NOTES / EXAMPLE or GRAPHIC REPRESENTATIONratio
proportion
INSTRUCTION 1: KHAN: Ratios INSTRUCTION 4: SOPHIA: Ratios
INSTRUCTION 2: KHAN: Proportions INSTRUCTION 5: SOPHIA: Ratio and Proportions
INSTRUCTION 3: KHAN: Ratio ,Proportions ,Units
Class work
Simplify the ratio.
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1. 15 in to 45 in
2. 27yd to 6yd
3. 12 days to 4 weeks
4. 6 years to 1 decade
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Solve the proportion
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5.
6.
7.
8.
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PMI-NJ Center for Teaching & Learning ~1~ NJCTL.org
9. The scale on the blueprint of a house is 0.04in = 1 foot. If the width of the kitchen on the blueprint is 1 inch, what is the actual width of the kitchen?
10. There are 350 people at the school basketball game. The ratio of the students to adults is 6:1. How many students attended the game?
Homework
Simplify the ratio.
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11. 40 feet to 12 feet
12. 8 days to 14 days
13. 150 feet to 1 mile
14. 20 ounces to 3 pounds
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Solve the proportion.
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15.
16.
17.
18.
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19. Mike, Angela, and Victor have $160 in a ratio of 7:5:4. How much do they each have?
20. You made a 3-foot model of your home, using a scale of 1:42. What is the actual height of your home?
Solve Problems using Similarity
INSTRUCTION 1: YOU TUBE: Shadow Problems
NOTES:
Class work
21 A basketball hoop in your backyard casts a shadow 109 inches long. You are 5 feet 8 inches tall and cast a shadow 62 inches long. Find the height of the basketball hoop in inches. Round your answer to the nearest whole number.
22. You want to know the approximate height of a very tall pine tree. You place a mirror on the ground and stand where you can see the top of the tree in the mirror. How tall is the tree? The mirror is 24 feet from the base of the tree. You are 24 inches from the mirror and your eyes are 6 feet above the ground. Round your answer to the nearest tenth.
23. To find the distance d across a lake, you locate the points as shown. Find d. Round your answer to the nearest tenth.
Homework
24. A yardstick casts a shadow 1 ft long. A nearby tree casts a 16 ft shadow. How tall is the tree? Round your answer to the nearest tenth.
25. You want to know the approximate height of a tall oak tree. You place a mirror on the ground and stand where you can see the top of the tree in the mirror. How tall is the tree? The mirror is 24 feet from the base of the tree. You are 36 inches from the mirror and your eyes are 5 feet above the ground. Round your answer to the nearest tenth.
26. To find the distance d across a lake, you locate the points as shown. Find d. Round your answer to the nearest tenth.
Similar Figures Unit Review
Multiple Choice –
Choose the correct answer for each question. No partial credit will be given.
1. Simplify the ratio 15 inches to 3 inches.
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a. 15 to 9
b. 1:5
c. 5/3
d. 5/1
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2. Solve the proportion.
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a. 30
b. 54
c. 24
d. 27
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3. Solve the proportion.
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a. x = 5
b. x = -5
c. x = 1
d. x = 0.5
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Short Constructed Response - Write the answer for each question. No partial credit will be given.
4. The scale on a map of the US, 1 inch = 250 miles. New York is 12 inches from California. What is the actual distance between the cities.
5. Your school casts a shadow 30 feet long. At the same time a person 6 feet casts a shadow 4 feet long. Sketch and label a diagram. Find the height of your school. Round your answer to the nearest tenth.
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Geometry-Similar Figures ~30~ NJCTL.org