Geo assessment ch-1-performance PDF

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Summary

homework for chapter 1 - questions for 2020-21...

Description

Name_________________________________________________________

Chapter

1

Date __________

Performance Task

Building Bridges Instructional Overview Launch Question

Beam, arch, truss, and suspension are all types of bridges. The type chosen for a specific span depends on many factors, including the length of the bridge and how it handles tension and compression. What mathematical concepts are involved in the complexities of building bridges?

Summary

This task applies basic geometric concepts included in the chapter to the construction of different types of bridges.

Teacher Notes

Students apply basic geometric concepts to the real world. To further explore the connection between geometry and the real world, have students research actual bridges, such as the Golden Gate Bridge in San Francisco, California, and how they are constructed.

Supplies

Handouts, Internet

Mathematical Discourse

What geometric shapes do you see in the bridges pictured throughout this task?

Writing/Discussion Prompts

What are the components engineers need to keep track of when they are designing a bridge? What are the benefits of using a suspension bridge rather than a beam bridge over a large span?

Curriculum Content Content Objectives

• Use the Segment Addition Postulate. • Find segment lengths using midpoints. • Use the Ruler Postulate. • Use the Midpoint Formula. • Use the Distance Formula. • Find perimeters of polygons in the coordinate plane. • Identify complementary and supplementary angles. • Use the Angle Addition Postulate to find angle measures. • Identify congruent angles.

Mathematical Processes

Mathematically proficient students apply the basic geometric concepts they know to find distances and angle measures used in the construction of different bridges.

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Geometry Assessment Book

13

Name _________________________________________________________ Date _________

Chapter

1

Performance Task (continued)

Rubric Building Bridges

Points

1. a. 27 ft b. 42 yd

4 1

Total possible points for each correct part

6

1

Total possible points for part (a) for part (b) for part (c) for part (d)

4 2

Total possible points for each correct part

4

The student correctly uses the postulates and formulas discussed in the chapter to answer each question. Partial credit may be awarded.

c. 1732 ft d. 688 m 2. a. 240 m b. yes; yes; AE = BC = 160 m, AB = CD = 40 c.

5m

3 1

(11, 6)

d. 80 + 80 5, or about 258.9 m 3. a. Sample answer: ∠ SVT ; ∠ TVU and ∠ TVR are supplementary angles, so m∠TVR = 90°. By the Angle Addition Postulate, m∠SVT + m∠SVR = 90°. b. 49°; Complementary angles have a sum of 90° and 90 ° − 41° = 49°. Mathematical Processes:

Mathematically proficient students apply the basic geometric concepts they know to find distances and angle measures used in the construction of different bridges. The students use multiple postulates and formulas they have learned to find different measurements. Total Points

14

Geometry Assessment Book

1

18 points

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Name_________________________________________________________

Chapter

1

Date __________

Performance Task (continued)

Building Bridges Beam, arch, truss, and suspension are all types of bridges. The type chosen for a specific span depends on many factors, including the length of the bridge and how it handles tension and compression. What mathematical concepts are involved in the complexities of building bridges? 1. The span of a bridge is the length of the bridge between supports. Find each distance. a. A footbridge has a span of 54 feet. A sign is

to be placed exactly halfway across the bridge. How far will the center of the sign be from each end of the bridge?

b. A beam bridge has a total length of

168 yards. The bridge is supported at both ends and has three additional supports in the water. What is the span between any two consecutive supports?

c. A suspension bridge has two support towers.

Each tower is 1152 feet from the end of the bridge. The total length of the bridge is 4036 feet. What is the span between the towers?

d. An arch bridge crosses a river. The bridge

is supported at each end and has seven additional supports in the water. The span of each arch is 86 meters. What is the distance across the river?

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Geometry Assessment Book

15

Name _________________________________________________________ Date _________

Chapter

1

Performance Task (continued)

2. The diagram to the right shows a truss bridge.

In the diagram, each unit represents 20 meters. a. What is the length of the bridge from point A

y 10

B

8

C

to point D? 6 4

b. Are A E and BC congruent? AB and CD ?

A

F

D

E

2

Explain. 0 0

2

4

6

8

10

12

14

x

c. What is the midpoint of EC ?

d. What is the perimeter of

ABF ?

3. Use the diagram below. The vertical posts are perpendicular to the floor of the bridge. T

S

41° R

V

U

a. Name a complementary angle to ∠SVR. Explain.

b. What is the measure of the angle you named in part (a)? Explain.

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Geometry Assessment Book

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Name_________________________________________________________

Chapter

1

Date __________

Performance Task (continued)

Teacher Notes:

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Geometry Assessment Book

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