name (s) class date geometry - cobb · pdf filejohnathan wants to paint the bottom of his...

Name (s) ______________________________________ Class_______________ Date_______________________________

Question # 0 ©Exceeding the CORE

7th Grade Common Core

Includes: * Angles * Triangles

* Scale Drawings * Area and Circumference of a Circle

* Volume of Prisms and Pyramids * Surface Area of Prisms and Pyramids

WORD PROBLEMS

ERROR ANALYSIS

GEOMETRY

Name (s) ______________________________________ Class_______________ Date_______________________________


Error Analysis – GEOMETRY Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then

share a strategy this student could use to prevent the same error in the future.

An engineer makes a model of a bridge using a scale of 1 inch = 4 yards. The length of the actual bridge is 60 yards. What is the length of the model?

Incorrect Work/Solution Identify and Explain the Error

x = the length of the model 1

4=

60

𝑥

x = 240 The model measures 240 inches.

Correct Work/ Solution Share a Strategy

Name (s) ______________________________________ Class_______________ Date_______________________________




A ramp makes an angle of 19˚ with respect to the ground as shown below. What is the value of x?


19 = x – 50 +50 + 50 69 = x The value of x is 69.


Name (s) ______________________________________ Class_______________ Date_______________________________




The supports of a picture frame is in the shape of a right triangle. Find the third angle of the triangle if the measure of one of the angles is 47°.


47+ x = 180 -47 -47 x= 133 The third angle of the triangular support measures 133°.


Name (s) ______________________________________ Class_______________ Date_______________________________




Marcia is placing a fence around the circular flower bed in her garden. The diameter of the flower bed is 3 feet. How much fencing should Marcia use? Use 3.14 for 𝝅. Round to the nearest tenth if necessary.


d = 3 r = 1.5 A = 𝜋𝑟2 A = 𝜋 (1.5)2

A =(3.14)(2.25) A = 7.065 A ≈ 7.1 Marcia needs to use 7.1 square feet of fencing.


Name (s) ______________________________________ Class_______________ Date_______________________________




Johnathan wants to paint the bottom of his swimming pool the color blue. The swimming pool has a diameter

of 50 feet. How many square feet will Johnathan need to paint? Use 3.14 for 𝝅.


d = 50 r = 25 A = 𝜋𝑟2

A = 𝜋 (25)2

A = (3.14)(50) A = 157 Johnathan will need to paint 157 square feet.


Name (s) ______________________________________ Class_______________ Date_______________________________




The window in Sandra’s dining room is in the shape of a semi-circle. The diameter of the window is 16 inches.

How many square inches is the window? Use 3.14 for 𝝅. Round to the nearest tenth.


𝐴 =1

2𝜋𝑟2

𝐴 =1

2𝜋(16)2

𝐴 = 0.5(3.14)(256)

𝐴 ≈ 401.9

The area of Sandra’s window is 401.9 square inches.


Name (s) ______________________________________ Class_______________ Date_______________________________



share a strategy this student could use to prevent the same error in the f4uture.

Jodi built a rectangular sandbox for her daughter. The sandbox measures 6 feet by 5 feet by 1.2 feet. Jodi purchases 20 cubic feet of sand to fill the sandbox. How much sand will the sandbox hold? Did Jodi purchase enough sand to fill the sandbox to the top?


V = Bh V = 6(5)

2(1.2)

V = 30

2(1.2)

V = (15)(1.2) V= 18 The sandbox will hold 18 cubic feet of sand. Jodi purchased enough sand to fill the sandbox to the top.


Name (s) ______________________________________ Class_______________ Date_______________________________




A glass pyramid has a height of 6 inches. Its rectangular base has a length of 9 inches and a width of 5 inches. Find the volume of glass used to create the pyramid.


V=1

3𝐵ℎ

V=1

3(9)(6)

V=1

3(54)

V=18 The volume of the glass pyramid is 18 cubic inches.


Name (s) ______________________________________ Class_______________ Date_______________________________




Larry is shipping a package in a cardboard box that measures 9.5 inches long, 13 inches high and 7 inches wide. He would like to wrap the box with paper. How much paper does Larry need?


V= 9.5 x 13 x 7 = 123.5 x 7 = 864. Larry will need 864.5 square inches of paper to wrap the cardboard box.


Name (s) ______________________________________ Class_______________ Date_______________________________




Tanya purchased a bottle of perfume that is in the shape of a square pyramid. The bottle has a slant height of 3 inches and base edges 2.5 inches long. What is the surface area of the bottle?


B= 2.52 = 6.25 P = 2.5 +2.5 = 5

S.A. = 𝐵 +1

2𝑃𝑙

S.A. = 6.25 +1

2(5)(3)

S.A. = 13.75 The surface area of the perfume bottle is 13.75 square inches.


Name (s) ______________________________________ Class_______________ Date_______________________________


Error Analysis – GEOMETRY Answer Key

Error Correct Sample Work Correct Answer

1. The proportion is not set up correctly. The number 60 should be in the denominator of the second ratio.

x = the length of the model 1

4=

x

60

4x = 60 x= 15 inches

The model measures 15 inches.

2. These angles are not congruent. They are supplementary. Therefore the sum of the angles is 180.

19 + x – 50 = 180 19 – 50 + x = 180 – 31 + x = 180 + 31 +31 x = 211

The value of x is 211.

3. The error in the solution is that the equation is missing the measurement of the right angle. Since, the support is in the shape of a right triangle, one of the angles measures 90°. The three angles in the triangle must have a sum of 180°.

90 + 47 + x = 180 137 + x = 180 -137 -137 x = 43

The third angle of the triangular support measures 43°.

4. The error in this solution is that the area of the flower bed was calculated instead of the circumference. Circumference measure the distance around the circle.

C =d 𝜋 C = 3 𝜋 C = 3(3.14) C = 9.42 C ≈ 9.4

Marcia needs to use 9.4 feet of fencing.

Name (s) ______________________________________ Class_______________ Date_______________________________


5. The error in this solution is that (25)2 was incorrectly simplified to 25(2) or 50. The expression (25)2 is equal to 25 x 25 or 625.

d = 50 r = 25 A = 𝜋𝑟2 A = 𝜋 (25)2

A = (3.14)(625) A = 1,962.5

Johnathan will need to paint 1,962.5 square feet.

6. The formula incorrectly uses the diameter to calculate the area. The radius of the semi-circle must be used when finding the area. The diameter, 16 inches, should have been divided by 2.

𝐴 =1

2𝜋𝑟2

𝐴 =1

2𝜋(8)2

𝐴 = 0.5(3.14)(64)

𝐴 ≈ 100.5

The area of Sandra’s window is 100.5 square inches.

7. The area of the base of the rectangular prism is calculated incorrectly. The area of the base is 6 x 5 or 30 cubic feet.

V = Bh V = (6)(5)(1.2) V = (30)(1.2) V = 36

The sandbox will hold 36 cubic feet of sand. Jodi did not purchase enough sand to fill the sandbox to the top.

8. This area of the rectangular base of the pyramid was not included in this solution The area of the rectangular base is 9 x 5 or 45 cubic feet.

V=1

3𝐵ℎ

V=1

3(9 ⋅ 5)(6)

V=1

3(45)(6)

V=90 The volume of the glass pyramid is 90 cubic inches.

The GEOMETRY of rolling a 6 and

choosing an M 1

42.

9. The surface area of the box must be calculated to determine the amount of paper needed to cover the box. This solution incorrectly uses the formula for volume. Volume determines the amount of space inside the box.

S.A. = 2𝑙ℎ + 2𝑙𝑤 + 2ℎ𝑤 = 2(9.5)(13) + 2 (9)(7) +2(13)(7) = 247 + 126 + 182 = 555

Larry will need 555 square inches of paper to wrap the cardboard box.

10. The error made in the solution to this problem is that the perimeter of the square base is not calculated correctly. The perimeter is 4(2.5) or 10 inches.

B= 2.52 = 6.25 P = 4(2.5) = 10

S.A. = 𝐵 +1

2𝑃𝑙

S.A. = 6.25 +1

2(10)(3)

S.A. = 21.25

The surface area of the perfume bottle is 21.25 square inches.

Name (s) ______________________________________ Class_______________ Date_______________________________


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