7th Grade Common Core
Name (s) ______________________________________
Class_______________
Date_______________________________
ERROR ANALYSIS
GEOMETRY
WORD PROBLEMS
©Exceeding the CORE
Includes:
* Angles * Triangles
* Scale Drawings
* Area and Circumference of a Circle
* Volume of Prisms and Pyramids
* Surface Area of Prisms and Pyramids
Question # 0
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 60
=
4
𝑥
x = 240
The model measures 240 inches.
Correct Work/ Solution
Share a Strategy
Question # 1
©Exceeding the CORE
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.
A ramp makes an angle of 19˚ with respect to the ground as shown below. What is the value of x?
Incorrect Work/Solution
Identify and Explain the Error
19 = x – 50
+50
+ 50
69 = x
The value of x is 69.
Correct Work/ Solution
Share a Strategy
Question # 2
©Exceeding the CORE
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.
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°.
Incorrect Work/Solution
Identify and Explain the Error
47+ x = 180
-47
-47
x= 133
The third angle of the triangular support
measures 133°.
Correct Work/ Solution
Share a Strategy
Question # 3
©Exceeding the CORE
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.
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.
Incorrect Work/Solution
Identify and Explain the Error
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.
Correct Work/ Solution
Share a Strategy
Question # 4
©Exceeding the CORE
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.
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.
Incorrect Work/Solution
Identify and Explain the Error
d = 50  r = 25
A = 𝜋𝑟2
A = 𝜋 (25)2
A = (3.14)(50)
A = 157
Johnathan will need to paint 157 square feet.
Correct Work/ Solution
Share a Strategy
Question # 5
©Exceeding the CORE
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.
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.
Incorrect Work/Solution
Identify and Explain the Error
1
𝐴 = 𝜋𝑟 2
2
1
𝐴 = 𝜋(16)2
2
𝐴 = 0.5(3.14)(256)
𝐴 ≈ 401.9
The area of Sandra’s window is 401.9 square
inches.
Correct Work/ Solution
Share a Strategy
Question # 6
©Exceeding the CORE
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 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?
Incorrect Work/Solution
Identify and Explain the Error
V = Bh
V = 6(5)
(1.2)
2
30
V = (1.2)
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.
Correct Work/ Solution
Share a Strategy
Question # 7
©Exceeding the CORE
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.
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.
Incorrect Work/Solution
Identify and Explain the Error
1
V=3 𝐵ℎ
1
V=3 (9)(6)
1
V=3 (54)
V=18
The volume of the glass pyramid is 18 cubic
inches.
Correct Work/ Solution
Share a Strategy
Question # 8
©Exceeding the CORE
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.
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?
Incorrect Work/Solution
Identify and Explain the Error
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.
Correct Work/ Solution
Share a Strategy
Question # 9
©Exceeding the CORE
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.
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?
Incorrect Work/Solution
B= 2.52 = 6.25
P = 2.5 +2.5 = 5
Identify and Explain the Error
1
S.A. = 𝐵 + 𝑃𝑙
2
1
S.A. = 6.25 + (5)(3)
2
S.A. = 13.75
The surface area of the perfume bottle is 13.75
square inches.
Correct Work/ Solution
Share a Strategy
Question # 10
©Exceeding the CORE
Name (s) ______________________________________
Class_______________
Date_______________________________
Error Analysis – GEOMETRY
Answer Key
1.
2.
Error
Correct Sample Work
Correct Answer
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
x
=
4 60
The model measures 15 inches.
These angles are not congruent. They are
supplementary. Therefore the sum of the angles
is 180.
4x = 60
x= 15 inches
19 + x – 50 = 180
The value of x is 211.
19 – 50 + x = 180
– 31 + x = 180
+ 31
+31
x = 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°.
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.
90 + 47 + x = 180
137 + x = 180
-137
-137
x = 43
C =d 𝜋
C=3𝜋
C = 3(3.14)
C = 9.42
C ≈ 9.4
The third angle of the triangular
support measures 43°.
Marcia needs to use 9.4 feet of
fencing.
Question # 11
©Exceeding the CORE
Name (s) ______________________________________
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.
6.
The formula incorrectly uses the diameter to
calculate the area. The radius of the semicircle must be used when finding the area.
The diameter, 16 inches, should have been
divided by 2.
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.
7.
8.
9.
10.
Class_______________
Date_______________________________
d = 50  r = 25
A = 𝜋𝑟2
A = 𝜋 (25)2
A = (3.14)(625)
A = 1,962.5
1
𝐴 = 𝜋𝑟 2
2
1
𝐴 = 𝜋(8)2
2
𝐴 = 0.5(3.14)(64)
𝐴 ≈ 100.5
V = Bh
V = (6)(5)(1.2)
V = (30)(1.2)
V = 36
Johnathan will need to paint
1,962.5 square feet.
The area of Sandra’s window is
100.5 square inches.
1
This area of the rectangular base of the
V=3 𝐵ℎ
pyramid was not included in this solution The
1
V=3 (9 ⋅ 5)(6)
area of the rectangular base is 9 x 5 or 45
1
V= (45)(6)
cubic feet.
3
V=90
The volume of the glass pyramid is 90 cubic
inches.
The surface area of the box must be
calculated to determine the amount of paper S.A. = 2𝑙ℎ + 2𝑙𝑤 + 2ℎ𝑤
= 2(9.5)(13) + 2 (9)(7) +2(13)(7)
needed to cover the box. This solution
= 247 + 126 + 182
incorrectly uses the formula for volume.
= 555
Volume determines the amount of space
inside the box.
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
1
S.A. = 𝐵 + 𝑃𝑙
2
P = 4(2.5) = 10
The sandbox will hold 36 cubic
feet of sand. Jodi did not
purchase enough sand to fill the
sandbox to the top.
The GEOMETRY of rolling a 6 and
1
choosing an M .
42
Larry will need 555 square
inches of paper to wrap the
cardboard box.
The surface area of the perfume
bottle is 21.25 square inches.
1
S.A. = 6.25 + 2 (10)(3)
S.A. = 21.25
Question # 12
©Exceeding the CORE
Name (s) ______________________________________
Class_______________
Date_______________________________
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©Exceeding the CORE