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Assessment Items
1. The Larson family just built a rectangular sandbox in their backyard. The sandbox is
2 feet deep, 4 feet wide, and 5 feet long. How much sand would they need to fill the
sandbox to the top?
A.
B.
C.
D.
11 cubic feet
40 cubic feet
56 cubic feet
76 cubic feet
2. Mr. Perez just purchased the fish tank shown below for his science classroom.
Using the measurements given in the picture, determine how much water is needed
to completely fill the fish tank.
12 inches
8 inches
24 inches
A.
B.
C.
D.
44 cubic inches
288 cubic inches
672 cubic inches
2,304 cubic inches
3. The juice box shown below holds 180 cubic cm of juice. The length of the box is 6
cm and the width is 3 cm, then what is the height of the box?
A.
B.
C.
D.
9 cm
10 cm
20 cm
71 cm
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Assessment Materials Page 1 of 19
4. Crunchy Cereal is packaged in a rectangular box that is 2 ½ inches wide, 7 ½ inches
long and 10 ½ inches high. Their leading competitor, Flakey Cereal, is packaged in
a rectangular box that is 2 inches wide, 7 inches long and 11 inches high. How do
the volumes of these two cereal packages compare?
A. The volume of Crunchy Cereal is larger.
B. The volume of Flakey Cereal is larger.
C. It is not possible to compare the volumes.
D. The volumes of Crunch Cereal and Flakey Cereal are the same.
5. Emiko wants to wrap the book she bought as a gift for her friend. Using the picture
of the book and its measurements shown below, how much wrapping paper will
Emiko need to wrap the book?
A.
B.
C.
D.
12 square inches
28 square inches
39 square inches
78 square inches
7 inches
1 inch
4 inches
6. Riley and Sarah built a tree house in a big elm tree in their backyard. The tree
house has four walls, a floor, and a flat roof all made out of wood. It measures 4
meters wide, 6 meters long, and 2.5 meters tall. How much wood did Riley and
Sarah use to build the tree house?
A.
B.
C.
D.
12.5 square meters
49 square meters
60 square meters
98 square meters
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Assessment Materials Page 2 of 19
7. Each of the rectangular boxes shown below hold the same amount of rice, but the
measurements of the boxes are all different. Which box has the smallest surface
area?
B
4 cm
A
6 cm
2 cm
1 cm
6 cm
1 cm
3 cm
2 cm
C
D
1 cm
12 cm
2 cm
4 cm
A. Box A
B. Box B
C. Box C
D. Box D
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Assessment Materials Page 3 of 19
8. Terry is making a cake with dimensions of 15 inches x 11 inches x 2 inches. If a
container of frosting covers 250 square inches, will Terry have enough frosting to
cover the top and four sides of the cake with one container of frosting?
•
Calculate the surface area of the top and four sides of the cake.
•
Determine whether Terry will have enough frosting for the cake.
•
Show work to support your answer using words, numbers and/or pictures.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
Is there enough frosting? ________
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Assessment Materials Page 4 of 19
9. The rectangular prism below has a volume of 12 cubic units. If a, b, and c are
whole numbers, find one possible length (a), width (b), and height (c), and then
calculate the surface area for the rectangular prism.
c
b
a
Show your work to support your answer using words, numbers, and/or pictures.
Length (side a) =
Width (side b) =
Height (side c) =
Surface Area =
Boxed In!
__________
__________
__________
__________
Assessment Materials Page 5 of 19
10. One small can of metallic paint covers 15 square feet. Jessie is going to paint the
outside of her toy chest. She will use two coats of paint to cover the entire toy
chest.
1.5 feet
2 feet
3 feet
How many small cans of paint will Jessie need to buy to paint the toy chest?
Show your work to support your answer using words, numbers, and/or pictures.
Length (side a) = __________
Width (side b) = __________
Height (side c) = __________
Jessie will need to buy __________ cans of paint.
Surface Area = __________
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Assessment Materials Page 6 of 19
11. Martin needs to buy wrapping paper for a gift for his mom. The gift fits into each of
the boxes shown below. Wrapping paper is expensive and Martin needs to use
the box that requires the least amount of wrapping paper.
Box A
Box B
16 cm
10 cm
6 cm
6 cm
14 cm
8 cm
Which box should Martin use? Explain your answer.
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
Martin should use Box _____
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Assessment Materials Page 7 of 19
12. Colton uses a backpack to carry his textbooks and binder. The backpack is 8
inches wide, 12 inches long, and 15 inches tall. Colton’s textbooks and binder fit
into his backpack and have the following measurements:
Binder
Mathematics
Social Studies
Science
Language Arts
Height
13 in.
11 in.
13 in.
11 in.
11 in.
Length
12 in.
8 in.
8 in.
8½ in.
8 in.
Width
2 in.
1 in.
2 in.
1 in.
2 in.
After Colton puts these items into his backpack, how much space is left in his
backpack to put other items like gloves, hat, and snacks? Give the dimensions of
the biggest lunchbox he could fit into the backpack when all of his books are in the
backpack.
Show your work to support your answer using words, numbers, and/or pictures.
Additional work space on next page
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Assessment Materials Page 8 of 19
Additional work space
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
____________________________________________________________________
Amount of space left for other items
Lunchbox Dimensions:
Boxed In!
_______
Length ______ Width ______ Height ______
Assessment Materials Page 9 of 19
13. A gardener has 84 square feet of plywood and 2 cubic yards of soil. She wants to
build a rectangular planter box with four sides and a bottom in her backyard using
these materials. The gardener wants a rectangular planter box that will give her
the largest planting surface or dirt area to plant. What would the length, width, and
height of the planter box need to be in order to accomplish this and use all of the
soil she has?
Make sure your answer uses all of the wood and soil.
Describe or show how you found your answer using words, pictures, and/or
numbers.
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
Length = _________
Boxed In!
Width = _________ Height = __________
Assessment Materials Page 10 of 19
Boxed In!
Assessment Items
Answer Key
1. The Larson family just built a rectangular sandbox in their backyard. The sandbox is
2 feet deep, 4 feet wide, and 5 feet long. How much sand would they need to fill the
sandbox to the top?
A.
B.
C.
D.
11 cubic feet
40 cubic feet
56 cubic feet
76 cubic feet
(2 ft. + 4 ft. + 5 ft.)
(Correct answer: 2 ft. x 4 ft. x 5 ft.)
(2 x 2 ft. x 4 ft. + 2 x 2 ft. x 5 ft. + 1 x 4 ft. x 5 ft.) No top
(2 x 2 ft. x 4 ft. + 2 x 2 ft. x 5 ft. + 2 x 4 ft. x 5 ft.)
2. Mr. Perez just purchased the fish tank shown below for his science classroom.
Using the measurements given in the picture, determine how much water is needed
to completely fill t the fish tank ?
12 inches
8 inches
24 inches
A.
B.
C.
D.
44 cubic feet
288 cubic feet
672 cubic feet
2,304 cubic feet(
(12 in. + 8 in. + 24 in.)
(24 in. x 12 in.)
(2 x 12 in. x 8 in. + 2 x 12 in. x 24 in. + 2 x 8 in. x 24 in.)
Correct answer: 12 in. x 8 in. x 24 in.)
3. The juice box shown below holds 180 cubic cm of juice. The length of the box is
6 cm and the width is 3 cm. What is the height of the box?
A.
B.
C.
D.
9 cm
10 cm
20 cm
71 cm
Boxed In!
(6 cm + 3 cm)
(Correct answer: 180 cm³ ÷ (6 cm x 3 cm))
(180 cm³ ÷ (6 cm + 3 cm))
(180 cm³ - 6 cm – 3 cm)
Assessment Materials Page 11 of 19
4. Crunchy Cereal is packaged in a rectangular box that is 2 ½ inches wide, 7 inches
long and 10 ½ inches tall. Their leading competitor, Flakey Cereal is packaged in a
rectangular box that is 2 inches wide, 7 inches long and 11 inches tall. How do the
volumes of these two cereal packages compare?
A. The volume of Crunchy Cereal is larger. (Correct Answer)
B. The volume of Flakey Cereal is larger.
C. It is not possible to compare the volumes.
D. The volumes of Crunch Cereal and Flakey Cereal are the same.
Crunchy Cereal’s volume: 2 ½ in. x 7 in. x 10 ½ in. = 183.75 cubic inches
Flakey Cereal’s volume: 2 in. x 7 in. x 11 in. = 154 cubic inches
5. Emiko wants to wrap the book she bought as a gift for her friend. Using the picture
of the book and its measurements shown below, how much wrapping paper will
Emiko need?
A.
B.
C.
D.
12 square inches(1 in. + 4 in. + 7 in.)
28 square inches(1 in. x 4 in. x 7 in.)
39 square inches(1 in.x4 in. + 1 in.x7 in. + 4 in.x7 in.)
78 square inches(Correct answer: 2 x 1 in. x 4 in. +
2 x 1 in. x 7 in. + 2 x 4 in. x 7 in.)
1 inch
7 inches
4 inches
6. Riley and Sarah built a tree house in a big elm tree in their backyard. The tree
house had four walls, a floor, and a flat roof all made out of wood. It was 4 meters
wide, 6 meters long, and 2.5 meters tall. How much wood did Riley and Sarah use
to build the tree house?
A.
B.
C.
D.
12.5 square meters
(4m + 6m + 2.5m)
49 square meters (4m x 6m + 4m x 2.5m + 6m x 2.5m)
60 square meters (4m x 6m x 2.5m)
98 square meters (Correct answer: 2 x 4m x 6m + 2 x 4m x 2.5m + 2 x
6m x 2.5m)
Boxed In!
Assessment Materials Page 12 of 19
7. Each of the rectangular boxes shown below hold the same amount of rice, but the
measurements of the boxes are all different. Which box has the smallest surface
area?
B
4 cm
2 cm
A
6 cm
1 cm
6 cm
1 cm
3 cm
2 cm
D
1 cm
12 cm
C
2 cm
4 cm
A. Box A (2 x 4cm x 6cm + 2 x 4cm x 1cm + 2 x 6cm x 1cm=68 square cm)
B. Box B (4 x 6cm x 2cm + 2 x 2cm x 2cm=56 square cm)
C. Box C (Correct answer:
2 x 3cm x 4cm + 2 x 3cm x 2cm + 2 x 2cm x 4cm=52 square cm)
D. Box D (2 x 2cm x 12cm+2 x 1cmx12cm +2 x 1cm x 2cm=76 square cm)
Boxed In!
Assessment Materials Page 13 of 19
Scoring Rubric Item 8
Strand: Measurement ME01
2-point response: The student shows an understanding of how to determine surface
area and then compare surface areas by doing the following:
• indicates 269 in² for the surface area of the frosting needed to frost 5 sides of the
cake
• shows work and/or explanation supporting the surface area calculated
• indicates that one container is NOT enough
• shows work and/or explanation supporting the shortage of frosting
Example:
Surface Area
Top of cake: 15 in. x 11 in. = 165 in.²
Sides of cake: 2 x 2 in. x 11 in. + 2 x 2 in. x 15 in. = 104 in.²
Total surface area: 165 sq. in. + 104 sq. in. = 269 sq. in.
Frosting Needed
Surface area of cake to be frosted 269 sq. in.
Frosting container covers
- 250 sq. in.
19 sq. in. of cake not frosted/short
Note: Allow one computation error as long as conceptual understanding is clear.
1-point response: The students does two or three of the following:
• indicates 269 in² for the surface area of the frosting needed to frost 5 sides of the
cake
• shows work and/or explanation supporting the surface area calculated
• indicates that one container is NOT enough
• shows work and/or explanation supporting the shortage of frosting
0-point response: The student shows very little or no understanding of how to
determine and compare surface area.
Boxed In!
Assessment Materials Page 14 of 19
Scoring Rubric Item 9
Strand: Measurement ME01
2-point response: The student shows an understanding of how to label
measurements of rectangular prisms to show understanding of the
relationships among linear dimensions, surface area, and volume of
rectangular prisms as well as how to use surface area to describe a
rectangular prism. The student shows these by doing the following:
• indicates one of the following as possible sets of dimensions for a rectangular
prism with 12 cubic units volume: 1u x 1u x 12u 1u x 2u x 6u 1u x 3u x 4u 2u x
2u x 3u
• shows work and/or explanation supporting the dimensions chosen
• indicates the correct corresponding surface area for the chosen set of dimensions
1u x 1u x 12u (4 x 12 x 1 + 2 x 1 x 1 = 50 square units)
1u x 2u x 6u (2 x 6 x 2 + 2 x 2 x 1 + 2 x 1 x 6 = 40 square units)
1u x 3u x 4u (2 x 3 x 4 + 2 x 4 x 1 + 2 x 3 x 1 = 38 square units)
2u x 2u x 3u (4 x 3 x 2 + 2 x 2 x 2 = 32 square units)
• shows work and/or explanation supporting the surface area
Example:
Dimensions/Volume
1u x 1u x 12u (1 x 1 x 12 = 12 cubic units)
1u x 2u x 6u (1 x 2 x 6 = 12 cubic units)
1u x 3u x 4u (1 x 3 x 4 = 12 cubic units)
2u x 2u x 3u (2 x 2 x 3 = 12 cubic units)
Surface Area
1u x 1u x 12u
1u x 2u x 6u
1u x 3u x 4u
2u x 2u x 3u
(4 x 12 x 1 + 2 x 1 x 1 = 50 square units)
(2 x 6 x 2 + 2 x 2 x 1 + 2 x 1 x 6 = 40 square units)
(2 x 3 x 4 + 2 x 4 x 1 + 2 x 3 x 1 = 38 square units)
(4 x 3 x 2 + 2 x 2 x 2 = 32 square units)
Note: Allow one computation error as long as conceptual understanding is clear.
1-point response: The students does two or three of the following:
• indicates one of the following as possible sets of dimensions for a rectangular
prism with 12 cubic units volume: 1u x 1u x 12u 1u x 2u x 6u 1u x 3u x 4u 2u x
2u x 3u
• shows work and/or explanation supporting the dimensions chosen
• indicates the correct corresponding surface area for the chosen set of dimensions
1u x 1u x 12u (4 x 12 x 1 + 2 x 1 x 1 = 50 square units)
1u x 2u x 6u (2 x 6 x 2 + 2 x 2 x 1 + 2 x 1 x 6 = 40 square units)
1u x 3u x 4u (2 x 3 x 4 + 2 x 4 x 1 + 2 x 3 x 1 = 38 square units)
2u x 2u x 3u (4 x 3 x 2 + 2 x 2 x 2 = 32 square units)
• shows work and/or explanation supporting the surface area
0-point response:
Boxed In!
The student shows very little or no understanding of how to
determine and compare surface area.
Assessment Materials Page 15 of 19
Scoring Rubric Item 10
Strand: Measurement ME01
2-point response: The student shows an understanding of how to determine surface
area and then compare surface areas by doing the following:
• indicates 27 square feet for the surface area of the toy chest
• shows work supporting the surface area calculated
• indicates that two cans of paint are needed
Example:
Surface Area
Front/back of toy chest: 2 x 2 feet x 3 feet = 12 square feet
Top/bottom of toy chest: 2 x 3 feet x 1.5 feet = 9 square feet
Sides of toy chest: 2 x 2 feet x 1.5 feet = 6 square feet
Total surface area: 12 square feet + 9 square feet + 6 square feet = 27 square feet
Paint Needed
Surface area to be painted
One paint can covers
27 square feet
- 15 square feet
12 square feet still to be covered
So, one more can is needed 12 – 15 = -3 square feet Will have paint left over to
cover 3 square feet
Note: Allow one computation error as long as conceptual understanding is clear.
1-point response: The students does two or three of the following:
• indicates 27 square feet for the surface area of the toy chest
• shows work supporting the surface area calculated
• indicates that two cans of paint are needed
0-point response: The student shows very little or no understanding of how to
determine and compare surface area.
Boxed In!
Assessment Materials Page 16 of 19
Scoring Rubric Item 11
Strand: Measurement ME01
2-point response: The student shows an understanding of how to compare the surface
area of two different rectangular prisms by doing the following:
• indicates 568 square cm for the surface area of Box A and 544 square cm for Box B
• shows work and/or explanation supporting the surface areas calculated
• indicates that Box B should be used by Martin as it would use the least amount of
wrapping paper
Example:
Surface Area
Box A (2 x 10cm x 14 cm + 2 x 10cm x 6cm + 2 x 14cm x 6cm = 568 square cm)
Box B (2x 8cm x 6cm + 2 x 8cm x 16cm + 2 x 16cm x 6cm = 544 square cm)
Wrapping Paper Needed
The surface area for Box B (544 square cm) is less than the surface area for
Box A (568 square cm), so Box B would use less wrapping paper
Note: Allow one computation error as long as conceptual understanding is clear.
1-point response: The students does two or three of the following:
• indicates 568 square cm for the surface area of Box A and 544 square cm for Box B
• shows work and/or explanation supporting the surface areas calculated
• indicates that Box B should be used by Martin as it would use the least amount of
wrapping paper
0-point response:
Boxed In!
The student shows very little or no understanding of how to
determine and compare surface area.
Assessment Materials Page 17 of 19
Scoring Rubric Item 12
Strand: Solves Problems Reasons Logically
(SR02)
Learning Target: (Construct Solutions) Select and organize relevant
information; use appropriate concepts and procedures from number sense,
measurement, geometric sense, probability and statistics, and algebraic
sense; use a variety of strategies and approaches; determine whether a
solution is viable, mathematically correct, and answers the question(s) asked
(GRE 2.2.1, 2.2.2, 2.2.3, and 2.2.4)
4-point response demonstrates mathematical reasoning by doing the following:
• Includes volume calculations of all six (6) items: lunchbox, backpack, mathematics,
social studies, science, and language arts textbooks.
Backpack: 15 x 12 x 8 = 1,440 cubic inches Binder: 13 x 12 x 2 = 312 cubic in.
Mathematics: 11 x 8 x 1=88 cubic inches
Science: 11 x 8.5 x 1=93.5 cubic in.
Lang. Arts: 11 x 8 x 2=176 cubic inches Social Studies: 13 x 8 x 2=208 cubic in.
Lunchbox: 12 x 8 x 2 = 192 cubic inches
Space left over: 1,440-312-88-93.5-176-208 = 562.5 cubic inches
• Presentation has a layout that is clear, organized, and sequencing is appropriate.
• Calculations are appropriate and accurate.
• Support and justification with a mathematical model and/or work is given for
possible dimensions of lunchbox.
3-point response includes three of the four listed above.
2-point response includes two of the four listed above.
1-point response includes one of the four listed above.
0-point response shows little or no mathematical understanding of the task.
Boxed In!
Assessment Materials Page 18 of 19
Scoring Rubric Item 13
Strand: Communicates Understanding
(CU02)
Learning Target: (Organize, Represent and Share Information) Organize,
clarify, and refine mathematical information for a given purpose; apply
communication skills to clearly and effectively express or present ideas and
situations using mathematical language or notation (4.2.1, 4.2.2)
4-point response demonstrates mathematical communication by doing the following:
• Includes all three (3) components: plywood, soil, and dimensions (length, width,
and height)
• Presentation has a layout that is clear, organized, includes identifications, and
sequencing is appropriate.
• Labels for at least two of the three components (ft., ft.², and ft.³) are used
sufficiently to demonstrate understanding of and appropriate use.
• Conversions between measurements such as cubic yards to cubic feet, and
calculations are appropriate and accurate.
Example: 2 cubic yards = 1 yard x 1 yard x 2 yards
= 3 feet x 3 feet x 6 feet
= 54 cubic feet
Possible dimensions: 2 x 3 x 3
or 1 x 6 x 9
Surface area:
4 x 2 feet x 3 feet + 2 x 3 feet x 3 feet=42 square feet
Correct answer: 2 x 1 foot x 6 feet + 2 x 1 foot x 9 feet + 2 x 6 feet x 9 feet
=84 square feet
3-point response includes three of the four listed above.
2-point response includes two of the four listed above.
1-point response includes one of the four listed above.
0-point response shows little or no mathematical understanding of the task.
Boxed In!
Assessment Materials Page 19 of 19