Name_________________________________________________________
CCSS
8.EE.2
Date __________
Nested Boxes
You buy a set of 4 gift boxes with different sizes. Each box is cube-shaped. The
boxes can be stacked completely inside each other.
D
C
A
B
1. The volume of box A is 64 cubic inches. The circumference of a regulation
baseball is at least 9 inches but no more than 9.25 inches. Can a baseball fit
in box A? Explain.
2. Box B has a surface area of 216 square inches. What is the ratio of the side
length of box B to the side length of box A?
3. The ratios of the side lengths of B to A, C to B, and D to C are the same.
How much more space do the boxes occupy when stored separately in a
closet than when they are stacked inside each other in the closet?
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Big Ideas Math
Performance Tasks
3
CCSS
8.EE.2
Common Core State Standard
8.EE.2 Use square root and cube root symbols to represent solutions to
equations of the form x 2 = p and x3 = p, where p is a positive
rational number. Evaluate square roots of small perfect squares and
cube roots of small perfect cubes. Know that 2 is irrational.
CCSS
8.EE.2
Grading Rubric
Answers
Score
1. yes; The diameter of the baseball is less than the side length of
2
box A. So, it will fit inside.
2. 3 to 2
1
3. 1009 in.3
1
Precision
1. Student calculates and compares the diameter of the baseball and
3
the side length of box A.
2
2. Student calculates the side length of box B and writes a ratio.
3. Student uses the ratios to calculate the side lengths and volumes of
the boxes. Student uses a sum of volumes for the answer.
Total Points
4
Big Ideas Math
Performance Tasks
3
12
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All rights reserved.