Georgia Department of Education
Common Core Georgia Performance Standards Framework Teacher Edition
Sixth Grade Mathematics Unit 5
Name______________________________________ Date ______________________________
CULMINATING TASK: STEM Fish Tank Foam Packing Design
The STEM (Science, Technology, Engineering, and Math) Club had entered the Fish Tank
Experts foam packaging design competition. Lately, Fish Tank Experts have had to recall their
15-gallon fish tank equipment due to breakage during shipment. They have found that their
equipment is breaking because the foam that encases the tank needs to be thicker and stronger.
The Fish Tank Experts are looking for a way to increase the size of the foam without affecting
the volume of the box. Round all answers to the nearest hundredth of an inch.
The 15-gallon
fish tank measures 24 ¼ x 12 ½ x 12 ¾ inches.
1. What size box is needed to ship the 15-gallon fish tank? Round to the nearest hundredth
of an inch.
2. The new foam package should be ¼ inch thick, adding an additional ½ inch on each
dimension of 15-gallon fish tank so that there is room for the tank in the package.
a. What is the fractional edge length of the foam packaging?
b. What is the volume of the foam packaging?
3. What is the difference in the volume of fish tank and foam packaging?
4. The Fish Tank Experts has a supply of the following boxes (rectangular prism) that must
be used for packaging:
Box 1 – 24 ¾ inches long x 12 ¾ inches wide x 13 ¼ inches height
Box 2 – 25 inches long x 13 ¼ inches wide x 13 ½ inches height
Box 3 – 25 ½ inches long x 13 ¼ inches wide x 13 ¼ inches height
Box 4 – 25 ½ inches long x 13 ¼ inches wide x 13 ½ inches height
MATHEMATICS  GRADE 6  UNIT 5: Area and Volume
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
April 2012  Page 69 of 69
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework Teacher Edition
Sixth Grade Mathematics Unit 5
a. Predict which box will best fit the tank and its’ foam case for packaging.
b. What is the volume of each box?
c. For each box determine if it will accommodate the tank and its foam case for
packaging? Why or why not?
Boxes
Box 1
Box 2
Box 3
Box 4
Volume
Rationale
5. Determine the dimensions of the smallest possible box that Fish Tank Experts could use
to package their 15-gallon tanks.
a. How much empty space will there between the foam case and the box?
b. Prove your answer by drawing a representation of the net on grid paper or
constructing the boxes.
MATHEMATICS  GRADE 6  UNIT 5: Area and Volume
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
April 2012  Page 70 of 69
All Rights Reserved
Georgia Department of Education
Common Core Georgia Performance Standards Framework Teacher Edition
Sixth Grade Mathematics Unit 5
6. Use mathematics to explain how you determined your answer. Use words, symbols, or
both in your explanation.
a. What steps did you take to find the volume of the box needed to package the 15gallon fish tank and its foam case?
Use your solution from #6a to solve problems 7-8.
7. Using your solution from #7a, find the surface area and sketch the net of the box used to
package the 15-gallon tank.
a. Surface area of the 15-gallon tank
b. Sketch and label (front, back, top, bottom, left and right side) the net for this 15gallon tank
8. The front side of the box for the 15-gallon tank must display a design that will help Fish
Tank Experts showcase and sell their product.
a. What are the dimensions for the front side of the box?
b. Decrease the dimensions for the front side of the box by 1-inch? Dimensions?
c. Using rectangles, triangles, and special quadrilaterals, compose a design of an
irregular polygon using graph paper. You must follow these requirements:
(1) Use isometric dot or grid paper
(2) Create a border around your design using your dimension in #10b,
(3) Identify a scale (for example, using grid paper 1-cm = 1 square inch)
(4) Area of design must not exceed 288 inches2
d. Calculate the area of your design.
e. What steps did you take to find the area of your design? Use mathematics (words,
symbols, or both) to explain how you determined your answer.
f. Describe your design for Fish Tank Experts.
MATHEMATICS  GRADE 6  UNIT 5: Area and Volume
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
April 2012  Page 71 of 69
All Rights Reserved