5.MD.5b
Volume Problem Solving Cards
Materials: Problem Solving Cards (6)
Problem Solving Blank Sheets (1 per student) or Notebooks-for student work
Pencils
Calculators
Answer Key
Self-Assessment
Time: 50-60 minutes
Objective: Students will be able to solve real-life application problems using the volume
formula. Students will be able to determine the volume, length, width, or height of an
object, depending on the information they were given.
Management: Students can either work in pairs or individually.
Pairs Suggestion:
1. The cards can be located at stations throughout the room. When students
answer the problem, they can move to the next station to answer the next
problem.
*Since cards are not in a specific order, they are not numbered. Instead
they have a picture symbol in the top to match with the answer key.
2. Continue problem solving with partners until all of the cards have been
completed.
3. You can either walk around the room using the observation checklist while
students are working in various stations, or you could set up one station where
you will sit and observe a specific problem of your choosing.
4. Allow the students to self-check their answers with the answer key and complete
the self-assessment.
Individual Suggestion:
1. Choose one or two problems of which you would like to assess the students’
understanding as a summative assessment.
2. Allow the students to complete the others as classwork/homework.
5.MD.5b
Mrs. Smith has a cabinet to store her classroom games. It is 40
inches wide, 16 inches deep, and 30 inches high. What is the
volume of the cabinet?
If a typical board game box measures 20 inches long, 8 inches wide,
and 15 inches high, what is the volume of the board game?
How many board games would fit in
the cabinet?
5.MD.5b
The Rodriguez’s built a new deck in their backyard. To keep it clean, they
purchased a storage box to store the hoses, sprinklers, and gardening
tools.
When they purchased it from Keep It Organized website, the dimensions
listed were: 5 feet long, 2 feet wide, and 3 feet tall.
Their son, Daniel, wanted to calculate the volume before it was shipped
to their house. He thought it was going to be 10 cubic feet. However, he
was surprised when it arrived because it was much larger.
What is the volume of the storage box?
What was Daniel’s error?
5.MD.5b
Jason wants to buy the most spacious compact car possible. He
decides to base his decision on the car with the greatest volume. He
looks at the dimensions of each car before he test drives one.
Jason believes he should buy Car #2, although the difference in the
heights of the cars is important to him, too. He is tall and does not
want his head to touch the roof.
Calculate the height of each car to decide which one is
the best car to buy based on the information in the table.
Car
1
2
Volume
Length
Width
706,112 cu.in.
706,230 cu.in.
176 in.
177 in
68 in.
70 in.
Height
A 50-pound bag of sand fills 1 cubic foot.
The height of a rectangular sandbox is 12 inches and the width of
the sandbox is 36 inches.
If it takes 12 bags of sand to fill the whole sandbox, what is the
length of the sandbox?
5.MD.5b
A shipping company packs merchandise in standard shipping boxes
measuring 2 feet by 3 feet by 2 feet. If there is extra space in the box,
workers fill it in with packing peanuts to ensure the merchandise is safe
and does not break.
If the merchandise box is 1 foot by 2 feet by 2 feet and it is packed
inside the shipping box, what remaining volume needs to be packed
with packing peanuts?
You have been hired by Fruity Fruit Juice Company to design a box
that holds juice. Your boss prefers small containers so that it is easy
for the children to hold.
If the container holds 24 cubic inches, list two possible sets of
dimensions for the juice box.
Choose which box dimension would be best
and explain your reasoning.
5.MD.5b
Student Work
Student Work
5.MD.5b
Student Work
Student Work
5.MD.5b
Student Work
Student Work
5.MD.5b
Volume of the bookshelf = 40 x 16 x 30 = 19,200 cubic inches
Volume of the board game = 20 x 8 x 15 = 2,400 cubic inches
19,200 ÷ 2,400 = 8 games
OR
2,400 x 8 = 19,200
Volume of storage box: 5 x 2 x 3 = 30 cubic feet
Daniel added the length, width, and height instead of
multiplying them
Car 1:
Car 2:
176 x 68 x height = 706,112
177 x 70 x height = 706,230
11,968 x height = 706,112
12,230 x height = 706,230
706,112 ÷ 11,968 = 59
706,230 ÷ 12,230 = 57
Height = 59 inches
Height = 57 inches
5.MD.5b
Height:will
12vary
inches = 1 foot
Reasons
Width: 36 inches = 3 feet
3 x 1 x length = 12 cubic feet
3 x length = 12 cubic feet
12 ÷ 3 = 4
Length = 4 feet or 4 inches
Shipping Box Volume:
2 feet x 3 feet x 2 feet = 12 cubic feet
Merchandise Box Volume:
1 foot x 2 feet x 2 feet = 4 cubic feet
To calculate the remaining volume for packing peanuts:
12 – 4 = 8 cubic feet OR v + 4 = 12
5.MD.5b
Possible Dimensions:
1 in x 1 in x 12 in
1 in x 2 in x 6 in
1 in x 3 in x 4 in
2 in x 2 in x 3 in
Reasons will vary
Student
Name: ___________________________________
Assessment: Volume Problem Solving Cards
Date: __________
Teacher: ________________________
Data:
Student’s overall score on assessment: ______________
Assessment will be retaken. Yes
No
Problem Solving Card
Calculate volume when length, width, height are given
Yes
No
Relate volume to the operations of multiplication to solve real-world problem by
determining the correct amount of games on the bookshelf
Calculate volume when length, width, height are given
Yes
Yes
No
No
Critique the reasoning of other by finding Daniel’s error and correcting it
Yes No
Calculate the height when the volume, length and width are given
No
Reason abstractly and quantitatively to decide the best car
Yes
Yes
No
Calculate the length when the volume, width and height are given Yes
Attend to precision (converted inches to feet)
Yes
No
No
Calculate volume when length, width, height are given Yes
No
Relate volume to the operations of addition to solve real-world problem by
determining the remaining volume left for packing peanuts
Found two possible dimensions for 12 cubic inches Yes
No
Yes
No
5.MD.5b
Reason abstractly and quantitatively to decide the best juice box
Strategy:
I did very well on….
I need to go back and work on….
Yes
No