Answers
Teacher Copy
Activity 26
Volume
Crystal Collections
Lesson 26-1
Volume of Cubes
Learning Targets
Find the volume of a right rectangular prism with fractional edge lengths.
Write equations that represent problems related to the volume of right rectangular prisms.
Close Reading (Learning Strategy)
Definition
Reading text word for word, sentence by sentence, and line by line to make a detailed analysis of
meaning
Purpose
Assists in developing a comprehensive understanding of the text
Paraphrasing (Learning Strategy)
Definition
Restating in your own words the essential information in a text or problem description
Purpose
Assists with comprehension, recall of information, and problem solving
Think Aloud (Learning Strategy)
Definition
Talking through a difficult text or problem by describing what the text means
Purpose
Helps in comprehending the text, understanding the components of a problem, and thinking
about possible paths to a solution
Visualization (Learning Strategy)
Definition
p. 331
Picturing (mentally and/or literally) what is read in the text
Purpose
Increases reading comprehension and promotes active engagement with the text
Vocabulary Organizer (Learning Strategy)
Definition
Using a graphic organizer to keep an ongoing record of vocabulary words with definitions,
pictures, notes, and connections between words
Purpose
Supports a systematic process of learning vocabulary
Construct an Argument (Learning Strategy)
Definition
Use mathematical reasoning to present assumptions about mathematical situations, support
conjectures with mathematically relevant and accurate data, and provide a logical progression of
ideas leading to a conclusion that makes sense
Purpose
Helps develop the process of evaluating mathematical information, developing reasoning skills,
and enhancing communication skills in supporting conjectures and conclusions
Create a Plan (Learning Strategy)
Definition
Analyzing the tasks in a problem and creating a process for completing the tasks by finding
information needed for the tasks, interpreting data, choosing how to solve a problem,
communicating the results, and verifying accuracy
Purpose
Assists in breaking tasks into smaller parts and identifying the steps needed to complete the
entire task
Use Manipulatives (Learning Strategy)
Definition
Using objects to examine relationships between the information given
Purpose
Provides a visual representation of data that supports comprehension of information in a problem
Look for a Pattern (Learning Strategy)
Definition
Observing information or creating visual representations to find a trend
Purpose
Helps to identify patterns that may be used to make predictions
Suggested Learning Strategies
Close Reading, Paraphrasing, Think Aloud, Visualization, Vocabulary Organizer, Construct an
Argument, Create a Plan, Use Manipulatives, Look for a Pattern
Crystals are solids formed by a regular repeated pattern of molecules connecting together. p. 333p. 332
They have a regular shape and flat sides. Some crystals form cubes while others grow into
columns with three or more sides. The figures shown below are crystals.
The collected atoms that make up crystals are called unit cells. They are the simplest repeating
unit in the crystal and are repeated in exactly the same arrangement throughout the solid.
Opposite faces of a unit cell are parallel. A simple cubic unit cell is in the shape of a cube.
Cubes are named for the lengths of their edges:
A 1-inch cube is a cube with edges that are 1 inch in length.
A 2-inch cube is a cube with edges that are 2 inches in length.
1
1
A 2 -inch cube is a cube with edges that are 2 inch in length.
Any size cube can be used to build larger cubes.
Math Tip
The cube in the diagram is an a-unit cube. Each edge is a units long.
Volume is a measure of the amount of space a solid occupies. It is measured in cubic units, such
as cubic inches (in.3), cubic feet (ft3), cubic centimeters (cm3), or cubic meters (m3).
One way to find the volume of a solid is to fill the solid with cubes. The volume is the total
number of cubes needed to fill the solid.
1. Halite, or table salt, is a mineral that is made up of cubic crystals. Use unit cubes,
provided by your teacher, as models of 1-inch cubes.
a. Use the unit cubes to build models of 2-inch and 3-inch cubes. Then complete the
table.
Length of Edge (in.)
Area of Face (in.2)
Volume of Cube
(in.3)
1
2
3
b. Describe any patterns you see in the table.
2. Make use of structure. Describe how you can use the patterns you found in the table to
determine the volume of a cube when you do not have enough unit cubes to build the
cube.
3. Let the variable e represent the length of the edge of a cube. Write a rule for finding the
volume, V, of a cube in terms of the length of an edge, e.
4. Model with mathematics. Print and cut out the nets of cubes, Figure 1 and Figure 2, on
page 341.
a. Fold each figure to form a cube.
b. How many of the smaller cubes made from Figure 1 will fit into the larger cube made
from Figure 2?
c. Look back at the table in Item 1. How many cubes with edge length 1 inch will fit into
the cube with edge length 2 inches?
5. Consider a cube with edge length 4 inches. How many of these smaller cubes will fit into
an 8-inch cube? Explain your thinking.
In Items 4 and 5, the ratio of the edge length of the smaller cube to the edge length of the larger
1
cube is 2 .
The rule you determined earlier in the activity to find the volume of a cube can also be used to
find the volume of a cube with fractional edge lengths.
6. Find the volume of each cube with the given edge length.
a.
2
3
b. 1
foot
1
4
inches
7. A storage shed shaped like a cube has sides that are 3.5 meters long. What is the volume
of the storage shed?
p. 334
Check Your Understanding
8. A cube has an edge length of 5 centimeters. What is the volume of the cube?
9. What is the volume of a cube with an edge length of
1
6
foot?
Lesson 26-1 Practice
For Items 10–13, find the volume of each cube.
10.
11.
12.
13.
14. A cube has an edge length of 4.3 meters. What is the volume of the cube?
15. What is the volume of a cube with an edge length of
1
4
yard?
16. A cube has a volume of 1,000 cubic feet. What is the edge length of the cube?
17. The area of one face of a cube is 36 cubic inches. What is the volume of the cube?
18. How much greater is the volume of a cube with edges that are feet long than a cube with
1
edges that are 2 2 feet long?
19. A fish tank shaped like a cube has sides that are 9 inches long. What is the volume of the
fish tank?
20. Reason quantitatively. A cube has a surface area of 96 square inches. What is the volume
of the cube? Explain your thinking.
21. Make sense of problems. A tower is made from three cubes stacked on top of each other.
The edges of the cubes are 4 inches, 6 inches, and 8 inches. What is the total volume of
the tower?
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