Lesson 14Fractional Lengths in Triangles and Prisms
Learning Goal
Let’s explore area and volume when fractions are involved.
Learning Targets
I can explain how to find the volume of a rectangular prism using cubes that have a unit fraction as their edge length.
I can use division and multiplication to solve problems involving areas of triangles with fractional bases and heights.
I know how to find the volume of a rectangular prism even when the edge lengths are not whole numbers.
Warm Up: Area of Triangle
Problem 1
Find the area of Triangle A in square centimeters. Show your reasoning.
Activity 1: Bases and Heights of Triangles
Problem 1
The area of Triangle B is 8 square units. Find the length of
Problem 2
The area of Triangle C is
Activity 2: Volumes of Cubes and Prisms
Problem 1
Use cubes or the applet to help you answer the following questions.
Here is a drawing of a cube with edge lengths of 1 inch.
How many cubes with edge lengths of
inch are needed to fill this cube? What is the volume, in cubic inches, of a cube with edge lengths of
inch? Explain or show your reasoning.
Print Version
Your teacher will give you cubes that have edge lengths of
Here is a drawing of a cube with edge lengths of 1 inch.
How many cubes with edge lengths of
inch are needed to fill this cube? What is the volume, in cubic inches, of a cube with edge lengths of
inch? Explain or show your reasoning.
Problem 2
Four cubes are piled in a single stack to make a prism. Each cube has an edge length of
Problem 3
Use cubes with an edge length of
For each prism, record in the table how many
-inch cubes can be packed into the prism and the volume of the prism. prism
length (in)prism
width (in)prism
height (in)number of
-inch
cubes in prismvolume of
prism (in3)Examine the values in the table. What do you notice about the relationship between the edge lengths of each prism and its volume?
Problem 4
What is the volume of a rectangular prism that is
Are you ready for more?
Problem 1
A unit fraction has a 1 in the numerator. These are unit fractions:
Find three unit fractions whose sum is
. An example is: How many examples like this can you find?
Find a box whose surface area in square units equals its volume in cubic units. How many like this can you find?
Lesson Summary
If a rectangular prism has edge lengths of 2 units, 3 units, and 5 units, we can think of it as 2 layers of unit cubes, with each layer having
To find the volume of a rectangular prism with fractional edge lengths, we can think of it as being built of cubes that have a unit fraction for their edge length. For instance, if we build a prism that is
A height of 1 cube, because
A width of 3 cubes, because
A length of 8 cubes, because
The volume of the prism would be
We know that each cube with a
The volume of the prism, in cubic inches, can also be found by multiplying the fractional edge lengths in inches: