IM 6.4.14 Lesson: Fractional Lengths in Triangles and Prisms

Find the area of Triangle A in square centimeters. Show your reasoning.

The area of Triangle B is 8 square units. Find the length of b. Show your reasoning.

The area of Triangle C is 54/5 square units. What is the length of h? Show your reasoning.

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 [math]\frac{1}{2}[/math] inch are needed to fill this cube?

What is the volume, in cubic inches, of a cube with edge lengths of [math]\frac{1}{2}[/math] inch? Explain or show your reasoning.[br]

Four cubes are piled in a single stack to make a prism. Each cube has an edge length of ½ inch. Sketch the prism, and find its volume in cubic inches.

For each prism, record in the table how many ½-inch cubes can be packed into the prism and the volume of the prism.

Examine the values in the table. What do you notice about the relationship between the edge lengths of each prism and its volume?

What is the volume of a rectangular prism that is [math]1\frac{1}{2}[/math]inches by [math]2\frac{1}{4}[/math]inches by 4 inches? Show your reasoning in the app below.

Show your reasoning.

A unit fraction has a 1 in the numerator.

[list][*]These are unit fractions: [math]\frac{1}{3}[/math],[math]\frac{1}{100}[/math],[math]\frac{1}{1}[/math].[/*][/list][list][*]These are [i]not[/i] unit fractions: [math]\frac{2}{9},\frac{8}{1},2\frac{1}{5}[/math].[br][/*][/list][br]Find three unit fractions whose sum is [math]\frac{1}{2}[/math]. An example is: [math]\frac{1}{8}+\frac{1}{8}+\frac{1}{4}=\frac{1}{2}[/math] How many examples like this can you find?[br]

Find a box whose surface area in square units equals its volume in cubic units. How many like this can you find?