Fishtank Learning

5th Grade Math
Unit 3: Shapes and Volume
Lesson 3

Objective

Find the volume of a right rectangular prism by thinking about its layers.

Anchor Tasks - Problem 1

What is the volume, in cubic units, of this figure?

(Teachers: Present students the open-top containers constructed from the net of the figure from Net D as well as no more than 14 centimeter cubes per student/group.)

Guiding Questions

What made finding the volume difficult?
What did you do to find the volume without having all of the cubes needed to pack it?
Write an equation that represents your strategy. (Write either $$9 + 9 + 9 + 9 + 9 + 9 = 54$$ or $$ 6 \times 9 = 54$$, assuming they used the side opposite the open top as the base.)

Notes

Because students will not have enough cubes to completely pack the figure, they’ll need to spatially structure the rectangular prism, hopefully by packing the bottom layer and figuring out how many layers there are. If students use the even more advanced strategy of figuring out the length and width of the bottom layer and multiplying those numbers together, hold off on that strategy as they’ll see it in Lesson 4.
Students may choose to pack the open-top container in the following way:

If there are not enough centimeter cubes or constructing enough figures for the whole class isn’t feasible, you could facilitate this Anchor Task as a whole class. Do so by presenting the figure and asking for strategies to pack the figure, then trying those different ideas out until students land on the strategy of packing the bottom layer and figuring out the number of layers.
The teacher and students will need an open-top container that measures 3 cm $$\times$$ 3 cm $$\times$$ 6 cm for this task. Construct this on cardstock from the net on Net D. The teacher and students will also need no more than 14 centimeter cubes each.

Anchor Tasks - Problem 2

How many layers are there in the following figure? How many cubes are in each layer? What is the volume of the figure?

Find another way to think of the layers in the figure.

Guiding Questions

How many layers are there in the rectangular prism? How many cubes are in each layer? (Draw lines along the prism to show the layers students are referring to.)
Write an expression to represent how you used the number of layers and the number of cubes in each layer to find the volume.
What is the volume of the figure? How did you figure that out?
I see layers in the rectangular prism in a different way. Can anyone see different layers in their prism?
Write an expression to represent how you can use these layers to find the volume.
There is a third way to see the layers in the prism. What do you predict the volume will be when we think about the layers in that other way? Why?

Notes

You can record the different ways of seeing of the layers in the pictorial figure in the three following ways:

You might choose to organize these different ways of seeing the layers in a table, such as the following:

Number of Layers Cubes in Each Layer Volume

2 15 30 cubic units

5 6 30 cubic units

3 10 30 cubic units
The teacher and students may need centimeter cubes for this task (make these available for students in case constructing the figure will help them, but don’t point them in the direction of what tool to use (MP.5)).

Anchor Tasks - Problem 3

a. Explain or show how the expression $$5\times24$$ represents the volume of this rectangular prism.

b. Explain or show how the expression $$6\times20$$ represents the volume of this rectangular prism.

c. Find a different way to calculate the volume of this rectangular prism. Explain or show your thinking.

d. Write an expression to represent the way you calculated the volume.

Problem Set

View Problem Set

Target Task

Use the figure below to answer the following questions.

a. Sasha says she sees 2 layers with 9 cubes in each layer the prism above. Draw lines on the prism to show the layers Sasha sees.

b. Yaritza says she sees 3 layers of 6 cubes in each layer in the prism above. Do you agree or disagree that there are 3 layers with 6 cubes in each layer in the prism? Explain.

c. Find the volume of the prism.

Word Problem

Malin has 240 cans of lemon-lime soda and 320 cans of root beer to sell during the field hockey game. She sells 92 during the game and puts the rest into boxes that hold 12 cans each to carry them home. How many boxes does she use?