5th Grade Centimeter Cube Volume Lesson
Standard
5.MD.C.5a Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the
volume is the same as would be found by multiplying the edge lengths,
equivalently by multiplying the height by the area of the base.
Represent threefold whole-number products as volumes, e.g., to
represent the associative property of multiplication.
Mathematical 5. Use appropriate tools strategically.
Practices
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Target
Materials
I can use unit cubes to determine the volume of a rectangular prism.
Interlocking centimeter cubes
Centimeter grid paper
Vocabulary
APK
volume, unit, cube, cubic units, rectangular prism
Have students count out 18 centimeter cubes. Model connecting nine
cubes to create a column. Have students create a column of nine.
Repeat the process one more time so that you have an area model of 9
cubes x 2 cubes. Discuss what they already know about this model.
Relate to their understanding of arrays. Discuss that it is a 2
dimensional model from which we can calculate area.
Model building three more models of 9x2 and stack each one on top of
the previous one. Show the rectangular prism that is 9x2x4. Think
aloud how you can look down at the top and see that it has the same
area as your APK model of 9x2. Think aloud how you notice that you
have 4 “layers” that contain 18 cubes each. Model taking the layers out
and counting individual cubes. If there are 18 cubes in the first two
layers, I can infer that there are 18 cubes in every layer so I can add 18
four times which would give me 72 cubes total.
Have students build four layers of centimeter cubes identical to the one
built in the APK. Every time they build a layer they are to count the
number of cubes and record it on their paper. After building four layers
they should count to see if they have 72 total cubes. Discuss together
how this is similar to area models and ask how it is different.
Explain how the layers makes a 3 dimensional figure that doesn’t just
have area, but also has volume. Volume is defined as the space occupied
by a three-dimensional object. It is measured in cubic units because it
has length, width, and height. Point out the length, width and height and
talk about how many units make up the length, width, and height.
Discuss that when we talk about volume we are using cubes and not flat
squares so our measurements are now going to be called cubic units
instead of square units.
Since we already have 72 cubes, could we create another rectangular
I DO/WE DO
WE DO
prism that would use the same amount of cubes but have different
lengths, widths, and heights? Model changing the 9x2x4 to a rectangular
prism with a base of 8x3. Ask students to guess how many layers will be
needed for the height. After they guess, have them build the model to
determine the height. They should determine: Length-8, Width-3, and
Height-3. Have them determine how many cubes total were used to
build the rectangular prism. They should determine that 8 x3 would be
24 cubes for the base and that since there are 3 “layers”, they would add
24 three times to get a volume of 72 cubes or 72 cubic units. Have
students discuss why we are saying 72 cubic units and not 72 square
units. What is the difference between square and cubic units? Have
students work together to build another model with the 72 cubes. Give
them the base of 6 x 6 and have them determine what the length, width
and height of the rectangular prism will be if they use all 72 cubes.
YOU DO
Students will build a model that is different from the 9x2x4, 8x3x3 and
6x6x2 used in previous models. Have them label their length, width,
and height.
Other models might include: 4x3x6, 12x2x3, 12x1x6
CLOSURE
Have students with different models share with the whole class. Putting
the different models (including the ones from I DO and WE DO), have
students do a quickwrite on what they notice about the different
models. Remind them that they all have the same number of cubes.
Have students use the vocabulary (cube, rectangular prism, volume, and
cubic) to explain what they understand about how volume is different
than area.
CFU/
Build a new model using any amount of cubes. Determine the length,
ASSESSMENT width, height and then use the same amount of cubes to create another
rectangular prism with different dimensions but same volume.