T584
Mathematics Success – Level G
LESSON 23: Volume of Rectangular Prisms
[OBJECTIVE]
The student will find the volume of rectangular prisms.
[MATERIALS]
Student pages S196–S202
Transparencies T592, T594, T596
Centimeter cubes (50 cubes per pair)
Colored paper for foldable (1 per student – or foldable made during Lesson 22)
[ESSENTIAL QUESTIONS]
1. What does volume measure?
2. Why is volume measured in cubic units?
3. Describe how the area of the base of a prism is related to the volume of the
prism.
[WORDS FOR WORD WALL]
volume, rectangular prism, base, height
[GROUPING]
Cooperative Pairs (CP), Whole Group (WG), Individual (I)
[LEVELS
OF
TEACHER SUPPORT]
Modeling (M), Guided Practice (GP), Independent Practice (IP)
[MULTIPLE REPRESENTATIONS]
SOLVE, Algebraic Formula, Verbal Description, Pictorial Representation, Concrete
Represenation, Graphic Organizer
[WARM-UP] (5 minutes – WG, IP, I) S196 (Answers on T591.)
• Have students turn to S196 in their books to begin the Warm-Up. Students will
find the area of rectangles to prepare for finding the volume of rectangular prisms.
Monitor students to see if any of them need help during the Warm-Up. Give
students 4 minutes to complete the problems and then spend 1 minute reviewing
the answers as a class. {Algebraic Formula, Verbal Representation}
[HOMEWORK] (5 minutes)
Take time to go over the homework from the previous night.
Mathematics Success – Level G
T585
LESSON 23: Volume of Rectangular Prisms
[LESSON] (50–60 minutes – M, GP, IP, WG, CP)
SOLVE Problem
(3 minutes – GP, WG) T592, S197 (Answers on T593.)
Have students turn to S197 in their books, and place T592 on the overhead. The
first problem is a SOLVE problem. You are only going to complete the S step with
students at this point. Tell students that during the lesson they will learn how to
find the volume of prisms. They will use this knowledge to complete this SOLVE
problem at the end of the lesson. {SOLVE}
Discovery Activity – Volume of Rectangular Prisms
(15 minutes – M, GP, WG) T592, S197 (Answers on T593.)
Pass out the cubes to each pair of students. Use the following activity to complete
the steps on S197 (T592) with your students. {Concrete Representation, Algebraic
Formula, Verbal Description}
T586
Mathematics Success – Level G
LESSON 23: Volume of Rectangular Prisms
MODELING
Volume of a Rectangular Prism
Step 1: Model creating a rectangle out of the cubes that is 5 cubes long and 2
cubes wide on the overhead. Be sure to point out that there is no space
between the cubes.
Step 2: Find the area of the bottom of the rectangle by counting the squares on
the bottom, or by using the area formula: A = lw = 5(2) = 10 square
units. Remind students that the area is the number of squares the shape
covers.
Step 3: Tell students that since you used cubes to make the figure, it not only
has length and width, but also height. It is a three-dimensional figure.
Record the number of cubes for each dimension: height (1), length (5),
and width (2).
Step 4: Count the number of cubes that make up the prism with students (10).
Add another layer to your prism by adding 10 more cubes on top of the
first layer.
Step 5: Ask students to tell you the area of the bottom (or base). Ask, “Has it
changed?” (No, it is still 10 square units.) Ask students to find the height
(2), length (5), and width (2) of the prism. Count the number of cubes
that make up the prism with students (20).
Step 6: Add another layer to your prism by adding 10 more cubes on top of the
first two layers.
Step 7: Ask students to tell you the area of the bottom (or base). Ask, “Has it
changed?” (No, it is still 10 square units.) Ask students to find the height
(3), length (5), and width (2) of the prism. Count the number of cubes
that make up the prism with students (30).
Mathematics Success – Level G
T587
LESSON 23: Volume of Rectangular Prisms
Step 8: Explain to students that the number of cubes it takes to make a rectangular
prism is called the prism’s volume. Ask students to look at the pattern
of the number of cubes that made up the prism each time a layer was
added. Each time a layer was added, 10 more cubes were added, and the
volume increased by 10.
Step 9: Ask students to look at the pattern created by the height, length, and
width at Steps 3, 5, and 7. Write the dimensions on the board.
Step 3
Step 5
Step 7
Length
Width
Height
5
5
5
2
2
2
1
2
3
Number
of Cubes
(Volume)
10
20
30
Ask students what formula they could use to find the volume of a
rectangular prism (V = lwh) or (V = Bh).
Practice – Volume of Rectangular Prisms
(12 minutes – M, GP, IP, WG, I)
T594, S198 (Answers on T595.)
5 minutes – M, GP, WG: Have students turn to S198 in their books, and place
T594 on the overhead. Use the following activity to
help students complete S198. {Pictorial Representation,
Algebraic Formula, Verbal Description, Graphic Organizer}
T588
Mathematics Success – Level G
LESSON 23: Volume of Rectangular Prisms
MODELING
Practice with Volume
Step 1: Have students look at Example 1 on S198. Remind students that to find
the volume, they can multiply the length, width, and height of the figure.
Have students label the length (5), the width (3), and the height (3).
Remind them to always start by writing the formula and then substituting
in the values. Explain that because the unit of measure of the prism in
the example is not specified, students will use “unit.” The answer will be
in units cubed (u3). If students have difficulty understanding the units
cubed, remind them that each unit is a cube. If they were to count the
number of cubes in Example 1, there would be 45 cubes. Each cube is 1
cubic unit, so that will be a total of 45 cubic units. (If you used cm cubes,
that measurement would be 45 cm3.)
Step 2: In the second column, model for students how to write the formula for
the volume of a rectangular prism (V = lwh).
Step 3: Look at Example 2 with students. Point out the length (5), width (4), and
height (8). Model writing the formula and then substituting the values to find
the volume. Also have students write the formula in the middle column.
Step 4: Look at Example 3 with students. After reading the problem, model how
to underline each of the dimensions in the problem. Then model writing
the formula and substituting the values to find the volume. Also have
students write the formula in the middle column.
Step 5: Look at Example 4 with students. After reading the problem, have students
underline each of the dimensions in the problem. Ask students how they
think you should find the volume, if you know the area of the base and
not the length and width. Remind them that area = length times width,
so they need to multiply the base area by the height. (You can also refer
back to the cube activity, where the area of the base was always the
same, and the height changed when students added another layer.)
7 minutes – IP, I, WG:
Have students complete Problems 5–8 in the third
column on S198. Give students 5 minutes to complete
the problems and then go over the answers as a class.
{Pictorial Representation, Algebraic
Description, Graphic Organizer}
Formula,
Verbal
Mathematics Success – Level G
T589
LESSON 23: Volume of Rectangular Prisms
Foldable
(10 minutes – M, GP, WG)
Give students a piece of colored paper. Follow the steps below to have each student
make a foldable. The foldable will include finding the volume of rectangular prisms.
(If you completed Lesson 22, the students have already made the foldable. Skip
to Step 2 to add information on finding the volume of a rectangular prism to the
foldable that is already started.) In later lessons, students can also add surface
area of prisms or include area of other shapes such as triangles, rectangles or
circles. {Algebraic Formula, Graphic Organizer}
MODELING
Foldable
Step 1: Fold one corner of the piece of paper down to the edge of the other side
of the paper. Cut off the strip at the bottom. A square should be left.
Step 2: Open the square. Fold each corner into the center. Write Volume of
Rectangular Prisms on one outside flap. Three outside flaps will be blank
to be written on later.
Step 3: Pull up the flap that says Volume of Rectangular Prisms. On the triangle
that sticks up, draw a rectangular prism with the length, base, and height
labeled. Underneath the prism, write the formula. On the square portion,
draw another prism with values for the dimensions. Find the volume using
the formula. See your foldable for the information.
T590
Mathematics Success – Level G
LESSON 23: Volume of Rectangular Prisms
SOLVE Problem
(5 minutes – GP, WG) T596, S199 (Answers on T597.)
Have students turn to S199 and place T596 on the overhead. Remind students that
the SOLVE problem is the same one from the beginning of the lesson. Complete
the SOLVE problem with your students. Ask them for possible connections from
the SOLVE problem to the lesson. (Students should say that they need to use the
volume formula.) {SOLVE, Algebraic Formula, Verbal Description}
If time permits…
(10 minutes – IP, I) S200 (Answers on T598.)
Have students complete the six volume problems on S200. Give students 8
minutes to complete the problems, and take 2 minutes to go over the answers.
{Algebraic Formula, Verbal Description}
[CLOSURE] (5 minutes)
To wrap up the lesson, go back to the essential questions and discuss them with
students.
• What does volume measure? (Volume measures the capacity of a 3-D figure.)
• Why is volume measured in cubic units? (When finding volume, three measurements
are multiplied, and a unit times a unit times a unit is units cubed, or units to the
third power.)
• Describe how the area of the base of a prism is related to the volume of the
prism. (The base is the area of the bottom of the prism, and the volume is the
base times the number of layers in the prism.)
[HOMEWORK] Assign S201 and S202 for homework. (Answers on T599 and T600.)
[QUIZ ANSWERS] T601–T603
The quiz can be used at any time as extra homework or to see how students did on
finding the volume of rectangular prisms.