T604
Mathematics Success – Level G
LESSON 24: Surface Area of Prisms
[OBJECTIVE]
The student will find the surface area of rectangular prisms.
[MATERIALS]
Student pages S203–S210
Transparencies T613, T615, T617, T619
Centimeter cubes (50 cubes per pair)
Colored paper for foldable (1 per student – or foldable made during Lesson 22)
[ESSENTIAL QUESTIONS]
1. How is surface area different from area?
2. Why is surface area measured in square units?
3. Tell how to find the surface area of a cube if you know the area of one face.
[WORDS FOR WORD WALL]
surface area, rectangular prism, cube, face, net, polyhedron
[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 – IP, I, WG) S203 (Answers on T612.)
• Have students turn to S203 in their books to begin the Warm-Up. Students
will find the areas of squares and rectangles to prepare for finding the surface
area 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
T605
LESSON 24: Surface Area of Prisms
[LESSON] (50–60 minutes – M, GP, IP, WG, I)
SOLVE Problem
(3 minutes – GP, WG) T613, S204, (Answers on T614.)
Have students turn to S204 in their books, and place T613 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 surface areas of rectangular prisms. They will use this knowledge to
complete this SOLVE problem at the end of the lesson. {SOLVE}
Discovery Activity – Surface Area of Rectangular Prisms (15 minutes – M, GP, WG)
T613, T615, S204, S205 (Answers on T614, T616.)
Pass out the cubes to each pair of students. Use the following activity to complete
the steps on S204 (T613) with your students. {Concrete Representation, Algebraic
Formula, Verbal Description, Pictorial Representation}
T606
Mathematics Success – Level G
LESSON 24: Surface Area of Prisms
MODELING
Surface Area of a Rectangular Prism
Step 1: Model creating a prism out of the cubes that is 4 cubes long, 3 cubes
wide, and 2 layers tall on the overhead.
Step 2: Ask students to look at the number of faces the prism has. Remind them
that each side of the prism is a face, so there are six faces.
Step 3: Model for students how to draw the base (bottom) rectangle on the graph
paper on S205 (T615). Be sure to tell students that the length of one
cube is the same as the length of one square on the graph paper. Draw
the bottom so that it is 4 squares long and 3 squares wide. Label it
“bottom.”
Ask students which faces would be touching the bottom face if students
were able to unfold the prism. They should say “front and back” and/or
“right and left.” Start by drawing the front and back so that they are
connected to the bottom. Make the back and front both rectangles that
are 4 squares long and 2 squares wide.
Mathematics Success – Level G
T607
LESSON 24: Surface Area of Prisms
Ask students where the top would connect to what you have already
drawn. Model how to draw the top so that it connects to the back. Have
students copy your work in their books.
Ask students where they think the sides of the prism would be drawn.
Model drawing the sides and have students copy your work in their
books.
Explain to students that what they have just drawn is a net of the
rectangular prism. Explain that a net is a two-dimensional representation
that can be folded to form a polyhedron.
Step 4: Ask students to find the area of each face of the prism, either by counting
the squares or using the formula A = lw.
Step 5: Explain to students that since surface area means “the area of all the
surfaces,” they need to add the areas they found in Step 4.
Step 6: Have students look at the areas they wrote in Step 4. Ask, “What do you
notice about the areas?” (The top and the bottom have the same area,
the front and the back have the same area, and the right and left side
have the same area.)
T608
Mathematics Success – Level G
LESSON 24: Surface Area of Prisms
Step 7: Ask students to think about a formula they could use to find the surface
area of any rectangular prism. Some students may tell you that you need
to find the area of all six faces and add them together. Have them look
at the areas in Step 4 again, and guide them toward finding the areas of
three of the sides (top, one side, front) and doubling those areas since
there are three pairs of congruent sides (SA = 2[top area] + 2[front
area] + 2[side area]).
Other students may realize that in finding the surface area, they use each
dimension twice in the formula: SA = 2lw
lw + 2lh + 2wh.
Practice – Surface Area of Rectangular Prisms (12 minutes – M, GP, WG) T617,
S206 (Answers on T618.)
Have students turn to S206 in their books, and place T617 on the overhead. Use
the following activity to help students complete the problems on S206 as you
model drawing the nets and finding the surface areas on the overhead. {Pictorial
Representation, Algebraic Formula, Verbal Description, Graphic Organizer}
MODELING
Practice with Surface Area
Step 1: Have students look at Example 1 on S206. Have them look at the length,
width, and height of the prism in units. Remind students that to find the
surface area, they can draw a net.
Step 2: In the middle column, model how to draw and label a net. Label each face
and explain how you are labeling the measurements. For example:
“When I look at the top, I can see that the top is five cubes long by 3
cubes wide. So, when I draw the rectangle for the top, I am going to
label it ‘5 units’ for the length and ‘3 units’ for the width. I know that
the bottom will be the same, but they are not connected on the net, so
I need to draw the front first. When I look at the front, I see that it is 5
cubes long by 4 cubes wide. When I draw the front and back, I do not
need to label every single side. Now I need to draw and label the left and
right sides of the prism. When looking at them, I can see that the sides
are 3 by 4 rectangles.”
Mathematics Success – Level G
T609
LESSON 24: Surface Area of Prisms
Step 3: In the third column, model for students how to write the formula for the
surface area of a rectangular prism: SA = 2(top area) + 2(front area) +
2(side area). Then have students use the formula to find surface area of
the prism.
Step 4: Look at Example 2 with students. Point out that the prism is a cube
because all three dimensions are the same.
Step 5: Help students to draw a net for the cube. Ask them what they think the
squares will look like. (They will all be the same.) Model drawing the net,
with four squares connected and one square on each side of the four.
Step 6: Have students find the surface area using the formula they came up with
on S204. Then point out that since all sides have exactly the same area,
they can find the area of one face and then multiply it by 6.
Step 7: Look at Example 3 with students. After reading the problem, have students
draw a prism to match the dimensions. Explain that this will help them to
be able to visualize and draw the net.
Step 8: Model how to draw the net, again asking students which sides would be
touching if the prism were unfolded.
Step 9: Model how to use the formula to find the surface area of the prism.
Foldable
(10 minutes – M, GP, WG)
Give students a piece of colored paper. Follow the steps below to have each
student make a foldable. (If you completed Lesson 22 or 23, students have
already made the foldable. Skip to Step 2 to add information on finding the
surface area of a rectangular prism. If there are empty spaces, have students
include areas of other shapes such as triangles, rectangles, and circles. {Algebraic
Formula, Graphic Organizer, Pictorial Representation}
T610
Mathematics Success – Level G
LESSON 24: Surface Area of Prisms
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 Surface Area 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 Surface Area 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
surface area using the formula. See your foldable for the information.
Mathematics Success – Level G
T611
LESSON 24: Surface Area of Prisms
SOLVE Problem
(7 minutes – GP, WG) T619, S207 (Answers on T620.)
Have students turn to S207 in their books, and place T619 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 find the surface area.) {SOLVE, Algebraic Formula, Verbal Description}
If time permits…
(10 minutes – IP, I) S208 (Answers on T621.)
Have students complete the five surface area problems on S208. Give students 8
minutes to complete the problems, and take 2 minutes to go over the answers.
{Algebraic Formula, Verbal Description}
[CLOSURE] (3 minutes)
To wrap up the lesson, go back to the essential questions and discuss them with
students.
• How is surface area different from area? (Area is the amount of space that is
covered by either a two-dimensional figure or the base of a three-dimensional
figure. The surface area is the area of all of the faces of a three-dimensional
figure added together.)
• Why is surface area measured in square units? (Because area is measured in
square units, and you add the areas of all the faces of the figure.)
• Tell how to find the surface area of a cube if you know the area of one face.
(Multiply the area of one face by six, since there are six faces that are exactly the
same.)
[HOMEWORK] Assign S209 and S210 for homework. (Answers on T622 and T623.)
[QUIZ ANSWERS] T624–T626
The quiz can be used at any time as extra homework or to see how students did on
finding the surface area of a rectangular prism.