Summary: Identify the relationship between the corresponding sides in two
similar figures and their volumes. Find volumes of similar figures.
Materials:
Attachments
Background For Teachers: Enduring Understanding (Big Ideas):
Indirect measures for similar figures
Essential Questions:
 How can we describe the relationship between
the corresponding sides of similar figures and
their volumes?
 How can this relationship help us determine the
volume for similar figures?
Skill Focus:
Use the relationship between
corresponding sides of similar figures to
find volume.
Vocabulary Focus:
Corresponding sides, similar figures, volume
Ways to Gain/Maintain Attention (Primacy):
Manipulatives, cheer, games, foldable
Instructional Procedures:
Starter:
 Find the area of rectangle
 These rectangles are similar. What is the scale
factor?
 Use the scale factor to find the area for the
larger rectangle
 Write 3, 200,000 using scientific notation
Lesson Segment 1: How can we describe the relationship between the
corresponding sides of similar figures and their areas?
Give each team of students 100 linking cubes. They will be building similar prisms and
comparing the ratio of corresponding sides to the ratio of the volumes. Work with
them to build prisms as they complete the “Investigating Similar Figures, Scale Factors
and Volume With Linking Cubes” investigation worksheet. If they have difficulty
building a rectangular prism, remind them to first build the base by forming lw, and
then stack the number of layers for h.
As they work together in small groups, ask them to rotate roles: Builder (handles the
cubes), Coach (tells builder how it should look and suggest ideas for building),
Draftsman (reminds all to sketch the prisms helping each of them with the drawing),
Encourager (makes sure there are no putdowns and that each person is taking a turn
with the roles). Have students build and sketch, and discuss the answers to the
questions as a class.
Predicting and testing the hypotheses: Remind students that in the last lesson,
when finding area (or the number of squares needed to cover a similar figure), they
used the scale factor squared. Ask students to predict what might happen with the
scale factor when finding volumes of similar figures. Have them look for a pattern that
relates the scale factor to the number of cube units in each prism. Make sure student
focus on the relationship between the scale factor and the new volume. They should
begin to see that the units of volume in the larger figure are always the original volume
multiplied by the cube of the scale factor. When they write the ratio for each make this
explicit: The volume of the larger figure is the cube of the scale factor multiplied by
the volume of the smaller figure. Help them make the connection between volume
being measured in cubed units and the scale factor being cubed when finding the
volume of the larger prism.
Lesson Segment 2: How can the relationship between volumes of similar
figures help us find missing areas?
Teach the students the following cheer. Have them compare this cheer to the cheer for
area from the last lesson. How are the procedures the same? Different?
Similar figures? I don’t cry.
I can find volume if I try.
Cube the scale factor and multiply
By the smaller volume! My oh My! 

Similar figures? I’m not scared!
I’ll find area if I’m dared.
Multiply the scale factor squared
By the smaller areaI’m prepared! 

Play Lie Detector again for completing the worksheet, Volume of Similar Figures.
Materials: Give each small group a Smart Pal with blank paper or large team board and
marker
Procedure: Divide the class into two teams, A and B. Team members work together to
complete one assigned part of the worksheet. Give students a little time to check with
team members and to work the part of the worksheet correctly. The team should then
decide if they are going to tell a lie or tell the truth. If they choose to tell the truth, a
scribe writes the responses to the worksheet correctly on the Smart Pal or Team Board.
If they decide to tell a lie, the scribe writes part of their response incorrectly on the
Smart Pal or team board. Teacher selects one person from team A to be The
Presenter. The Presenter stands in the front of the room shows the team board and
explains what was done (either telling the truth, or telling a lie about the problem).
The class is given a little time to discuss the response in small groups. The Presenter
then chooses one person from Team B to be the Lie Detector and to tell whether they
believe the explanation was truth or lie. If The Lie Detector thinks the explanation was
a lie, he/she has to explain where the lie occurred and correct it. If the Lie Detector is
correct, Team B gets a point. If not, The Presenter tells whether their explanation was
the truth or a lie. If it was a lie, The Presenter tells why. The game proceeds with
each team taking a turn to be Presenter and Lie Detector.
Journal:
Students should make the foldable and fill in the blanks to show each step.
Application review of the affect of scale factor on length, area, and volume.
Have student play Jenga as described on the attached worksheet.
Attachments
Assessment Plan: Performance task, observation of student groups,
questions
Bibliography: This lesson plan was created by Linda Bolin. Author: Utah LessonPlans
Created Date : May 14 2009 14:19 PM
