Summary: Identify the relationship between the corresponding sides in two
similar figures and their areas. Find area of similar figures.
Main Curriculum Tie: Mathematics Grade 7 Draw construct, and describe geometrical figures and describe the relationships between them. 1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 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 areas?
 How can this relationship help us determine the area for
similar figures?
Skill Focus:
Use the relationship between
corresponding sides of similar
figures to find area.
Vocabulary Focus:
Corresponding sides, similar figures
Ways to Gain/Maintain Attention (Primacy):
Manipulatives, cheer/movement, game, writing
Instructional Procedures:
Starter:
 Find the perimeter of this rectangle.
 Find the area for the rectangle
 If these rectangles are similar, what is the
measure of side EF?
 What scale factor was used on the smaller
rectangle to get the larger dimensions?
Lesson Segment 1: How can we describe the relationship between the
corresponding sides of similar figures and their areas?
Have students review the journal Frayer Models: Defining Similar Figures and Defining
Scale Factor. Ask students to read through their definitions, examples and nonexamples.
Tell them they will be using what they know about similar figures,
corresponding sides and scale factor for today’s learning goal.
Give each team of students 16 of each pattern block: orange squares, green triangles,
blue rhombi. They will be building growing patterns, or growing generations of similar
figures. Geometry Standard in the 7th Grade Utah Mathematics Core uses the terms "scale drawings" rather than generations. Make clear to students that each generation is a scale drawing of the original figure. Work with them in completing the Growing Generations of Similar Figures
investigation worksheet , discussing the answers to the questions on page 2 of the
worksheet through # 2 on the second page. Ask them to be looking for a pattern that
relates the scale factor to the number of area units in each generation.
To help students visualize the figures in the table for # 3 on the second page of
Growing Generations of Similar Figures, give each a Centimeter Paper. Students can
sketch each of the generations listed in the table for the “5 cm²” shape (as shown in
red on the attached key for the Centimeter Paper) as well as the 2nd and 3rd generation
listed in the table for the “4 yd²” shape as shown in green. As they sketch the figures,
compare the areas, and complete these first six rows of the table on the worksheet,
have them focus on the relationship between the scale factor and the original area.
They should begin to see that the units of area in the larger figure are always the
original area multiplied by the square of the scale factor. Help them make the
connection between area being measured in square units and the scale factor being
squared when finding the area of the larger generation. Students should then be able
to complete the last four rows of the table by using the pattern described rather than
needing to sketch.
Lesson Segment 2: How can the relationship between areas of similar figures
help us find missing areas?
Teach the students the following cheer. Have teams create moves for the cheer or a
rap to present to class.
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 for completing the worksheet, Area 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: Have students take the roll of expert explaining a student who had just come
into the class. Students should write a complete explanation for how to answer the
following question using words, drawings and math symbols. An evaluation for math
writings has been attached. Students should do the writing on the back of the
evaluation.
Question: You have a great photo that is 3” by 5”. You want to enlarge the area of
the picture using a scale factor of 3. What is the area of the larger picture? Will it fit
on your 9 x 12 scrapbook page?
Assign text practice as needed.
Attachments
Assessment Plan: Performance task, observation of student groups,
written response
Bibliography: This lesson plan was created by Linda Bolin. Author: Utah LessonPlans
Created Date : May 14 2009 13:30 PM
