Lesson Title: Similar Figures
Date: _____________ Teacher(s): ____________________
Course: Common Core Geometry, Unit 1
Start/end times: _________________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which Mathematical
Practices do you expect students to engage in during the lesson?
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they
are similar; explain using similarity transformations the meaning of similarity for triangles as the equality
of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
This lesson will take two 50 minute periods to complete.
MP1: Make sense of problems and persevere in solving them..
MP3: Construct viable arguments and critique the reasoning of others.
MP4: Model with mathematics.
.MP7: Look for and make use of structure.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Ask what needs to be true for proportions (ratios) to be
equal. As a formative assessment, have students, in
small groups or pairs, decide which of these pairs of
ratios are equal
1
5 18
42 6
15
,
,
,
and
and
and
6
30 6
14 10
30
8
20 12
8
,
and
and
14
35 9
6
1
6
5
18
42
6
15
8
20
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.
Refer to closure lesson sheet.
Note: In each part of this activity, students first write
what the features of the similar figures are. Then they are
asked to do some extension and find some measures with
the concept of proportionality. This could be done as a
whole group or individually. The extension could be put
off for the next day in class.
12
, 30 6 , 14 10 , 30
,
,Have students
14 35
9
justify their answers. Have groups compare similarities
and differences between strategies used. (Look for
evidence of MP3)
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson?
1. Have students draw a geometric figure. (Recommend that they draw a triangle or quadrilateral.) Have students
exchange their drawing with another student.
2. Have each student draw a “matching” or “similar” version of the figure they were given, either twice or half as
large (the option will avoid some problems with size limitations).
3. Have students discuss and share how they created their similar figure. During whole group sharing, highlight the
necessity for angles to be the same and all three pairs of sides to be proportional by 2:1 or 1:2 (as in the lesson
launch).
4. Ask, “What must be the same and what does not for the figures to be similar?” Once it is established that the
angles must be equal in measure (start using “congruent”) If students have not yet discovered the proportional
nature of the sides, then have them measure with a ruler and record the lengths of the sides of they have drawn.
Have students discuss in their pairs what the criteria is for the corresponding sides. Have each pair write their
conjecture and explain how the conjecture is verified. Refer to the opening activity for guidance, if necessary.
(MP1, MP2, MP3, MP5, MP6, MP7 in evidence)
5. Group the students into 4 or 8 groups (depending on the size or your class and what size groups your are
comfortable with). Set up the 4 stations described below. (If you have 8 groups you will need 2 of each station.)
Have groups visit each station and complete the task. Each station should take about 10 minutes depending on
ability level
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Similar Figures
Course: Common Core Geometry, Unit 1
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
 Station 1 – Refer to activity sheet one. Make enough copies for each student. It contains several pairs of
polygons. Groups are to decide whether or not each pair is similar and justify their assertion. Each
student should complete a sheet. (MP2)
 Station 2 – Place enough rectangular and triangular cut pieces of patty paper for each group to have one
of each. They should be large enough to fold. Each group should fold their two figures to create a
similar figure. They should write on the figure why it is similar (MP1,MP3,MP5)
 Station 3 – Refer to activity sheet three. Make enough copies for each student. It has a trapezoid on a
graph grid. Groups are to create two figures (one exactly congruent and one similar) on the grid and
justify their figures as such.(MP1,MP2, MP4,MP5)
 Station 4 – Place a computer with this web site loaded.
http://www.mathopenref.com/similartriangles.html. Allow students to explore the applets. Ask
each group to write one observation about similar triangles and transformations. Use these
questions to guide them: 1) What happens to the angles when transformations are applied?
What happens to the sides when transformations are applied? Do these things always happen?
(Look for evidence of MP3 and MP5)
6. Assign each group a particular station for which to summarize their findings. Probe groups to highlight, more
exactly, the conditions for similarity of angle equality and side proportionality. (Look for evidence of MP2)
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student mastery? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened (and conceptual) understanding.
Students will be able to determine if figures are similar by comparing their sides and angles
Students will be able to create similar figures by maintaining angle measure and creating proportional sides
Students may be able to find lengths of sides of proportional figures given enough information about their
proportionality.
Mastery can be assessed during each of the three parts of the lesson, by monitoring group discussion and class
discussion for accurate conjectures and use of those conjectures.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Proportional, Similar, Congruent.
A common misconception is that similarity and congruence are independent. Congruence is a special case of
similarity with sides having a 1:1 ratio.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Activity Sheets for stations 1 and 3
Patty paper triangles and rectangles for station 2
Computer(s) with Internet connections for station 4
Activity Sheet for Closure
Rulers and Protractors
To be determined by teacher
Lesson Reflections: What questions, connected to the lesson objectives and evidence of success, will you use to
reflect on the effectiveness of this lesson?
How effectively did students discover the requirements for similarity on their own?
Can students identify similar figures by comparing their angles for congruence and sides for proportionality?
Can students create similar figures, in a variety of settings, by copying the angles and keeping the sides proportional?
What modifications do I need to make to tomorrow’s lesson based on the students’ current understanding?
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Similar Figures
Date: _____________ Teacher(s): ____________________
Course: Common Core Geometry, Unit 1
Start/end times: _________________________
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.