Similarity
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to compare four images. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.
Launch
Arrange students in groups of 2–4. Display the images for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed 3 images that go together and can explain why. Next, tell students to share their response with their group, and then together find as many sets of three as they can.
Student Task
Which 3 go together? Why do they go together?
Sample Response
Sample responses:
A, B, and C go together because:
-
Both triangles in each pair are scaled copies of each other.
-
Both triangles in each pair are dilations of each other.
A, B, and D go together because:
-
Both triangles in each pair are “facing” the same direction.
A, C, and D go together because:
-
None of the triangles in each pair overlap each other.
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None of the triangles in each pair share a common vertex.
B, C, and D go together because:
-
Both triangles in each pair are different sizes.
Activity Synthesis (Teacher Notes)
Invite each group to share 1 reason why a particular set of 3 go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.
During the discussion, prompt students to explain the meaning of any terminology they use, such as “scaled copies” and “dilation,” and to clarify their reasoning as needed. Consider asking:
-
“How do you know . . . ?”
-
“What do you mean by . . . ?”
-
“Can you say that in another way?”
Standards
- 8.G.4·Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
- 8.G.A.4·Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
20 min
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Similarity
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to compare four images. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.
Launch
Arrange students in groups of 2–4. Display the images for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed 3 images that go together and can explain why. Next, tell students to share their response with their group, and then together find as many sets of three as they can.
Student Task
Which 3 go together? Why do they go together?
Sample Response
Sample responses:
A, B, and C go together because:
-
Both triangles in each pair are scaled copies of each other.
-
Both triangles in each pair are dilations of each other.
A, B, and D go together because:
-
Both triangles in each pair are “facing” the same direction.
A, C, and D go together because:
-
None of the triangles in each pair overlap each other.
-
None of the triangles in each pair share a common vertex.
B, C, and D go together because:
-
Both triangles in each pair are different sizes.
Activity Synthesis (Teacher Notes)
Invite each group to share 1 reason why a particular set of 3 go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.
During the discussion, prompt students to explain the meaning of any terminology they use, such as “scaled copies” and “dilation,” and to clarify their reasoning as needed. Consider asking:
-
“How do you know . . . ?”
-
“What do you mean by . . . ?”
-
“Can you say that in another way?”
Standards
- 8.G.4·Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
- 8.G.A.4·Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.