Unit 7, Lesson 17
Parameters and Graphs
Extra Support Materials for Algebra 1
17.1
Warm-up
Which Three Go Together: Triangles
Instructional Routines
Which Three Go Together?Materials
NoneActivity Narrative
This Warm-up prompts students to carefully analyze and compare figures that are transformed in the plane. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminology students know and how they talk about transformations. Terms like “translation” and “reflection” are great, but for the purposes of this lesson and the associated Algebra 1 lesson, less formal terms like “shift” or “flip” are also acceptable.
Launch
Arrange students in groups of 2–4. Display the figures for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three images that go together and can explain why. Next, tell students to share their response with their group and then to work together to find as many sets of three as they can.
Activity
NoneEach figure shows triangle
ATwo triangles in an x y plane. Horizontal axis scale negative 5 to 5 by 1s. Vertical axis scale negative 5 to 5 by 1s. Triangle P Q R. Point P is at 0 comma 0. Point Q is at 0 comma 2. Point R is at 3 comma 0. Triangle P prime Q prime R prime. Point P prime is at negative 1.5 comma 0. Point Q prime is at negative 1.5 comma 4. Point R prime is at 4.5 comma 0.
BTwo triangles in an x y plane. Horizontal axis scale negative 5 to 5 by 1s. Vertical axis scale negative 5 to 5 by 1s. Triangle P Q R. Point P is at 0 comma 0. Point Q is at 0 comma 2. Point R is at 3 comma 0. Triangle P prime Q prime R prime. Point P prime is at 0 comma 0. Point Q prime is at negative 1.5 comma 1.414 comma negative 1.414. Point R prime is at negative 2.12 comma negative 2.121.
CTwo triangles in an x y plane. Horizontal axis scale negative 5 to 5 by 1s. Vertical axis scale negative 5 to 5 by 1s. Triangle P Q R. Point P is at 0 comma 0. Point Q is at 0 comma 2. Point R is at 3 comma 0. Triangle P prime Q prime R prime. Point P prime is at negative 2 comma negative 3. Point Q prime is at negative 2 comma negative 1. Point R prime is at 1 comma negative 3.
DTwo triangles in an x y plane. Horizontal axis scale negative 5 to 5 by 1s. Vertical axis scale negative 5 to 5 by 1s. Triangle P Q R. Point P is at 0 comma 0. Point Q is at 0 comma 2. Point R is at 3 comma 0. Triangle P prime Q prime R prime. Point P prime is at 0 comma 0. Point Q prime is at 0 comma negative 2. Point R prime is at 3 comma 0.
Activity Synthesis
Invite each group to share one reason why a particular set of three 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 that the reasons given are correct.
During the discussion, ask students to explain the meaning of any terminology they use, such as “slide,” “shift,” “flip,” “translate,” “rotate,” or “dilate,” 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?”
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