Transformations and Angle Relationships

Lesson 1

Math

Unit 3

8th Grade

Lesson 1 of 22

Objective


Understand the rigid transformations that move figures in the plane (translation, reflection, rotation).

Common Core Standards


Core Standards

  • 8.G.A.1.A — Lines are taken to lines, and line segments to line segments of the same length.
  • 8.G.A.1.B — Angles are taken to angles of the same measure.
  • 8.G.A.1.C — Parallel lines are taken to parallel lines.
  • 8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Criteria for Success


  1. Understand different ways that figures can be moved while maintaining their original shape and size through translation, reflection, and rotation.
  2. Define and prove congruence between two figures; if a figure can be moved to overlap perfectly with the other figure, without stretching or breaking it, then those two figures are congruent.

Tips for Teachers


  • This lesson introduces students to the concept of rigid transformations. Students will have prior-learned language to describe these movements, like “flip,” “turn,” or “slide.” Allow students to use these descriptions to enable them to talk freely about what they see; however, be sure to introduce the formal names of these movements so students can begin to internalize them. 
  • Throughout the unit, students may find it valuable to use patty paper (transparency paper), graph paper, and/or rulers. It may be helpful to set up a station in the classroom where students can access these tools whenever they need them.

Lesson Materials

  • Ruler (1 per student)
  • Graph Paper (2-3 sheets per student)
  • Patty paper (transparency paper) (several sheets per student)
  • Scissors (1 per small group)
  • Optional: Tape (1 per small group)
  • 180° Protractor (1 per student)
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Anchor Problems


Problem 1

Watch the 5 videos of Ms. Pac-Man from from Robert Kaplinsky's How Did They Make Ms. Pac-Man?. After each video, discuss the question in each part.

a.   Watch the first video of Ms. Pac-Man under “The Situation.” 
Discuss: How can you describe Ms. Pac-Man’s movements? 

b.   Watch the next video (“Translations Only”).
Discuss: What do you think “translation” means? What other movements did Ms. Pac-Man make in the original video? 

c.   Watch the next video (“Translations and Reflections Only”).
Discuss: What do you think “reflection” means? Did Ms. Pac-Man make any other movements in the original video? 

d.   Watch the next video (“Translation, Reflections, and Rotations”).
Discuss: How can we get more precise to describe how far she translates, in what direction she rotates, etc.? 

e.   Lastly, watch the video with the coordinate plane (“Translations, Reflections, Rotations, and Coordinate Plane”).
Discuss: How does the coordinate plane help us communicate about movements more precisely? 

Guiding Questions

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References

Problem 2

For each pair of figures, decide whether these figures are the same size and same shape. Be prepared to justify your reasoning. You may use mathematical tools to make your decision.
 

Set A:
Set B:
Set C:
Set D:
Set E:
 

Guiding Questions

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References

Illustrative Mathematics Same Size, Same Shape?

Same Size, Same Shape?, accessed on Oct. 13, 2017, 1:11 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 3

For each set, determine if the two figures are congruent. Explain how you would move one figure to get to the other figure, and what transformations you would use.

a.   

b.   

c.   Lines $$P$$ and $$Q$$ are parallel and are transformed to map onto lines $$P'$$ and $$Q'$$

Guiding Questions

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Problem Set

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Target Task


Triangle $${{{CDE}}}$$ underwent a transformation that created triangle $${{{C'D'E'}}}$$.

a.   Describe how triangle $${{{CDE}}}$$ was transformed to become triangle $${{{C'D'E'}}}$$.

b.   What features stayed the same?

c.   What features changed? 

d.   Is triangle $${{{CDE}}}$$ congruent to triangle $${{{C'D'E'}}}$$? Explain how you know. 

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Examples where students are given two figures to 1) determine if the figures are congruent and 2) explain using rigid transformations; be sure to include congruent and non-congruent examples, similar to Anchor Problem #3
  • Example where either a reflection or a rotation may map one figure to another (see below) 
    • Malik says that the figure below was reflected, but Shayla says it was rotated. Who is right? Explain your answer.

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Lesson 2

Lesson Map

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Topic A: Congruence and Rigid Transformations

Topic B: Similarity and Dilations

Topic C: Angle Relationships

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