Curriculum / Math / 8th Grade / Unit 3: Transformations and Angle Relationships / Lesson 1
Math
Unit 3
8th Grade
Lesson 1 of 22
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Understand the rigid transformations that move figures in the plane (translation, reflection, rotation).
The core standards covered in this lesson
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
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?
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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.
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.
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 $$Q'$$
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15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
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.
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Describe and perform translations between congruent figures. Use translations to determine if figures are congruent.
Topic A: Congruence and Rigid Transformations
Standards
8.G.A.1.A8.G.A.1.B8.G.A.1.C8.G.A.2
Describe and apply properties of translations. Use coordinate points to represent relationships between translated figures.
8.G.A.1.A8.G.A.1.B8.G.A.1.C8.G.A.28.G.A.3
Describe and perform reflections between congruent figures. Use reflections to determine if figures are congruent.
Describe sequences of transformations between figures using reflections and translations. Use coordinate points to represent relationships between reflected figures.
Describe and perform rotations between congruent figures.
Describe sequences of transformations between figures using rotations and other transformations.
Describe a sequence of rigid transformations that will map one figure onto another.
Describe multiple rigid transformations using coordinate points.
8.G.A.28.G.A.3
Review rigid transformations and congruence between two figures.
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Topic B: Similarity and Dilations
Define a dilation as a non-rigid transformation, and understand the impact of scale factor.
8.G.A.4
Describe and perform dilations.
Describe a sequence of dilations and rigid motions between two figures. Use coordinate points to represent relationships between similar figures.
8.G.A.38.G.A.4
Determine and informally prove or disprove if two figures are similar or congruent using transformations.
8.G.A.28.G.A.4
Find missing side lengths in similar figures. Find scale factor between similar figures.
Use properties of similar triangles to model and solve real-world problems.
Topic C: Angle Relationships
Define and identify corresponding angles in parallel line diagrams. Review vertical, supplementary, and complementary angle relationships.
8.G.A.28.G.A.5
Define and identify alternate interior and alternate exterior angles in parallel line diagrams. Find missing angles in parallel line diagrams.
Solve for missing angle measures in parallel line diagrams using equations.
8.G.A.5
Define and use the interior angle sum theorem for triangles.
Define and use the exterior angle theorem for triangles.
Define and use the angle-angle criterion for similar triangles.
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