Students investigate congruence and similarity by studying transformations of figures in the coordinate plane, and apply these transformations to discover new angle relationships.
Math
Unit 3
8th Grade
In Unit 3, eighth-grade students bridge their understanding of geometry from middle school concepts to high school concepts. Until now, standards in the geometry domain have been either supporting or additional to the major standards. In eighth grade, geometry standards, especially the standards highlighted in this unit, are part of the major work of the grade and play a critical role in setting students up well for success in high school.
In this unit, students begin their work with transformations using patty paper (transparency paper) to experiment with, manipulate, and verify hypotheses around how shapes move under different transformations (MP.5). They use precision in their descriptions of transformations and in their justifications for why two figures may be similar or congruent to each other (MP.6). Students then apply their understanding of transformations to discover new angle relationships in parallel line diagrams and triangles.
Prior to eighth grade, students developed their understanding of geometric figures and learned how to draw them, calculate measurements, and model real-world situations. In seventh grade, students were introduced to the concept of scaling through scale drawings, and they solved for various measurements using proportional reasoning. Students will draw on these prior skills when they investigate dilations and similar triangles.
In high school geometry, students spend significant time studying congruence and similarity in-depth. They build off of the informal proofs and reasoning developed in eighth grade to hone their definitions of transformations, prove geometric theorems, and derive trigonometric ratios.
Pacing: 26 instructional days (22 lessons, 3 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 2021-2022 school year, see our 8th Grade Scope and Sequence Recommended Adjustments.
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This assessment accompanies Unit 3 and should be given on the suggested assessment day or after completing the unit.
To see all the materials needed for this course, view our 8th Grade Course Material Overview.
alternate interior and exterior angles
corresponding angles
reflection
similar
translation
rigid transformation
rotation
congruent/ congruence
dilation
scale factor
vertical angles
To see all the vocabulary for this course, view our 8th Grade Vocabulary Glossary.
Topic A: Congruence and Rigid Transformations
Topic B: Similarity and Dilations
Topic C: Angle Relationships
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 2
Solving One-Variable Equations
Unit 4
Functions