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)
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The following assessments accompany Unit 3.
Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Have students complete the Mid-Unit Assessment after lesson 10.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.
Unit Launch
Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning.
alternate interior and exterior angles
congruent/ congruence
corresponding angles
dilation
reflection
rigid transformation
rotation
scale factor
similar
translation
vertical angles
To see all the vocabulary for Unit 3, view our 8th Grade Vocabulary Glossary.
To see all the materials needed for this course, view our 8th Grade Course Material Overview.
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