Unit Plan 27 (Grade 8 Math): Geometry Mixed Review—Transform, Compare, Solve
8th graders integrate geometry’s big ideas—transformations, similarity, angle reasoning, and Pythagorean applications—through real-world, multi-step problems. They choose strategies, justify methods, and model with precision across diagrams and coordinates.
Focus: Synthesize transformations, similarity, angle relationships, and Pythagorean applications in integrated tasks.
Grade Level: 8
Subject Area: Mathematics (Geometry • Coordinate Geometry • Modeling)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week pulls together the big geometry ideas: rigid motions and congruence, dilations and similarity, angle relationships, the Pythagorean Theorem and distance, and volume of round solids. Students will switch flexibly among representations (diagrams, coordinates, and words), choose the right tool (transform, compare, solve), and justify their choices. The emphasis is on multi-step, real contexts where more than one concept shows up in the same problem.
Essential Questions
- Which approach—transformations, similarity, or Pythagorean—best fits a given problem, and why?
- How do angle relationships (parallel lines, triangle sum, exterior angle) support similarity or congruence arguments?
- How do I move confidently between diagrams and coordinates, and explain my reasoning clearly?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Use sequences of rigid motions to argue congruence and describe precise moves on the plane.
- Use dilations and similarity (including scale drawings and indirect measurement) to determine unknown lengths.
- Apply angle relationships to set up similarity or to compute unknown angles in multi-step diagrams.
- Apply the Pythagorean Theorem and the distance formula to solve coordinate and real-world problems; make reasonableness checks.
- Tackle integrated tasks that may require more than one idea and communicate concise justifications.
Standards Alignment — CCSS Grade 8 (spiral emphasis this week)
- 8.G.1–8.G.3: Rigid motions and their coordinate effects; invariants; congruence via sequences.
- 8.G.2: Congruence through rigid motions; describe a sequence.
- 8.G.3–8.G.4: Coordinate rules for dilations; similarity via transformations and sequences.
- 8.G.5: Informal arguments about angle sum, exterior angle, and angles with parallel lines.
- 8.G.6–8.G.8: Pythagorean Theorem, its converse, and distance on the coordinate plane.
- 8.G.9: Volume of cylinders, cones, spheres (light touch via one composite application).
- Mathematical Practices MP.1–MP.4: Make sense of problems, reason abstractly, construct viable arguments, and model with mathematics.
Success Criteria (student-friendly)
- I can choose a strategy (transform, compare, or solve with Pythagorean) and explain why it fits.
- I can show congruence or similarity with a clear sequence and matching parts.
- I can compute missing measures with units and a reasonableness check.
- I can communicate short, precise justifications that others can follow.