Unit Plan 18 (Grade 7 Math): Midyear Synthesis—Rates, Equations, and Geometry
7th graders engage in integrated performance tasks combining proportions, equations, inequalities, and geometry. They select appropriate models, apply unit reasoning, validate results with estimates, and communicate precise, well-justified mathematical conclusions.
Focus: Mixed performance tasks connecting proportions, equations/inequalities, and geometric reasoning with units.
Grade Level: 7
Subject Area: Mathematics (Integrated Review • Modeling & Reasoning)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This midyear synthesis weaves together ratios & proportional relationships, equations/inequalities, and geometry. Students rotate through studio-style tasks that demand modeling, unit reasoning, and clear mathematical communication. They choose among contexts (pricing plans, scale maps, design builds, angle puzzles), show multiple representations (tables, graphs, equations, diagrams), and justify decisions with estimates, checks, and units.
Essential Questions
- How do I choose the best model (table, graph, y = kx, equation, inequality) for a situation?
- Where do units and scale matter most in making a result believable?
- How do algebraic and geometric ideas support each other in solving real problems?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Model contexts with proportional relationships (find/interpret k, use y = kx, compare strategies with tables/graphs).
- Write and solve equations and inequalities from word problems; justify steps and check reasonableness.
- Apply scale drawings, angle relationships, cross-sections, and triangle construction conditions to analyze or create geometric representations.
- Use estimation, bounds, and unit analysis to validate results.
- Communicate solutions with clear diagrams, labels, and conclusions tied to the question asked.
Standards Alignment — CCSS Grade 7
- 7.RP.1–3: Analyze proportional relationships and use them to solve real-world and mathematical problems.
- 7.EE.1–4: Use properties of operations to generate equivalent expressions; solve real-life problems using equations and inequalities; assess reasonableness.
- 7.G.1–3, 7.G.5 (spiral): Solve problems with scale drawings; draw geometric shapes with given conditions; describe cross-sections; use angle facts to write and solve equations.
- Mathematical Practices emphasized: MP.1–MP.6 (make sense, reason, argue, model, use tools, attend to precision).
Success Criteria — Student Language
- I can pick a representation that fits the situation (table, graph, equation, inequality, diagram).
- I can keep track of units and scale, and use estimates to check my answers.
- I can justify algebraic steps and explain what my solution means in the context.
- I can create/read a scale drawing and explain a geometric choice (angle facts, cross-section).
- I can write a clear final statement that answers the question asked.