Unit Plan 36 (Grade 6 Math): Cumulative Synthesis & Exhibition
6th graders demonstrate mastery across all math strands—ratios, number system, expressions, geometry, and statistics—by solving integrated real-world problems. Students model, calculate, and present claims with clear reasoning, evidence, and precise mathematical communication.
Focus: Show what you know with integrated problems blending ratios/percents, number system, expressions & equations, geometry, and statistics; present and defend your reasoning.
Grade Level: 6
Subject Area: Mathematics (Comprehensive Spiral — 6.RP, 6.NS, 6.EE, 6.G, 6.SP)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This capstone week is a showcase of Grade 6 mathematics in action. Student teams select or are assigned a real-world scenario, plan a solution path, produce models and calculations (tables, graphs, equations, nets, summaries), and deliver a 5-minute presentation with Q&A. Emphasis is on modeling, precision, assumptions, and clear communication.
Essential Questions
- Which representations (table, graph, equation, net, summary) best fit the problem and why?
- What assumptions and units are necessary, and how do they affect the result?
- How do we check reasonableness and revise models when evidence changes?
- How do we present a claim–evidence–reasoning argument that others can follow?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Plan a solution pathway that identifies needed math strands and representations.
- Model situations with ratio tables, double number lines, equations/inequalities, nets, graphs, and statistical displays.
- Compute accurately with fractions/decimals, percents, unit rates, conversions, area/surface area/volume, and coordinate distances; include units.
- Justify conclusions with evidence and assumptions, and critique peer reasoning.
- Present findings clearly and respond to questions with mathematical language.
Standards Alignment — CCSS Grade 6 (Comprehensive Spiral)
- 6.RP.1–3: Ratios, unit rates, percent problems, conversions.
- 6.NS.1–3, 5–8: Fraction/decimal operations; rational order/absolute value; coordinate plane and grid distances.
- 6.EE.1–4, 5–9: Exponents/order; expressions & equivalence; one-step equations/inequalities; two-variable relationships (y in terms of x).
- 6.G.1–4: Area of polygons; volume of right rectangular prisms (including fractional edges); polygons on coordinate plane; surface area via nets.
- 6.SP.1–5: Statistical questions; displays (dot plot, histogram, box plot); center/variability; summaries in context.
- Mathematical Practices MP.1–MP.8 emphasized and observable in planning, modeling, precision, structure, and reflection.
Success Criteria — Student Language
- I can choose and explain the representations that fit my problem.
- I can calculate with correct units and show my assumptions.
- I can connect ratios/percents, algebra, geometry, and statistics in one solution.
- I can defend my claim with evidence and respond to questions clearly.
- I can revise my model when feedback or data suggests a better approach.