Unit Plan 36 (Grade 7 Math): Cumulative Synthesis & Exhibition

Focus: Show what you know: teams tackle integrated problems and defend reasoning with clear representations, units, and critique.

Grade Level: 7

Subject Area: Mathematics (Integrated Synthesis • Modeling • Communication)

Total Unit Duration: 5 sessions (one week), 45–60 minutes per session

I. Introduction

This week is a culminating exhibition of Grade 7 mathematics. Students work in teams on multi-part problems that weave ratios/proportions, rational number operations, expressions/equations/inequalities, geometry (circles, surface area, volume), and statistics/probability. Emphasis: choose an appropriate model, show coherent representations, track units, justify reasoning, and respond to critique.

Essential Questions

• How do I decide which mathematical tools and models best fit a complex, real situation?
• How do representations (diagrams, graphs, tables, equations) strengthen a mathematical argument?
• How can I communicate uncertainty, limits, and assumptions while defending my conclusions?

II. Objectives and Standards

Learning Objectives — Students will be able to…

1. Decompose complex contexts and select appropriate models (proportion, equation/inequality, geometric formulas, probability).
2. Move flexibly among representations and keep quantities and units consistent.
3. Solve multistep problems that integrate 7.RP, 7.NS, 7.EE, 7.G, 7.SP content; check results for reasonableness.
4. Construct and present a clear argument, citing evidence from calculations, graphs, and diagrams; respond to peer critique.
5. Identify assumptions/limitations and use precise mathematical language.

Standards Alignment — CCSS Grade 7 (comprehensive spiral)

• 7.RP: Proportional relationships; unit rates; multistep percent/rate problems.
• 7.NS: Operations with signed rational numbers in real contexts.
• 7.EE: Expressions/equations/inequalities modeling, solving, interpreting.
• 7.G: Circles, area, surface area, volume; angle relationships; nets.
• 7.SP: Sampling/inference; comparing populations; probability models; compound events/simulations.
• Mathematical Practices MP.1–MP.8 threaded throughout.

Success Criteria — Student Language

• I can choose a fitting model, explain why, and keep units straight.
• I can represent my thinking with a diagram/graph/table/equation and show how they connect.
• I can check answers (estimate, bounds, domain) and explain reasonableness.
• I can state assumptions/limits and answer questions about my choices.
• I can present a clear claim with evidence and revise after feedback.

III. Materials and Resources

Tasks & Tools (teacher acquires/curates)

• Integrated problem sets and project prompts (price plans, packaging/SA-volume, survey-and-decision, route planning, game-of-chance design).
• Graph paper, rulers, protractors, compasses, measuring tape, nets; calculators.
• Chance devices (dice, coins, non-uniform spinners) and small data sets for sampling comparisons.
• Posters or slide templates for exhibition; rubric and peer feedback forms.

Preparation

• Curate 3–4 choice tasks that each touch at least three strands (for example, RP/EE + G + SP).
• Create deliverable templates: Claim → Model(s) → Compute → Represent → Check → Conclude → Limits.
• Prepare exhibition schedule and norms for critique.

Common Misconceptions to Surface

• Treating any straight line as proportional (ignoring origin or additive fees).
• Confusing circumference vs area; square vs cubic units.
• Solving inequalities without interpreting solution sets or units.
• Overclaiming from small samples or assuming uniform probability without checking.
• Dropping signs or rounding too early in multistep computations.

IV. Lesson Procedure

(Each day: Launch → Explore (teams) → Discuss/Consolidate → Reflect)

Session 1: Launch & Planning (All domains; MP.1–MP.4)

• Launch (8–10 min): Review exhibition expectations and rubric. Quick mini-case: identify which strands the case taps and which representations would help.
• Explore (20–25 min): Teams select a choice task and complete a planning sheet: variables, units, models needed, data/measurements, and a timeline.
• Discuss (5–7 min): Share plans; class builds a checklist (models, representations, units, checks, limits).
• Reflect (Exit Ticket): Submit your plan with a first-pass estimate of the final quantity you’ll report.

Session 2: Modeling & Representation Build (RP/NS/EE/G/SP as needed; MP.5–MP.7)

• Launch (5–7 min): Strategy spotlight—moving between table ↔ graph ↔ equation and labeling units.
• Explore (25–30 min): Teams gather data, compute, and construct representations (graphs, diagrams, nets, tables). Include at least one estimation check and one assumption statement.
• Discuss (5–7 min): Midpoint check with another team: what’s convincing so far, what’s missing?
• Reflect (Exit Ticket): List one representation to improve tomorrow and why.

Session 3: Analysis, Checks, and Draft Claims (All domains; MP.2, MP.6)

• Launch (5–7 min): Reasonableness tools—bounds, domain restrictions, and unit audits.
• Explore (25–30 min): Finalize computations; run probability simulations or sampling comparisons if your task includes SP; compute circle/SA/volume if geometry is involved; write a draft claim with evidence and limits.
• Discuss (5–7 min): Quick gallery—post draft claims; classmates place sticky notes with questions and suggestions.
• Reflect (Exit Ticket): One revision you will make based on feedback.

Session 4: Rehearse & Peer Critique (MP.3, MP.6, MP.8)

• Launch (5–7 min): Presenting tips—front-load the claim, then walk the audience through model → representation → check → limits.
• Explore (25–30 min): Peer review rounds (triads): one team presents, one panel questions, one records action steps; rotate.
• Discuss (5–7 min): Whole-group debrief—common strengths and last-mile fixes.
• Reflect (Exit Ticket): Final checklist: units verified, assumptions stated, visuals readable, timing tight.

Session 5: Exhibition & Reflection (All domains; MP.1–MP.8)

• Task (35–40 min): Exhibition (posters or short slide talks). Each team:
  1. Claim and context.
  2. Models used (proportion/equation/inequality/geometry/probability) with labeled units.
  3. Representations (graph/diagram/table/net) and how they connect.
  4. Checks (estimate/bounds/domain) and assumptions/limitations.
  5. Conclusion and implications/next steps.
• Reflect (Exit Ticket): Individual written reflection—“What math choice most improved our argument, and what would we change with more time?”

V. Differentiation and Accommodations

Advanced Learners

• Add a sensitivity analysis: how much does your decision change if a parameter varies by ±10%?
• Create a break-even inequality between two competing models and interpret domain restrictions.
• Optimize a design (fixed volume, minimize surface area) and justify choice.

Targeted Support

• Provide a “Which Tool?” decision tree and unit/representation checklists.
• Offer scaffolded templates for graphs/nets and sentence frames for claims and limits.
• Allow number-choice simplifications first, then generalize to messier values.

Multilingual Learners

• Mini-glossary: claim, evidence, assumption, limitation, model, representation, estimate, bound, domain.
• Frames: “We used __ because __.” “This graph shows __; it connects to our equation __.” “A reasonable bound is __ to __ because __.”
• Allow bilingual prep; final claim in clear English with units.

IEP/504 & Accessibility

• Large-print graph paper and nets; high-contrast visuals; manipulatives for volume and probability.
• Chunked deadlines with mini-conferences; option to scribe; extended time.
• Clear rubrics; verbal + written directions.

VI. Assessment and Evaluation

Formative Checks (daily)

• S1: Approved plan with models/representations identified and a preliminary estimate.
• S2: Draft representations (graph/diagram/net/table) with units and at least one assumption.
• S3: Completed calculations with checks (estimate/bounds/domain) and draft claim.
• S4: Peer-critique notes and revision plan.
• S5: Exhibition product (poster/slides) and individual reflection.

Summative (end of week; 0–2 per criterion, total 10)

1. Model Selection & Integration (7.RP, 7.NS, 7.EE, 7.G, 7.SP as applicable; MP.1, MP.4)
   • 2: Appropriate models chosen and coherently integrated
   • 1: Minor mismatch or missing link
   • 0: Inappropriate or unclear models
2. Representations & Units (MP.5, MP.6, MP.7)
   • 2: Accurate, connected representations with correct and consistent units
   • 1: Minor unit/connection issues
   • 0: Misleading or unitless
3. Computation & Reasonableness (All content; MP.2)
   • 2: Correct calculations with estimates/bounds/domain checks
   • 1: Minor slip or weak check
   • 0: Off-track or unchecked
4. Argument & Communication (MP.3, MP.6)
   • 2: Clear claim, evidence, and responses to questions; precise language
   • 1: Partially supported or vague language
   • 0: Unclear, unsupported
5. Assumptions & Limitations (MP.1, MP.4)
   • 2: Explicit, sensible assumptions; thoughtful limits and next steps
   • 1: Partial or generic
   • 0: Missing

Feedback Protocol (use in Sessions 4–5)

• Step 1 — Read & Restate (1 minute): Reviewer restates the claim and key models/units used.
• Step 2 — TAG Feedback (2–3 minutes):
  • Tell a strength (representation clarity, solid unit work).
  • Ask a question (about assumptions, domain, sensitivity).
  • Give a suggestion (add a bound, label axes, connect table to graph).
• Step 3 — Evidence Check (1 minute): Point to the computation/visual that backs the claim.
• Step 4 — Author Response (1–2 minutes): Team records one revision they will implement.

VII. Reflection and Extension

Reflection Prompts

• Which representation most helped your audience understand your reasoning—and why?
• Where did an estimate or bound catch a possible error?
• If you repeated this exhibition, which assumption would you test or refine?

Extensions

• Publish a short math brief for a real audience (school newsletter or bulletin board).
• Turn your task into an assessment item: write a clear prompt, provide data/visuals, and include an answer key with rubrics.
• Create a mini-lesson teaching one technique you mastered (for example, comparing models with a break-even inequality).

Standards Trace — When Each Domain Is Addressed

• 7.RP — Sessions 2–5 (unit rates, proportional checks, percent/rate problems in projects).
• 7.NS — Sessions 2–3 (signed rational operations within contexts).
• 7.EE — Sessions 2–4 (equations/inequalities modeling and solving; interpretations).
• 7.G — Sessions 2–3 (circle, surface area, volume; nets and diagrams).
• 7.SP — Sessions 2–3 (sampling/inference, probability models, compound events/simulations).
• MP.1–MP.8 — Embedded throughout planning, modeling, precision, structure, tools, argument, and reflection.