Unit Plan 36 (Grade 6 Math): Cumulative Synthesis & Exhibition

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:

1. Plan a solution pathway that identifies needed math strands and representations.
2. Model situations with ratio tables, double number lines, equations/inequalities, nets, graphs, and statistical displays.
3. Compute accurately with fractions/decimals, percents, unit rates, conversions, area/surface area/volume, and coordinate distances; include units.
4. Justify conclusions with evidence and assumptions, and critique peer reasoning.
5. 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.

III. Materials and Resources

Tasks & Tools (teacher acquires/curates)

• Math notebooks; graph paper (coordinate and dot); rulers; colored pencils/highlighters; scissors/tape for nets; sticky notes.
• Templates: Project Plan, Computation Log, Assumptions & Units Sheet, Figure List, Presentation Outline.
• Scenario sets (choose a few):
  • Café Combo Optimizer: unit pricing, percent discounts/tax/tip, decision with 6.RP and 6.NS.3.
  • Park Plan & Packaging: composite area, surface area via nets, volume for bins; tradeoffs (6.G.1–4).
  • Route & Schedule: constant speed comparisons, unit conversions, coordinate maps and grid distances (6.RP.3b, 6.NS.8).
  • Class Survey: design a statistical question, collect data, build dot/histogram/box plot, report center & spread (6.SP.1–5).
  • Small-Business Budget: markups/discounts, recipe scaling (fraction division), monthly cost projection with equations/graphs (6.RP, 6.NS.1, 6.EE.9).
• Exit tickets and peer-feedback cards.

Preparation

• Anchor charts: Claim–Evidence–Reasoning, Units & Assumptions, Choosing Representations, Quality Graph & Net Checklist.
• Provide small, realistic datasets or allow quick class-data collection.

Common Misconceptions to Surface

• Comparing options without unit rate or forgetting tax/tip.
• Mixing perimeter and area, square vs cubic units.
• Forcing proportional models when b ≠ 0 (nonzero start).
• Using diagonal distance instead of horizontal/vertical grid distance.
• Statistical summaries that ignore context, outliers, or variability.

Key Terms (highlighted in lessons)

• ratio, unit rate, percent, conversion, expression, equation/inequality, variable, y in terms of x, compose/decompose, net, surface area, volume, coordinate plane, horizontal/vertical distance, statistical question, center (mean/median), variability (MAD/IQR), assumption, reasonableness.

IV. Lesson Procedure

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

Session 1: Launch & Project Planning (all strands; MP.1, MP.4)

• Launch (8–10 min): Showcase a brief exemplar of claim–evidence–reasoning.
• Explore/Build (20–25 min): Teams pick a scenario; complete Project Plan (goal, needed data, chosen representations, assumptions/units, timeline). Begin first computations (e.g., unit rates or rough area sketches).
• Discuss (8–10 min): Quick stand-ups: each team states claim-in-progress and one assumption.
• Reflect (Exit Ticket): “Our claim might be ___ because ___; to confirm, we must ___.”

Session 2: Investigation Day — Ratios, Percents, and Number System (6.RP, 6.NS; MP.6)

• Launch (5–7 min): Mini-lesson on estimate → compute → compare for percent/decimal work.
• Explore/Build (20–25 min): Teams finalize unit rates, percent calculations, conversions, and fraction/decimal operations; log work on the Computation Log with unit sentences.
• Discuss (8–10 min): Gallery pause to scan for precision and units.
• Reflect (Exit Ticket): Note one assumption and one reasonableness check you used.

Session 3: Investigation Day — Algebra, Geometry, and Statistics (6.EE, 6.G, 6.SP; MP.4, MP.7)

• Launch (8–10 min): Quick reminders: y in terms of x for simple relationships; net checklist; display selection (dot/histogram/box).
• Explore/Build (20–25 min): Produce equations/graphs (if applicable), draw nets and compute SA/Volume, build statistical displays with center & variability; document choices on the Figure List.
• Discuss (8–10 min): Peer micro-critique: does each figure support the claim? Are units and labels present?
• Reflect (Exit Ticket): Identify one figure that most strengthens your claim and why.

Session 4: Synthesis & Presentation Build (MP.3, MP.6, MP.8)

• Launch (5–7 min): Model a strong conclusion that states claim + numeric evidence + limitation.
• Explore/Build (20–25 min): Draft the Presentation Outline:
  1. Problem & assumptions, 2) Methods & representations, 3) Results with units, 4) Decision/Design, 5) Limitations & next steps. Rehearse; prepare visuals (boards or slides).
• Discuss (8–10 min): Structured peer feedback (see protocol below).
• Reflect (Exit Ticket): Record one specific revision you will make.

Session 5: Exhibition & Reflection (MP.1–MP.8 in action)

• Task (25–30 min): Teams deliver 5-minute presentations with visual evidence; Q&A from peers.
• Discuss (5–7 min): Whole-class debrief: Which assumptions mattered most? Which representations were most persuasive?
• Reflect (Exit Ticket): Personal reflection: “What I do confidently now… What I will refine next year…”.

V. Differentiation and Accommodations

Advanced Learners

• Sensitivity analysis: Vary a key assumption (tax rate, dimensions) and report impact.
• Optimization prompt: Given a fixed SA, compare volumes (qualitative); or fixed budget, maximize outcome.
• Piecewise model: Model a start fee + per-unit rate; justify non-proportional choice.

Targeted Support

• Provide worked-example libraries for each strand; scaffolded Project Plan with checkboxes.
• Assign team roles (Data, Computation, Diagrams, Speaker).
• Frequent conferences to verify units, labels, and figure-purpose alignment.

Multilingual Learners

• Visual glossary for project terms; bilingual stems for claim, evidence, assumption, limitation.
• Sentence stems: “Our claim is ___ because the ratio/graph/net shows ___,” “A key assumption is ___, which affects ___.”

IEP/504 & Accessibility

• Timers and chunked deliverables; large-print grids; manipulatives for nets.
• Option to scribe; extended time; calculators permitted with emphasis on setup and units.
• Quiet practice space for rehearsal.

VI. Assessment and Evaluation

Formative Checks (daily)

• S1: Project Plan with at least one assumption and chosen representations.
• S2: Percent/ratio computations with unit sentences and an estimate check.
• S3: At least one algebraic, one geometric, and one statistical artifact with correct labels/units.
• S4: Presentation Outline with a defensible conclusion and noted limitations.
• S5: Presentation delivered; active participation in Q&A.

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

1. Modeling & Representations (MP.4; 6.RP/6.EE/6.G/6.SP)
   • 2: Chosen representations are appropriate, accurate, and support the claim
   • 1: Mostly appropriate; minor mismatches or omissions
   • 0: Inappropriate or inaccurate representations
2. Computation & Precision (MP.6; 6.NS/6.RP)
   • 2: Correct calculations with units, reasonable rounding, and checks
   • 1: Minor arithmetic/label slip; overall sound
   • 0: Frequent errors; missing units
3. Connections Across Strands (MP.7/MP.2)
   • 2: Clear integration of at least three strands with explicit links
   • 1: Two strands connected; links somewhat implicit
   • 0: Isolated skills with no connections
4. Argument & Evidence (MP.3)
   • 2: Claim–Evidence–Reasoning is coherent; addresses assumptions/limitations
   • 1: Claim present; evidence thin or reasoning partial
   • 0: Unsupported or unclear claim
5. Communication & Presentation (SL-like; MP.1, MP.8)
   • 2: Clear visuals, pacing, vocabulary; fielded Q&A with math-based answers
   • 1: Generally clear; minor gaps in visuals or Q&A
   • 0: Hard to follow; incomplete presentation

Feedback Protocol (for Session 4 rehearsals and Session 5 peer review)

• Read & Restate (1 minute): Reviewer restates the team’s claim and primary evidence.
• TAG (2–3 minutes): Tell a strength (strong unit tracking or clear graph), Ask a question (about an assumption or method), Give a suggestion (clarify a figure or add a limitation).
• Evidence Pointer (1 minute): Reviewer points to a specific calculation/figure that could be clearer.
• Author Response (1–2 minutes): Team names one revision and how it improves the argument.

VII. Reflection and Extension

Reflection Prompts

• Which assumption most influenced your result? How would changing it alter your decision?
• Which representation carried the most persuasive weight and why?
• Where did estimation or unit analysis prevent an error?

Extensions

• Public Posting: Turn your project into a one-page math brief with figures and a QR link to your slides.
• Real Data Check: Gather a small new sample or price check and update your model; report changes.
• Next-Level Challenge: Add a constraint (budget, material limit, time window) and re-optimize.

Standards Trace — When Each Standard Is Addressed

• 6.RP.1–3 — Sessions 2–5 (unit rates, percent, conversions used in decisions).
• 6.NS.1–3, 5–8 — Sessions 2–4 (fraction/decimal operations; order/absolute value; plotting and grid distances).
• 6.EE.1–4, 5–9 — Sessions 3–4 (order/exponents; expressions/equivalence; equations/inequalities; y in terms of x).
• 6.G.1–4 — Sessions 3–5 (area, SA via nets, volume; polygons on coordinate plane).
• 6.SP.1–5 — Sessions 3–5 (statistical question; displays; center/variability; summaries).
• MP.1–MP.8 — Evident throughout planning, modeling, precision, structure, tool use, reasoning, regularity, and communication.