Unit Plan 36 (Grade 5 Math): Cumulative Synthesis & Exhibition

Focus: Show what you know with integrated tasks blending NBT, NF, OA, MD, and G; students present and defend reasoning with clear models, units, and explanations.

Grade Level: 5

Subject Area: Mathematics (Comprehensive Spiral)

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

I. Introduction

This capstone week lets students apply the year’s learning in authentic, multi-step problems that cut across place value/decimals (NBT), fractions (NF), expressions & patterns (OA), measurement/data (MD), and geometry (G). Teams design solutions, justify methods, and exhibit their work to peers.

Essential Questions

• How do I choose the most efficient strategy across multiple domains?
• What counts as evidence when defending a mathematical decision?
• How do representations (tables, graphs, diagrams, equations, models) strengthen a clear mathematical argument?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Tackle multi-step, real-world problems requiring combined skills from 5.OA, 5.NBT, 5.NF, 5.MD, 5.G.
2. Select and justify efficient strategies (e.g., equivalent fractions vs. decimals, unit conversions vs. scaling).
3. Use representations (diagrams, number lines, coordinate graphs, line plots, volume sketches) to support claims.
4. Communicate with precision: correct units, labels, and reasonableness checks.
5. Present and defend solutions using mathematical language, responding to questions and counterexamples.

Standards Alignment — CCSS Grade 5 (spiral across the unit)

• 5.OA: Write/interpret numerical expressions; analyze patterns and relationships.
• 5.NBT: Place value patterns; decimal operations; powers of ten.
• 5.NF: Add/subtract/multiply/divide fractions (including mixed numbers) and apply in context.
• 5.MD: Conversions, line plots with fractional units, volume formulas and additive reasoning.
• 5.G: Coordinate plane (first quadrant) and classification/attribute reasoning.
• Mathematical Practices (MP.1–MP.8) threaded throughout.

Success Criteria — Student Language

• I can plan a multi-step solution, show models, and explain why it works.
• I can choose fractions or decimals strategically and keep units accurate.
• I can present my thinking and answer questions using math vocabulary and evidence.

III. Materials and Resources

Tasks & Tools (teacher acquires/curates)

• Math notebooks; rulers; grid/graph paper; coordinate plane templates; line-plot templates; unit cubes or cube nets.
• Mixed project cards (e.g., school fair planning, class garden boxes, supply orders, route maps).
• Conversion strips (customary/metric), fraction equivalence charts, volume anchor charts.
• Feedback rubrics and TAG (Tell–Ask–Give) peer-review slips.

Preparation

• Anchor charts: Estimate–Compute–Check, Choosing a Representation, Units & Conversions, Defending a Claim.
• Sentence stems: “I chose ___ because ,” “My model shows ** therefore ,” “A potential error is **, we avoided it by ___.”

Common Misconceptions to Surface

• Dropping units between steps.
• Mixing surface area and volume.
• Adding unlike denominators without making equivalent fractions.
• Rounding too early; converting in the wrong direction.
• Assuming a coordinate graph’s “looks like” means the classification is proven (need evidence).

Key Terms (highlighted in lessons)

• estimate, representation, equivalent fractions, decimal place value, conversion factor, line plot, volume, base area, coordinate plane, hierarchy, claim, evidence, counterexample, reasonableness.

IV. Lesson Procedure

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

Session 1: Capstone Task Launch — Plan Your Approach (OA, NBT, NF, MD; MP.1, MP.4)

• Launch (8–10 min): Introduce a rich scenario (e.g., planning snack packs: fractional recipes, unit conversions, and cost/quantity with decimals).
• Explore (15–20 min): Teams identify sub-problems and map a plan (What must we convert? Where do we use fraction vs. decimal? What should we graph or model?).
• Discuss (8–10 min): Share planning choices; highlight diverse but valid routes.
• Reflect (Exit Ticket): Write your solution plan: operations, representations, and where to estimate.

Session 2: Data & Geometry Crossover — Graphs, Plots, and Grids (MD, G; MP.5, MP.6)

• Launch (5–7 min): Mini-lesson: choose displays—line plot vs. table/graph; when to use a coordinate grid.
• Explore (15–20 min): Teams incorporate a data display (line plot of measurements or bar graph of costs) and, if relevant, a coordinate diagram (layout, route, or bin design).
• Discuss (10–12 min): Evaluate clarity: titles, labels, units, readable scales.
• Reflect (Exit Ticket): One improvement to your representation and why.

Session 3: Fraction & Decimal Decisions — Efficiency and Accuracy (NF, NBT; MP.2, MP.7)

• Launch (8–10 min): Compare two approaches: operate in fractions vs. decimals; which is more efficient and why?
• Explore (15–20 min): Teams compute critical subtotals both ways (where sensible) to confirm accuracy; document the chosen method and rationale.
• Discuss (8–10 min): Share places where equivalents, LCD, or powers of ten saved time.
• Reflect (Exit Ticket): “We chose fractions/decimals for ___ because ___.”

Session 4: Build the Argument — Write, Check, and Anticipate (OA, All; MP.3, MP.6)

• Launch (5–7 min): Model a short defense paragraph: claim → evidence (work + representation) → units → reasonableness.
• Explore (15–20 min): Teams draft their argument; add a counterexample check (what might a skeptic ask?).
• Discuss (10–12 min): Peer micro–Q&A: partners ask for clarifications; teams tighten explanations.
• Reflect (Exit Ticket): Note one anticipated question and your prepared response.

Session 5: Exhibition — Present, Question, Revise (All domains; MP.1–MP.8)

• Task (25–30 min): Present your solution board (problem statement; plan; work with units; data/graph; model like volume sketch or grid; final conclusion; reasonableness).
• Peer Review (TAG, 5–7 min):
  • Tell a strength (clarity of model/units).
  • Ask a question (method choice, rounding, or conversion).
  • Give a suggestion (representation or explanation to tighten).
• Reflect (Exit Ticket): “We revised ___ because ___.”

V. Differentiation and Accommodations

Advanced Learners

• Add a constraint (budget cap, dimension limit) and optimize under it; compare two near-optimal solutions and defend the better choice.
• Require two distinct representations leading to the same answer; discuss pros/cons.

Targeted Support

• Provide checklists (units present, labels, estimate, computation, check).
• Offer scaffolded conversion tables and equivalence ladders (fractions ↔ decimals).
• Small, well-chosen numbers to keep cognitive load on reasoning rather than arithmetic.

Multilingual Learners

• Visual sentence frames: “Our claim is ___ because ___,” “The graph/model shows ___,” “We rounded because ___ (context).”
• Word/visual glossary for key terms used in this unit.

IEP/504 & Accessibility

• Option for oral presentation with a partner scribe; large-format graph/coordinate paper.
• Chunk the task into milestones with quick checks each day.

VI. Assessment and Evaluation

Formative Checks (daily)

• S1: Coherent plan with sub-problems identified.
• S2: Accurate, well-labeled representations (units/scales).
• S3: Appropriate choice and accurate use of fractions/decimals.
• S4: Clear written argument with reasonableness check.
• S5: Effective presentation and responsive Q&A.

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

1. Mathematical Accuracy (All domains)
   • 2: Correct computations and conversions with units
   • 1: Minor errors not affecting the conclusion
   • 0: Major errors or unsupported results
2. Strategy & Representation (MP.4, MP.5, MP.7)
   • 2: Efficient strategy; representations fit the purpose and are well-labeled
   • 1: Strategy mostly sound; minor labeling issues
   • 0: Inefficient or mismatched representations
3. Reasoning & Argument (MP.2, MP.3)
   • 2: Clear claim, evidence, and counterexample awareness
   • 1: Partially justified or vague in places
   • 0: Assertions without support
4. Precision & Communication (MP.6)
   • 2: Units, rounding, and symbols precise; readable work
   • 1: Minor precision lapses
   • 0: Disorganized or imprecise
5. Collaboration & Presentation (MP.1, MP.8)
   • 2: Equitable teamwork; addresses feedback thoughtfully
   • 1: Uneven participation or limited revisions
   • 0: Minimal collaboration or dismisses feedback

Feedback Protocol (Exhibition)

• Read & Restate (1 min): Reviewer restates the team’s claim and goal.
• TAG (2–3 min): Tell a strength, Ask a focused question, Give a concrete suggestion.
• Evidence Check (1 min): Reviewer points to a representation or calculation that supports—or challenges—the claim.
• Author Response (1–2 min): Team records one revision and why it improves the solution.

VII. Reflection and Extension

Reflection Prompts

• Where did your estimate catch a possible error?
• If you had one more day, what data display or model would you add and why?
• Which math practice helped your team the most?

Extensions

• Alternate Scenario: Rework your solution under a new constraint (budget change; size limit).
• Two-Method Proof: Solve a core step two ways (fractions vs. decimals, table vs. equation) and compare.
• Community Share: Turn your exhibition board into a family-night or hallway display with QR audio explanations.

Standards Trace — When Each Domain Is Addressed

• 5.OA — Sessions 1, 3, 4, 5 (planning operations, expressions, argument structure).
• 5.NBT — Sessions 1, 3 (place value, decimal operations, powers of ten in context).
• 5.NF — Sessions 1, 3 (fraction operations, equivalence, reasonableness).
• 5.MD — Sessions 1, 2 (conversions; line plots; volume where applicable).
• 5.G — Session 2 (coordinate modeling) and as needed for layout/classification claims.
• MP.1–MP.8 — All sessions (perseverance, reasoning, argument, modeling, tools, precision, structure, regularity).