Unit Plan 36 (Grade 4 Math): Cumulative Synthesis & Exhibition

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

Grade Level: 4

Subject Area: Mathematics (Comprehensive Spiral)

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

I. Introduction

This capstone week invites students to apply the year’s learning in authentic, multi-step problems that cut across operations & algebraic thinking, place value/multi-digit computation, fractions, measurement & data, and geometry. Teams plan approaches, create representations, justify decisions, and exhibit their work.

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, diagrams, number lines, coordinate grids, equations) strengthen a clear argument?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Tackle multi-step, real-world problems requiring combined skills from 4.OA, 4.NBT, 4.NF, 4.MD, 4.G.
2. Select and justify efficient strategies (e.g., equivalent fractions vs. decimals, unit conversions vs. scaling).
3. Use representations (area/perimeter sketches, number lines, line plots, coordinate grids) 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 4 (spiral across the unit)

• 4.OA: Solve multi-step word problems; represent with equations; analyze patterns & rules.
• 4.NBT: Use place value understanding; perform multi-digit addition, subtraction, multiplication, division (by 1-digit).
• 4.NF: Explain equivalence; compare; add/subtract (like denominators); multiply fractions by whole numbers; connect to decimals.
• 4.MD: Measurement conversions within a system; perimeter/area of rectangles; line plots with fractional data; angles.
• 4.G: Draw/identify lines, angles; classify figures; symmetry.
• 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/decimals and units strategically and check reasonableness.
• 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, protractors, graph paper, coordinate plane templates; line-plot templates.
• Mixed project cards (e.g., playground design, snack-pack planning, garden bed layouts, field-trip timing).
• Conversion charts (customary/metric), fraction equivalence charts, area/perimeter anchor charts, angle reference sheets.
• 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 possible error is ___; we avoided it by ___.”

Common Misconceptions to Surface

• Dropping units between steps or converting the wrong direction.
• Confusing area and perimeter or surface and volume.
• Adding fractions without matching denominators when needed.
• Rounding too early; misreading scales on plots/axes.
• Assuming a figure’s “look” proves a classification (need property evidence).

Key Terms (highlighted in lessons)

• representation, estimate, reasonableness, equivalent fractions, decimal, conversion factor, perimeter, area, angle, line plot, coordinate plane, parallel, perpendicular, symmetry, claim, evidence, counterexample.

IV. Lesson Procedure

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

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

• Launch (8–10 min): Introduce a rich scenario (e.g., plan a class fair: costs with decimals, fraction recipes, time schedules).
• Explore (15–20 min): Teams identify sub-problems and map a plan (What needs conversion? Where use fractions vs. decimals? What to graph or model?).
• Discuss (8–10 min): Share plan choices; highlight multiple valid routes.
• Reflect (Exit Ticket): Write your solution plan: operations, representations, and where to estimate.

Session 2: Compute & Model — Decimals and Fractions (NBT, NF; MP.2, MP.7)

• Launch (5–7 min): Mini-lesson: choosing equivalents/common denominators vs. moving to decimals; keep units visible.
• Explore (15–20 min): Teams compute key subtotals two ways (where sensible) to confirm accuracy; document chosen method and rationale.
• Discuss (10–12 min): Share places where powers of ten, equivalents, or decomposition saved time.
• Reflect (Exit Ticket): “We chose fractions/decimals for ___ because ___.”

Session 3: Data & Measurement — Tables, Plots, and Units (MD; MP.4, MP.6)

• Launch (5–7 min): When to use a table, bar/line plot, or coordinate grid; set scales and labels.
• Explore (15–20 min): Build a display (e.g., line plot of item lengths, table of costs, grid layout). Solve questions using fraction/decimal operations and conversions.
• Discuss (10–12 min): Evaluate clarity and precision of units, titles, and scales.
• Reflect (Exit Ticket): One improvement to your representation and why.

Session 4: Geometry Connections — Properties & Unknowns (G, MD; MP.3, MP.5)

• Launch (8–10 min): Quick review: parallel/perpendicular, angle types, symmetry, area/perimeter of rectangles.
• Explore (15–20 min): Apply geometry to the scenario (e.g., design a booth with given area; find an unknown angle; justify classification).
• Discuss (8–10 min): How does the geometry support your overall solution?
• Reflect (Exit Ticket): State a claim about your design and cite evidence (measurement, angles, classification).

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—e.g., area/perimeter sketch or coordinate map; final conclusion; reasonableness).
• Peer Review (TAG, 5–7 min): Tell a strength (clarity of model/units); Ask a focused question (method choice, rounding, conversion); Give a suggestion (representation or explanation).
• Reflect (Exit Ticket): “We revised ___ because ___.”

V. Differentiation and Accommodations

Advanced Learners

• Add a constraint (budget cap, dimension limit) and optimize; compare 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.

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 project into milestones with quick checks each day.

VI. Assessment and Evaluation

Formative Checks (daily)

• S1: Coherent plan with sub-problems identified.
• S2: Appropriate choice and accurate use of fractions/decimals with units.
• S3: Accurate, well-labeled representations (tables/plots/grids) tied to questions.
• S4: Correct geometry application with property-based evidence.
• 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 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 short QR audio explanations.

Standards Trace — When Each Domain Is Addressed

• 4.OA — Multi-step Problems/Patterns: Sessions 1, 2, 4, 5.
• 4.NBT — Place Value & Multi-Digit Operations: Sessions 1–3.
• 4.NF — Fraction Reasoning & Operations: Sessions 1–3.
• 4.MD — Conversions, Data Displays, Perimeter/Area, Angles: Sessions 1–4 (and in 5 as evidence).
• 4.G — Lines/Angles, Classification, Symmetry: Session 4 (referenced in 5).
• MP.1–MP.8 — Practices: All sessions (perseverance, reasoning, argument, modeling, tools, precision, structure, regularity).