Unit Plan 36 (Grade 8 Math): Cumulative Synthesis & Exhibition

Focus: Show what you know—multi-standard tasks blending functions, linear models, geometry, and statistics; students present solutions and defend reasoning.

Grade Level: 8

Subject Area: Mathematics (Integrated Algebra • Functions • Geometry • Statistics & Probability • Modeling)

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

I. Introduction

This final unit asks students to synthesize their Grade 8 learning in authentic, multi-part performance tasks. Teams will plan, solve, and present solutions that integrate number system reasoning, equations/functions and linear models, geometry and measurement, and statistics. Emphasis: tool choice, units and precision, evidence-based claims, and defense of reasoning through written and oral explanations.

Essential Questions

• How do I decide which mathematical tools (algebraic, geometric, graphical, statistical) fit a problem and why?
• How do assumptions, units, and precision affect decisions and results?
• What does a convincing mathematical argument look and sound like for a real audience?

II. Objectives and Standards

Learning Objectives — Students will be able to…

1. Plan an approach to a complex task, selecting appropriate representations (equations, tables, graphs, diagrams) and justifying method choices.
2. Apply Grade 8 content to integrated problems: build/interpret functions and linear models; solve equations and systems; use the Pythagorean Theorem, distance, and volume; construct/interpret scatter plots, lines of fit, and two-way tables.
3. Communicate solutions with clear units, sensible precision, and reasonableness checks; compare alternatives and note limitations.
4. Present and defend conclusions; critique others’ reasoning using mathematical language and evidence.

Standards Alignment — CCSS Grade 8 (Comprehensive Spiral)

• 8.NS.1–8.NS.2 (Number System)
• 8.EE.1–8.EE.8 (Expressions & Equations; includes scientific notation, exponent rules, equations, systems)
• 8.F.1–8.F.5 (Functions; modeling with linear functions)
• 8.G.1–8.G.9 (Geometry; transformations, similarity, Pythagorean, distance, volume)
• 8.SP.1–8.SP.4 (Statistics & Probability; scatter plots, lines of fit, two-way tables)
• Mathematical Practices MP.1–MP.8 integrated throughout

Success Criteria — Student Language

• I can choose a good strategy and say why it fits.
• I can show my work in more than one way (diagram, graph, equation, table) and keep units and precision straight.
• I can check if an answer makes sense (bounds, order of magnitude, looks right on the graph).
• I can explain my thinking clearly and respond to questions with evidence.
• I can give feedback to a classmate that is specific, kind, and mathematical.

III. Materials and Resources

Tasks & Tools (teacher acquires/curates)

• Graph paper, rulers/straightedges, protractors, calculators; large poster paper or slide templates for exhibitions.
• Mixed-domain performance tasks (3–5 choices), e.g.:
  • Transit Ramp Design: Slope criteria (functions), right-triangle/Pythagorean checks (geometry), material volume estimate (measurement), cost comparison (equations).
  • School Energy Snapshot: Two-variable data (scatter plot), line of best fit and prediction with cautions (statistics/functions), unit conversions and order-of-magnitude checks (number system).
  • Plan Comparison: Two linear pricing plans (functions/systems), break-even analysis, sensitivity to slope/intercept, present recommendation.
  • Water Tank Build: Composite solids (cylinder + cone), capacity vs fill rate (functions), precision and units.
  • Sports Data Brief: Two-way table for categorical variables, conditional percentages and association, short memo with limitations.
• Anchor charts: Method Match, Units & Precision, Argument Frames, Feedback Stems.

Preparation

• Provide task briefs with required deliverables (calculations, diagram/graph, written justification, final claim).
• Create planning organizers (Assumptions • Data/Measures • Tools • Steps • Checks • Limitations).
• Prepare rubrics aligned to content and practices; set norms for Q&A.

Common Misconceptions to Surface

• Choosing a method out of habit rather than fit to structure.
• Mixing rate vs initial value or misreading slope/intercept.
• Using slant height instead of perpendicular height in cones; radius vs diameter.
• Overstating causal claims from associations; ignoring units/precision.

IV. Lesson Procedure

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

Session 1: Kickoff — Plan the Investigation (MP.1–MP.4)

• Launch (8–10 min): Showcase a sample solution excerpt and model the planning organizer.
• Explore (15–20 min): Teams choose a task, list assumptions, identify needed measurements/data, and select tools/representations.
• Discuss (8–10 min): Share plans; peer questions focus on fit of methods and missing data.
• Reflect (Exit Ticket): “Our first method choice is ___ because ___.”

Session 2: Build the Math — Models, Diagrams, and Data (8.EE, 8.F, 8.G, 8.SP)

• Launch (5–7 min): Quick mini-lessons on common hurdles (e.g., unit conversions, reading slope from context).
• Explore (15–20 min): Teams construct graphs/diagrams, set up equations/systems, and compute with units.
• Discuss (10–12 min): Midpoint check—each team states one evidence-backed claim and one open question.
• Reflect (Exit Ticket): “The most sensitive number in our model is ___ because ___.”

Session 3: Analyze, Check, and Revise (MP.3, MP.6)

• Launch (8–10 min): Model a reasonableness check (bounds, order of magnitude, visual fit).
• Explore (15–20 min): Teams run checks, compare alternatives (e.g., through-origin vs y = mx + b), adjust assumptions if justified, and finalize computations.
• Discuss (8–10 min): Pair critique: exchange work and give specific feedback using sentence stems.
• Reflect (Exit Ticket): “One revision we made and why it matters: ___.”

Session 4: Craft the Argument — Poster/Slides and Rehearsal (MP.2, MP.4, MP.6)

• Launch (5–7 min): Presentation checklist: Claim • Evidence (math) • Reasoning • Limits/Next Steps.
• Explore (15–20 min): Teams assemble a poster or slide deck with: problem restatement, assumptions, visuals (diagram/graph), key calculations with units, final claim, limitations.
• Discuss (10–12 min): Rehearsal with timed run-through and targeted peer Q&A.
• Reflect (Exit Ticket): “The question I hope the audience asks is ___ because ___.”

Session 5: Exhibition & Defense (MP.1–MP.8)

• Task (25–30 min): Gallery walk or short talks (2–3 minutes/team) with live Q&A. Presenters must justify method choice, precision, and limitations.
• Discuss (5–7 min): Debrief—highlight strong uses of multiple representations and clear unit reasoning.
• Reflect (Exit Ticket): “If we had one more day, we would ___ to strengthen our argument.”

V. Differentiation and Accommodations

Advanced Learners

• Compare two competing models; compute a small error snapshot (e.g., average absolute error) or run a brief sensitivity test (change slope/intercept or a dimension by 5%).
• Add a constraint (budget, maximum height) and re-optimize the recommendation.

Targeted Support

• Provide scaffolded templates for graphs, tables, and formula selection; curated number sets to reduce computational load while preserving reasoning.
• Conference checkpoints with one required representation switch (table → graph, or diagram → equation).

Multilingual Learners

• Mini-glossary and argument frames: “We chose ___ because the problem has ___.” “Our graph shows ___; therefore ___.” “A limitation is ___ because ___.”
• Allow bilingual drafting; final display uses clear English labels and units.

IEP/504 & Accessibility

• Large-format, high-contrast templates; chunk tasks with checklists.
• Option to submit a recorded narration; roles within teams (data, visuals, speaker) to leverage strengths.
• Extended time as needed.

VI. Assessment and Evaluation

Formative Checks (daily)

• S1: Completed planning organizer with justified method choices.
• S2: Interim visuals (graph/diagram) plus at least one computed result with units.
• S3: Documented reasonableness check and one revision.
• S4: Draft poster/slides meeting the checklist.

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

1. Modeling & Method Choice (MP.1–MP.4)
   • 2: Methods fit structure; assumptions stated; choices justified
   • 1: Methods workable; limited justification
   • 0: Poor fit or unjustified
2. Algebra/Functions Reasoning (8.EE, 8.F)
   • 2: Correct equations/models; slope/intercept or system solution interpreted with units
   • 1: Minor slips; interpretation thin
   • 0: Incorrect or unsupported
3. Geometry & Measurement (8.G)
   • 2: Accurate diagrams; correct use of Pythagorean/distance/volume with units and precision
   • 1: Minor unit/rounding or setup issue
   • 0: Incorrect or unlabeled
4. Statistics & Data Evidence (8.SP)
   • 2: Appropriate plots/tables; valid descriptions of association/fit; cautious claims
   • 1: Partial or vague evidence
   • 0: Misinterpretation or missing
5. Communication & Defense (MP.3, MP.6, MP.7, MP.8)
   • 2: Clear claim–evidence–reasoning; attends to structure/regularity; handles Q&A with evidence
   • 1: Mostly clear; limited defense
   • 0: Disorganized; cannot defend

VII. Reflection and Extension

Reflection Prompts

• Which representation switch unlocked the problem for you and why?
• Where did units/precision matter most in your result?
• How did a limitation or assumption change your conclusion?

Extensions

• Stakeholder Memo: Convert your presentation to a one-page memo for a non-math audience (principal, coach, facilities).
• Iterate with New Data: Add 3–5 new data points or a new constraint and note how the recommendation changes.
• Peer Repository: Contribute your task, solution outline, and rubric notes to a shared “Grade 8 Math Exhibition” bank.

Standards Trace — When Each Standard Is Taught/Assessed

• 8.NS.1–8.NS.2 — As needed for approximations, unit conversions, and order-of-magnitude checks; assessed in criteria 1 and 5.
• 8.EE.1–8.EE.8 — Sessions 2–5 within modeling, equations, and systems; assessed in criteria 2 and 5.
• 8.F.1–8.F.5 — Sessions 2–5 for building/interpreting linear functions and qualitative graphs; assessed in criteria 2 and 5.
• 8.G.1–8.G.9 — Sessions 2–5 for diagrams, Pythagorean/distance, and volume; assessed in criterion 3.
• 8.SP.1–8.SP.4 — Sessions 2–5 for plots/fit/tables and association; assessed in criterion 4.
• MP.1–MP.8 — Embedded all week; emphasized in method choice, structure, precision, strategic tool use, repeated reasoning, and presentation defense.