Unit Plan 1 (Grade 4 Math): Building Our Math Community & Problem-Solving Norms

Focus: Establish discourse routines, math notebooks, error analysis, and estimation with rich whole-number tasks (comparison and place-value games).

Grade Level: 4

Subject Area: Mathematics (Community Launch • Place Value & Problem Solving)

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

I. Introduction

This launch week builds a shared culture for productive struggle and mathematical talk while revisiting whole-number place value and comparisons. Students set up notebooks, practice partner and group norms, and use estimation and place-value reasoning to make and defend decisions.

Essential Questions

• How do collaborative norms help us solve problems more effectively?
• When is estimation better than exact calculation?
• How does understanding place value help us compare, compose, and explain large numbers?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Establish discussion norms (listening, turn-taking, using sentence stems) and organize math notebooks for clear work.
2. Use place-value reasoning to compose/decompose multi-digit numbers and to compare with symbols and language.
3. Choose and justify estimation or exact computation in everyday contexts.
4. Represent thinking with models (place-value charts, base-ten sketches, number lines) and explain choices.
5. Engage in error analysis and revise solutions based on peer feedback.

Standards Alignment — CCSS Grade 4 (spiral across the unit)

• 4.NBT: Generalize place value understanding for multi-digit whole numbers; read, write, compare (light intro to 4.NBT.1–2).
• 4.OA: Interpret multiplicative comparisons and represent situations with equations (light spiral to 4.OA.1 via contexts).
• Mathematical Practices (MP.1–MP.8) threaded throughout.

Success Criteria — Student Language

• I can explain our discussion norms and use them during problem solving.
• I can compare multi-digit numbers using place-value reasoning and correct symbols.
• I can decide when to estimate and when to compute exactly—and explain why.
• I can show my strategy clearly in my notebook and revise after feedback.

III. Materials and Resources

Tasks & Tools (teacher acquires/curates)

• Math notebooks; dividers; place-value charts; base-ten blocks/disks; digit cards; number lines; hundreds charts.
• Rich task cards (comparison games, “closest estimate wins,” number-building challenges).
• Sentence stems posters; mini whiteboards; feedback rubrics and TAG (Tell–Ask–Give) slips.

Preparation

• Anchor charts: Community Norms for Math Talk, Estimate–Compute–Check, Show Your Thinking Clearly.
• Prepare notebook setup guide (labels, date, problem number, model, explanation).
• Create exemplar and non-exemplar notebook pages for a quick “noticings/wonderings” routine.

Common Misconceptions to Surface

• Treating the value of a digit as its face value (e.g., thinking the 3 in 3,000 is “3” not 3 thousands).
• Comparing by length of the numeral string instead of highest place.
• Believing estimation is “guessing” rather than reasoned approximation.
• Dropping labels/units or leaving work unlabeled in notebooks.

Key Terms (highlighted in lessons): place value, digit, period, expanded form, standard form, compare, greater than ( > ), less than ( < ), equal to ( = ), estimate, round, reasonableness, representation, multiplicative comparison, strategy, error analysis.

IV. Lesson Procedure

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

Session 1: Community Norms & Notebook Setup (MP.1, MP.3, MP.6)

• Launch (8–10 min): Co-create Math Talk Norms; model sentence stems (“I agree because…”, “I noticed…”, “Can you clarify…?”).
• Explore (15–20 min): Notebook setup + quick error-hunt in two sample pages; students mark strengths and fixes.
• Discuss (8–10 min): Share “non-negotiables” for clarity (titles, dates, models, labels).
• Reflect (Exit Ticket): Write two norms you’ll use and why they matter.

Session 2: Place-Value Building — Make the Biggest/Smallest (4.NBT; MP.2, MP.7)

• Launch (5–7 min): Mini-lesson on 10×/1⁄10 of a value using base-ten sketches (conceptual, not procedural drill).
• Explore (15–20 min): Digit-card games: build numbers to meet constraints (e.g., “largest number with a 6 in the thousands place”).
• Discuss (10–12 min): Compare strategies; highlight how place drives value.
• Reflect (Exit Ticket): Explain how moving a digit to a different place changed the number’s value.

Session 3: Compare & Justify — Symbols and Sentences (4.NBT; MP.3, MP.6)

• Launch (8–10 min): Model comparing two numbers using expanded form and a comparison sentence.
• Explore (15–20 min): Stations: (A) expanded-form races, (B) number line placement, (C) true/false comparison cards with justifications.
• Discuss (8–10 min): Emphasize precise language and symbols (>, <, =).
• Reflect (Exit Ticket): “I know ___ is greater than ___ because ___.”

Session 4: Estimate or Exact? Decisions in Context (4.OA.1 light; MP.1, MP.5, MP.6)

• Launch (5–7 min): Present two scenarios (class supply order vs. prize tickets). Ask: estimate or compute exactly? Why?
• Explore (15–20 min): Small groups solve a set of mixed contexts; label each as estimate/exact, then solve and defend.
• Discuss (10–12 min): Share decision rules; connect to reasonableness checks.
• Reflect (Exit Ticket): State one situation from today where an estimate was better, and why.

Session 5: Error Analysis & Mini-Exhibition (4.NBT, 4.OA.1; MP.3, MP.6, MP.8)

• Task (20–25 min): Mixed problems (compare, build-to-spec, estimate/exact). Include one intentional error per set.
• Peer Review (TAG, 5–7 min):
  • Tell a strength (clear model, labels).
  • Ask a focused question (place-value choice, symbol use, estimation reasoning).
  • Give a suggestion (representation to add or clarify).
• Discuss (5–7 min): Groups share one revision sparked by feedback.
• Reflect (Exit Ticket): “The most helpful feedback we received was ___ because ___.”

V. Differentiation and Accommodations

Advanced Learners

• Add constraints (fixed digits/places) and require two valid solutions with different strategies.
• Write and justify a general rule about how value changes when a digit shifts one place to the left/right.

Targeted Support

• Provide scaffolded place-value charts and expanded-form frames.
• Use smaller numbers first; then scale to larger values once reasoning is solid.

Multilingual Learners

• Visual sentence frames and icon-supported word bank for compare, estimate, because.
• Partner rehearsal before whole-group share; accept labeled diagrams as part of explanation.

IEP/504 & Accessibility

• Large-print digit cards, high-contrast number lines; option to dictate reflections.
• Break tasks into short milestones with quick checks.

VI. Assessment and Evaluation

Formative Checks (daily)

• S1: Student states and applies at least two discussion norms in partner talk.
• S2: Notebook shows labeled models and clear place-value reasoning.
• S3: Justified comparisons with correct symbols and sentences.
• S4: Correctly identifies estimate vs. exact with rationale.
• S5: Revision notes reflect peer feedback and improved clarity.

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

1. Mathematical Accuracy (4.NBT, 4.OA)

• 2: Correct comparisons/compositions; estimation or exact choice used correctly and computed accurately.
• 1: Minor errors that do not change conclusions.
• 0: Major errors; conclusions unsupported.

2. Strategy & Representation (MP.4, MP.5, MP.7)

• 2: Efficient strategy; models/notations fit purpose and are well-labeled.
• 1: Mostly sound; minor labeling or model mismatches.
• 0: Inefficient or mismatched representations.

3. Reasoning & Justification (MP.2, MP.3)

• 2: Clear claim with place-value evidence; addresses a counterexample or potential error.
• 1: Partially justified or vague in spots.
• 0: Assertions without support.

4. Precision & Communication (MP.6)

• 2: Symbols, vocabulary, and notebook conventions precise and readable.
• 1: Minor precision lapses.
• 0: Disorganized or imprecise.

5. Collaboration & Presentation (MP.1, MP.8)

• 2: Equitable teamwork; responds to feedback thoughtfully.
• 1: Uneven participation or limited incorporation of feedback.
• 0: Minimal collaboration; dismisses feedback.

Feedback Protocol (Exhibition)

• Read & Restate (1 min): Reviewer restates the team’s claim/goal.
• TAG (2–3 min): Tell a strength, Ask a focused question, Give a concrete suggestion.
• Evidence Check (1 min): Point to a model/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

• Which norm helped your group the most, and how did it show up in your work?
• Where did estimation save time without hurting accuracy?
• How did your representation make your explanation clearer?

Extensions

• Constraint Challenge: Build the largest/smallest number meeting two conditions (e.g., fixed thousands and tens digits); justify.
• Two-Method Proof: Compare two numbers using expanded form and a number line; explain which felt more convincing.
• Community Share: Post notebook exemplars with captions that name the strategy and representation used.

Standards Trace — When Each Domain Is Addressed

• 4.NBT — Sessions 2, 3, 5 (compose/decompose, compare, place-value arguments).
• 4.OA — Sessions 4–5 (light multiplicative-comparison contexts; choose estimate vs. exact).
• MP.1–MP.8 — All sessions (perseverance, reasoning, argument, modeling, tools, precision, structure, regularity).