Unit Plan 1 (Grade 6 Math): Building Our Math Community & Problem-Solving Norms

Focus: Establish discourse routines, math notebooks, self-checking, and error analysis with rich ratio/rate and number sense tasks.

Grade Level: 6

Subject Area: Mathematics (Classroom Routines • Ratios • Number Sense)

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

I. Introduction

Launch a safe, productive math space where students talk, reason, and revise. This week sets class norms, builds a shared problem-solving routine, and warms up content with ratios (light intro to 6.RP.1) and multi-digit division (light spiral of 6.NS.2). Students practice self-checking and error analysis while building stamina and confidence.

Essential Questions

• What does productive math talk look and sound like in our classroom?
• How do I organize my thinking so others can follow—and I can check my own work?
• What does a ratio mean, and how does it connect to “for every” and “per”?
• How can estimation help me verify multi-digit division results?

II. Objectives and Standards

Learning Objectives — Students will be able to…

1. Use and reference class discourse norms and a problem-solving routine (Read → Represent → Solve → Check → Reflect).
2. Explain a ratio using “for every,” “to,” and clear unit language; represent with tape diagrams or double number lines.
3. Apply estimation, partial quotients, and standard division to check or compute multi-digit division with whole numbers.
4. Conduct error analysis on sample work and write a self-check note that corrects or improves a solution.
5. Share mathematical thinking using diagrams, labels, complete sentences, and units.

Standards Alignment — CCSS Grade 6

• 6.RP.1 (light intro): Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
• 6.NS.2 (light spiral): Fluently divide multi-digit numbers using the standard algorithm.
• Mathematical Practices (threaded all week): MP.1–MP.8 (make sense, reason, argue/critique, model, use tools, attend to precision, look for structure, express regularity).

Success Criteria — Student Language

• I can describe a ratio with units (for example, “3 cups of juice for every 2 cups of soda”).
• I can represent a ratio with a tape diagram or double number line and explain my steps.
• I can estimate and divide multi-digit numbers and tell whether my answer is reasonable.
• I can spot and correct errors and write a brief reflection about what changed.
• I can speak, listen, and write using our class norms and sentence starters.

III. Materials and Resources

Tasks & Tools (teacher acquires/curates)

• Chart paper or whiteboard for class norms and problem-solving routine anchor charts.
• Math notebooks, pencils, highlighters, sticky notes.
• Ratio visuals: images (trail mix, paint, fruit baskets), tape-diagram and double-number-line templates.
• Manipulatives: counters/cubes, measuring cups (for ratio demos), number lines.
• Division practice sets (friendly and mixed numbers), error-analysis work samples (intentional mistakes).
• Exit ticket slips; timers for “think → pair → share.”

Preparation

• Draft starter anchor charts: Math Talk Norms and Problem-Solving Routine.
• Print ratio task cards (increasing complexity) and division sets with estimation prompts.
• Prepare two short student-work samples containing common errors (ratio mislabeling; division place-value slip).
• Create sentence stems: “I notice…,” “I wonder…,” “I disagree because…,” “The ratio means…,” “I checked by…”.

Common Misconceptions to Surface

• Reversing the order in a ratio (A:B vs B:A) or dropping units.
• Treating “per” as multiply instead of a comparison/for-every relationship.
• In division: digit misalignment, ignoring estimation, or misinterpreting remainders.
• Believing there is only one “right” representation; neglecting self-checks.

IV. Lesson Procedure

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

Session 1: Community Launch + Norms in Action (MP.1–MP.3, MP.6)

• Launch (8–10 min): “Which One Doesn’t Belong?” number set to spark multiple correct answers. Capture talk norms.
• Explore (15–20 min): Introduce notebook setup and the Problem-Solving Routine. Students solve a low-floor task and write a self-check note (What did I try? How did I check?).
• Discuss (8–10 min): Share two exemplar notebooks; highlight precise labeling and reflection.
• Reflect (Exit Ticket): One norm you used today and one goal for tomorrow.

Session 2: Ratios—Meaning and Language (6.RP.1; MP.4, MP.6)

• Launch (5–7 min): Quick demo (for example, 2 cups juice to 3 cups soda). Ask: “How would you say this as a ratio?”
• Explore (15–20 min): Use tape diagrams and double number lines to describe and compare ratios from images/contexts. Students write ratios with units and a sentence (“for every…”).
• Discuss (10–12 min): Share multiple representations; emphasize order and unit language.
• Reflect (Exit Ticket): Write one context sentence for a given ratio card.

Session 3: Number Sense—Division Estimates and Algorithms (6.NS.2; MP.7, MP.8)

• Launch (8–10 min): Estimation challenge: “About how many groups?” before computing.
• Explore (15–20 min): Practice partial quotients and standard algorithm; check with multiplication; note remainders in context.
• Discuss (8–10 min): Compare strategies; when estimation reveals a place-value error.
• Reflect (Exit Ticket): Solve one division problem and justify reasonableness with an estimate.

Session 4: Error Analysis & Self-Checking Routines (6.RP.1, 6.NS.2; MP.3, MP.6)

• Launch (5–7 min): Display a flawed solution (ratio order swapped or missing units).
• Explore (15–20 min): In triads, annotate what’s right, what’s wrong, how to fix (ratio sample and division sample).
• Discuss (10–12 min): Build a class Error-Analysis Checklist (estimate, units, labels, inverse check, explain).
• Reflect (Exit Ticket): Revise one step of your own work using the checklist.

Session 5: Team Challenge—Ratios Meet Division (Integrated; MP.1–MP.6)

• Launch (5–7 min): Present a mini-project (for example, mix a classroom “sports drink”: ratio concentrate to water; scale for 28 students).
• Explore (25–30 min): Teams plan quantities using ratios and division to scale and portion; show at least one representation and a self-check (estimate or inverse).
• Discuss (5–7 min): Gallery walk; tag clear units and effective checks.
• Reflect (Exit Ticket): Write a 2–3 sentence reflection: What representation helped most? What will you carry into next week?

V. Differentiation and Accommodations

Advanced Learners

• Generalize ratio statements using variables (a:b = ka:kb).
• Design two equivalent recipes and justify equivalence with a double number line.
• Create a division “stress test” with large or composite numbers; provide an estimate band your answer must fall within.

Targeted Support

• Provide ratio sentence frames and pre-drawn tape diagrams.
• Use scaffolds for partial quotients (recording sheets) and multiplication-as-check.
• Offer worked example → “my turn” pairs with explicit unit labeling.

Multilingual Learners

• Mini-glossary with visuals: ratio, for every, per, unit, estimate, quotient, remainder.
• Sentence frames: “The ratio of __ to __ is : because…,” “I checked my division by…,” “My answer is reasonable because…”.
• Allow bilingual notes; require final statements with units in clear English.

IEP/504 & Accessibility

• Larger grid paper for alignment; manipulatives for ratio builds and place value.
• Chunked directions; checklists; option to scribe; extended time as needed.
• Frequent verbal checks for understanding and restatements of norms.

VI. Assessment and Evaluation

Formative Checks (daily)

• S1: Exit slip on norms and a quick self-check note.
• S2: Ratio exit with a labeled diagram and a “for every” sentence (6.RP.1).
• S3: Division problem with estimate and inverse check (6.NS.2).
• S4: Annotated error-analysis card (identify, explain, fix).
• S5: Team artifact with representation, units, and a written self-check.

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

1. Community & Process (MP.1–MP.3)
   • 2: Consistently follows norms and routine; clear collaboration evidence
   • 1: Partial or inconsistent
   • 0: Minimal evidence
2. Ratio Understanding (6.RP.1)
   • 2: Correct language/units and accurate visual representation
   • 1: Minor slips
   • 0: Off-track
3. Division Fluency (6.NS.2)
   • 2: Accurate computation and estimate/reverse check
   • 1: Minor arithmetic/placement error
   • 0: Incorrect or unchecked
4. Representations & Precision (MP.4, MP.6)
   • 2: Diagrams/tables labeled; units precise; work legible
   • 1: Partially clear
   • 0: Vague or unitless
5. Reflection & Revision (MP.8)
   • 2: Thoughtful self-check and concrete improvement noted
   • 1: Partial reflection
   • 0: Missing

Feedback Protocol (use in Session 5 peer review)

• Read & Restate (1 minute): Reviewer summarizes the team’s plan, representation, and result.
• TAG (2–3 minutes): Tell a strength (clear units), Ask a question (“How did you estimate?”), Give a suggestion (“Add an inverse check”).
• Evidence Check (1 minute): Point to the step where the conclusion is justified.
• Author Response (1–2 minutes): Team writes one concrete revision.

VII. Reflection and Extension

Reflection Prompts

• Which norm helped your group work better this week?
• Where did estimation change your approach or catch an error?
• Which representation (tape diagram, double number line, table) felt most useful—and why?

Extensions

• Recipe Remix: Create two equivalent mixes; prove equivalence with a double number line and words.
• Division Detective: Write a problem where a wrong estimate leads to a place-value mistake; then fix it and explain.
• Math Talk Coach: Draft mini “talk move” cards for partners (press for reasoning, revoice, add on).

Standards Trace — When Each Standard Is Addressed

• 6.RP.1 — Sessions 2, 4, 5 (ratio meaning, language, and representations).
• 6.NS.2 — Sessions 3, 4, 5 (estimation, partial quotients, standard algorithm, inverse check).
• MP.1–MP.8 — Embedded daily through routine, representation, precision, structure, and critique.