Unit Plan 1 (Grade 5 Math): Building Our Math Community & Problem-Solving Norms

Focus: Establish routines for discourse, math notebooks, self-checking, and error analysis using rich place-value and estimation tasks.

Grade Level: 5

Subject Area: Mathematics (Community Norms, Place Value, Estimation)

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

I. Introduction

This launch week builds a collaborative math culture while refreshing core ideas we’ll use all year. Students co-create math-talk norms, practice estimation and reasonableness checks, and explore place-value patterns (how digits shift by factors of 10). We emphasize productive struggle, respectful discourse, and consistent self-check routines.

Essential Questions

• What does productive math talk look and sound like?
• How can place value and powers of ten help me reason mentally?
• What makes a solution reasonable, and how do I self-check it?
• How do we give useful feedback that helps a classmate improve?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Co-create and apply discussion norms and feedback protocols during problem solving.
2. Explain that a digit in one place is 10 times what it is to the right and one tenth of what it is to the left; use this to reason mentally about size and shifts.
3. Use estimation strategies (rounding, front-end estimation, compatible numbers) to predict results and check reasonableness.
4. Use a self-check checklist (Estimate → Compute → Compare → Explain) and perform error analysis on sample work.
5. Communicate thinking with precise vocabulary, units, and clear notebook organization.

Standards Alignment — CCSS Grade 5

• 5.NBT.1: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left (light introductory emphasis).
• Mathematical Practices (MP.1–MP.8): Make sense of problems; reason abstractly and quantitatively; construct viable arguments and critique the reasoning of others; model with mathematics; use tools strategically; attend to precision; look for structure; look for repeated reasoning (threaded throughout the unit).

Success Criteria — Student Language

• I can state and follow our class math-talk norms.
• I can explain the 10-times / one-tenth idea and use digit shifts to reason about number size.
• I can choose an estimation strategy and justify why it fits a problem.
• I can use a self-check checklist and spot errors in sample work.
• I can show my thinking clearly in my notebook with labels and units.

III. Materials and Resources

Tasks & Tools (teacher acquires/curates)

• Math notebooks; pencils/highlighters; sticky notes; place-value charts (ones to thousandths), base-ten blocks or place-value disks; number lines; sentence-stem cards.
• Launch tasks: “Notice and Wonder” images, Which One Doesn’t Belong? numerals/representations.
• Error-analysis cards (common place-value/rounding mistakes).
• Exit tickets (half-sheets) for daily checks.

Preparation

• Anchor charts: Math Talk Norms, Estimation Strategies, Place-Value Shifts (10^n), Self-Check Checklist.
• Post sentence stems: “I agree/disagree because…”, “Can you clarify…?”, “Another way is…”.

Common Misconceptions to Surface

• “Multiplying by 10 just adds a zero” (counter with digit shift and decimals).
• Rounding rules applied mechanically without thinking about reasonableness.
• Confusing magnitude (how big) with value after a shift (e.g., 3 in tens vs 3 in hundreds).
• Skipping units and labels in notebooks.

Key Terms (highlighted in lessons)

• place value, power of ten, ten times, one tenth, digit shift, round, estimate, front-end estimation, compatible numbers, reasonableness, math talk, error analysis, self-check.

IV. Lesson Procedure

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

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

• Launch (8–10 min): Quick puzzle with multiple solution paths (no calculators). Students share how they approached it.
• Explore (15–20 min): Co-create Math Talk Norms and Self-Check Checklist. Try sentence stems with a short estimation problem.
• Discuss (8–10 min): What helped you understand a partner’s idea? Record norms on an anchor chart.
• Reflect (Exit Ticket): “One norm I used today was ___, and it helped because ___.”

Session 2: Place Value Patterns — Ten Times and One Tenth (5.NBT.1)

• Launch (5–7 min): Predict how the value of a digit changes when it moves one place left or right.
• Explore (15–20 min): Use place-value charts and disks to model shifts (e.g., 3.5 → 35 → 350; 640 → 64). Connect to language ten times/one tenth.
• Discuss (10–12 min): Contrast “add a zero” vs true digit shift reasoning, including decimals.
• Reflect (Exit Ticket): Explain how the 6 changes in 6.2, 62, and 0.62.

Session 3: Estimation Strategies That Make Sense (MP.1, MP.4, MP.6)

• Launch (8–10 min): “Which estimate is more reasonable? Why?” (two student estimates posted).
• Explore (15–20 min): Practice rounding, front-end estimation, and compatible numbers in short word problems; label chosen strategy.
• Discuss (8–10 min): Share pairs of exact vs estimated answers; when is exact necessary? when is estimate sufficient?
• Reflect (Exit Ticket): Solve one new problem and write: “I used ___ because ___, so a reasonable estimate is ___.”

Session 4: Error Analysis and Self-Checking Routines (MP.3, MP.6, MP.7)

• Launch (5–7 min): Show a worked solution with a subtle place-value or rounding error.
• Explore (15–20 min): Use the Self-Check Checklist to find, fix, and explain errors; then create a brief “trap problem” for peers.
• Discuss (10–12 min): What error patterns did we notice? Which checklist step caught them?
• Reflect (Exit Ticket): Name the checklist step that helped you most and why.

Session 5: Mini-Performance — Supply Order Sense-Making (5.NBT.1; MP.1–MP.6)

• Task (25–30 min): Teams use estimation and place-value reasoning to plan a school-supply order (bundles, per-item costs, approximate totals). Must include: chosen strategy, an estimate, a quick reasonableness check, and a short note on assumptions.
• Discuss (5–7 min): Gallery walk; tag clear notebook setups and strongest justifications.
• Reflect (Exit Ticket): “Next time I will improve my ___ by ___.”

V. Differentiation and Accommodations

Advanced Learners

• Generalize to 10^n shifts with decimals; justify why moving two places is “100 times.”
• Create a real-world scenario where two different estimation strategies lead to different but reasonable decisions; compare.

Targeted Support

• Provide place-value mats and disks; number lines with tenths/hundredths.
• Sentence frames for justification (“I rounded to ___ because ___”).
• Worked-example → faded-example sequences for rounding and estimation.

Multilingual Learners

• Visual glossary for ten times, one tenth, estimate, reasonableness.
• Structured partner talk with stems: “I think ___ because ___,” “Can you show the digit shift?”
• Encourage sketches/models before full-sentence explanations.

IEP/504 & Accessibility

• Chunk tasks; allow manipulatives and larger-format charts.
• Option to scribe or use audio notes for reflections.
• Frequent checks for understanding; offer re-teach with concrete → representational → abstract sequence.

VI. Assessment and Evaluation

Formative Checks (daily)

• S1: Exit ticket citing a norm used.
• S2: Quick write explaining a digit shift comparison.
• S3: Estimation problem with strategy named and why.
• S4: Error-analysis correction with the checklist step identified.
• S5: Team artifact (estimate, assumptions, reasonableness statement).

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

1. Place-Value Understanding (5.NBT.1)
   • 2: Correct ten-times/one-tenth reasoning applied to whole and decimal numbers
   • 1: Generally correct; minor slips
   • 0: Off-track or missing
2. Estimation Strategy & Reasonableness (MP.1, MP.6)
   • 2: Appropriate strategy chosen and well-justified; estimate matches context
   • 1: Strategy partially justified or estimate loosely connected
   • 0: Inappropriate or unsupported estimate
3. Error Analysis & Self-Check (MP.3, MP.7)
   • 2: Accurately identifies/corrects errors and cites checklist step
   • 1: Partial identification or fix
   • 0: Not identified or incorrectly corrected
4. Mathematical Communication (MP.3, MP.6)
   • 2: Clear notebook organization, labels, units, and vocabulary
   • 1: Minor clarity/label issues
   • 0: Disorganized or unclear
5. Collaboration & Discourse (MP.1–MP.8)
   • 2: Uses norms, listens/responds to peers, builds on ideas
   • 1: Inconsistent use of norms
   • 0: Limited participation

Feedback Protocol (use in Session 5 peer review)

• Read & Restate (1 minute): Reviewer restates the team’s claim/estimate and assumptions.
• TAG (2–3 minutes): Tell a strength (clear digit-shift explanation), Ask a question (about rounding choice), Give a suggestion (tighten reasonableness check).
• Evidence Check (1 minute): Point to a specific notebook entry or calculation.
• Author Response (1–2 minutes): Team records one revision to improve clarity or accuracy.

VII. Reflection and Extension

Reflection Prompts

• Which norm helped you most in understanding a classmate’s idea?
• When did estimation save you from a mistake this week?
• How will you use the Self-Check Checklist on future tasks?

Extensions

• Digit-Shift Detective: Given several numbers, describe the effect of moving each digit left or right and justify with words and models.
• Estimate, Then Compute: Create a two-step context (e.g., supplies + tax). Share your estimate first, then compute and compare.
• Poster Build: Design a mini-poster of your favorite estimation strategy with an example and “when it’s best.”

Standards Trace — When Each Standard Is Addressed

• 5.NBT.1 — Sessions 2 and 5 (explicit), applied in Sessions 3–4 for reasonableness and error checks.
• MP.1–MP.8 — Visible daily: sense making and perseverance (MP.1), argument/critique (MP.3), modeling and precision (MP.4, MP.6), structure and repeated reasoning during digit shifts and estimation (MP.7–MP.8).