Unit Plan 1 (Grade 7 Math): Building Our Math Community & Problem-Solving Norms

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

Grade Level: 7

Subject Area: Mathematics (Classroom Culture • Problem Solving • Number Sense)

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

I. Introduction

Launch the year by building a thinking classroom: norms for partner/group talk, math notebook setup, routines for self-checking and error analysis, and shared expectations for perseverance and clarity. Math-wise, students engage with accessible-but-deep tasks featuring ratios/unit rates (preview of 7.RP) and integers on the number line (spiral of 7.NS) so culture and content grow together.

Essential Questions

• What does productive math talk look/sound like, and how do we make space for everyone’s ideas?
• How do I check my own work, analyze mistakes, and revise a solution?
• How do unit rates and number line models help me reason about real situations quickly and accurately?

II. Objectives and Standards

Learning Objectives — Students will be able to…

1. Use agreed discussion norms and sentence frames to explain thinking, ask clarifying questions, and build on peers’ ideas.
2. Organize a math notebook (date, title, goal, worked examples, error analysis, reflection) and use it to track growth.
3. Apply unit rate reasoning in simple ratio contexts and justify the constant of proportionality informally (light intro).
4. Model integer addition/subtraction on a number line and interpret results in context (spiral).
5. Employ a self-check routine (estimate → compute → verify → reflect) and document error analyses of sample work.

Standards Alignment — CCSS Grade 7

• Mathematical Practices MP.1–MP.8 (threaded throughout: make sense, reason, argue, model, use tools, precision, structure, regularity).
• 7.RP.1 (light introduction): Compute unit rates including complex fractions; interpret rate and units.
• 7.NS.1a–d (light spiral): Add/subtract rational numbers; represent on number line; show that subtraction is adding the additive inverse; apply properties; apply to contexts.

Success Criteria — Student Language

• I can listen, explain, and question using our class talk stems.
• I can set up my notebook so someone else can follow my work.
• I can find a unit rate and say what it means with correct units.
• I can use a number line to show integer addition/subtraction and explain my steps.
• I can check my answer and write a short error analysis when I find (or am given) a mistake.

III. Materials and Resources

Tasks & Tools (teacher acquires/curates)

• Chart paper or whiteboard space for class norms; sticky notes; markers; sentence-stem cards.
• Math notebook supplies (composition books or binders), page layout template.
• Task cards: quick ratio/rate scenarios (recipes, speed, cost per item) and integer contexts (elevation, temperature, gains/losses).
• Large number line posters; mini number lines; rulers.
• “My Self-Check” and “Error Analysis” mini-forms; exit ticket slips.
• Optional: visible random groups, non-permanent vertical surfaces for group problem solving.

Preparation

• Draft initial talk norms and feedback stems to co-create with students.
• Prepare 2–3 worked examples with planted errors (unit slip, sign error, missing units).
• Select one rich low-floor/high-ceiling task blending rates or integers for Day 5 performance.

Common Misconceptions to Surface

• Treating rate with missing or mismatched units; confusing “per 1” with “per 100.”
• On integers, misreading direction on number line; subtract-as-“move left” always.
• Believing a single answer without units/representation is “complete.”

IV. Lesson Procedure

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

Session 1: Norms + Math Identities (MP.1, MP.3, MP.6)

• Launch (8–10 min): Quick puzzle (Which One Doesn’t Belong?) to model talk moves.
• Explore (15–20 min): Co-create discussion norms and notebook setup (date, title, goal, examples, reflection). Short rate warm-ups (cost per item).
• Discuss (8–10 min): Share strategies; post anchor charts: Talk Stems, Notebook Anatomy, My Self-Check.
• Reflect: Exit Ticket—“One norm I’ll commit to and why.” Plus a 1-sentence unit rate with units.

Session 2: Self-Check Routine with Ratios (MP.1, MP.4, MP.6; 7.RP.1 intro)

• Launch (5–7 min): Estimation first—Which is larger: 3 for 4 dollars or 7 for 10 dollars? Why?
• Explore (15–20 min): Mini-set of unit rate problems; require estimate → compute → verify → reflect; highlight units.
• Discuss (10–12 min): Share multiple paths (tables, scaling, double number line).
• Reflect: Exit Ticket—Write a complete solution with a unit rate statement in words.

Session 3: Error Analysis Workshop (MP.3, MP.6)

• Launch (8–10 min): Present a flawed solution (wrong unit, arithmetic slip, or unjustified step).
• Explore (15–20 min): In triads, annotate what went wrong, fix it, and write a short feedback note using evidence.
• Discuss (8–10 min): Build an Error Analysis Checklist: identify assumption, show corrective step, restate final answer with units.
• Reflect: Exit Ticket—One thing I’ll check first next time and why.

Session 4: Integers on the Line (MP.2, MP.7; 7.NS.1 spiral)

• Launch (8–10 min): Context: temperature change over a day; sketch on a number line.
• Explore (15–20 min): Model addition as movement and subtraction as adding the additive inverse; create two original word problems showing each.
• Discuss (8–10 min): Share and critique models for clarity and precision.
• Reflect: Exit Ticket—Solve two integer expressions and justify with a brief number line or inverse explanation.

Session 5: Performance Task—Plan, Solve, Check, Communicate (MP.1–MP.6)

• Task (25–30 min): Mixed rate + integer scenario (e.g., hike elevation changes plus snack pricing). Deliverables:
  1. Notebook page with strategy and units,
  2. Final answer with self-check box,
  3. One-paragraph explanation using a sentence frame.
• Discuss (5–7 min): Gallery share; highlight precise units and clear representations.
• Reflect: Exit Ticket—“What I’ll keep in my notebook as a model for future problems and why.”

V. Differentiation and Accommodations

Advanced Learners

• Compare two unit-rate strategies (ratio table vs scaling vs equation) and argue efficiency.
• Create a context where subtracting a negative is essential; justify using additive inverse language.
• Add a constraint (budget/time) to the performance task and re-optimize the plan.

Targeted Support

• Provide sentence stems (“I think ___ because ___.” “Can you explain how you got from ___ to ___?”).
• Scaffolded notebook template and self-check checklist.
• Number-line overlays for integer moves; curated numbers to reduce computation load.

Multilingual Learners

• Mini-glossary: unit rate, per, constant of proportionality, integer, additive inverse, estimate, verify, reflect.
• Frames: “The unit rate is __ per 1 __.” “I checked by __.” “Subtracting __ means adding __.”
• Allow bilingual drafting; final statements include English units.

IEP/504 & Accessibility

• High-contrast materials; large number lines; explicit step checklists.
• Flexible roles in triads (reader, recorder, reporter); option to scribe or use audio notes.
• Extended time as needed.

VI. Assessment and Evaluation

Formative Checks (daily)

• S1: Exit ticket on norms plus a unit-rate sentence with units.
• S2: Worked example using estimate → compute → verify → reflect.
• S3: Annotated error analysis (identify error, correct, justify).
• S4: Integer addition/subtraction with number line or inverse explanation.
• S5: Performance-task notebook page with self-check and written explanation.

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

1. Participation in Mathematical Practices (MP.1–MP.8)
   • 2: Consistently uses norms, representations, and precision; supports/asks questions
   • 1: Partial use; occasional prompting needed
   • 0: Minimal engagement
2. Unit Rate Reasoning (7.RP.1 — intro level)
   • 2: Correct unit rates with clear units and interpretation
   • 1: Minor slip or incomplete interpretation
   • 0: Incorrect or missing units
3. Integer Reasoning (7.NS.1 — spiral level)
   • 2: Accurate integer models and justifications (number line or inverse)
   • 1: Correct answer with thin reasoning
   • 0: Incorrect or unsupported
4. Self-Check & Error Analysis Quality
   • 2: Evidence of estimate/verify; error analysis identifies cause and fix
   • 1: Partial check or generic fix
   • 0: No check or unclear analysis
5. Communication & Notebook Organization
   • 2: Well-organized pages; headings, representations, units; readable to others
   • 1: Mostly organized; minor clarity issues
   • 0: Disorganized or hard to follow

Feedback Protocol (for peer review during Session 3 and Session 5)

• Step 1 — Read & Restate (1 minute): Reviewer quietly reads the work, then restates the goal of the problem in their own words.
• Step 2 — TAG Feedback (2–3 minutes):
  • Tell something specific you notice/like (representation, units, clear step).
  • Ask a focused question (“How did you verify ___?” “Where did the unit rate come from?”).
  • Give one actionable suggestion (“Label the number line arrows; add units to the final statement.”).
• Step 3 — Evidence Check (1 minute): Reviewer underlines where the evidence supports the answer (calculation, diagram, unit statement).
• Step 4 — Writer Response (1–2 minutes): Author notes one revision they will make immediately.

VII. Reflection and Extension

Reflection Prompts

• Which norm or strategy helped you most this week and why?
• When did a self-check catch a mistake? What will you check first next time?
• How did using units make your explanation clearer?

Extensions

• Norms in Action: Create a short sketchnote page that models an ideal solution (strategy, units, self-check).
• Rate Remix: Find two everyday rates (nutrition label, speed, cost) and write a short comparison with per-1 statements.
• Integer Stories: Write and solve two context problems (one addition, one subtraction) that require the additive inverse idea.

Standards Trace — When Each Standard Is Addressed

• MP.1–MP.8 — Sessions 1–5 (norms, error analysis, modeling, precision).
• 7.RP.1 (intro) — Sessions 2 and 5 (unit rate meaning and units).
• 7.NS.1a–d (spiral) — Session 4 (models/contexts) and Session 5 (application).