Unit Plan 1 (Grade 8 Math): Building Our Math Community & Problem-Solving Norms

Focus: Establish routines for math discourse, notebooks, self-checking, and error analysis. Launch with rich tasks that preview Grade 8 themes (linear patterns, exponents, and transformations).

Grade Level: 8

Subject Area: Mathematics (Number System • Expressions & Equations • Functions • Geometry • Mathematical Practices)

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

I. Introduction

This launch week builds a thinking classroom: norms for math talk, notebooks, self-checking, and error-as-data mindsets. Students will solve rich, low-floor/high-ceiling tasks that preview key Grade 8 ideas—linear patterns (slope/rate), functions (input→output), integer exponents, and rigid motions—while practicing the Mathematical Practices (MP.1–MP.8) every day.

II. Objectives and Standards

Learning Objectives — Students will be able to…

1. Use and reflect on problem-solving routines (understand → plan → try → revise) and discourse norms to explain reasoning and critique ideas (MP.1, MP.3).
2. Track thinking in a math notebook, apply self-check strategies (estimation, inverse operations, unit checks), and use error analysis to revise work (MP.6, MP.7, MP.8).
3. From tasks, preview Grade 8 content: interpret slope as rate of change in proportional situations and recognize a function as a rule assigning each input exactly one output (8.EE.5, 8.F.1).

Standards Alignment — CCSS Grade 8

• 8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph; compare two different proportional relationships represented in different ways (e.g., by tables, graphs, equations).
• 8.F.1: Understand that a function is a rule that assigns to each input exactly one output; the graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
• Standards for Mathematical Practice (MP.1–MP.8):
  • MP.1: Make sense of problems and persevere in solving them.
  • MP.2: Reason abstractly and quantitatively.
  • MP.3: Construct viable arguments and critique the reasoning of others.
  • MP.4: Model with mathematics.
  • MP.5: Use appropriate tools strategically.
  • MP.6: Attend to precision.
  • MP.7: Look for and make use of structure.
  • MP.8: Look for and express regularity in repeated reasoning.

Success Criteria — student language

• I can explain my plan and revise it after checking against estimates or a graph.
• I can use evidence (table, graph, example) to support or critique a solution.
• I can describe slope as a rate in context and say what a function means (one input → one output).
• I can write clear, labeled work in my notebook and identify an error and how I fixed it.

III. Materials and Resources

Tasks & Tools — teacher acquires/curates

• Two rich tasks involving proportional relationships/linear patterns (e.g., stair-step pattern growth, constant-speed travel) and a function-mapping task (input→output tables/graphs).
• One short exponents pattern prompt (powers table showing regularity) and a transformations mini-challenge (translate/reflect a shape on a grid).
• Graph paper, straightedges, sticky notes, colored pens/highlighters, whiteboards or chart paper; access to a graphing tool (handheld or digital).
• Posters/handouts: Problem-Solving Routine, Discussion Stems, Self-Check Menu (estimate, inverse, different representation), Error Analysis Guide.

Preparation — before Session 1

1. Arrange vertical whiteboard spaces or large paper for group work.
2. Pre-select student work samples (correct and with common errors) for error analysis.
3. Prepare notebook setup pages (table of contents, date/learning target headers, reflection prompts).

IV. Lesson Procedure

Each session follows: Launch → Explore (groups) → Discuss/Consolidate → Reflect (exit ticket)

Session 1: Our Math Community & Problem-Solving Routine (MP.1, MP.3, MP.6)

• Launch (10–12 min): Co-create norms: “Everyone solves • Everyone explains • Errors welcome.” Teach the Problem-Solving Routine (Understand → Plan → Try → Check → Revise).
• Explore (15–20 min): Quick puzzle task with multiple solution paths. Teacher models notebook setup and prompts: underline givens, list assumptions, sketch.
• Discuss (8–10 min): Gallery walk; groups present a strategy and a self-check they used.
• Reflect: Exit ticket—“Where did I get stuck, what did I try next?”

Session 2: Linear Patterns & Slope as Rate (preview 8.EE.5; MP.2, MP.4, MP.6)

• Launch (8–10 min): Introduce a constant-rate scenario (e.g., biking speed). Ask: What is changing? How can we represent it?
• Explore (15–20 min): Groups create a table, graph, and equation (if/when ready). Identify unit rate and slope; label axes/units.
• Discuss (10 min): Compare two groups’ representations; which is steeper and why?
• Reflect: Exit ticket—State the unit rate and one sentence interpreting the slope.

Session 3: What Is a Function? (preview 8.F.1; MP.2, MP.5, MP.7)

• Launch (8–10 min): Mapping cards: some rules give one output per input, others don’t.
• Explore (15–20 min): Sort/justify which relations are functions; graph one example and identify ordered pairs.
• Discuss (8–10 min): Share a non-function example and explain the conflict (two outputs for one input).
• Reflect: Exit ticket—Finish the stem: “A function is ___; in my example, input __ gives output __.”

Session 4: Structure & Regularity—Exponent Patterns (MP.7, MP.8; light preview)

• Launch (5–7 min): Build a powers table (…, 2^–1, 2^0, 2^1, 2^2, …). What pattern do you notice?
• Explore (15–18 min): Extend to other bases; predict the next value using the pattern, not a rule given by the teacher.
• Discuss (10 min): Connect to precision and structure: why does 2^0 = 1 make sense?
• Reflect: Exit ticket—Describe the regularity you noticed and one way it helps check work later.

Session 5: Transformations Teaser & Error Analysis (MP.3, MP.5, MP.6; spiral)

• Launch (8–10 min): On a grid, translate and reflect a simple polygon; record coordinate changes informally.
• Explore (12–15 min): Mixed mini-set (one linear pattern item, one function card, one transformation).
• Discuss (10–12 min): Error analysis: examine two anonymous student solutions; identify the error type (misread scale, swapped x/y, arithmetic slip) and write a revision.
• Reflect: Exit ticket—Set a personal process goal (e.g., “Use a quick sketch to check reasonableness,” “Label axes every time”).

V. Differentiation and Accommodations

Advanced Learners

• Justify slope equivalence using similar triangles on a line (connection to 8.EE.6, preview only).
• Create a realistic context for a given graph and explain intercept meaning.
• Extend exponent patterns to negative bases; discuss sign patterns.

Targeted Support

• Provide sentence frames (“The unit rate is __ because for every 1 __, __ changes by __.”).
• Offer partially filled tables/graphs and manipulatives (number lines, tiles).
• Use worked-example pairs: correct vs. flawed with “Which? Why?” prompts.

Multilingual Learners

• Mini-glossary with visuals: slope, rate, function, input, output, translate, reflect, exponent.
• Allow bilingual notes; require math words in English in final share-outs.
• Partner reading of task stems; teacher models revoicing student ideas.

IEP/504 & Accessibility

• Provide large-grid graph paper; color coding for axes and points.
• Chunk directions into numbered steps; offer extra time for notebook setup.
• Option to demonstrate understanding verbally with teacher scribing.

VI. Assessment and Evaluation

Formative Assessment — Daily

• Notebook checks for labeled representations and self-check notes.
• Quick exit tickets (unit rate statement; function definition with example; exponent pattern).
• Discourse tracker: evidence of cite/critique/build (MP.3) during discussions.

Summative Assessment — End of Week; 0–2 per criterion, total 10

1. Problem-Solving Process (MP.1, MP.6)
   • 2: Clear plan, revisions based on checks/estimates.
   • 1: Plan present; limited checking.
   • 0: Minimal process evidence.
2. Reasoning & Communication (MP.2, MP.3)
   • 2: Uses representations and justifies choices; critiques ideas with evidence.
   • 1: Some reasoning; limited justification.
   • 0: Assertions without support.
3. Representations & Tools (MP.4, MP.5)
   • 2: Appropriate tables/graphs/equations; tools used strategically.
   • 1: Representations partially correct or inefficient.
   • 0: Missing/misused.
4. Precision & Structure (MP.6, MP.7, MP.8)
   • 2: Careful labeling/units; notices patterns and uses them.
   • 1: Minor precision issues; patterns noted but not applied.
   • 0: Frequent errors; patterns ignored.
5. Content Preview (8.EE.5, 8.F.1)
   • 2: Correctly identifies unit rate/slope and recognizes function vs. non-function.
   • 1: Partially correct.
   • 0: Off target.

Feedback Protocol

• Two strengths (e.g., “Your table → graph transition showed rate clearly”) and one next step (e.g., “Add a quick unit check before you decide”).
• Micro-goals: label axes every time, write one because sentence per solution, log one error fix per task.

VII. Reflection and Extension

Reflection Prompts

• “Which self-check helped you catch an error this week?”
• “How did using tables and graphs change your approach to the problem?”
• “Where did you notice a pattern you can reuse next time?”

Extensions

• Design-a-Task: Create a short constant-rate scenario and provide a correct table/graph pair.
• Function Hunt: Find three real-life input→output pairs at home/school; explain why each is (or isn’t) a function.
• Transformation Trail: Draw a shape and write directions to move it (translate/reflect) so a partner can reproduce it.

Standards Trace — When Each Standard Is Taught/Assessed

• 8.EE.5 introduced Session 2; assessed in Summative criterion 5.
• 8.F.1 introduced Session 3; assessed in Summative criterion 5.
• MP.1–MP.8 embedded Sessions 1–5; assessed in Summative criteria 1–4.