Unit Plan 1 (Grade 3 Math): Building Our Math Community & Problem-Solving Norms

Focus: Establish discourse routines, math journals, self-checking, and error analysis with rich number/riddle tasks; preview arrays and equal groups.

Grade Level: 3

Subject Area: Mathematics (Community, Problem Solving, Early OA/NBT)

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

I. Introduction

Launch the math year by building shared norms for talking about math, organizing math journals, and using self-checking strategies. Students tackle short, engaging number riddles and explore equal groups/arrays to preview multiplication while reinforcing place-value language.

Essential Questions

• How do we explain our thinking and listen to others in math?
• What does it mean to check if an answer is reasonable?
• How do equal groups and arrays help us see multiplication?

II. Objectives and Standards

Learning Objectives — Students will be able to:

1. Follow and contribute to math discourse routines (turn-and-talk, agree/disagree with reasons).
2. Use math journals to show representations (drawings, arrays, number lines) and written explanations.
3. Solve number/riddle tasks and self-check using estimation, inverse thinking, or another strategy.
4. Describe and build equal groups/arrays; connect repeated addition to early multiplication ideas.
5. Use precise place-value language (hundreds, tens, ones) when reading and composing numbers.

Standards Alignment — CCSS Grade 3 (light academic launch)

• 3.OA.1 (light intro): Interpret products of whole numbers as equal groups (e.g., 4 × 6 as 4 groups of 6).
• 3.NBT.1 (place-value/rounding language): Use place value understanding to reason about tens/hundreds (build language now; rounding in later units).
• Mathematical Practices (MP.1–MP.8) threaded: Make sense & persevere, reason abstractly/quantitatively, construct arguments, model, use tools, attend to precision, look for structure/regularity.

Success Criteria — Student Language

• I can explain my strategy and listen for others’ ideas.
• I can show my work with arrays/diagrams and check if it makes sense.
• I can use place-value words (hundreds/tens/ones) to describe numbers.

III. Materials and Resources

Tasks & Tools (teacher acquires/curates)

• Math journals; dot/grid paper; two-color counters or linking cubes; 100 charts; place-value mats.
• Quick number riddles (mystery number with place-value clues), array card tasks, equal-groups task cards.
• Anchor charts: Discussion Norms, Solve–Check–Explain, What Is an Array?, Place-Value Words.
• Sentence stems and mini-rubrics for TAG feedback (Tell–Ask–Give).

Preparation

• Post discourse norms and success criteria; set up journal template (date, problem, model, explanation, check).
• Prepare “array museum” pictures (real-world arrays: egg cartons, windows, muffin tins).

Common Misconceptions to Surface

• Mixing up rows and columns in an array.
• Treating groups with unequal sizes as “equal groups.”
• Skipping the check step or changing numbers during copying.
• Using place-value words imprecisely (e.g., saying “10 hundreds” without linking to 1,000 conceptually).

Key Terms (highlighted in lessons)

• array, equal groups, row, column, skip count, repeated addition, multiplication, product, place value, hundreds/tens/ones, estimate, representation, reasonableness, error analysis, math talk.

IV. Lesson Procedure

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

Session 1: Community & Norms — How We Do Math Here (MP.1, MP.3, MP.6)

• Launch (8–10 min): Teach Discussion Norms and journal structure; model a short explanation with a simple number puzzle.
• Explore (15–20 min): Number riddles (mystery number between 300 and 400 with 4 tens and 6 ones, etc.). Students write clues using place-value words.
• Discuss (8–10 min): Share two student solutions; peers use TAG to celebrate clarity and ask a question.
• Reflect (Exit Ticket): “One norm I used today was ___; it helped because ___.”

Session 2: Equal Groups — From Pictures to Math (3.OA.1 intro; MP.2, MP.4)

• Launch (5–7 min): Show real-life pictures of equal groups; label rows/columns.
• Explore (15–20 min): Build equal groups with counters (e.g., 3 groups of 4); record as repeated addition and early multiplication (3 groups of 4 → 4 + 4 + 4 → “3 by 4 array”).
• Discuss (10–12 min): Compare two representations of the same total (groups vs. array).
• Reflect (Exit Ticket): Draw an array for 2 groups of 5 and explain rows/columns.

Session 3: Array Museum — Structure & Language (3.OA.1 intro; MP.7, MP.8)

• Launch (5–7 min): Revisit array features; highlight structure (equal rows/columns).
• Explore (15–20 min): “Array museum walk”: students label arrays (e.g., 4 rows, 5 columns), skip count, and write matching equations (4 + 4 + 4 + 4 and 4 × 5).
• Discuss (10–12 min): Where did structure help? How did skip counting support your total?
• Reflect (Exit Ticket): Write two sentences using array, row, column correctly.

Session 4: Place-Value Power — Read, Compose, Describe (3.NBT.1 language; MP.6, MP.7)

• Launch (8–10 min): Quick place-value warm-up: build a 3-digit number with cards; describe using hundreds/tens/ones.
• Explore (15–20 min): Journal tasks: “I am a number with 6 hundreds, 0 tens, and 9 ones. What am I? Show two ways to represent me.”
• Discuss (8–10 min): Emphasize precision in place-value language; connect to reasonableness checks.
• Reflect (Exit Ticket): Write a mystery-number clue using place-value words.

Session 5: Problem-Solving Showcase — Solve, Check, Explain (MP.1–MP.6)

• Task (25–30 min): Mixed menu: one array task, one equal groups story, one place-value riddle. Students solve–check–explain in journals with representations.
• Peer Review (TAG, 5–7 min): Tell a strength, Ask a question, Give a suggestion (clarify model/words).
• Reflect (Exit Ticket): “One self-check I used was ___; it changed my work by ___.”

V. Differentiation and Accommodations

Advanced Learners

• Create two different arrays for the same total; explain which is easier to count and why.
• Write your own number riddle with two valid solutions; justify both.

Targeted Support

• Provide row/column frames and pre-drawn grids; sentence frames for math talk.
• Use small numbers and manipulatives; model the check step explicitly.

Multilingual Learners

• Picture glossary cards for array, row, column, hundreds/tens/ones; stems: “I see…,” “My model shows…,” “I checked by…”.
• Encourage labeled drawings before full sentences.

IEP/504 & Accessibility

• Offer larger grid paper, color-coding (rows one color, columns another).
• Partner scribe or voice-to-text for journal explanations.

VI. Assessment and Evaluation

Formative Checks (daily)

• S1: Uses norms and journals correctly; attempts an explanation.
• S2: Builds equal groups and records repeated addition.
• S3: Correctly labels rows/columns; connects to a total with skip counting.
• S4: Uses place-value words precisely to describe/build numbers.
• S5: Shows solve–check–explain with a clear representation.

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

1. Mathematical Accuracy

• 2: Correct totals, models, and place-value descriptions
• 1: Minor mistakes not changing the result
• 0: Major errors or unsupported answers

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

• 2: Efficient strategy; models (arrays/equal groups/place value) fit the task
• 1: Mostly sensible; some mismatched or incomplete models
• 0: Inefficient or unclear strategy/models

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

• 2: Clear explanation connecting model → math words → total
• 1: Partially justified or missing a link
• 0: Little/no explanation

4. Precision (MP.6)

• 2: Correct place-value words; neat labels; accurate counts
• 1: Minor precision lapses
• 0: Disorganized or imprecise work

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

• 2: Uses norms, gives/uses TAG feedback, notes self-check
• 1: Uneven participation or limited reflection
• 0: Minimal collaboration or reflection

Feedback Protocol (Showcase)

• Read & Restate (1 min): Peer restates the solver’s claim/answer.
• TAG (2–3 min): Tell a strength, Ask a focused question, Give a suggestion.
• Evidence Check (1 min): Point to a representation that supports/challenges the claim.
• Author Response (1–2 min): Record one revision and why it improves clarity or correctness.

VII. Reflection and Extension

Reflection Prompts

• Which check caught a possible error?
• How did using an array help you explain your thinking?
• Which math practice did you use most today?

Extensions

• Array Hunt: Photograph or sketch real-world arrays at home/school; label rows/columns, write the total.
• Two Ways: Solve a problem with equal groups and as an array; compare which was clearer and why.
• Riddle Author: Create a multi-clue place-value riddle for a partner to solve.

Standards Trace — When Each Idea Is Addressed

• 3.OA.1 — Equal Groups/Arrays (intro): Sessions 2–3, 5.
• 3.NBT.1 — Place-Value Language (foundation for rounding later): Sessions 1, 4, 5.
• MP.1–MP.8 — Practices: All sessions (perseverance, reasoning, argument, modeling, tools, precision, structure, regularity).