Division Patterns

Year 3 Mathematics — 60-minute lesson

---

Curriculum Context

This lesson aligns with the New Zealand Curriculum Refresh for Mathematics and Statistics, with a focus on Number strategies in Phase 1 (Years 0–3). Students will consolidate understanding of multiplication and division facts, particularly division by 2, 4, and 8, by using equal grouping, skip counting, and familiar patterns. Learning builds on prior knowledge of skip counting and multiplication, progressing towards confident recall of division facts and use in problem-solving.

Relevant curriculum expectations:

• Recall multiplication and corresponding division facts for 2s, 4s, and 8s.
• Multiply and divide using equal grouping or skip counting.
• Represent division problems using materials, diagrams, number lines, and equations.
• Use correct mathematical language to describe operations.
• Decode and solve word problems involving division facts.
• Develop fluency through games, table grids, and other engaging activities.

Key competencies:

• Thinking and reasoning as they notice patterns in division.
• Using language, symbols, and texts in mathematics discussions.
• Managing self by engaging with challenges.
• Participating and contributing in group activities.

Teaching considerations include modelling efficient problem-solving methods, valuing mistakes as learning opportunities, and using student backgrounds to make mathematics meaningful.

---

Learning Objectives (WALT)

• We Are Learning To recall basic division facts for 2, 4, and 8.
• We Are Learning To use equal grouping and skip counting to solve division problems.
• We Are Learning To represent division with materials, diagrams, and equations.
• We Are Learning To explain division problems in our own words.

---

Success Criteria

• I can recall division facts for 2, 4, and 8 confidently.
• I can divide objects into equal groups using counters or drawings.
• I can solve simple word problems involving division by 2, 4, and 8.
• I can use division vocabulary correctly (e.g., share equally, equal groups, divide).

---

Lesson Outline

Time	Activity	Details / Resources
0–10	Introduction and Activation	Warm up with skip counting by 2s, 4s, 8s together as a class using chanting and clapping. Connect to prior knowledge of multiplication facts for these numbers.
10–25	Exploration with materials: Equal grouping	In small groups, students use counters, cubes, or paper shapes to create equal groups to divide sets of objects by 2, 4, and 8. Use number cards (e.g., 16, 24). Encourage students to show how many groups and how many in each group. Provide 10s frames and number lines for support.
25–35	Whole class modelling and vocabulary	Model how to write the division equation for problems (e.g., 16 ÷ 4 = 4). Highlight connection to multiplication families (4 × 4 = 16). Discuss vocabulary: divide, groups of, share equally. Use a simple bar model to represent grouping visually.
35–50	Guided practice: solving word problems	Present simple story problems involving division by 2, 4, and 8 (e.g., “There are 24 apples, shared equally into 8 bags. How many apples in each bag?”). Students work in pairs to draw diagrams, solve, and write the division equation. Circulate to support and ask guiding questions.
50–60	Reflection, success criteria check & extension	Students share one solution with the class. Discuss different ways to check answers (e.g., multiply to confirm). For early finishers: provide extension tasks with larger numbers or missing number problems (e.g., 48 ÷? = 6). Use table grids or digital games if available.

---

Differentiation Strategies

• Support for diverse learners:
• Use concrete materials and visual aids for all learners.
• Provide sentence starters for writing equations (e.g., “___ divided by ___ equals ___”).
• Work in mixed-ability groups to promote peer learning.
• Offer one-on-one support or adapted numbers for students needing confidence building (e.g., numbers divisible by 2 only initially).
• Extension for advanced learners:
• Challenge students with missing factor or divisor questions (e.g., “_ ÷ 4 = 5”).
• Explore division beyond the basic facts, including word problems involving remainders.
• Encourage the use of number lines and bar models to represent division problems independently.
• Investigate patterns (e.g., multiples) that help predict division results.

---

Materials and Resources

• Counters, cubes, or small objects for grouping
• Number cards (multiples of 2, 4, 8)
• 10s frames and number lines
• Whiteboard for modelling and vocabulary
• Paper and pencils for drawing bar models and diagrams
• Table grids for facts practice
• Optional: digital tools for multiplication/division games

---

Mathematical Language

• divide, division, groups of, sharing equally, divisor, quotient, multiply, multiplication, sets, equal groups, skip counting

---

Assessment for Learning

• Use observations during group work to identify who is confidently recalling facts and who is still developing understanding.
• Listen for correct use of language in explaining division.
• Review completed equations and word problem solutions.
• Use exit questions such as: “Can you tell me how many groups you made?” or “How did you check your answer?”

---

This lesson plan supports Year 3 students to build fluency and conceptual understanding of division facts by 2, 4, and 8 through active, collaborative learning embedded in the New Zealand Mathematics Curriculum framework. It emphasises multiple representations of division and connects multiplication and division as related operations, fostering both procedural skill and thinking strategies.