Division Foundations

Year Level

Year 3

Duration

60 minutes

Class size

25 students

---

Learning Objectives (New Zealand Curriculum Refresh aligned)

• Recall division facts using equal grouping and sharing with one-digit divisors (e.g., 24 ÷ 3) with no remainders.
• Use arrays and number lines as visual representations of division problems.
• Solve simple division word problems involving equal sharing and grouping.
• Develop and practise mental calculation strategies and fluency for basic division facts.
• Use correct mathematical language related to division (e.g., divide, share equally, groups of, sets of).

Relevant curriculum references:

• Operations: Divide whole numbers by a one-digit divisor with no remainders, using grouping (Year 3)
• Represent multiplication and division problems using diagrams, arrays, number lines, and words (Year 3)
• Use materials and images to model division as sharing or grouping
• Develop fluency with multiplication and division facts for 2s, 3s, 5s, 10s, including corresponding division facts
• Mathematical competencies: Thinking, Using language, symbols and texts, and Participating and contributing

---

WALT (We Are Learning To)

• Understand division as equal sharing and grouping.
• Recall and use basic division facts for 2s, 3s, 5s, and 10s.
• Represent division problems using arrays and number lines.
• Solve simple division word problems.
• Develop mental calculation strategies to improve fluency.

---

Success Criteria

Students will be able to:

• Explain what division means using correct mathematical language.
• Model division problems by drawing arrays or using number lines.
• Divide numbers into equal groups using counters or other materials.
• Solve simple word problems involving division.
• Recall division facts for selected times tables confidently and mentally.

---

Lesson Outline and Activities

1. Introduction & Recap (10 minutes)

• Start with a short discussion: "What does division mean?" Use everyday language and examples (e.g., sharing 12 biscuits equally among 3 friends).
• Show a simple sharing problem using counters or marbles.
• Introduce key vocabulary: divide, share equally, groups of.

Teacher talk and engage students in sharing what they know about dividing things equally.

2. Exploring Division Through Grouping and Sharing (15 minutes)

• Activity 1: Equal sharing with concrete materials. Provide each student/group with counters or cubes. Ask them to share 12 counters equally between 3 groups and find out how many counters are in each group. Repeat with 24 ÷ 4 and 20 ÷ 5.

• Activity 2: Use arrays to visualise division. Draw or use grid paper to create arrays (e.g., a 12-dot array arranged as 3 rows of 4). Discuss how looking at rows and columns relates to division (12 ÷ 3 = 4). Students draw their own arrays for given division facts.

3. Division on Number Lines (10 minutes)

• Demonstrate how to use a number line to model division as repeated subtraction or jumps.
• Example: "If we have 12, jump back in 3s until you get to zero - how many jumps?"
• Students practice with their own number lines for simple division facts.

4. Word Problems in Context (10 minutes)

• Present simple, relatable division word problems:

• "There are 18 apple slices to share equally among 6 students. How many slices does each student get?"

• "You have 20 marbles and want to put them into bags of 5. How many bags do you fill?"

• Model decoding the problem, identifying the numbers, operation (division), and solving using grouping or sharing methods.

• Students work in pairs to solve 2-3 word problems using drawings or physical materials.

5. Fluency Practice and Mental Strategies (10 minutes)

• Quick-fire questions on division facts in 2s, 3s, 5s, 10s. Use games or choral responses.
• Introduce and practise mental calculation strategies such as:
• Using related multiplication facts (e.g., if 5 × 4 = 20, then 20 ÷ 5 = 4)
• Doubling or halving known division facts.

6. Reflection & Plenary (5 minutes)

• Discuss with the class: What did they learn today?
• Ask students to explain division in their own words or to show one of their arrays or number lines.
• Highlight the success criteria and check if objectives were met.

---

Differentiation Strategies

• For diverse learners:

• Use concrete materials (counters, cubes) and visual aids (arrays, number lines) for hands-on learning.

• Provide sentence starters or word banks to support verbal explanations of division concepts.

• Pair learners strategically, mixing stronger with developing students for peer support.

• Use simplified word problems with images.

• For advanced learners:

• Challenge learners to create their own division word problems for peers.

• Extend to division problems involving larger numbers or missing numbers in division sentences (e.g.,? ÷ 4 = 6).

• Encourage exploration of the multiplicative identity and commutative property (e.g., understanding 12 ÷ 4 = 3 and 3 × 4 = 12).

• Introduce early concepts of division with remainders or two-digit dividends divided by one-digit divisors without remainders.

---

Assessment Opportunities

• Observe students using materials to form equal groups and arrays.
• Listen to explanations during partner work and plenary for use of correct mathematical language.
• Check solution strategies in written or drawn work for understanding equal sharing and grouping.
• Use oral questioning in fluency practice to gauge rapid recall of division facts.
• Review ability to solve simple division word problems independently or with minimal support.

---

Materials Required

• Counters or small cubes
• Grid paper for arrays
• Whiteboard and markers
• Number lines printed or drawn for students
• Word problem cards or worksheets
• Visual aids with arrays and sharing examples

---

This lesson aligns specifically with the New Zealand Curriculum Refresh Phase 1 Year 3 expectations on division skills, mental strategy development, and using multiple representations including arrays and number lines for division. It incorporates mathematical competencies such as language use, thinking, and participation through interactive and collaborative learning strategies. The inclusion of differentiation and extension tasks ensures that diverse learners are supported and challenged appropriately, reflecting effective classroom practice in New Zealand primary schools.