Halves and Sharing

Lesson Overview

Year Level: Year 5
Duration: 30 minutes
Subject: Mathematics
Australian Curriculum Reference:
ACMNA101 — "Compare and order common unit fractions and locate and represent them on a number line."
ACMNA100 — "Use equivalent number sentences involving multiplication and division to describe and verify mathematical relationships."

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Learning Intention

We are learning to understand that division can sometimes result in halves and fractions, and that this connects to the commutative property of multiplication and division.

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Success Criteria

By the end of this lesson, students will be able to:

• Identify when a division problem results in a fraction or a half.
• Explain how the commutative property works for multiplication (but not division).
• Use visual models to represent division problems that lead to halves.
• Justify their thinking using mathematical language.

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Materials Needed

• Mini whiteboards and markers (1 per student)
• Counters (or any manipulatives like buttons, blocks – at least 30 per group)
• Large chart paper with a number line (0 to 2 marked by halves)
• PowerPoint slides / Display screen
• A4 printed cards with simple division scenarios (e.g., 5 ÷ 2, 6 ÷ 3, etc.)
• Fraction circles or fraction bars
• Teacher’s example board / blackboard

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Vocabulary

• Division
• Halves
• Commutative Property
• Equal Groups
• Remainders
• Fraction

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‘I Do, We Do, You Do’ Sequence

I Do (10 minutes)

Teacher Led Explanation and Modelling

1. Hook / Prior Knowledge Activation (2 minutes):
   Ask: “Who remembers what happens when we divide something and it doesn’t go in evenly?”
   Example: “If I had 5 apples and 2 people, how many each?”
   Use fraction bars to show that sometimes we get halves.

2. Explicit Teaching (8 minutes)
   Use the board to model this sequence:

   • Write:
     6 ÷ 2 = ?
     and explain—“Two equal groups. How many in each?”

   • Then:
     5 ÷ 2 = ?
     Ask: “Can I split 5 into 2 equal WHOLE numbers?” (No!)

   • Model this using real counters and group into halves:
     2 + 2 + 1 left over becomes two 2.5s
     So, write: 5 ÷ 2 = 2½

   • Highlight:
     “Notice how the answer includes a half because it didn’t divide equally."

   • Introduce the commutative property:

     • 6 × 2 = 12 and 2 × 6 = 12 ✔︎
     • But: 12 ÷ 2 = 6 and 2 ÷ 12 = ❌ (not interchangeable!)
     • Reinforce: Multiplication is commutative; division is not. But they are related.

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We Do (10 minutes)

Guided Practice

1. Group Activity (Pairs or groups of 3):
   Each group gets counters and cards with division questions like:

   • 4 ÷ 2
   • 9 ÷ 2
   • 6 ÷ 3
   • 7 ÷ 2

   For each, they:

   • Solve using counters.
   • Use fraction bars when needed.
   • Write their answer in both "mixed numeral" and "fraction" (e.g., 3½ or 7/2)
   • Draw it on the number line.

2. Share out one tricky question to the class
   Group presents how they got their ‘half’.

   • Teacher questions: “Why do we get a half here? Could we see a half in the original problem?”

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You Do (7 minutes)

Independent Practice

• Hand out individual mini-whiteboards.

• Display 3 new division problems that should result in fractional answers:

  1. 7 ÷ 2 = ?
  2. 10 ÷ 4 = ?
  3. 5 ÷ 2 = ?

• Students draw:

  • Equal groups with any remainder split into fractions.
  • Number line representing their answer.

• Ask students to write a sentence: “I know this answer has a half because...”

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Plenary (3 minutes)

Mini-Quiz Showdown!
Ask quick-fire questions:

• “Is multiplication always commutative?”
• “Can I do 6 ÷ 2 the same as 2 ÷ 6?”
• “Why would I have a half when dividing?”
• “Give me a number sentence that equals 7/2”

Catch misconceptions live and correct them for the whole class.

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Differentiation

• Support:
  Provide scaffolded cards with visual models already started.
  Use simpler numbers and allow use of manipulatives more freely.

• Extension:
  Ask deeper questions like “Can a division ever give you quarters?”
  Ask them to write a real-life word problem where a fractional answer is needed.

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Assessment Strategies

• Observation during ‘You Do’ and group tasks.
• Check for correct use of fractions and visuals.
• Do students explain reasoning using mathematical vocabulary?
• Collect whiteboards or snapshots of number lines.

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Reflection

Post-Lesson Reflection Prompt for Teacher:

• Did students grasp the idea that fractions can result naturally from division?
• Were students able to distinguish between the properties of multiplication versus division?
• How confident were students when asked to explain “why” an answer includes a half?

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By using visual aids, relatable group work, and high-value vocabulary, this lesson aims to deepen understanding of division and connect it meaningfully to broader number sense expectations in Year 5.

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Teaching Tip
Try leaving up the number line post-lesson as a reference point for follow-up maths sessions — a visual cue works wonders for anchoring new ideas!