Sharing and Grouping

Overview

Year Level: Year 3
Subject: Mathematics
Duration: 45 minutes
Class Size: 18 students

Australian Curriculum Alignment

Curriculum Area: Number and Algebra → Number and place value
Content Descriptor (ACMNA057):
“Represent and solve problems involving multiplication and division using efficient mental and written strategies and appropriate digital technologies.”

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Learning Intentions

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

• Understand division as repeated subtraction
• Draw arrays to model division problems
• Identify:
  • What is being divided (the dividend)
  • How many groups or items are in each group
  • Whether the problem is about sharing or grouping

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Success Criteria

Students will demonstrate success by:

• Drawing an appropriate array to show equal groups
• Solving at least three division problems using repeated subtraction
• Explaining the difference between sharing and grouping using their own words and an illustration

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Materials and Resources

• Whiteboard and markers
• Pre-cut paper counters (3 sets of 18 per student)
• A3 coloured paper for array drawing
• “Division Detectives” worksheet (provided below)
• Dice (1 per pair)
• Mini whiteboards or clipboards for student working
• Visuals of arrays and repeated subtraction examples

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Warm-Up – 5 mins

"Where did they go?" (Informal Chat)

Objective: Activate prior knowledge about equal groups.

Prompts:

• "Imagine you have 12 cupcakes to share between 4 friends. How would you do it?"
• "What are some ways to show that 12 things can be shared into equal groups?"

Strategy: Encourage open talk around terms like “groups”, “sharing”, “each”, “fair”, and “equal”.

Teacher notes observations on the board (no right or wrong answers yet).

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Explicit Teaching – 10 mins

Exploring Division: Repeated Subtraction and Arrays

**Step 1: Introduce division as repeated subtraction
Use the whiteboard to model:

• “12 divided by 3 = ?”
• Ask: “How many times can I subtract 3 from 12?”
• 12 − 3 = 9 → 9 − 3 = 6 → 6 − 3 = 3 → 3 − 3 = 0
  You subtracted 3 four times. So, 12 ÷ 3 = 4

Add a number line to show the jumps being subtracted each time.

Step 2: Link to Arrays
Present a real-life example:

• “You have 15 stickers and want to group them with 5 in each group.”
• Draw an array: 3 rows of 5
• Highlight: 3 groups (rows), 5 in each group
• Point out: We divided 15 by 5 and got 3 groups

Use a think-aloud:

• “What is being divided?” (15 stickers – the total)
• “How many are in each group?” (5 per group)
• “How many groups did we make?” (3)

Interactive questioning throughout for participation.

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Guided Practice – 10 mins

“Shake, Roll & Group” (Hands-On Activity in Pairs)

Grouping: Pairs
Materials: Dice, counters, A3 paper

Instructions:

1. Both roll a die.
2. First number = number of items (dividend)
   Double the number (e.g. roll a 4 → 8 is total items)
3. Second number = group size (divisor)
4. Use counters to physically group and then draw the matching array.
5. Record:
   • Number sentence (16 ÷ 4 = 4)
   • Repeated subtraction method (16 − 4 = 12… until 0)
   • Labeled array

Teacher circulates and prompts:

• “What are you dividing?”
• “How many groups did you make?”
• “Can you explain your thinking?”

Extension: If students complete early, ask them to make up their own story problems for their equation.

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Independent Task – 15 mins

“Division Detectives” Worksheet

Each student receives the worksheet with 3 real-world problems. All involve division, but phrased either as sharing or grouping.

Example Problem 1:
"You have 20 apples. You give 5 to each friend. How many friends get apples?"
(division by grouping)

They must:

• Use repeated subtraction to find the answer
• Create a matching array
• Identify what is being divided and how many in each group

Challenge Box:
“Can you write your own problem using 24 items?”
Draw the array and write the division sentence.

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Plenary – 5 mins

“Explain and Show!” (Student-Led Presentations)

Volunteers (2–3 students) come up to:

• Share one problem they solved
• Explain whether it was a grouping or sharing problem
• Show the array and how it helped them

Teacher prompts the rest of the class to give them “Wow” or “Wonder” feedback.

Wrap-Up Message:

“Today, we found that dividing isn’t just one thing – it can be about sharing equally or finding how many groups we can make. Arrays and subtraction helped us every step of the way!”

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Differentiation

Support:

• Use visual aids and simplified tasks with smaller numbers
• Provide a “Division Helper Card” showing subtraction steps and labelled array vocabulary

Extension:

• Create their own “division menu” of 5 story problems for peers to solve
• Use 2-digit numbers and link to multiplication facts

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Assessment

Formative assessment through:

• Observation during pair and independent work
• Questions during plenary to gauge vocabulary use and understanding
• Review of worksheet – focus on correct use of arrays and accurate application of repeated subtraction

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Reflection (for Teacher Use)

• Were students able to explain the difference between sharing and grouping?
• Did they independently use repeated subtraction correctly?
• Were arrays used effectively to support reasoning?

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Notes for Teacher

Consider using today’s observations to set up tomorrow’s lesson on division with remainders, building on today’s hands-on learning with clear visual strategies.

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This fun, practical, and rigorous session will help your Year 3 learners build a solid conceptual understanding of division—not just as a mathematical operation, but as a meaningful activity connected to their world.