Sharing with Remainders

WALT (We Are Learning To)

• Model division with remainders using concrete materials.
• Understand how division can result in left-over amounts.
• Use hands-on activities to represent and solve division problems with remainders.

Alignment with Australian Curriculum (v9)

• Mathematics > Number and Algebra > Number and place value
• Year 4 Content Description: Recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator - Elaborations focus on using materials and diagrams to explain division and related multiplication facts, which supports modelling of division with remainders concretely.

Success Criteria

• I can use objects (such as counters or blocks) to divide a number into equal groups.
• I can identify when there are some objects left over (a remainder).
• I can write a division number sentence that shows the remainder.
• I can explain what the remainder means in a real-life context.

Lesson Duration

• 45 minutes

Class Size

• 25 students

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Resources

• Counters or small blocks (enough for each student to have around 30)
• Whiteboards and markers
• Division flashcards (numbers, e.g., 23 ÷ 4)
• Division chart showing division sentences with remainders
• Large paper or chart for creating a whole-class model
• Digital tool or app simulating division with remainders (optional)

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Lesson Outline

1. Introduction (5 minutes)

• Begin with a brief review of multiplication facts related to division (e.g., 4 x 5 = 20, so 20 ÷ 4 = 5).
• Introduce today's learning goal using WALT and success criteria.
• Explain that sometimes when we divide, things don’t split evenly and there can be leftovers called "remainders."

2. Hands-on Modelling Activity (15 minutes)

• Concrete Modelling with Counters:
• In pairs, students receive 23 counters.
• Teacher presents the division problem: "Divide 23 counters into groups of 4."
• Students physically divide their counters into equal groups of 4.
• After grouping, students count how many groups of 4 they have and how many counters are left over.
• Guide students to understand the remainder—there are 5 groups of 4 with 3 left over.
• Discuss as a class and represent the division as: 23 ÷ 4 = 5 remainder 3.
• Use a large paper or chart to create a visual model showing the 5 groups of 4 and remainder 3.

3. Explanation and Number Sentence Writing (10 minutes)

• Teach students how to write a division sentence with a remainder:

For example: 23 ÷ 4 = 5 R3

• Provide multiple practice examples (e.g., 19 ÷ 3, 30 ÷ 7), with students using counters to solve and write the number sentences.
• Discuss what the remainder means in each context (e.g., 3 leftover counters that cannot be grouped evenly).

4. Collaborative Problem Solving (10 minutes)

• Students work in small groups.
• Each group is given a real-life word problem involving division with remainder, such as:
• "You have 29 apples and boxes that hold 6 apples each. How many boxes can you fill? How many apples will be left over?"
• Groups use counters and whiteboards to model and solve.
• Groups share their solution and explanation with the class.

5. Extension for Advanced Learners

• Introduce concept of interpreting remainders in different contexts:
• Sometimes a remainder means “left over.”
• Sometimes a remainder might mean needing another whole group (e.g., boxes must be full).
• Challenge students to rewrite number sentences accordingly (e.g., 23 ÷ 4 = 6 boxes if you can’t leave any apples unpacked).

6. Differentiation Strategies

• For diverse learners who need extra support:
• Use smaller numbers initially.
• Provide one-on-one guidance with hands-on materials.
• Use visual step-by-step charts to remind of the process.
• For students needing enrichment:
• Challenge their thinking by providing larger numbers or two-digit divisors.
• Encourage explanation of division and remainder using drawings and words.

7. Conclusion and Reflection (5 minutes)

• Recap the lesson using WALT and success criteria.
• Invite students to explain in their own words what a remainder is and how to model division with remainders.
• Collect one example division problem solved with counters and written as a number sentence from each student on a mini whiteboard.

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Additional Notes

• Encourage the use of mathematical language such as "quotient," "divisor," "dividend," and "remainder."
• Use First Nations Australians’ cultural approaches to sharing and grouping where relevant, to connect mathematics with local contexts.
• Consider integrating a fun game where students “divide” a set of cards or tokens and identify remainders to reinforce learning.

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This lesson plan allows students to explore division with remainders through physical, social, and reflective learning activities that align tightly with the Australian Curriculum Year 4 Mathematics content and elaborations. The concrete hands-on models ensure young learners not only understand division conceptually but also see how remainders arise naturally and what they represent in realistic scenarios, supporting rich mathematical thinking and communication.