Division Sharing

Overview

In this lesson, students deepen their understanding of division by modelling “sharing” and “grouping” situations using concrete materials, diagrams and number sentences. They connect these models to multiplication/division relationships and use strategies to solve and explain division problems.

Learning intentions

Students will:

• understand division as sharing equally and as grouping into equal sets
• represent division problems using number sentences, arrays or part-part-whole diagrams
• choose an appropriate strategy to solve division problems with one- and two-digit numbers
• explain their thinking using words, diagrams and mathematical notation

Success criteria

Students can:

• state whether a situation is “sharing” or “grouping” and explain why
• draw or build a model that matches the division story
• write a correct number sentence for a division problem and check if it makes sense
• use a strategy (repeated subtraction, skip counting, arrays, known facts) to find the answer

Curriculum links

• Number — multiplication and division (one- and two-digit numbers), representing problems using number sentences and diagrams, and using a variety of calculation strategies
• Algebra — recall multiplication facts for 3, 4, 5 and 10 and use related division facts
• Number — using part-part-whole and comparative models to represent multiplicative relationships

Lesson structure (60 minutes)

1. 0–5 min · Hook (Think–Pair–Share). Teacher reads a short scenario: “12 lollies shared equally into 3 bags.” Students discuss in pairs what “shared equally” means and what question we could ask.

2. 5–15 min · Direct teach: sharing vs grouping. Teacher demonstrates with counters:

• Sharing: 12 counters into 3 equal groups (each group gets 4).
• Grouping: 12 counters grouped into piles of 4 (how many piles?). Students record a quick T-chart: “Sharing =? in each group” and “Grouping =? groups.”

3. 15–25 min · Guided practice: models to number sentences. Teacher shows two problems on the board:

• A: “20 apples shared equally among 4 children.”
• B: “20 apples packed into bags of 5.” Students, in small groups, use counters and draw a diagram. They then write a number sentence that matches their model (e.g., “20 ÷ 4 = 5” or “20 ÷ 5 = 4”). Teacher circulates, prompting correct alignment between story, model and equation.

4. 25–40 min · Strategy station rotation (calculation and reasoning). Three stations run for ~5 minutes each:

• Station 1: Arrays/Equal groups drawings for “sharing” and “grouping.”
• Station 2: Repeated subtraction or “how many equal jumps” number line strategy.
• Station 3: Known facts and skip counting for division with links to multiplication facts. Students solve two teacher-provided problems (one sharing, one grouping) and explain one strategy choice in words on a mini response sheet.

5. 40–52 min · Whole-class consolidation: represent and check. Teacher selects two student examples (one correct, one with a common error such as swapping sharing/grouping). Students help correct the equation by referring back to the model. Teacher emphasises checking: “Does the answer match the size and number of groups?” Students revise their own thinking if needed.

6. 52–60 min · Exit ticket (independent). Students complete:

• Scenario 1 (sharing): “18 biscuits shared equally into 3 plates. How many per plate?”
• Scenario 2 (grouping): “18 biscuits packed into groups of 3. How many groups?” They must draw a simple model and write the division number sentence for each.

Resources

• Counters (or Unifix cubes) for modelling equal groups
• Base-ten blocks or place-value mats (optional for students who prefer visual structure)
• Division problem cards (sharing and grouping)
• Mini response sheets with space for a diagram and number sentence
• Whiteboards/slates and markers
• T-chart template: Sharing vs Grouping
• Number line prints for strategy station 2
• Sticky notes for student explanations during consolidation

Assessment

• Formative: teacher listens for correct identification of “sharing” vs “grouping” during pair discussions and station work
• Formative: teacher checks that students’ diagrams match their number sentence (during guided practice and consolidation)
• Summative (quick): exit ticket for correct division equation plus model alignment and brief reasoning

Differentiation

• Support:
• Sentence starters: “This is sharing because…”, “I know because…”, “The groups are equal because…”
• Provide a model scaffold: partially drawn circles/groups with prompts to fill in
• Use fewer digits at first (e.g., 12 ÷ 3) then move to larger numbers once the structure is secure
• Targeted practice:
• Offer an “inverse check” prompt: “If 20 ÷ 5 = 4, what multiplication matches?”
• Extension for faster students:
• Challenge students to create a new sharing and grouping story for a given number sentence (e.g., “24 ÷ 6 = 4”)
• Ask them to compare strategies: “Which strategy is fastest for this problem and why?”
• EAL/SEN considerations:
• Use consistent visuals and gestures for “each”, “equal”, “bags/piles”
• Reduce written load: allow oral explanation plus a labelled diagram, then copy only the final equation

Differentiation for advanced learners

• Provide an additional task during stations: “Choose whether each situation is sharing or grouping. Then solve and explain using a diagram and an equation.” Include one two-digit dividend problem that requires a strategy beyond basic counting (e.g., 36 biscuits shared into 6 groups; 36 biscuits packed into groups of 9).