Multiplication and division with equal groups and arrays

Students build multiplication and division ideas from equal groups rather than memorising isolated rules. They make arrays, describe repeated addition, share collections fairly, make groups of a given size and explain how multiplication and division are connected.

• Make and name arrays such as 3 groups of 4 and 4 groups of 3.
• Connect an array to repeated addition and a multiplication statement.
• Partition an array into known facts to find a total efficiently.
• Share a collection into a known number of equal groups.
• Make groups of a known size and count how many groups can be formed.
• Use materials, diagrams, bar models, skip counting and Think Boards to explain solutions.

Content description: multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays and partitioning to support a variety of calculation strategies.

• E1: make and name arrays and use bar models to solve multiplication and sharing problems; recognise equivalent array orientations such as 3 fours and 4 threes.
• E2: find array totals by partitioning arrays and using subitising and known number facts.
• E3: distinguish dividing a set into a known number of equal groups from dividing it into groups of a known size.
• E4: use Think Boards, materials, diagrams and skip counting to solve partition and quotition division problems and interpret the unit of the answer.
• E5: use materials, diagrams, repeated addition and skip counting to solve repeated equal-quantity multiplication problems.

Key idea: Multiplication counts equal groups. Division shares equally or finds groups. Arrays make rows, columns and repeated addition visible.

Remember

• Make equal groups
• Use arrays
• Write repeated addition
• Model division
• Explain sharing

Quick questions

• Show 4 groups of 3.
• Write repeated addition for 5 groups of 2.
• Share 16 into 4 equal groups.
• Explain why 3, 4 and 5 is not an equal grouping.

If an answer is uncertain, return to the model and explain what each part represents before calculating or drawing a conclusion.

• Unequal groups: multiplication and equal-sharing models need equal group sizes.
• Counting every object in an array: prompt students to use rows, columns, doubles or known facts.
• Mixing up number of groups and group size: ask what each number represents in the story.
• Assuming all division means sharing: contrast “share into 3 groups” with “make groups of 3”.
• Writing a correct number without a unit: identify whether the answer is people, dollars, groups, objects or another quantity.

Begin with physical equal groups, then move to arrays, drawings, bar models and number sentences. Mix multiplication, sharing and grouping tasks so students must interpret the structure rather than rely on a memorised keyword.

Students build multiplication and division ideas from equal groups rather than memorising isolated rules. They make arrays, describe repeated addition, share collections fairly, make groups of a given size and explain how multiplication and division are connected.

• Make and name arrays such as 3 groups of 4 and 4 groups of 3.
• Connect an array to repeated addition and a multiplication statement.
• Partition an array into known facts to find a total efficiently.
• Share a collection into a known number of equal groups.
• Make groups of a known size and count how many groups can be formed.
• Use materials, diagrams, bar models, skip counting and Think Boards to explain solutions.

• Australian Curriculum Version 9.0
• Victorian Curriculum F–10
• NSW Curriculum

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