AC9M2N05: 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.

Multiplication describes repeated equal quantities. If there are 4 trays with 6 biscuits on each tray, the repeated addition is 6 + 6 + 6 + 6 = 24.

Students should say what the numbers mean: 4 groups of 6 make 24. The groups must be equal; a collection split into unequal groups does not model multiplication in this way.

An array organises objects into equal rows and equal columns. Twelve objects can be arranged as 3 rows of 4, 4 rows of 3, 2 rows of 6 or 6 rows of 2.

The same array can be viewed in two directions. A 3-by-4 array shows both 3 groups of 4 and 4 groups of 3; both have a total of 12.

Rotate or redraw arrays so students focus on the equal-group structure rather than the picture orientation.

Students do not need to count every item in a large array. They can split it into familiar parts.

For a 3-by-5 array, a student might see 2 groups of 5 as 10, then one more group of 5: 10 + 5 = 15.

For 6 groups of 4, they might use 5 groups of 4 = 20, then add one more 4 to make 24.

Two division situations can start with the same total but ask different questions.

Sharing (partition division): 12 counters are shared equally between 3 children. Each child gets 4.

Grouping (quotition division): 12 counters are put into groups of 3. There are 4 groups.

Ask students to identify what the answer represents: the size of each group or the number of groups.

A Think Board can show the same problem in several connected forms: the story, materials, a drawing/bar model, skip counting and a number sentence.

Example: $36 is shared equally between 4 people. Students can make 4 equal groups, draw 4 equal bars and skip count 4 groups of 9 to confirm that each person receives $9.

The unit matters: the answer is 9 dollars per person, not 9 people.

A multiplication bar model shows several equal parts making one whole. A division bar model can show either an unknown part size or an unknown number of equal parts.

For 4 groups of 6, draw 4 equal bars labelled 6. The whole is 24. For 24 shared between 4 groups, the whole is known and each equal bar is unknown.

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.

• Support: use counters, cups, egg cartons, grid paper and pre-drawn bar models.
• Core: move between an array, repeated addition, a bar model and a spoken equal-group statement.
• Extension: ask students to find several different arrays for the same total and explain why each is valid.

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.

1. Draw an array for 3 groups of 4. What is the total?
2. Write repeated addition for 5 groups of 3.
3. Explain two different arrays that show 12.
4. Share 20 counters equally between 4 groups. How many are in each group?
5. Make groups of 4 from 20 counters. How many groups are there?
6. Explain the difference between the previous two division questions.

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.

Curriculum equivalents for Multiply and divide by one-digit numbers using repeated addition, equal...

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

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.

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

• AC9M2N04: Addition and subtraction strategies
• AC9M2N06: Mathematical modelling and money
• AC9M2A03: Multiplication facts for twos and related division facts