Multiplication & Division Activities for Primary Schools

Building Conceptual Understanding of Multiplication and Division

Multiplication and division are more than memorising times tables — they are fundamental operations that underpin fractions, ratios, algebra, and problem solving across the curriculum. Students who understand why multiplication and division work, not just how to perform them, develop the flexible number sense needed for success in upper primary and secondary mathematics.

In the Australian Curriculum v9, multiplication and division sit within the Number strand and are developed progressively from Year 2 through Year 6. The curriculum emphasises building conceptual understanding first — through equal groups, arrays, and the connection between multiplication and division — before moving to procedural fluency and formal algorithms.

This guide focuses on conceptual understanding and problem-solving strategies for multiplication and division. For times tables fluency and fact recall, see our Times Tables Chart page. For multiplication and division games, see our Maths Games guide. Browse the teacher-created resources below to find worksheets, activities, and hands-on materials organised by concept and year level.

Understanding multiplication and division develops through several connected concepts. Each stage builds on the one before, and students need secure understanding at each level before moving to the next.

Equal Groups

Multiplication begins with the concept of equal groups. Before students learn the multiplication symbol, they need extensive experience with:

• Making equal groups: "Put 12 counters into groups of 3. How many groups did you make?" This is the basis of division (sharing and grouping)
• Describing equal groups: "There are 4 bags with 5 apples in each bag. How many apples altogether?" This is the basis of multiplication
• Skip counting: Counting by 2s, 5s, 10s, and then 3s and 4s reinforces the idea of adding equal groups repeatedly

Activities at this stage are entirely hands-on — students use counters, blocks, food items, and real objects to make and describe equal groups.

Repeated Addition

Repeated addition is the bridge between addition and multiplication. Students learn that 3 + 3 + 3 + 3 is the same as 4 groups of 3, which is the same as 4 × 3. Activities include:

• Number line jumps: Students show repeated addition as jumps on a number line — four jumps of 3 from zero to 12
• Repeated addition to multiplication sentences: Students write the repeated addition, then rewrite it as a multiplication sentence
• Story problems: "Sam ate 2 biscuits every day for 5 days. How many biscuits did he eat altogether?" Students represent this as 2 + 2 + 2 + 2 + 2 = 10, then as 5 × 2 = 10

Arrays

Arrays are rectangular arrangements of objects in rows and columns. They are one of the most powerful models for multiplication because they make several key concepts visible:

• Commutativity: A 3 × 4 array has the same number of objects as a 4 × 3 array — just rotated. Students can physically turn the array to see that the total is the same
• Connection to area: An array of squares is essentially an area model, connecting multiplication to measurement
• Fact families: A single array generates four related facts (e.g., 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 4 = 3, 12 ÷ 3 = 4)

Array activities include:

• Building arrays with counters or tiles: Students arrange objects into rows and columns and write the matching multiplication sentence
• Array snap: Students match array cards to multiplication sentence cards
• Finding arrays in the real world: Egg cartons (2 × 6), chocolate blocks (4 × 5), window panes, floor tiles

Area Model

The area model extends arrays to larger numbers. Students draw a rectangle and label the sides with the factors. For single-digit multiplication, this looks like a standard array. For multi-digit multiplication, students partition the rectangle:

• 24 × 3: Partition 24 into 20 + 4. Draw a rectangle split into two sections: 20 × 3 = 60 and 4 × 3 = 12. Total: 72
• 23 × 15: Partition both numbers: (20 × 10) + (20 × 5) + (3 × 10) + (3 × 5) = 200 + 100 + 30 + 15 = 345

The area model makes the distributive property visible and provides a conceptual foundation for the formal long multiplication algorithm.

Fact Families (Multiplication and Division)

Multiplication and division are inverse operations — each undoes the other. Understanding this relationship is critical. Activities include:

• Fact family triangles: A triangle with three numbers (e.g., 3, 5, 15) at the corners. Students write all four related facts: 3 × 5 = 15, 5 × 3 = 15, 15 ÷ 3 = 5, 15 ÷ 5 = 3
• Missing number problems: 4 × _ = 20. Students use their knowledge of the inverse to solve
• Array-based fact families: Given an array, students write all four facts it represents

For foundational number work that supports multiplication and division, see our Addition & Subtraction Activities guide.

As with addition and subtraction, the Australian Curriculum expects students to develop mental strategies before moving to formal written algorithms. Here are the key strategies, roughly in the order they are typically introduced.

Mental Multiplication Strategies

Doubling and halving: To multiply by 4, double twice. To multiply by 8, double three times. To multiply by 5, multiply by 10 and halve. These strategies build on students' strong doubles knowledge from addition and subtraction.

Using known facts: Students use facts they know to derive facts they don't. If a student knows 6 × 6 = 36, they can work out 6 × 7 = 36 + 6 = 42. This builds multiplicative reasoning.

Distributive property (split strategy): Break a factor into parts. For example, 7 × 8 = (5 × 8) + (2 × 8) = 40 + 16 = 56. This strategy is the mental version of the area model and directly prepares students for multi-digit multiplication.

Compensation: Round one factor to make the calculation easier, then adjust. For example, 9 × 6: think 10 × 6 = 60, then subtract one group of 6: 60 − 6 = 54.

Mental Division Strategies

Using multiplication facts: Division is the inverse of multiplication, so knowing that 7 × 8 = 56 means you also know 56 ÷ 8 = 7. This is the most efficient division strategy for basic facts.

Halving: Dividing by 2 is halving. Dividing by 4 is halving twice. Dividing by 8 is halving three times. These strategies mirror the doubling strategies for multiplication.

Chunking: For larger division problems, students subtract known multiples of the divisor. For example, 96 ÷ 4: subtract 10 groups of 4 (40) to get 56, then subtract 10 more groups (40) to get 16, then subtract 4 groups (16) to get 0. Total: 10 + 10 + 4 = 24 groups.

Formal Written Methods

Short multiplication: The traditional algorithm where students multiply each digit of the larger number by the single-digit multiplier, carrying as needed. This is typically introduced in Year 4 after students have a solid understanding of place value and the distributive property.

Long multiplication: For multiplying by a two-digit number. Students multiply by the ones digit, then by the tens digit, and add the partial products. Introduced in Year 5 or 6, building on the area model.

Short division (bus stop method): Students divide each digit of the dividend by the divisor, carrying remainders across. This is typically introduced in Year 4.

Long division: For dividing by a two-digit number. This is the most complex primary algorithm and is typically introduced in Year 5 or 6.

The Australian Curriculum v9 develops multiplication and division progressively within the Number strand.

Year 2

Year 2 is where multiplication and division are formally introduced. Students explore equal groups, sharing equally, and skip counting by 2s, 5s, and 10s. They represent multiplication as repeated addition and use arrays to model problems. Division is introduced through sharing (partitive) and grouping (quotitive) contexts. Students are not expected to know times tables at this stage — the focus is on understanding the concepts.

Year 3

Year 3 students develop recall of multiplication facts for 2, 3, 5, and 10. They use arrays and the area model to represent multiplication, and explore the commutative property (3 × 4 = 4 × 3). Division is connected to multiplication through fact families. Students begin to solve one-step multiplication and division word problems.

Year 4

Year 4 extends to multiplication facts for all numbers to 10 × 10. Students develop fluency with these facts and apply them to mental and written multiplication and division. They learn to multiply two-digit numbers by one-digit numbers using mental strategies and the short multiplication algorithm. Division with remainders is introduced, and students interpret remainders in context (round up, round down, or express as a fraction).

Year 5

Year 5 students multiply and divide by two-digit numbers. They use the area model and long multiplication to multiply multi-digit numbers. Division extends to dividing four-digit numbers by one-digit numbers. Students apply multiplication and division to problems involving fractions and decimals, and connect multiplication to area and volume calculations.

Year 6

Year 6 consolidates multi-digit multiplication and division, including long division. Students solve complex multi-step problems and apply their skills across all areas of the curriculum — ratios, percentages, rates, and algebraic thinking. Estimation and reasonableness checking become increasingly important.

Hands-On Activities for Each Year Level

Year 2: Egg carton maths (sharing counters equally into cups), skip counting with a hundred chart, making equal groups with counters, simple array building

Year 3: Array snap card games, multiplication war (two players flip cards and multiply), times tables board games, fact family triangles, word problem sorting

Year 4: Area model drawings, multiplication bingo, division with remainders using counters, real-world multiplication problems (calculating total cost, area of a room), place value connections

Year 5–6: Multi-digit multiplication challenges, division problem-solving tasks, fraction connections (3/4 of 24), ratio and proportion activities, mathematical investigations that require multiplication and division