Free Printable Year 2 Multiplication and Division Worksheets

About This Year 2 Maths Topic

In Year 2, children begin developing multiplication and division understanding through practical experiences rather than memorising formal procedures.

Multiplication is introduced as repeated equal quantities. For example, 4 trays with 6 biscuits on each tray can be represented as 4 equal groups of 6.

Children may record the situation as repeated addition:

6 + 6 + 6 + 6 = 24

Division is explored through sharing and grouping. Children learn that these are related but different questions.

• Sharing 12 objects among 3 people asks how many each person receives.
• Dividing 12 objects into groups of 3 asks how many groups can be made.

Arrays, bar models, physical materials, diagrams, skip counting and Think Boards help children represent these relationships and explain their calculation strategies.

These activities support Australian Curriculum Version 9.0 content descriptor AC9M2N05 and its associated elaborations.

The Big Idea for Parents

Multiplication combines equal groups to find a total. Division begins with a total and separates it into equal groups or groups of a chosen size.

For example, 3 groups of 4 can be shown as:

• 3 groups with 4 objects in each group;
• 4 + 4 + 4;
• an array with 3 rows of 4;
• a bar model divided into 3 equal parts;
• a total of 12.

Learning Intentions

Children will learn to:

• recognise multiplication as repeated equal groups;
• represent multiplication using repeated addition;
• make and name arrays;
• identify rows and columns in arrays;
• turn arrays and recognise that the total remains unchanged;
• use bar models to represent equal groups;
• partition arrays to find totals efficiently;
• use subitising and known number facts;
• use skip counting to find totals;
• recognise division situations;
• share collections into equal groups;
• divide collections into groups of a chosen size;
• distinguish between sharing and grouping division;
• use Think Boards to represent division problems;
• explain what the answer represents in the problem.

Student Success Criteria

Key Vocabulary

Teacher Guide for Parents

Teachers normally introduce multiplication and division using physical materials and familiar situations before introducing symbolic number sentences.

At home, follow this sequence: make it, arrange it, draw it, count it and explain it.

1. Begin with Equal Groups

Give your child counters, buttons, blocks or other small objects. Ask them to make equal groups.

For example:

“Make 4 groups with 3 counters in each group.”

Count the number in each group and check that all groups contain the same quantity.

2. Connect Equal Groups to Repeated Addition

Once the groups have been made, write an addition sentence using the same quantity repeatedly.

Four groups of 3 can be written as:

3 + 3 + 3 + 3 = 12

Ask your child to point to each group as they say each addend. This helps connect the written number sentence to the physical model.

3. Use Skip Counting

Instead of counting every object individually, encourage your child to skip count by the number in each group.

For 4 groups of 3:

3, 6, 9, 12

Explain that each skip represents another equal group being added.

4. Make Arrays

Arrange objects into straight rows and columns.

For example, 12 objects could be arranged as:

• 3 rows of 4;
• 4 rows of 3;
• 2 rows of 6;
• 6 rows of 2.

Ask your child to describe each arrangement using equal-group language such as “3 fours” or “4 threes”.

5. Turn the Array

Build an array with 3 rows of 4. Turn it so it becomes 4 rows of 3.

Ask:

• Did the number of objects change?
• What changed?
• What stayed the same?

Children should notice that the arrangement changes but the total remains 12.

6. Use Bar Models for Equal Groups

Draw one long bar divided into equal sections.

For 3 groups of 4, divide the bar into 3 equal sections and label each section 4.

The complete bar represents the total:

4 + 4 + 4 = 12

Bar models help children connect the group size, number of groups and total.

7. Partition Arrays to Find Totals

Children do not always need to count every object in an array. They can divide the array into smaller known parts.

For a 3-by-5 array:

• see 2 rows of 5 as 10;
• see 1 more row of 5;
• combine 10 and 5 to make 15.

Encourage your child to explain:

“I saw 2 fives, which is 10, and then 5 more, which makes 15.”

8. Use Known Number Facts

Arrays can be broken into familiar facts.

For example, a 4-by-6 array could be partitioned into:

• 2 rows of 6 and another 2 rows of 6;
• 12 and another 12;
• a total of 24.

Children may also recognise doubles, groups of 5 or groups of 10.

9. Introduce Sharing Division

Sharing division begins with a total and a known number of groups.

Example:

“Share 12 counters equally between 3 people.”

Deal one counter to each person in turn until all counters have been shared.

Each person receives 4 counters.

10. Introduce Grouping Division

Grouping division begins with a total and a known group size.

Example:

“Place 12 counters into groups of 3.”

Make groups containing exactly 3 counters until all counters have been used.

Four groups can be made.

11. Compare Sharing and Grouping Division

Use the same total to compare the two division situations.

With 12 objects:

• sharing into 3 equal groups gives 4 objects in each group;
• making groups of 3 gives 4 groups.

Both answers involve 4, but the 4 represents something different.

12. Use Think Boards

A Think Board allows children to represent the same problem in several ways.

A division Think Board may include:

• the word problem;
• physical materials;
• a drawing or diagram;
• a bar model;
• skip counting;
• a number sentence;
• a written explanation.

For example:

“A prize of $36 is shared equally between 4 people.”

Children may draw 4 groups, share $36 equally, skip count or use repeated subtraction to determine that each person receives $9.

The answer 9 represents dollars received by each person.

13. Solve Repeated Equal-Quantity Problems

Read a problem such as:

“There are 4 trays with 6 biscuits on each tray. How many biscuits are there altogether?”

Ask your child to:

1. identify the number of groups;
2. identify the number in each group;
3. draw or build the groups;
4. write repeated addition;
5. skip count to find the total;
6. write the answer with the correct unit.

The repeated addition sentence is:

6 + 6 + 6 + 6 = 24

14. Explain the Meaning of the Answer

A numerical answer is incomplete if the child cannot explain what it represents.

Ask:

• Does the answer represent objects?
• Does it represent groups?
• Does it represent people?
• Does it represent dollars?
• Does it represent objects in each group?

Recommended Teaching Sequence at Home

1. Make repeated equal groups with objects.
2. Write the matching repeated addition sentence.
3. Use skip counting to find the total.
4. Arrange the objects into rows and columns.
5. Name and turn arrays.
6. Partition arrays using known number facts.
7. Represent multiplication with bar models.
8. Share collections into a known number of groups.
9. Make groups of a known size.
10. Compare the two types of division.
11. Use a Think Board to represent a problem.
12. Explain what the answer represents.

Common Misconceptions and How Parents Can Help

Simple Home Multiplication and Division Activities

Questions Parents Can Ask

• How many equal groups are there?
• How many objects are in each group?
• Are all the groups equal?
• What repeated addition sentence matches the groups?
• What number will you skip count by?
• How many skips will you make?
• How many rows are in the array?
• How many columns are in the array?
• How could you name this array?
• What happens when the array is turned?
• How could you partition the array?
• What known number facts can help?
• Are you sharing into a number of groups?
• Are you making groups of a chosen size?
• What is known in the problem?
• What are you trying to find?
• Does the answer represent groups or objects in each group?
• Can you show the problem with a bar model?
• Can you represent the problem another way?
• How can you check your answer?

Mathematical Sentence Starters

Supporting Different Learners at Home

Children Who Need More Support

• use small totals such as 6, 8, 10 and 12;
• begin with groups of 2, 5 and 10;
• use physical objects before drawings;
• keep all groups visible;
• label the number of groups and group size separately;
• use grid paper for arrays;
• practise counting rows and columns;
• compare one sharing problem with one grouping problem;
• provide a partially completed Think Board;
• allow oral explanations before written responses.

Children Ready for Extension

• find several arrays for the same total;
• compare turned arrays;
• partition larger arrays in different ways;
• use more than one strategy to find a total;
• write multiplication stories for given arrays;
• write sharing and grouping stories for the same total;
• solve problems with an unknown number of groups;
• solve problems with an unknown group size;
• identify and correct an incorrect array or division model;
• explain why two representations show the same calculation.

Quick Parent Check

Use these questions to check whether your child understands the main ideas.

1. Make 4 equal groups with 3 objects in each group.
2. Write the matching repeated addition sentence.
3. Build and name an array representing 12.
4. Turn the array and describe the new arrangement.
5. Find the total in a 3-by-5 array without counting every dot.
6. Share 12 objects equally into 3 groups.
7. Place 12 objects into groups of 3.
8. Explain how the two division problems are different.
9. Draw a bar model showing 4 groups of 6.
10. Explain what the answer represents in a division problem.

A child shows secure understanding when they can represent equal groups, find totals efficiently, distinguish between sharing and grouping, and explain what the answer means.

Quick Exit Ticket

1. Draw an array showing 3 groups of 4.
2. Write the matching repeated addition sentence.
3. Explain the difference between sharing into 3 groups and making groups of 3.

Printable Teacher, Parent and Student Resources

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Home Learning Summary

Multiplication and division understanding grows through repeated practical experiences with equal groups, arrays and sharing.

Use this simple routine:

1. identify the total, groups and group size;
2. represent the problem with objects;
3. arrange or share the objects equally;
4. draw an array, diagram or bar model;
5. write repeated addition or skip count;
6. explain what the answer represents.

Related Foundation, Year 1 and Year 2 Maths Topics

Children who need additional support can revisit these earlier counting, grouping, sharing and addition topics.