Mathematics · Year 2

Active learning ideas

Flexible Partitioning

Breaking numbers apart in flexible ways helps students move beyond rigid counting strategies and develop true number sense. Active learning lets them see, touch, and test different partitions, which builds mental flexibility needed for addition, subtraction, and place value understanding.

• ACARA Content Descriptions
• AC9M2N01
• AC9M2N02

• 15–40 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Gallery Walk
• 30 min · Small Groups

Gallery Walk: Number Splitting

Small groups are given a target number (e.g., 72) and must find as many ways to partition it as possible on a large sheet of paper. Groups then rotate to see other teams' ideas, adding a 'tick' to ones they also found and a 'star' to unique ones.

In what different ways can we decompose 100 using tens and ones?

Facilitation Tip

During Gallery Walk, label each poster with the original number so students compare totals, not just the parts.

What to look for

Present students with a number, like 73. Ask them to write down three different ways to partition it using tens and ones, or other combinations. For example: 70 + 3, 60 + 13, 50 + 23.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Role Play
• 40 min · Pairs

Role Play: The Change Makers

Students act as shopkeepers in a 'Bush Tucker' cafe. When a customer pays with a large 'note' (a bundle of 100), the shopkeeper must partition that 100 into different combinations of tens and ones to give change for various items.

How does partitioning a number make it easier to add or subtract mentally?

Facilitation Tip

When students act as Change Makers, give each pair a different target amount so they experience multiple partitions of the same number.

What to look for

Pose a problem: 'Sarah has 45 stickers and gets 20 more. How can she figure out how many she has now using partitioning?' Ask students to share different ways they could break apart 45 or 20 to make the addition easier.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Which Split is Best?

The teacher presents a problem like 52 - 8. Students think about whether it is easier to split 52 into 50+2 or 40+12. They share their preference with a partner, explaining why their choice makes the subtraction easier.

Why might one way of breaking a number be more useful than another in a specific problem?

Facilitation Tip

For Which Split is Best, use a timer to push students to defend their chosen partition within 30 seconds.

What to look for

Give students a subtraction problem, such as 62 - 15. Ask them to show one way they could partition 62 or 15 to solve it mentally. For example, partitioning 15 into 10 + 5, or partitioning 62 into 52 + 10.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach flexible partitioning by modeling how to break a number slowly, talking through each step aloud. Avoid rushing to the standard partition; instead, celebrate all valid splits. Research shows that repeated, short bursts of partitioning practice build stronger mental agility than long, single sessions.

Students show they can decompose numbers in more than one way and explain why the total stays the same. They choose partitions that make calculations easier and justify their choices to peers.

---

Watch Out for These Misconceptions

• During Gallery Walk, watch for students who assume the total changes when parts change.

  Ask each group to place their MAB blocks on a balance scale to prove the total mass does not shift regardless of how they are grouped.

• During the Role Play activity, students may resist breaking tens into ones.

  Hand each pair a set of ten sticks and ten individual cubes, then instruct them to ‘break’ one ten stick into ten ones to prove the value stays 45.

---

Methods used in this brief

• Gallery Walk
• Role Play
• Think-Pair-Share