Mathematics · Year 2

Active learning ideas

Inverse Relationships

Active learning works well for inverse relationships because students need to physically manipulate numbers to see how addition and subtraction connect. When children move objects or rearrange numbers themselves, they build mental models that last beyond the lesson.

• ACARA Content Descriptions
• AC9M2N03
• AC9M2A02

• 15–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Role Play
• 25 min · Small Groups

Role Play: The Fact Family Reunion

Students are given cards with numbers (e.g., 5, 8, 13). They must find their 'family members' and stand together. Once grouped, they must act out the four equations they can make (two addition, two subtraction) using large plus, minus, and equals props.

How can an addition fact be used to solve a subtraction problem?

Facilitation Tip

During Role Play: The Fact Family Reunion, assign each student a role as a number in the family so they physically act out both the addition and subtraction equations.

What to look for

Present students with an addition sentence, such as 9 + 4 = 13. Ask them to write two related subtraction sentences. Observe if they correctly use the numbers from the original fact.

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

Activity 02

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: Part-Part-Whole Mats

Using hula hoops on the floor as a giant part-part-whole model, students move items (like beanbags) between the 'parts' and the 'whole'. They record the equations as they move the items, observing how the same three numbers keep appearing in different positions.

Why does the order of numbers matter in subtraction but not in addition?

Facilitation Tip

When using Part-Part-Whole Mats, have students verbalize the relationship between the numbers as they move counters between parts and wholes.

What to look for

Show students a part-part-whole mat with 6 in the whole, and 2 and 4 in the parts. Ask: 'How can we write an addition sentence using these numbers? How can we write two subtraction sentences? Why can we write two subtraction sentences but only one addition sentence?'

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: The Missing Link

The teacher shows a subtraction problem like 15 - ? = 9. Students think about what addition fact could help them solve it (9 + ? = 15). They share their 'helper fact' with a partner and explain why it works.

What is the relationship between part-part-whole models and equations?

Facilitation Tip

For The Missing Link, provide sentence stems like 'If I know __ + __ = __, then I also know __ - __ = __' to scaffold student thinking.

What to look for

Give each student a card with a part-part-whole diagram (e.g., whole=15, part=8, part=7). Ask them to write the complete fact family for these numbers and explain in one sentence why knowing 8 + 7 = 15 helps them solve 15 - 8.

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

A few notes on teaching this unit

Teach inverse relationships by always starting with hands-on materials before moving to symbols. Avoid rushing to abstract equations; let students verbalize the connections between operations first. Research shows that students who manipulate objects while explaining their thinking develop stronger number sense.

Successful learning looks like students recognizing that every addition sentence has two matching subtraction sentences, and using this to check their work independently. You will see them confidently switching between operations without hesitation.

---

Watch Out for These Misconceptions

• During Role Play: The Fact Family Reunion, watch for students who reverse the order of subtraction without considering the quantities. For example, they might write 5 - 10 = 5 even after acting out the scene.

  Use the physical role play to redirect them. Have the student holding 5 items 'give away' to the student holding 10, then ask what happens when you try to take more than you have. Ask the class to discuss what it means to 'have' versus 'give' in the context of the numbers.

• During Collaborative Investigation: Part-Part-Whole Mats, watch for students who treat addition and subtraction as separate unrelated facts rather than connected equations.

  Use the triangular fact cards placed on the mat corners to show the permanent bond between the three numbers. Ask students to trace the edges of the triangle as they read each equation aloud, reinforcing that the same three numbers create all four equations.

---

Methods used in this brief

• Role Play
• Inquiry Circle
• Think-Pair-Share