Mathematics · Year 2

Active learning ideas

Number Bonds to 20 and Beyond

Students need to experience the commutative property through movement and conversation to move beyond rote memorization of number facts. When learners manipulate objects, switch positions, and explain their thinking aloud, they build durable mental models of why 15 + 5 equals the same total as 5 + 15.

• National Curriculum Attainment Targets
• KS1: Mathematics - Addition and Subtraction

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

Activity 01

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: The Commutative Challenge

Give students an addition sentence and ask them to find its 'twin'. Then give a subtraction sentence and ask if it has a twin. Pairs discuss why it works for one but not the other.

Explain how knowing 7 + 3 helps us solve 70 + 30.

Facilitation Tip

During the Think-Pair-Share, provide sentence stems like 'I noticed that adding 7 and 3 is the same as adding 3 and 7 because...'.

What to look for

Present students with a part-whole diagram where the whole is 20 and one part is 8. Ask: 'What is the missing part?' Then, present a similar diagram with the whole as 80 and one part as 50. Ask: 'What is the missing part?'

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

Activity 02

• Simulation Game
• 20 min · Small Groups

Simulation Game: The Human Part-Whole Model

Three students represent the parts and the whole. They move positions to show how the two 'part' students can swap places while the 'whole' stays the same, then try to do the same for subtraction.

Predict the missing number in an addition or subtraction sentence using number bonds.

Facilitation Tip

During the Human Part-Whole Model, position the larger number on the left side of the room so students physically experience 'starting with the bigger number.'

What to look for

Give each student a card with a number bond fact, such as 6 + 4 = 10. Ask them to write two related facts: one addition sentence up to 20 and one addition sentence up to 100. For example, 10 - 6 = 4 and 100 - 60 = 40.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 03

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: Fact Family Houses

Groups are given three numbers (e.g., 3, 7, 10). They must build a 'house' using blocks and write all four addition and subtraction facts that belong to that family, checking each other's work.

Justify why mastering number bonds makes mental calculations faster.

Facilitation Tip

During the Fact Family Houses, require students to label the roof with the whole and the windows with the parts before writing any equations.

What to look for

Pose the question: 'How does knowing 9 + 1 = 10 help you solve 90 + 10?' Encourage students to use the terms 'number bond' and 'related fact' in their explanations.

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

A few notes on teaching this unit

Teach the commutative property early in the unit through stories and real objects so students feel the equivalence before seeing the symbols. Avoid relying solely on flashcards or worksheets; frequent verbal exchanges and quick physical switches keep the concept alive. Research shows that children who link symbols to actions develop stronger number sense and avoid the swap-in-subtraction trap later on.

By the end of these activities, students will confidently use the commutative property to swap addends, explain why subtraction does not commute, and generate related facts up to 100 without counting each time. You will see them choose the larger addend first to lighten their mental load.

---

Watch Out for These Misconceptions

• During the Human Part-Whole Model, watch for students who physically swap the two groups without noticing the total stays the same.

  Stop the action and ask the group to recount the total before and after the swap, emphasizing that the count does not change even though the positions do.

• During the Think-Pair-Share, listen for students who say 5 + 2 and 2 + 5 are two different problems they need to solve from scratch.

  Prompt them to explain the rule to their partner using their own words, then run a quick speed round where they must instantly give the second sum after seeing the first.

---

Methods used in this brief

• Think-Pair-Share
• Simulation Game
• Inquiry Circle