Mathematics · Year 1

Active learning ideas

Fact Families for Addition and Subtraction

Active learning lets students physically manipulate objects and discuss their thinking, which helps them see the inverse relationship between addition and subtraction. This hands-on approach makes abstract number relationships concrete and memorable for young learners.

• ACARA Content Descriptions
• AC9M1N03

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

Activity 01

• Numbered Heads Together
• 20 min · Pairs

Pairs: Counter Fact Families

Provide pairs with counters and cups to model part-part-whole. One student hides some counters, the partner finds the total, then they write all four sentences. Switch roles and repeat with new numbers under 20.

Construct a fact family for a given set of three numbers.

Facilitation Tip

During the Counter Fact Families activity, circulate and ask each pair, 'How does taking away counters show the subtraction sentences?' to reinforce the inverse connection.

What to look for

Provide students with three numbers, for example, 5, 8, and 13. Ask them to write the four number sentences that make up the fact family for these numbers.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 02

• Numbered Heads Together
• 30 min · Small Groups

Small Groups: Domino Matching Game

Distribute dominoes showing parts and totals. Groups sort them into fact family cards, write the four equations, and share one with the class. Extend by creating their own dominoes from paper.

Explain how knowing one addition fact helps us solve two subtraction facts.

Facilitation Tip

For the Domino Matching Game, model how to sort dominoes by total first, then match addition and subtraction pairs before students work independently.

What to look for

Show students a partially completed fact family, such as 7 + 2 = 9, __ + 7 = 9, 9 - 7 = __, 9 - __ = 7. Ask them to fill in the missing numbers and explain how they found them.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 03

• Numbered Heads Together
• 25 min · Whole Class

Whole Class: Fact Family Human Chain

Students hold number cards (e.g., 7, 5, 12). Form chains linking addition to subtraction facts by passing cards to show relationships. Discuss predictions for missing numbers as a group.

Predict the missing number in a fact family based on the known numbers.

Facilitation Tip

In the Fact Family Human Chain, stand near students who are struggling to remind them to look at the largest number as the total before creating their human sentences.

What to look for

Ask students: 'If you know that 5 + 3 = 8, how can you use that one fact to figure out 8 - 5?' Listen for explanations that describe the inverse relationship between addition and subtraction.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 04

• Numbered Heads Together
• 15 min · Individual

Individual: Ten-Frame Families

Each student uses ten-frames to fill with two colours of counters for given numbers, then records the fact family. Check work by rebuilding with a partner.

Construct a fact family for a given set of three numbers.

What to look for

Provide students with three numbers, for example, 5, 8, and 13. Ask them to write the four number sentences that make up the fact family for these numbers.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

A few notes on teaching this unit

Teach fact families by starting with concrete objects like counters or ten-frames, then move to pictorial representations like dominoes, and finally to abstract symbols. Avoid rushing to worksheets; give students time to verbalize their reasoning. Research shows that explaining relationships aloud strengthens understanding of inverse operations more than silent practice.

Students will confidently identify and generate four related number sentences from three numbers. They will explain how addition and subtraction facts connect within each family and solve for missing parts using these relationships.

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Watch Out for These Misconceptions

• During Pairs: Counter Fact Families, watch for students who treat addition and subtraction as unrelated operations.

  Ask each pair to model an addition sentence with counters, then physically remove counters to 'undo' the addition and record the subtraction sentence that matches their action.

• During Small Groups: Domino Matching Game, watch for confusion about why the order of numbers matters in subtraction but not addition.

  Have students sort dominoes into addition pairs first, then discuss why subtraction dominoes must start with the total on the left side of the equation.

• During Individual: Ten-Frame Families, watch for students who think fact families only work with certain numbers.

  Ask students to use any three numbers they choose within 20 on their ten-frame, then share their families with the class to see the variety of examples.

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Methods used in this brief

• Numbered Heads Together