Mathematics · Grade 1

Active learning ideas

Subtraction Strategies: Related Facts

Active learning helps students grasp the connection between addition and subtraction when they physically manipulate objects and see relationships unfold in real time. For this topic, hands-on work with counters, cards, and frames builds concrete understanding that abstract equations often miss. When students see how 10 - 2 relates to 2 + 8, they begin to trust the strategy and apply it independently.

• Ontario Curriculum Expectations
• 1.OA.B.4
• 1.OA.C.6

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Numbered Heads Together
• 25 min · Pairs

Fact Family Houses: Counter Exploration

Students draw a house with two bottom rooms for addends and a top room for the sum. They use counters to model numbers like 4, 6, and 10, then write all four related facts on the house. Pairs share and compare their houses.

Explain why we can solve a subtraction problem by thinking about addition.

Facilitation Tip

During Fact Family Houses, circulate and ask each group to explain why their four equations belong together, focusing on the total number in the roof.

What to look for

Provide students with a fact family (e.g., 5, 8, 13). Ask them to write two addition and two subtraction sentences that belong to this family. Then, ask them to solve 13 - 5 by thinking of the addition fact.

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

Activity 02

• Numbered Heads Together
• 30 min · Small Groups

Related Facts Matching Game: Cards

Create cards with addition facts, subtraction facts, and numbers. Students match related facts, such as 8 + 2 with 10 - 2. Small groups play by flipping cards and discussing connections before laying matches.

Construct a fact family for the numbers 4, 6, and 10.

Facilitation Tip

Before starting the Related Facts Matching Game, model how to check for matching totals by pairing an addition card with its subtraction partner.

What to look for

Write a subtraction problem on the board, such as 9 - 4. Ask students to hold up fingers to show the related addition fact (e.g., 4 + 5 = 9). Then, ask them to write the answer to 9 - 4 on a mini-whiteboard.

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

Activity 03

• Numbered Heads Together
• 20 min · Pairs

Ten Frame Think Addition: Subtraction Puzzles

Provide ten frames and counters for puzzles like 10 - 3. Students fill the frame to 10 and remove 3, or add to 3 to reach 10. They record the related addition fact and explain to a partner.

Analyze how knowing 8 + 2 = 10 helps you solve 10 - 2.

Facilitation Tip

When using Ten Frame Think Addition, pause after each puzzle to have students whisper the related addition fact aloud before recording the answer.

What to look for

Pose the question: 'How does knowing 7 + 3 = 10 help you figure out 10 - 7?' Facilitate a discussion where students share their strategies, emphasizing the inverse relationship.

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

Activity 04

• Numbered Heads Together
• 35 min · Pairs

Story Problem Pairs: Related Scenarios

Pairs write two stories for numbers, one addition and one subtraction, like making 10 cookies and eating 4. They solve using counters and draw pictures showing the related facts.

Explain why we can solve a subtraction problem by thinking about addition.

Facilitation Tip

During Story Problem Pairs, invite students to act out the scenarios with counters to make the inverse relationship visible.

What to look for

Provide students with a fact family (e.g., 5, 8, 13). Ask them to write two addition and two subtraction sentences that belong to this family. Then, ask them to solve 13 - 5 by thinking of the addition fact.

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

A few notes on teaching this unit

Teach subtraction strategies by starting with counters and ten frames so students see the 'take apart' meaning of subtraction as clearly as the 'take away' meaning. Avoid rushing to memorization before students can explain why 7 + 3 helps solve 10 - 7. Research shows that students who verbalize the inverse relationship during hands-on work transfer the strategy to new problems more successfully.

Students will confidently explain how subtraction and addition are related by generating complete fact families and solving problems using the 'think addition' strategy. They will also articulate why knowing one fact helps them solve its inverse, demonstrating flexible thinking with numbers up to 20.

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Watch Out for These Misconceptions

• During Fact Family Houses, watch for students who only write one addition and one subtraction fact, ignoring inverses.

  Prompt students to place all four equation cards in the house, then ask them to read each one aloud while pointing to the related counters in the frame. Reinforce that every family has four members by counting them together.

• During Related Facts Matching Game, watch for students who pair cards based on numbers alone, without checking the total.

  Have students lay out their pairs, then use a whiteboard to write the total for each card. Ask them to explain why the numbers on each pair add up to the same amount before gluing them down.

• During Ten Frame Think Addition, watch for students who solve subtraction by counting backward instead of using the linked addition fact.

  Pause the activity and ask students to cover the counters they are taking away, then count the remaining ones while whispering the related addition fact aloud. Repeat with a new example until the strategy feels automatic.

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Methods used in this brief

• Numbered Heads Together