Foundations of Mathematical Thinking · 2nd Year

Active learning ideas

The Relationship of Addition and Subtraction

Active learning works well for this topic because students need to physically and visually connect addition and subtraction. Moving objects, writing equations, and moving along a number line help them see the inverse relationship rather than just hear about it. These concrete experiences build the mental models that lead to fluency and confidence with fact families and commutative property.

• NCCA Curriculum Specifications
• NCCA: Primary - Algebra
• NCCA: Primary - Number

• 15–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Collaborative Problem-Solving
• 25 min · Pairs

Partner Game: Fact Family Match-Up

Pairs draw cards with numbers like 6, 7, 13 and create all four fact family sentences on mini-whiteboards. Switch roles after two minutes, checking work together. End with sharing one new insight per pair.

If you know 6 + 7 = 13, how can that help you solve 13 − 7?

Facilitation Tip

During Partner Game: Fact Family Match-Up, circulate and ask pairs to explain how they knew their matches were correct, reinforcing the link between addition and subtraction.

What to look for

Present students with a fact family, for example, 5, 8, 13. Ask them to write all four equations in the fact family on a mini-whiteboard. Observe their ability to correctly apply inverse operations and the commutative property.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 02

• Collaborative Problem-Solving
• 30 min · Small Groups

Small Groups: Domino Fact Families

Provide dominoes showing addends and sums. Groups write the four related sentences for each domino, then sort into fact family charts. Discuss commutative swaps as a group.

What do you notice when you swap the numbers in 5 + 3 to make 3 + 5?

Facilitation Tip

For Small Groups: Domino Fact Families, remind students to turn the domino so they see both orientations, this helps them notice the commutative property in action.

What to look for

Give each student a card with a single addition equation, such as 9 + 4 = 13. Ask them to write one related subtraction equation and explain in one sentence how the addition fact helped them find the subtraction answer.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 03

• Collaborative Problem-Solving
• 35 min · Whole Class

Whole Class: Human Number Line

Students line up to represent numbers, acting out addition by joining and subtraction by separating. Call out problems like 13 - 7; class adjusts positions to show the answer. Debrief patterns observed.

What is 10 more than 24?

Facilitation Tip

When running Whole Class: Human Number Line, encourage students to step backward as well as forward to explicitly show subtraction as the reverse of addition.

What to look for

Pose the question: 'If you know that 15 - 6 = 9, what other number fact do you also know?' Facilitate a class discussion where students share their answers and explain their reasoning, highlighting the inverse relationship.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 04

• Collaborative Problem-Solving
• 15 min · Individual

Individual: Ten-Frame Challenges

Students use ten-frames to model '10 more than 24,' then create subtraction facts. Record in journals and share one with a neighbor.

If you know 6 + 7 = 13, how can that help you solve 13 − 7?

Facilitation Tip

With Individual: Ten-Frame Challenges, ask students to describe how filling the ten-frame relates to both the addition and subtraction equations they write.

What to look for

Present students with a fact family, for example, 5, 8, 13. Ask them to write all four equations in the fact family on a mini-whiteboard. Observe their ability to correctly apply inverse operations and the commutative property.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

A few notes on teaching this unit

Start with concrete tools like counters, dominoes, and number lines before moving to abstract equations. Ask students to verbalize their thinking as they build fact families. Avoid rushing to symbols; let students discover patterns through repeated hands-on practice. Research shows that students who manipulate objects and discuss relationships develop deeper understanding of inverse operations and number flexibility.

Successful learning looks like students confidently generating all four equations in a fact family and explaining how addition and subtraction relate. They should use the commutative property to switch addends without hesitation and use subtraction to solve for missing addends. Watch for flexible thinking when solving number puzzles and discussions that reference inverse operations naturally.

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Watch Out for These Misconceptions

• During Partner Game: Fact Family Match-Up, watch for students who treat addition and subtraction facts as unrelated. Redirect by asking them to explain how the addition card helps them find the matching subtraction card using their counters.

  Prompt students to verbalize that knowing 6 + 7 = 13 means they also know 13 - 7 = 6 by physically removing 7 counters from a group of 13.

• During Small Groups: Domino Fact Families, watch for students who only write one addition equation per domino orientation. Redirect by asking them to write both addition equations and the corresponding subtraction equations to show the commutative property holds.

  Have students rotate the domino and write 5 + 3 = 8 and 3 + 5 = 8, then write 8 - 3 = 5 and 8 - 5 = 3 to see all four equations.

• During Whole Class: Human Number Line, watch for students who only move forward to add and backward to subtract. Redirect by asking them to explain how moving backward from 13 to 6 is the same as subtracting 7 from 13.

  Ask students to stand at 13, take 7 steps backward, and then explain the equation that matches their movement: 13 - 7 = 6.

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Methods used in this brief

• Collaborative Problem-Solving