Subtraction Strategies: Fact Families

Active learning works for subtraction fact families because students need to see the connections between numbers in different operations. Moving from counting to using relationships between numbers builds fluency and confidence. These activities give students chances to explain their thinking, compare strategies, and apply ideas in real contexts.

• Grade 2
• Mathematics
• 3 activities
• 25 min–35 min

Concept Mapping

⏱ 30 min·Individual

Fact Family Houses

Students draw a 'house' with three rooms. The largest number goes on the roof, and the other two numbers go in the foundation rooms. Students then write the four fact family sentences around the house, connecting the numbers.

Prepare & details

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

Facilitation Tip: During the Strategy Gallery Walk, assign each student a different strategy card so every method gets represented when they rotate.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 25 min·Pairs

Number Bond Manipulatives

Provide students with number bonds (circles with three connecting lines). Students place three chosen numbers into the bond and then write the corresponding addition and subtraction sentences on whiteboards or paper.

Prepare & details

Justify how knowing 8+5=13 helps solve 13-5=8.

Facilitation Tip: For the Think-Pair-Share, give pairs a timer for 30 seconds to explain their strategy to each other before sharing with the class.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 35 min·Small Groups

Fact Family Matching Game

Create cards with individual number sentences (e.g., 9 + 3 = 12). Students work in small groups to find matching cards that belong to the same fact family and lay them out together.

Prepare & details

Differentiate between addition and subtraction in a word problem context.

Facilitation Tip: In the Mental Math Market simulation, provide play money and price tags set at friendly numbers so students practice 'making tens' naturally in context.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Teaching This Topic

Teachers often start by modeling how fact families connect addition and subtraction with visuals like number bonds or triangles. Avoid rushing to abstract symbols before students see the patterns in real problems. Research shows that students benefit most when they first talk through their own strategies, then compare them to others. Keep examples small at first, like 5, 7, 12, so the patterns are clear.

What to Expect

By the end of these activities, students should explain how fact families show the same numbers in addition and subtraction. They should choose efficient strategies like making tens or using doubles without teacher prompts. Students should also recognize when one strategy works better than another for a given problem.

Watch Out for These Misconceptions

Common Misconception

During the Strategy Gallery Walk, watch for students who rely only on counting on fingers for every problem.

What to Teach Instead

Have these students stand at the 'making tens' station first to see how peers break numbers apart, then ask them to try one example using that strategy before returning to their original method.

Common Misconception

During the Think-Pair-Share, watch for students who assume the teacher's method is the only correct way to solve a problem.

What to Teach Instead

After pairs share, ask each group to vote on which strategy they think is most efficient and explain why, highlighting that different problems may need different tools.

Assessment Ideas

Exit Ticket

After the Strategy Gallery Walk, provide students with a fact family triangle containing three numbers (e.g., 8, 6, 14). Ask them to write all four number sentences on their exit ticket.

Quick Check

During the Mental Math Market simulation, display a sign with: 'Liam had 11 marbles. He gave 5 to his sister. How many does he have left?' Ask students to write the related addition sentence and subtraction sentence on a sticky note before trading items at the market.

Discussion Prompt

After the Think-Pair-Share, pose the question: 'If you know that 7 + 8 = 15, how does that help you figure out 15 - 7?' Facilitate a class discussion where students explain the inverse relationship using examples from their own fact family work.

Extensions & Scaffolding

• Challenge early finishers to create their own fact family word problems using three related numbers.
• Scaffolding for struggling students: Provide counters or a number line during activities so they can see the jumps between numbers.
• Deeper exploration: Have students research how fact families appear in real life, like combining groups of items or splitting a total into parts.