Foundations of Mathematical Thinking · 1st Year

Active learning ideas

Subtraction within 10

Active subtraction work with small groups, pairs, and whole class builds fluency through movement and talk. When students move counters, step along number lines, or act out stories, they connect the abstract symbols to their lived experience, turning '6 - 4' into a visible action. Concrete materials let children repeatedly try, check, and revise, which strengthens number sense faster than worksheets alone.

• NCCA Curriculum Specifications
• NCCA: Primary - Number

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

Activity 01

• Problem-Based Learning
• 25 min · Small Groups

Small Groups: Counter Take-Away

Give each group 10 counters, cups, and problem cards like 8 - 3. Students count out the first number into the cup, remove the second number, count what remains, and draw it. Groups share one solution with the class.

Compare 'taking away' with 'finding the difference'.

Facilitation Tip

During Counter Take-Away, circulate and ask each group to say the full equation aloud after each turn so language and action align.

What to look for

Provide students with 5 counters and a card showing '7 - 3'. Ask them to use the counters to show the subtraction and write the answer. Then, ask them to draw a number line showing the same problem.

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

Activity 02

• Problem-Based Learning
• 20 min · Pairs

Pairs: Number Line Hops

Draw number lines 0-10 on the floor or paper. Partners draw a card like 7 - 2; one starts at 7 and hops back 2 spaces, the other verifies with counters. Record the jump and equation.

Explain how a number line can help us subtract.

Facilitation Tip

For Number Line Hops, position two students at opposite ends of the line so they can compare their hops and agree on the difference.

What to look for

Present students with two groups of objects, for example, 9 apples and 6 apples. Ask: 'What is the difference between the number of apples?' Observe if they can find the difference by counting or by removing. Ask: 'How many more apples are there?'

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

Activity 03

• Problem-Based Learning
• 30 min · Whole Class

Whole Class: Story Problem Theatre

Students work in pairs to write a subtraction story, like '9 birds on a branch, 4 fly away.' Class acts it out using toy birds or fingers, solves together, and discusses the strategy used.

Design a story problem that requires subtraction.

Facilitation Tip

In Story Problem Theatre, give shy students quiet roles like prop manager before they speak on stage.

What to look for

Pose the problem: 'Sarah had 8 sweets and gave 5 to her friend. How many does she have left?' Ask students to explain two different ways they could solve this problem, encouraging them to use the terms 'take away' and 'find the difference'.

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

Activity 04

• Problem-Based Learning
• 15 min · Individual

Individual: Draw and Solve Journal

Provide worksheets with problems within 10. Students draw sets of objects, cross out the subtracted amount, circle the remainder, and write the number sentence. Share one drawing with a partner.

Compare 'taking away' with 'finding the difference'.

What to look for

Provide students with 5 counters and a card showing '7 - 3'. Ask them to use the counters to show the subtraction and write the answer. Then, ask them to draw a number line showing the same problem.

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

A few notes on teaching this unit

Research shows students grasp subtraction better when they experience both 'take away' and 'difference' before formal symbols appear. Avoid rushing to abstract equations; instead, let children build internal number relationships through repeated, varied experiences. Use consistent language—'remove' for take-away, 'gap' or 'how many more' for difference—so your words match the actions they perform.

Successful learners explain subtraction in two ways: as taking away and as finding the difference. They choose tools appropriately, count accurately, and record answers with confidence. Most importantly, they articulate how each method solves the same problem, showing flexible thinking rather than memorized procedures.

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Watch Out for These Misconceptions

• During Counter Take-Away, watch for students who always remove counters even when the problem calls for finding a difference.

  Pause the activity and ask the group to model both meanings with the same starting set: first remove to find what’s left, then line up two sets to measure the gap. Have them label each result with the correct term.

• During Number Line Hops, watch for students who count the starting number as one of the hops, leading to off-by-one errors.

  Use a pointer to tap each number as they hop and count aloud together, emphasizing that the first hop lands on 9 after starting at 10, not counting 10 as a hop.

• During Story Problem Theatre, watch for students who insist the answer must always be smaller than both numbers in the story.

  After the performance, ask the class to consider 'how many more' questions and rephrase the original problem to highlight the part-whole relationship, using the phrase 'out of the original eight, five were given away, so how many remain?'

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Methods used in this brief

• Problem-Based Learning