Foundations of Mathematical Thinking · 1st Class

Active learning ideas

Subtraction of Numbers to 20

Active learning helps students move beyond counting on fingers to mental strategies that build speed and confidence. For subtraction up to 20, hands-on stations and peer discussions make abstract concepts concrete and memorable. Movement and collaboration turn 'doubles' and 'near-doubles' from abstract rules into tools students can use in real time.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Number - N.1.1
• NCCA: Junior Cycle - Strand 3: Number - N.1.2

• 15–40 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Stations Rotation
• 40 min · Small Groups

Stations Rotation: The Strategy Circuit

Set up stations for different mental tricks: one for 'Doubles' using mirrors, one for 'Adding 9' (add 10, subtract 1), and one for 'Near Doubles' using ladybird spots. Students rotate and practice each specific mental shortcut.

What does it mean to take away some objects from a group?

Facilitation Tip

During The Strategy Circuit, place a timer at each station so students practice using doubles and near-doubles under gentle pressure.

What to look for

Provide students with 10 counters. Ask them to show 15 take away 6. Have them write the number sentence and the answer on a slip of paper.

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

Activity 02

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: How Did You Get There?

The teacher presents a problem like 7 + 8. Students solve it mentally, then explain their specific strategy to a partner (e.g., 'I doubled 7 and added 1' or 'I made a ten'). This surfaces different ways of thinking.

How can you use counters or a number line to find the answer to a subtraction?

Facilitation Tip

In How Did You Get There?, circulate with a clipboard and listen for clear, concise explanations of mental steps.

What to look for

Draw a number line from 0 to 20 on the board. Pose a subtraction problem, such as 18 - 5. Ask students to come up and demonstrate how to solve it by jumping backward on the number line.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Simulation Game
• 20 min · Whole Class

Simulation Game: The Human Number Line

Students stand on a large number line. To solve 9 + 6, the '9' student explains how they can 'jump' to 10 first and then add the remaining 5. This physical 'bridging' makes the mental strategy visible and concrete.

Can you tell a take-away story using objects from the classroom?

Facilitation Tip

For The Human Number Line, step in only if students lose focus or need help aligning jumps with the correct direction.

What to look for

Present a scenario: 'There were 11 birds on a branch, and 4 flew away.' Ask students: 'What does it mean to take away the birds? How can we find out how many birds are left?' Encourage them to use objects or drawings to explain their thinking.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

A few notes on teaching this unit

Teach doubles as a gateway to near-doubles: once students know 5+5 quickly, show 5+6 as 5+5 plus one more. Avoid letting students stay in counting-all habits by modeling speed and accuracy yourself. Research shows that frequent, short bursts of practice with immediate feedback build fluency faster than long drills. Use errors as stepping stones by asking, 'What part feels tricky? Can we use a known double to help?'

By the end of the activities, students should solve subtraction problems up to 20 without relying on fingers or tally marks. They will explain their mental steps using doubles or near-doubles and share strategies with peers. Fluency and confidence in mental calculation will be visible in quick, accurate responses during group work.

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Watch Out for These Misconceptions

• During The Strategy Circuit, watch for students who still count on fingers or tally marks for every problem.

  Redirect them to use the doubles chart at the station to find a related double and adjust by one. Partner with a student who models quick mental use of near-doubles and ask them to share their strategy.

• During The Strategy Circuit, watch for students who limit doubles to numbers below 5.

  Set up a base-ten block station where students model doubling 10, 11, and 12, then write the corresponding number sentences. Encourage them to compare patterns with smaller doubles.

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Methods used in this brief

• Stations Rotation
• Think-Pair-Share
• Simulation Game