Foundations of Mathematical Thinking · Junior Infants

Active learning ideas

Operations with Integers: Addition & Subtraction

Active learning works for operations with integers because concrete models like number lines and counters make abstract rules visible. Students need to physically move along a number line or pair counters to see why subtracting a negative shifts direction. These kinesthetic experiences turn symbolic rules into memorable patterns.

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

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

Activity 01

• Collaborative Problem-Solving
• 30 min · Pairs

Number Line Walks: Integer Journeys

Mark a floor number line from -10 to 10 with tape. Students start at zero and follow cards with instructions like '+3' or '-2'. Pairs discuss and predict endpoints before moving, then record results on worksheets. End with sharing one justification.

Predict the outcome of adding a positive and a negative integer.

Facilitation Tip

During Integer War, circulate and listen for students verbalizing the rule 'change the sign and add' as they play.

What to look for

Present students with a number line. Ask them to model the problem -3 + 5 by moving their finger or a marker. Then, ask them to write the final answer and explain their steps in one sentence.

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

Activity 02

• Collaborative Problem-Solving
• 25 min · Small Groups

Two-Color Counters: Zero Pairs Game

Provide red (negative) and yellow (positive) counters. Students model problems like -3 + 5 by pairing opposites to make zeros, then count leftovers. Switch to subtraction by removing pairs. Groups compete to solve 10 problems fastest with explanations.

Justify why subtracting a negative number is equivalent to adding a positive number.

What to look for

Give each student a card with a subtraction problem involving a negative number, such as 7 - (-2). Ask them to rewrite the problem as an addition problem and then solve it, showing their work.

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

Activity 03

• Collaborative Problem-Solving
• 35 min · Pairs

Elevator Challenges: Real-World Integers

Print elevator floor cards from -5 to 15. Students draw sequences like 'down 4, up 7' and track position on personal number lines. Pairs create their own problems, trade, and solve while noting absolute values of floors.

Differentiate between the sum and the difference of two integers.

What to look for

Pose the question: 'If you have €10 in your pocket and you owe your friend €5, how would you represent this using integers? What happens to your 'money' if you pay them back?' Guide students to discuss the meaning of negative numbers and subtraction in this context.

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

Activity 04

• Collaborative Problem-Solving
• 20 min · Pairs

Integer War Card Game

Use cards labeled -10 to 10. Players flip two cards per round, add or subtract based on color rules, and compare results. Highest absolute value wins the round. Debrief misconceptions as a class.

Predict the outcome of adding a positive and a negative integer.

What to look for

Present students with a number line. Ask them to model the problem -3 + 5 by moving their finger or a marker. Then, ask them to write the final answer and explain their steps in one sentence.

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

A few notes on teaching this unit

Teachers should avoid rushing to symbolic rules before concrete experiences. Instead, let students struggle with models first, then ask them to articulate the pattern they notice. Research shows this gradual abstraction—first movement, then counters, then symbols—builds deeper understanding than memorizing rules upfront.

Successful students will confidently model integer addition and subtraction with at least two different methods. They will justify their steps using zero pairs or distances on the number line. Missteps should be caught through peer discussion or immediate teacher feedback.

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Watch Out for These Misconceptions

• During Number Line Walks, watch for students moving left when subtracting a negative, indicating they see the negative sign as a direction sign rather than an operation.

  Pause the walk and ask the student to explain their movement step-by-step. Use language like 'subtracting means opposite direction' and have them redo the step while verbalizing 'subtracting -3 means move right 3.'

• During Two-Color Counters, watch for students ignoring zero pairs and treating each counter as a separate value.

  Ask the group to recount their counters and physically remove zero pairs before counting the remaining ones. Reinforce that zero pairs cancel out first.

• During Elevator Challenges, watch for students treating 'down' as always negative regardless of starting point.

  Have them annotate their vertical number line with starting floors and movement arrows. Ask: 'If you start on floor 2 and go down 3, where do you land?' to reframe direction as relative movement.

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Methods used in this brief

• Collaborative Problem-Solving