Foundations of Mathematical Thinking · 1st Class

Active learning ideas

Mental Maths: Quick Adding and Subtracting

Active learning helps students build speed and confidence in mental math by engaging multiple senses and movement. For quick adding and subtracting to 20, physical games and partner work make abstract strategies visible and memorable, turning calculations into something students can see, hear, and do together.

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

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

Activity 01

• Think-Pair-Share
• 20 min · Pairs

Pairs: Make Ten Snap

Partners hold cards with numbers to 10. They snap pairs summing to 10 and explain the strategy, like '8 needs 2'. Switch roles after 10 rounds and record three new pairs.

How can you add small numbers quickly in your head?

Facilitation Tip

During Pairs: Make Ten Snap, circulate and listen for students verbalizing the ‘make 10’ step aloud as they play.

What to look for

Present students with a series of addition problems on a whiteboard (e.g., 8 + 5, 7 + 7, 9 + 10). Ask students to write down the answer and the strategy they used to solve it on a mini-whiteboard. Review responses to identify students needing more support with specific strategies.

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

Activity 02

• Think-Pair-Share
• 30 min · Small Groups

Small Groups: Doubles Relay

Form lines of 4-5 students. Teacher calls a double fact; first student solves aloud and tags next for a near double. Group celebrates correct chains and discusses strategies used.

What trick can you use when adding any number to 10?

Facilitation Tip

For Doubles Relay, position yourself near the back of the line to quickly observe and correct any missteps in doubling.

What to look for

Give each student a card with a problem like 'Use doubles to help you solve 6 + 7'. Ask them to write the doubles fact they used and then the answer. Collect these to gauge understanding of the near doubles strategy.

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

Activity 03

• Think-Pair-Share
• 25 min · Whole Class

Whole Class: Counting On Chant

Students stand in a circle. Teacher starts a problem like 12 + 4; class counts on chorally: '13, 14, 15, 16'. Rotate leaders to model from larger number.

Can you use doubles, like 4 + 4, to help you work out 4 + 5?

Facilitation Tip

Lead the Counting On Chant by modeling strong, rhythmic counting and pausing to let students echo back the next number.

What to look for

Pose the question: 'What is the quickest way to add 9 to any number?' Facilitate a class discussion where students share their strategies, focusing on the 'add 10, subtract 1' method. Encourage them to explain why it works.

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

Activity 04

• Think-Pair-Share
• 15 min · Individual

Individual: Strategy Journal

Each student solves 10 problems on a worksheet, notes the strategy used (e.g., make 10), and draws a quick picture. Share one with a partner afterward.

How can you add small numbers quickly in your head?

Facilitation Tip

When students complete their Strategy Journal, read their written strategies and add brief, encouraging feedback in the margin.

What to look for

Present students with a series of addition problems on a whiteboard (e.g., 8 + 5, 7 + 7, 9 + 10). Ask students to write down the answer and the strategy they used to solve it on a mini-whiteboard. Review responses to identify students needing more support with specific strategies.

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

A few notes on teaching this unit

Teach strategies explicitly, then embed them into games where speed and accuracy matter. Use partner talk and peer modeling to normalize flexible thinking. Avoid teaching counting from one as the default, as it slows down fluent calculation. Research shows that children who learn to use derived facts and known relationships become more confident and accurate over time.

Successful learning looks like students using efficient strategies such as counting on, making 10, or doubling without relying on counting from one. They explain their thinking clearly and apply these strategies flexibly across different problems, showing fluency and confidence in their calculations.

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Watch Out for These Misconceptions

• During Pairs: Make Ten Snap, watch for students counting both cards from one instead of scanning for pairs that make ten.

  Prompt pairs to say the two numbers aloud, then decide together if their sum is ten before snapping. Model this language during the first round.

• During Doubles Relay, watch for students believing that doubles facts only produce even totals.

  Ask each group to show 5 + 6 on their fingers and talk through how it equals double 5 plus one, reinforcing near doubles with concrete models.

• During Counting On Chant, watch for students always counting back to subtract instead of using related facts.

  Pause the chant to ask, ‘What plus 6 equals 14?’ and have students respond with 8, linking subtraction to known addition facts during the activity.

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Methods used in this brief

• Think-Pair-Share