Mathematical Explorers: Building Foundations · 2nd Class

Active learning ideas

Number Facts and Mental Maths Strategies

Active learning helps students internalize number facts and mental strategies by connecting abstract ideas to movement, discussion, and visuals. For this topic, movement-based games and partner talks make recall faster and more flexible than worksheets alone. Students need to hear, see, and verbalize the reasoning behind strategies to move beyond rote memory.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Algebra - A.2.1

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

Activity 01

• Simulation Game
• 20 min · Pairs

Simulation Game: Doubles Dash

Prepare cards with doubles facts to 20 and near-doubles. Pairs take turns drawing a card, solving mentally, and racing to write the answer before a 30-second timer. Switch roles after five cards; discuss any errors as a pair to refine strategies.

What addition and subtraction facts do you already know by heart?

Facilitation Tip

During Doubles Dash, circulate and model calling out doubles facts aloud with students to keep the pace lively and accurate.

What to look for

Present students with a whiteboard or paper. Write a problem like 34 + 25. Ask students to write down the answer and one strategy they used to find it. Review responses to see who can correctly calculate and articulate a strategy.

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

Activity 02

• Peer Teaching
• 25 min · Pairs

Partner Strategy Share: Making Ten

Give pairs two-digit addition problems without renaming, like 34+16. One student models partitioning on a mini-whiteboard (30+10=40, 4+6=10), the partner repeats with a new problem. Pairs then invent their own problems to swap and solve.

How can knowing doubles or near-doubles help you add quickly?

Facilitation Tip

During Partner Strategy Share: Making Ten, provide sentence starters like 'I made ten by...' to guide clear explanations.

What to look for

Pose the question: 'How does knowing that 6 + 6 = 12 help you figure out 26 + 6?' Listen for student explanations that involve adding the tens first (20 + 6 = 26) and then using the known fact (26 + 6 = 32).

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

Activity 03

• Peer Teaching
• 30 min · Whole Class

Whole Class: Fact Family Bingo

Distribute bingo cards with facts to 20 and strategy clues (e.g., 'double 7'). Call out verbal problems; students mark answers mentally and justify to a neighbor. First full row wins a group cheer; review strategies class-wide.

Can you use a mental maths strategy to find the answer to a two-digit addition or subtraction?

Facilitation Tip

During Fact Family Bingo, allow students to use mini whiteboards to jot down facts quickly before marking their cards.

What to look for

Give each student a card with a problem, such as 41 + 37. Ask them to write the answer and then draw a small picture or write one sentence showing how they used place value to solve it.

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

Activity 04

• Peer Teaching
• 15 min · Individual

Individual: Strategy Number Line Hunt

Students draw a number line from 0-100 and solve 10 two-digit additions without renaming by jumping tens then ones. They note the strategy used (e.g., doubles) beside each. Share one favorite with the class.

What addition and subtraction facts do you already know by heart?

Facilitation Tip

During Strategy Number Line Hunt, ask students to mark their starting point and jumps with different colors to track their thinking.

What to look for

Present students with a whiteboard or paper. Write a problem like 34 + 25. Ask students to write down the answer and one strategy they used to find it. Review responses to see who can correctly calculate and articulate a strategy.

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

A few notes on teaching this unit

Teach number facts as a network of connected ideas rather than isolated bits of information. Use games to build speed and accuracy, and class discussions to highlight patterns like how near-doubles relate to doubles. Avoid rushing students to written algorithms before they can explain their mental steps. Research shows that students who verbalize strategies during partner work develop stronger number sense than those who only write answers.

Students should confidently recall addition and subtraction facts to 20, explain at least two mental strategies they use, and solve two-digit sums without counting every single number aloud. They should also compare their methods with peers and adjust their thinking based on feedback. Success looks like students choosing strategies that make sense to them and using them efficiently.

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Watch Out for These Misconceptions

• During Doubles Dash, watch for students who always start adding from the ones digit mentally, even when it slows them down.

  Remind students to start with the larger number and use doubles or near-doubles from there. Ask them to explain their first step aloud to their partner before racing ahead.

• During Partner Strategy Share: Making Ten, watch for students who treat number facts as isolated facts without connections to other strategies.

  Guide them to link their facts to doubles or near-doubles during the share. For example, if they say '7 + 3 = 10,' ask how that helps with '17 + 3' or '7 + 13.'

• During Strategy Number Line Hunt, watch for students who rely on counting every single number rather than using jumps or partitioning.

  Ask them to circle the larger number and draw a jump first, then add the rest. Model this on their number line with a different color.

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Methods used in this brief

• Simulation Game
• Peer Teaching