Foundations of Mathematical Thinking · Senior Infants

Active learning ideas

Big and Small Numbers

Active learning helps children grasp the abstract idea of magnitude by making big and small numbers tangible and visible. When students move, sort, and build with numbers, they develop an intuitive sense of which numbers are greater, preparing them for place value work.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.12

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Simulation Game
• 30 min · Pairs

Simulation Game: Number Line Hop

Mark a floor number line from 1 to 100 with tape. Call out two numbers; pairs hop to them and decide which is bigger. Switch roles, then order three numbers by hopping in sequence.

Which number is bigger , 20 or 12?

Facilitation Tip

During Number Line Hop, place sticky notes with numbers at uneven intervals to prevent counting by rote and encourage true magnitude comparison.

What to look for

Present two number cards, for example, '15' and '8'. Ask students, 'Which number is bigger? How do you know?' Observe their responses and reasoning.

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

Activity 02

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Size Sort Stations

Prepare stations with cards: one for ordering 1-20, one for biggest/smallest in 10s, one for naming largest number with digit blocks. Small groups rotate, recording sorts on clipboards.

Can you put these number cards in order from smallest to biggest?

Facilitation Tip

At Size Sort Stations, provide written labels like 'teens' and 'twenties' to guide early grouping before abstract sorting.

What to look for

Give each student a small set of number cards (e.g., 3, 7, 1). Ask them to arrange the cards on their desk from smallest to biggest and show their teacher.

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

Activity 03

• Experiential Learning
• 25 min · Whole Class

Whole Class: Giant Number Chain

Students stand in circle; each adds a digit to build biggest class number by saying and writing it. Discuss why it grows larger, then shrink to smallest by rules like no zeros.

What is the biggest number you can say?

Facilitation Tip

For Giant Number Chain, model how to hold up both hands to represent tens and fingers for ones, then gradually release this scaffold.

What to look for

Hold up a large foam number '50' and a smaller number card '25'. Ask the class, 'If we were counting these toys, which group has more? What does 'more' mean for numbers?'

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Experiential Learning
• 20 min · Individual

Individual: Number Tower Build

Provide linking cubes; children build towers for given numbers, compare heights to decide bigger/smaller. Label towers and sequence by size on desks.

Which number is bigger , 20 or 12?

Facilitation Tip

When building Number Tower, ask children to predict how tall a tower of 50 cubes will be, then compare predictions to the actual height.

What to look for

Present two number cards, for example, '15' and '8'. Ask students, 'Which number is bigger? How do you know?' Observe their responses and reasoning.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Start with concrete, physical representations before moving to symbols. Use games and stations where children manipulate numbers so they feel the difference between 19 and 20, not just see it on paper. Avoid rushing to abstract symbols; let students verbalize their thinking first. Research shows that when children physically arrange numbers, their accuracy in comparing and ordering improves significantly.

Successful learning shows when students confidently compare, order, and name numbers beyond 20, using reasoning like 'I know 100 is bigger because it has a 1 in the hundreds place.' Children should explain their choices using visual or physical tools from the activities.

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Watch Out for These Misconceptions

• During Number Tower Build, watch for children who assume a stack of 99 cubes is taller than 100 cubes because 99 has more digits.

  Have them build both towers side by side, counting each cube in groups of ten. Ask, 'Which group has more tens? How does that change the height?'

• During Giant Number Chain, listen for children who hesitate or guess when naming numbers above 50.

  Encourage peer echoing: one child names a number, the next repeats and adds one. Gradually increase the starting number to build confidence.

• During Size Sort Stations, observe if students exclude numbers like 15 or 23 from 'small' sets.

  Ask, 'Is 15 smaller than 10? Why or why not?' Then have them sort a mixed set including teens and twenties to see patterns.

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Methods used in this brief

• Simulation Game
• Stations Rotation
• Experiential Learning