Foundations of Mathematical Thinking · Senior Infants

Active learning ideas

Comparing and Ordering Numbers

Active learning works because comparing and ordering numbers requires students to move beyond abstract symbols to real, tangible experiences. When students manipulate objects, arrange themselves, and estimate quantities, they build mental models that make numerical relationships concrete and memorable.

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

• 15–25 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Gallery Walk
• 25 min · Pairs

Gallery Walk: The Estimation Station

Place several jars with different amounts of items around the room. Students walk around in pairs, estimating which has the most and which has the least, then work together to count and order the jars by their actual totals.

Which number is bigger , 5 or 8? How do you know?

Facilitation Tip

During The Estimation Station, circulate and ask students to explain their estimates out loud to reinforce the connection between quantity and language.

What to look for

Present students with two small groups of objects (e.g., 3 blocks and 5 blocks). Ask: 'Which group has more objects? How do you know?' Then, ask: 'Which group has fewer objects?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Inquiry Circle
• 15 min · Pairs

Inquiry Circle: Is it Fair?

Give two students unequal amounts of 'treats' (cubes). They must use one-to-one correspondence by lining them up side-by-side to prove who has more and then figure out how to make the sets equal or 'fair.'

Can you put these number cards in order from 1 to 10?

Facilitation Tip

For Is it Fair?, listen carefully to how students justify their answers to uncover misconceptions about fairness and quantity.

What to look for

Give each student a card with two numbers (e.g., 7 and 4). Ask them to circle the larger number. On the back, have them draw a set of objects that shows 'fewer than' the number 6.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Simulation Game
• 20 min · Whole Class

Simulation Game: The Human Number Line

Give each student a card with a different number of dots. Without speaking, they must organize themselves into a line from the fewest dots to the most dots, checking their neighbors' cards to ensure the order is correct.

Show me which group has fewer counters.

Facilitation Tip

In The Human Number Line, place yourself between two students to model the midpoint and clarify the structure of the line.

What to look for

Provide students with number cards from 1 to 5. Ask: 'Can you arrange these cards from the smallest number to the largest number? Explain how you decided on the order for each card.'

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

A few notes on teaching this unit

Teachers should start with hands-on materials before moving to abstract symbols. Avoid rushing students to written work; instead, let them verbalize comparisons using objects first. Research suggests that pairing physical actions (like lining up objects) with spoken language strengthens understanding of relative magnitude.

By the end of these activities, students will confidently use comparative language like 'more than,' 'fewer than,' and 'equal to' while explaining their reasoning. They will also arrange numbers in order and recognize small differences in quantity with precision.

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Watch Out for These Misconceptions

• During The Estimation Station, watch for students who assume a spread-out group has more items because it takes up more space.

  Have students pair objects from both groups using string or place them in matching rows on a grid. This visual proof shows that the number of items, not the arrangement, determines 'more' or 'less.'

• During Is it Fair?, watch for students who confuse 'more' and 'less' when the difference is one.

  Ask students to build towers with one-block increments, such as 4 and 5. Point to the taller tower and say, 'This is one more than the shorter one,' to anchor the vocabulary in a physical comparison.

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Methods used in this brief

• Gallery Walk
• Inquiry Circle
• Simulation Game