Foundations of Mathematical Thinking · Senior Infants

Active learning ideas

Number Systems: Natural Numbers and Integers

Active learning transforms abstract numbers into tangible experiences for young learners. When children move, touch, and discuss objects while counting, they build durable connections between symbols, words, and quantities. This hands-on approach meets their developmental need for concrete experiences and reduces reliance on memorization alone.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.1
• NCCA: Junior Cycle - Number - N.2

• 10–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Stations Rotation
• 30 min · Small Groups

Stations Rotation: The Counting Circuit

Set up four stations with different materials like conkers, buttons, and shells. Students move in small groups to count the sets and record the total using tally marks or numeral cards, checking each other's work as they go.

Can you count these cubes and tell me how many there are?

Facilitation Tip

During Station Rotation: The Counting Circuit, position yourself near the station where students are counting two different sizes of the same object to observe if they equate quantity with size.

What to look for

Provide students with two small groups of manipulatives (e.g., buttons, blocks). Ask them to count each group and then state which group has more. Observe if they can accurately count and compare.

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

Activity 02

• Inquiry Circle
• 15 min · Pairs

Inquiry Circle: The Messy Set

Give pairs a large pile of counters spread out randomly. Ask them to find the total, then rearrange the counters into a circle or a straight line and predict if the total has changed before re-counting to verify.

Which group has more , show me how you know.

Facilitation Tip

For Collaborative Investigation: The Messy Set, circulate with a small whiteboard to jot down student observations about how rearranging objects does not change the count.

What to look for

Give each student a card with three numbers (e.g., 5, 2, 8). Ask them to write the numbers in order from smallest to largest. For a challenge, include 0 or a negative number if appropriate for the group.

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

Activity 03

• Think-Pair-Share
• 10 min · Pairs

Think-Pair-Share: The Counting Mistake

The teacher intentionally counts a set of blocks incorrectly (skipping one or counting one twice). Students think about what went wrong, discuss it with a partner, and then share the 'rule' for correct counting with the class.

Can you put these numbers in order from smallest to biggest?

Facilitation Tip

In Think-Pair-Share: The Counting Mistake, listen for students to explain their reasoning aloud so you can identify where one-to-one correspondence breaks down.

What to look for

Present a simple number line on the board showing 0 and a few positive and negative integers. Ask students: 'What does the number 0 tell us here?' and 'What does a number like -3 tell us compared to 3?'

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

A few notes on teaching this unit

Begin with concrete objects and real-world examples that matter to children, like snacks or toys. Avoid abstract symbols until students can count and compare sets with accuracy. Research shows that students who practice counting with physical objects develop stronger number sense than those who only count in their heads or on worksheets. Model counting slowly and deliberately, emphasizing that each object receives exactly one count.

Successful learning looks like students confidently pairing each object with one number word, recognizing that the last number spoken names the total quantity. They should also begin to understand that zero represents the absence of objects and that negative numbers extend counting beyond familiar territory.

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Watch Out for These Misconceptions

• During Station Rotation: The Counting Circuit, watch for students who assume that a taller stack of blocks means a larger number.

  Prompt students to recount using the same blocks but arrange them in a single line, then ask if the count changed. Reinforce that the number stays the same no matter how the objects are arranged.

• During Collaborative Investigation: The Messy Set, watch for students who rush their pointing while counting aloud.

  Model moving each object into a new container one at a time as you count, then invite the student to try the same method with your guidance.

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Methods used in this brief

• Stations Rotation
• Inquiry Circle
• Think-Pair-Share