Mathematics · Junior Infants

Active learning ideas

Prime and Composite Numbers

Active learning helps students see the difference between prime and composite numbers through touch and sight. Using arrays, games, and visual tools builds a lasting understanding of factors and multiples in a way that abstract rules cannot. Hands-on work makes the invisible structure of numbers visible for young learners.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Number - N.1.9

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 25 min · Pairs

Array Hunt: Primes vs Composites

Provide counters and grid mats numbered 2-20. Students build rectangular arrays for each number. Primes form only 1xN arrays; composites form multiple shapes. Pairs compare and sort into prime/composite piles.

Differentiate between prime and composite numbers.

Facilitation Tip

During Array Hunt, ask students to explain why a prime number cannot form more than one rectangle with its dots.

What to look for

Present students with a list of numbers (e.g., 15, 17, 21, 23, 25). Ask them to circle the prime numbers and put a square around the composite numbers. Then, ask them to write the factors for one composite number.

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

Activity 02

• Stations Rotation
• 35 min · Small Groups

Factor Chain Game: Small Groups

In groups, roll dice to generate numbers up to 30. Chain link paper strips for each factor pair. Primes get single links; composites multiple. Discuss longest chains for GCF practice with shared numbers.

Explain the utility of prime factorization in finding GCF and LCM.

Facilitation Tip

During Factor Chain Game, move between groups to listen for precise language like 'factor of' and 'multiple of' when students describe their chains.

What to look for

Give each student a card with two numbers (e.g., 8 and 12). Ask them to find the prime factorization for each number, then identify the GCF and LCM of the pair. Collect these to gauge understanding of factorization and GCF/LCM.

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

Activity 03

• Stations Rotation
• 40 min · Whole Class

Prime Factor Trees: Whole Class Demo

Project a number like 24. Class suggests factors, building a tree to primes (2x2x2x3). Then pairs draw trees for 18 and 20, finding GCF/LCM by comparing branches.

Construct a method for determining if a large number is prime.

Facilitation Tip

During Prime Factor Trees, model pausing after each branch to ask, 'Is this factor prime? How do you know?' before continuing.

What to look for

Pose the question: 'How can we be sure a number like 29 is prime without checking every single number less than it?' Guide students to discuss divisibility rules and the idea of checking only prime divisors up to a certain point, connecting to their method for testing primality.

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

Activity 04

• Stations Rotation
• 20 min · Individual

Is It Prime? Individual Test

Give students number cards 10-50. They circle test divisors up to sqrt(N) using divisibility rules. Mark primes with stars, justify with drawings.

Differentiate between prime and composite numbers.

Facilitation Tip

During Is It Prime?, provide a checklist with 'yes' and 'no' options and a space for factor pairs to guide systematic testing.

What to look for

Present students with a list of numbers (e.g., 15, 17, 21, 23, 25). Ask them to circle the prime numbers and put a square around the composite numbers. Then, ask them to write the factors for one composite number.

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

A few notes on teaching this unit

Teachers should start with concrete visuals before moving to symbols. Use dot cards and bead strings to build arrays, then transition to written factor pairs. Avoid rushing students to memorize rules before they can explain why a number is prime. Research shows that hands-on decomposition and repeated exposure to small numbers before 30 builds the strongest foundation.

By the end of these activities, students will confidently identify prime and composite numbers up to 30. They will explain why a number is prime or composite using factor pairs and visual models. They will also begin to use factor trees and divisibility rules to break down composite numbers.

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Watch Out for These Misconceptions

• During Array Hunt, watch for students who label 1 as prime because it appears to be a single dot or bead.

  Have students build arrays for 1 and compare it to arrays for 2 and 3. Ask them to count the rows and columns to see that 1 only forms one shape, not a rectangle with equal rows and columns like primes do.

• During Factor Chain Game, watch for students who assume any even number greater than 2 is prime.

  If a student selects 4 or 6 in the game, pause to build its array and list all factor pairs aloud. Have peers describe why multiple rectangles mean the number is composite.

• During Prime Factor Trees, watch for students who only divide by 2 or stop at partial factorization.

  Ask students to trace the tree back up after completing it. If they missed a branch, prompt them to rebuild the tree with all prime factors, using blocks to represent each factor visually.

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Methods used in this brief

• Stations Rotation