Mastering Mathematical Thinking: 4th Class · 4th Class

Active learning ideas

Properties of Integers: Factors, Multiples, Primes

Active learning helps students grasp factors, multiples, and primes by letting them manipulate objects and see patterns firsthand. These topics are abstract when taught through rules alone, so games and hands-on tasks make relationships visible and memorable for all learners.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.3
• NCCA: Junior Cycle - Number - N.4

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Simulation Game
• 30 min · Small Groups

Simulation Game: Factor Bingo

Prepare bingo cards with numbers 1-100. Call out factors, and students mark multiples on their cards. First to complete a line shouts 'Factors!'. Discuss winning cards to identify prime and composite numbers. Extend by having students create their own cards.

Differentiate between prime and composite numbers, providing examples of each.

Facilitation Tip

During Factor Bingo, circulate to listen for students who confuse factors with multiples and redirect them with a quick example like 'Is 15 a factor of 5 or a multiple of 5?' to clarify.

What to look for

Present students with a list of numbers (e.g., 15, 17, 21, 23). Ask them to circle the prime numbers and underline the composite numbers. Then, have them write the factors for one composite number from the list.

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

Activity 02

• Think-Pair-Share
• 45 min · Pairs

Hands-On: Sieve of Eratosthenes

Print a 1-100 number grid. Students circle multiples of 2, then 3, crossing out composites. Remaining primes spark discussion on patterns. Pairs test larger numbers using divisibility checks.

Explain how prime factorisation can be used to find the greatest common divisor (GCD) and least common multiple (LCM).

Facilitation Tip

When running the Sieve of Eratosthenes, model how to cross out multiples starting from 2, then 3, and ask students to explain why 4 is already crossed out to reinforce the process.

What to look for

Give each student a number (e.g., 36). Ask them to complete two tasks: 1. Write the prime factorisation of the number. 2. Explain in one sentence whether the number is prime or composite and why.

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

Activity 03

• Stations Rotation
• 40 min · Small Groups

Stations Rotation: Factor Trees

Set up stations with dice to generate numbers, tree templates, and coloured markers for primes. Students build factor trees, then swap to find GCD or LCM of pairs. Rotate every 10 minutes with peer feedback.

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

Facilitation Tip

In Factor Tree Station Rotation, provide colored pencils so students can trace each branch of the tree and spot missed factors more easily.

What to look for

Pose the question: 'If you wanted to find the greatest common divisor of 24 and 30, what are two different methods you could use?' Facilitate a class discussion comparing the factor listing method and the prime factorisation method.

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

Activity 04

• Think-Pair-Share
• 25 min · Small Groups

Relay: Multiple Chains

Teams line up. First student writes a number's first multiple, next adds the next, racing to 100. Correct chains earn points. Debrief on LCM connections with factorisation.

Differentiate between prime and composite numbers, providing examples of each.

Facilitation Tip

For the Multiple Chains Relay, set a timer and call on pairs to explain their chain before moving to the next number to encourage precision over speed.

What to look for

Present students with a list of numbers (e.g., 15, 17, 21, 23). Ask them to circle the prime numbers and underline the composite numbers. Then, have them write the factors for one composite number from the list.

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

A few notes on teaching this unit

Teach these topics by starting concrete and moving toward abstract. Use physical objects like counters or tiles to build arrays for factors, then transition to skip-counting for multiples. Avoid rushing to formal definitions; let students discover rules through repeated exposure in varied contexts. Research shows that students who construct their own understanding of primes through systematic elimination (like the Sieve) retain concepts longer than those who memorize lists.

Students will confidently identify factors, multiples, primes, and composites, and explain their reasoning using correct terminology. They will use prime factorisation to break down numbers systematically and justify their classifications with evidence from their work.

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Watch Out for These Misconceptions

• During Factor Bingo, watch for students who mark 1 as prime.

  Pause the game and ask the group to list the factors of 1 using their bingo cards, then count aloud to show it has only one distinct factor, so it belongs in a separate category.

• During the Sieve of Eratosthenes, watch for students who skip odd numbers beyond 3.

  Have them test 9 and 15 with counters, counting groups of 3 and 5 to reveal their composite nature, then resume the sieve with odd primes.

• During Factor Trees Station Rotation, watch for students who stop after dividing by 2 repeatedly.

  Prompt pairs to check if the result is prime; if not, they must branch again, using their colored pencils to track each new prime factor until only primes remain.

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Methods used in this brief

• Simulation Game
• Think-Pair-Share
• Stations Rotation