Mathematical Explorers: Building Number and Space · 3rd Class

Active learning ideas

Prime Numbers, Factors, and Multiples

Active learning works well for prime numbers, factors, and multiples because students need to manipulate numbers, test divisibility, and visualize relationships. These concepts are abstract, so hands-on sorting, building, and games make them concrete and memorable. Students retain rules better when they construct knowledge through movement and discussion rather than passive listening.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.8
• NCCA: Junior Cycle - Number - N.9

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Trading Cards
• 30 min · Small Groups

Sorting Relay: Primes vs Composites

Prepare cards numbered 1-50. Divide class into teams. One student per team runs to board, sorts card into prime or composite column, returns to tag next teammate. Discuss errors as a class after each round.

Analyze the difference between a prime number and a composite number.

Facilitation Tip

During Sorting Relay, circulate and ask students to justify why they placed a number in the prime or composite pile, focusing on factor counts.

What to look for

Present students with a list of numbers (e.g., 15, 17, 21, 29, 33). Ask them to circle the prime numbers and underline the composite numbers. For two of their choices, have them write down all the factors.

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

Activity 02

• Trading Cards
• 25 min · Pairs

Factor Pairs Hunt

List numbers 12-48 on worksheets. Students work in pairs to circle factor pairs that multiply to each number, then highlight common factors across numbers. Share one discovery per pair with class.

Construct a factor tree to find the prime factorization of a given number.

Facilitation Tip

For Factor Pairs Hunt, provide grid paper so students can visually organize pairs and spot missing factors quickly.

What to look for

Give each student a number (e.g., 24). Ask them to construct a factor tree for this number and write its prime factorization. Then, ask them to list the first 5 multiples of their number.

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

Activity 03

• Trading Cards
• 35 min · Pairs

Factor Tree Tournament

Provide numbers like 24, 36, 48. Pairs build factor trees on mini-whiteboards, racing to prime factorization. Rotate partners to compare trees and verify steps.

Justify the importance of prime numbers in cryptography and number theory.

Facilitation Tip

In Factor Tree Tournament, require students to label each branch with the factor used and the quotient to avoid skipping steps.

What to look for

Pose the question: 'Why are prime numbers considered special in mathematics?' Guide students to discuss their unique properties (only two factors) and their importance in breaking down other numbers (prime factorization) and in cryptography.

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

Activity 04

• Trading Cards
• 20 min · Whole Class

Multiples Chain Game

Call a number; students in circle add next multiple aloud or with claps. If error, group discusses correction. Extend to listing multiples of primes.

Analyze the difference between a prime number and a composite number.

Facilitation Tip

Play Multiples Chain Game with a timer visible to create urgency and encourage quick recognition of multiples.

What to look for

Present students with a list of numbers (e.g., 15, 17, 21, 29, 33). Ask them to circle the prime numbers and underline the composite numbers. For two of their choices, have them write down all the factors.

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

A few notes on teaching this unit

Teach these concepts through structured play and guided discovery. Start with sorting and pairing to build foundational understanding before moving to abstract factorization. Avoid rushing to definitions—instead, let students experience the properties first. Research shows that building factor trees collaboratively helps students avoid repeated errors and reinforces the concept of prime factorization as a unique decomposition.

By the end of these activities, students will confidently identify prime and composite numbers, list factor pairs quickly, and break down numbers into prime factors. They will also recognize multiples in sequences and explain why 1 and even numbers greater than 2 are not always prime. Clear communication about their reasoning shows true understanding.

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Watch Out for These Misconceptions

• During Sorting Relay, watch for students grouping 1 with prime numbers because it has one factor.

  Have students test 1 with the sieve cards; its single factor becomes obvious, and peers can explain why primes require exactly two distinct factors.

• During Factor Pairs Hunt, watch for students labeling all even numbers greater than 2 as prime.

  Ask them to write the factor pair for an even number like 10 (2 and 5) and compare it to 2, which only pairs with 1 and itself.

• During Factor Tree Tournament, watch for students only dividing by 2, missing odd prime factors.

  Circulate and ask, 'What other factors could you try?' to guide them toward options like 3 or 5 before confirming their trees.

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Methods used in this brief

• Trading Cards