Mathematics · Year 5

Active learning ideas

Prime and Composite Numbers

Active learning helps students grasp prime and composite numbers because the concepts rely on patterns in factors that are best discovered through hands-on work. Moving beyond memorization, students build number sense by physically manipulating numbers, which strengthens their ability to justify mathematical claims with evidence.

• ACARA Content Descriptions
• AC9M5N04

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

Activity 01

• Gallery Walk
• 35 min · Whole Class

Whole Class: Sieve of Eratosthenes

Provide a printed 1-100 number grid for each student. Direct students to cross out multiples of 2 starting from 4, then 3 from 6, continuing with each subsequent prime. Circle remaining unmarked numbers as primes and discuss patterns observed.

Explain what makes a prime number the fundamental building block of all other whole numbers.

Facilitation Tip

During Sieve of Eratosthenes, circulate with a checklist to ensure every student crosses out multiples correctly and records reasons for each step.

What to look for

Present students with a list of numbers (e.g., 10, 13, 15, 17, 21, 23). Ask them to circle the prime numbers and underline the composite numbers. For two of their choices, they must list all factors.

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

Activity 02

• Gallery Walk
• 25 min · Pairs

Pairs: Factor Pairs Race

Give pairs a list of numbers from 14 to 50. Pairs race to write all factor pairs for each, marking primes with just two factors. Compare lists and correct as a class, noting why composites have more pairs.

Justify why no even number, other than two, can be a prime number.

Facilitation Tip

For Factor Pairs Race, set a timer so the pressure encourages quick mental math but still allows time for partner discussion after each round.

What to look for

Pose the question: 'Why is the number 1 not considered a prime number?' Facilitate a class discussion where students share their reasoning based on the definition of prime numbers and the unique factorization theorem.

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

Activity 03

• Gallery Walk
• 40 min · Small Groups

Small Groups: Prime Chain Builders

Supply linking chains or paper strips in colours. Groups build chains representing factor pairs for given numbers; primes use only two links. Classify chains into prime or composite piles and explain choices.

Differentiate between prime and composite numbers using factor analysis.

Facilitation Tip

In Prime Chain Builders, provide different colored tiles for each prime group to help students visualize the growing chains and spot composite breaks visually.

What to look for

Give each student a card with a composite number (e.g., 24, 30, 36). Ask them to write the prime factorization of that number. Then, ask them to write one sentence explaining why their number is composite, not prime.

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

Activity 04

• Gallery Walk
• 20 min · Individual

Individual: Prime Hunt Journal

Students hunt primes up to 100 in a classroom number chart, logging them with factor checks. They draw factor trees for composites nearby and note one property per prime in journals.

Explain what makes a prime number the fundamental building block of all other whole numbers.

Facilitation Tip

For Prime Hunt Journal, model how to organize factor lists and number sentences before students begin independent recording.

What to look for

Present students with a list of numbers (e.g., 10, 13, 15, 17, 21, 23). Ask them to circle the prime numbers and underline the composite numbers. For two of their choices, they must list all factors.

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

A few notes on teaching this unit

Experienced teachers encourage students to verbalize their thinking during these activities, using precise language like 'distinct factors' and 'unique factorization.' Avoid rushing to definitions before students have grappled with examples, as research shows that early exposure to misconceptions helps students refine their understanding later. Use peer discussion to resolve disagreements, as explaining to others solidifies conceptual understanding.

By the end of these activities, students will confidently identify prime and composite numbers up to 100, explain why 1 is neither, and justify their reasoning using factor lists and divisibility. They will also connect primes to the building blocks of multiplication through prime factorization.

---

Watch Out for These Misconceptions

• During Whole Class: Sieve of Eratosthenes, watch for students who skip 1 or circle it as prime.

  Pause the sieve at 1 and ask students to list all factor pairs for 1 through 10 together. Ask them to explain why 1 does not meet the prime definition before continuing.

• During Whole Class: Sieve of Eratosthenes, watch for students who assume all odd numbers are prime.

  After completing the sieve to 20, highlight the odd composites like 9 and 15. Ask students to explain why these numbers are crossed out, connecting to multiples of 3 and 5.

• During Pairs: Factor Pairs Race, watch for students who label even numbers above 2 as prime.

  Have students build arrays for these even numbers (e.g., 4, 6, 8) and discuss why they always form rectangles with a side of 2. Compare this to the array for 2, the only even prime.

---

Methods used in this brief

• Gallery Walk