Prime Time Discovery

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📚 Curriculum Links

Australian Curriculum – Mathematics (v9.0)
Year 5 Achievement Standard

• Solve problems involving multiplication and division of large numbers by one- and two-digit numbers using efficient written strategies and digital technologies.
• Identify and describe factors and multiples of whole numbers.

Year 6 Achievement Standard

• Identify and describe properties of prime, composite, square and triangular numbers.
• Extend and apply knowledge of factors and multiples using strategies for compensation and flexibility with number facts.

Strand: Number and Algebra
Sub-strand: Number and place value
Elaborations:

• Exploring factors and using them to solve problems (AC9M6N03)
• Identify and explain properties of prime and composite numbers (AC9M6N02)

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⏰ Duration

45 minutes
Class Size: 16 students
Lesson 4 of 5 in Unit: "Mastering Multiples & Factors"

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🎯 WALT (We Are Learning To)

• Identify and describe prime and composite numbers
• Understand how factors relate to prime and composite numbers
• Construct and use factor trees to explore number composition
• Classify numbers based on their factor properties

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✅ Success Criteria

By the end of the lesson, students will be able to:

• Define prime and composite numbers using their own words
• Correctly identify prime and composite numbers up to 100
• Use a factor tree to find all the prime factors of a number
• Accurately categorise a set of numbers into prime and composite groups

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🧠 Prior Knowledge

Students should already have:

• A strong understanding of factors and multiples (covered in Lesson 3)
• The ability to use multiplication and division facts
• An understanding of arrays and grouping as it relates to multiplication

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🏫 Lesson Outline

1. Welcome & Quick Warmup (5 mins)

Activity: "Factor Snap"

• Hand out small cards with numbers between 10 and 50.
• In pairs, students take turns flipping their cards and must quickly name one factor of the number.
• This mentally activates their knowledge of multiples and factors in a fun, fast-paced way.
• Teacher circulates and joins in enthusiastically.

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2. Mini-Lesson: Explicit Teaching (10 mins)

Conversational and Visual Anchor Explanation:

Gather students on the floor. Use a large whiteboard to draw the numbers 1–20 as a list.

Say:

• Let’s become ‘Number Detectives’ to work out what makes a number prime or composite.
• Define prime number: a number with exactly two factors—1 and itself.
• Define composite number: a number with more than two factors.

Use colour-coded sticky notes (green for primes, red for composites) and place them on the list of numbers between 1–20 as the class identifies their type.

Demonstrate a factor tree live with 24:

     24
   /   \
  4     6
 / \   / \
2  2  2  3

Focus students on how the end numbers are primes — the unique "building blocks" of all other numbers.

Ask:

• “What do you notice about the numbers at the ends of the branches?”
• “Why do you think ‘1’ is not considered a prime number?”

Teacher Prompt: Use real conversational tone—“Okay mathematicians, challenge me—what’s a number you want to test?”

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3. Student Exploration (20 mins)

💡 Activity 1: Prime or Composite? Sorting Challenge (10 mins)

In groups of 4, students receive a deck of number cards (from 1 to 100).
Their task: Sort the cards into “Prime”, “Composite” and “Not Sure” piles using a sorting mat.

• Once sorted, each student chooses a number from the “Not Sure” pile to investigate deeply using factor trees or lists.
• Encourage collaborative discussions: “What’s the mathematical evidence we have for this one?”

Teacher Role: Roam between groups, question thinking, and coach without providing answers.

• Example question: “Have you found all the factors yet? How do you know?”

Differentiation Notes:

• Provide calculators and printed multiplication tables for support.
• Offer “scaffolded” factor trees with some branches started for students who need a hand.

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🔍 Activity 2: Factor Forest Investigation (10 mins)

Each student receives a “Factor Tree Forest” worksheet with 4 trunk numbers: 12, 30, 45, 60.

Their challenge:

• Complete the factor trees for each number.
• Circle the prime factors in green.
• Colour code composite offshoots in blue.

Optional Extension:

• Advanced learners can be challenged to find numbers with more than 2 distinct prime factors OR discover the smallest number with exactly 4 distinct prime factors.

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4. Class Reflection & Check-In (5 mins)

Return to the carpet. Ask a few student volunteers to share one number they sorted and why.

Use this time to unpack misconceptions:

• E.g., “Why is 2 the only even prime number?”
• Use mini whiteboards if time allows for students to write down one prime and one composite number they now feel confident identifying.

Peer pairs: “Turn and tell your partner ONE thing you’re proud of in maths today.”

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🌈 Differentiation Strategies

For support:

• Provide a list of prime numbers under 20 as hints for students who need scaffolding.
• Use visual number tiles or manipulatives to form arrays when thinking about factor sets.
• Partner struggling students with peer mentors.

For challenge:

• Encourage deeper exploration:
  • Research historical mathematicians and how primes were used (e.g., Eratosthenes’ Sieve).
  • Explore codes and why prime numbers are used in encryption.
  • Challenge: “Can you find a number between 90–100 that is prime? Justify it.”

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🧩 Materials & Resources

• Prime/composite sorting mats (laminated for reuse)
• Number cards 1–100
• Factor tree worksheets
• Sticky notes – green (prime), red (composite)
• Calculators (optional)
• Whiteboards and markers
• Anchor chart: “How To Tell If a Number Is Prime”

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📋 Assessment Opportunities

• Observe student discussions during sorting activity – are they justifying their decisions?
• Review accuracy and logic in completed factor forests.
• Collect and review “Not Sure” investigations—did the student use logical reasoning?
• Use whiteboard exit ticket: “What is one new thing you learned about prime numbers today?”

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🧠 Reflection & Looking Forward

This was Lesson 4 of 5 in the unit. The next lesson will explore Least Common Multiples (LCMs) and Highest Common Factors (HCFs) using prime factorisation.

Let students know after today, they have the tools needed to crack into those concepts—even the "big scary" numbers.

Teacher Tip: Optional journaling task at end of day:
🎁 “What makes prime numbers important in the world?” (Let them surprise you!)

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Let the Prime Time investigations begin 🔍🌳