Mathematics · Year 6 · The Power of Place Value and Calculation · Autumn Term

Prime Numbers and Composite Numbers

Students will identify prime numbers up to 100 and understand their unique properties.

• National Curriculum Attainment Targets
• KS2: Mathematics - Number and Place Value

About This Topic

Prime numbers are whole numbers greater than 1 with exactly two distinct factors: 1 and the number itself. Composite numbers have more than two factors. Year 6 students identify primes up to 100, justify why 1 is neither prime nor composite, predict the next prime in a sequence, and compare properties with composites. This topic aligns with the KS2 Number and Place Value objectives in the National Curriculum, building on place value and calculation skills from the Autumn term unit.

Students connect primes to factors, multiples, and divisibility rules, forming a base for prime factorisation used in fractions, ratios, and later algebra. Exploring patterns, such as primes beyond 2 being odd, develops logical reasoning and justification, key mathematical competencies. Collaborative tasks reveal these patterns through discussion and prediction.

Active learning benefits this topic greatly. When students sieve numbers together, sort factor cards, or debate sequences, abstract properties become concrete. Physical manipulation and peer explanation solidify definitions, address confusions like 1's status, and encourage precise reasoning, leading to deeper retention and confidence.

Key Questions

1. Justify why 1 is not considered a prime number.
2. Predict the next prime number in a sequence and explain your reasoning.
3. Compare the properties of prime numbers with composite numbers.

Learning Objectives

• Classify numbers up to 100 as either prime or composite, providing justification for each classification.
• Explain why the number 1 is neither prime nor composite, referencing the definition of prime numbers.
• Analyze sequences of numbers to predict the next prime number, articulating the reasoning based on divisibility rules.
• Compare and contrast the properties of prime numbers with composite numbers, identifying key differences in their factors.

Before You Start

Factors and Multiples

Why: Students need to understand the concept of factors to identify whether a number has exactly two factors (prime) or more than two factors (composite).

Number Properties (Even and Odd)

Why: Knowledge of even and odd numbers helps students quickly identify many composite numbers (all even numbers greater than 2) and narrow down possibilities for prime numbers.

Key Vocabulary

Prime Number	A whole number greater than 1 that has only two factors: 1 and itself. For example, 7 is prime because its only factors are 1 and 7.
Composite Number	A whole number greater than 1 that has more than two factors. For example, 10 is composite because its factors are 1, 2, 5, and 10.
Factor	A number that divides exactly into another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Divisibility Rule	A shortcut or guideline used to determine if a number can be divided by another number without a remainder. For example, a number is divisible by 2 if its last digit is even.

Watch Out for These Misconceptions

Common Misconception

1 is a prime number.

What to Teach Instead

1 has only one factor, itself, so it fits neither definition. Active pair discussions of factor lists for 1, primes, and composites clarify this. Students physically count factors on charts, building consensus through shared reasoning.

Common Misconception

All odd numbers greater than 2 are prime.

What to Teach Instead

Odd composites like 9, 15, and 21 have multiple factors. Group sieving activities expose this by crossing out odd multiples. Peer teaching during sorts reinforces checking all factors up to the square root.

Common Misconception

Even numbers cannot be prime.

What to Teach Instead

2 is the only even prime, as it has exactly two factors. Whole-class chains starting with 2 highlight this exception. Students defend predictions, using active testing to internalise the rule.

Active Learning Ideas

Small Groups: Sieve of Eratosthenes Grid

Provide each group with a 1-100 number grid. Starting from 2, students use coloured pens to cross out multiples collaboratively. Remaining numbers are primes; groups justify exclusions and note 1 separately. Share findings class-wide.

35 min·Small Groups

Pairs: Factor Pairs Card Sort

Prepare cards with numbers 1-100 and possible factor pairs. Pairs sort into prime, composite, or neither piles, testing factors systematically. Discuss borderline cases like 1 and 2, then verify with multiplication checks.

25 min·Pairs

Whole Class: Prime Prediction Chain

Display a prime sequence on the board. Students suggest and justify the next prime in turn, using divisibility tests. Class votes and tests predictions together, extending to spotting patterns beyond 100.

30 min·Whole Class

Individual: Prime Hunt Scavenger

Give students a 1-100 chart with hidden primes marked. They hunt, list, and explain three properties of their finds. Pairs then swap lists to verify and discuss predictions for larger numbers.

20 min·Individual

Real-World Connections

• Cryptography, the practice of secure communication, relies heavily on prime numbers. Large prime numbers are used to create encryption keys that protect sensitive data, such as online banking transactions and private messages.
• In number theory, prime numbers are fundamental building blocks, similar to atoms in chemistry. Mathematicians study their distribution and properties, which has led to advancements in fields like computer science and theoretical physics.

Assessment Ideas

Quick Check

Present students with a list of numbers from 1 to 30. Ask them to circle all the prime numbers and underline all the composite numbers. Then, ask them to write one sentence explaining their choice for the number 29.

Discussion Prompt

Pose the question: 'If you were to create a new number system, would you include prime numbers? Why or why not?' Facilitate a class discussion where students use their understanding of prime and composite properties to justify their ideas.

Exit Ticket

Give each student a card with a number (e.g., 49, 53, 77). Ask them to write down whether the number is prime or composite, list all its factors, and explain their reasoning in one to two sentences.

Frequently Asked Questions

Why is 1 not considered a prime number?

Prime numbers must have exactly two distinct positive factors: 1 and themselves. 1 has only one factor, so it is neither prime nor composite. Teach this through factor pair sorts where students list divisors for 1 alongside primes like 7, revealing the distinction. This builds precise vocabulary and reasoning for sequences and predictions.

How do you identify prime numbers up to 100?

List numbers from 2 to 100 and eliminate multiples of each prime starting from 2 using a sieve. Remaining numbers are primes. Hands-on grids let students cross out systematically, discuss patterns like odd primes, and memorise the 25 primes up to 100 efficiently through repetition and justification.

What are the key differences between prime and composite numbers?

Primes greater than 1 have exactly two factors; composites have more. For example, 7 is prime (factors: 1,7), while 8 is composite (1,2,4,8). Compare via card sorts or sieves, where students test divisibility and articulate properties, strengthening comparison skills for the curriculum.

How can active learning help students understand prime numbers?

Active methods like group sieving or pair factor hunts make abstract factor rules tangible. Students cross out multiples collaboratively, debate 1's status, and predict sequences aloud, addressing misconceptions instantly. This fosters reasoning, boosts engagement, and improves retention over rote memorisation, aligning with National Curriculum emphasis on justification.