Mathematics · Year 8

Active learning ideas

Prime Factors, HCF, and LCM

Active learning transforms abstract concepts like prime factors, HCF, and LCM into concrete, visual processes. Students manipulate numbers directly, which builds number sense and reveals patterns they might miss with only textbook exercises.

• National Curriculum Attainment Targets
• KS3: Mathematics - Number

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 30 min · Small Groups

Relay Race: Prime Factor Trees

Divide class into teams of four. Each student runs to board, factors one number using a tree, tags next teammate. First team to complete all correctly wins. Review trees as class for errors.

Differentiate between prime numbers and composite numbers.

Facilitation Tip

During the Relay Race, circulate and ask each group to explain one step of their factor tree aloud before passing the marker to keep everyone engaged.

What to look for

Provide students with the number 36. Ask them to: 1. List all its factors. 2. Identify if it is prime or composite. 3. Write its prime factorisation. 4. Calculate the LCM of 36 and 48.

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

Activity 02

• Stations Rotation
• 25 min · Pairs

Card Sort: HCF and LCM Pairs

Provide cards with numbers and pre-calculated HCF/LCM values. Pairs match sets where HCF or LCM matches. Extend by having them verify with prime factors.

Construct the prime factorisation of a given number.

Facilitation Tip

In the Card Sort, listen for students to verbalize why a pair belongs together, such as ‘Both numbers share 2 and 3, so the HCF is 6.’

What to look for

Display pairs of numbers on the board, e.g., (18, 24) and (15, 25). Ask students to work in pairs to find the HCF for each pair using a method of their choice (factor list or prime factors). Circulate to check understanding and address misconceptions.

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

Activity 03

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Real-World Problems

Set up three stations: HCF for dividing paint cans equally, LCM for cicada cycles, prime factors for simplifying ratios. Groups rotate, solve one problem per station, present findings.

Explain the practical applications of HCF and LCM in real-world problems.

Facilitation Tip

At the Stations, provide calculators only after students attempt the prime factorisation by hand to prevent skipping the core skill.

What to look for

Pose this scenario: 'A baker has 42 cookies and 30 brownies. What is the largest number of identical treat bags the baker can make using all the cookies and brownies?' Ask students to explain their reasoning, identifying whether they used HCF or LCM and why.

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

Activity 04

• Stations Rotation
• 20 min · Whole Class

Bingo: Prime Factorisation

Students get bingo cards with numbers. Call out prime factorisations; they mark matching numbers. First to line wins, then class verifies winners' workings.

Differentiate between prime numbers and composite numbers.

Facilitation Tip

For Bingo, have students call out their prime factors as they mark squares to reinforce the connection between factors and multiples.

What to look for

Provide students with the number 36. Ask them to: 1. List all its factors. 2. Identify if it is prime or composite. 3. Write its prime factorisation. 4. Calculate the LCM of 36 and 48.

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

A few notes on teaching this unit

Teach prime factorisation first through factor trees or repeated division, as these methods build a visual and procedural foundation. Avoid rushing to the formula for LCM = (a×b)/HCF before students understand why it works. Research shows that students who construct factorisations themselves retain the concept longer than those who memorize shortcuts too early.

Students will confidently break down composite numbers into primes, pair common factors correctly for HCF, and combine primes appropriately for LCM. They will explain their method and justify their answers using clear reasoning.

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Watch Out for These Misconceptions

• During the Card Sort: HCF and LCM Pairs, watch for students who pair numbers based on their difference rather than common factors.

  Have students write the prime factors of each number on the cards first, then physically group cards with matching primes to find the HCF.

• During the Relay Race: Prime Factor Trees, watch for students who mark even numbers greater than 2 as prime.

  Pause the race and ask the group to factor out 2 immediately for any even number, reinforcing that all evens over 2 are composite.

• During the Stations: Real-World Problems, watch for students who confuse HCF with LCM when solving for identical groupings.

  Ask them to list the prime factors of both quantities first, then decide whether to take the lowest or highest powers before calculating.

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Methods used in this brief

• Stations Rotation