Grade 6: Factors

Warm up with a quick recall on the board. Find factors by pairing (arrays or divisibility), list them in order, and connect to multiples as the same relationship from the other side.

A factor divides a number exactly: 1, 2, 3, 4, 6 and 12 are the factors of 12. A multiple is the result of multiplying: 12, 24, 36 are multiples of 12. The two words are opposite directions of the same fact family, and they underpin fractions, primes and algebra. Model the method clearly, thinking aloud:

• Build factor pairs with arrays: 12 counters can make a 1×12, 2×6 or 3×4 rectangle, each rectangle is a factor pair.
• List factors systematically in pairs from the outside in (1 and 12, 2 and 6, 3 and 4) so none get missed.
• Contrast the words directly: factors of 12 are 12 or smaller and run out; multiples of 12 are 12 or bigger and never end.
• Play fizz-buzz style games for multiples; use divisibility checks (even numbers, digit sums for 3) for factors.
• Link to primes: a prime has exactly two factors, 1 and itself.

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the worksheet independently. Hand out the three difficulty levels below so every child works at the right stretch.

Circulate and look for these, they are the usual sticking points:

• Mixing up the words, listing 24, 36 as 'factors' of 12.
• Missing factor pairs by listing randomly instead of in order.
• Forgetting 1 and the number itself are always factors.
• Thinking a number with many factors must be big (60 has more factors than 61).
• Missing a factor pair (especially 1 and the number itself) and confusing factors with multiples.

Pull the class back together. Ask one child to explain factors in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.