Factors and multiples with biscuits: a kitchen-table lesson for Class 5

Ask a Class 5 child for the factors of 12 and you'll often get a quick, confident list: 1, 2, 3, 4, 6, 12. Then ask what a factor actually is, and things go quiet. Reciting a list isn't the same as knowing what it means. A pack of biscuits, a handful of beads or a few coins can fix that in about ten minutes.

Twelve biscuits, laid out in rows

Count out 12 biscuits. Ask your child to lay them in neat rows, with the same number in every row, using all of them. No leftovers, no eating yet.

• 1 row of 12
• 2 rows of 6
• 3 rows of 4
• 4 rows of 3
• 6 rows of 2
• 12 rows of 1

Every number that shows up, either as the number of rows or the number in a row, is a factor of 12: 1, 2, 3, 4, 6 and 12. So a factor is a number that divides another number exactly, with nothing left over. Your child has just seen that with their own hands, which is a lot harder to forget than a definition.

Now try 7 biscuits. You'll find only two layouts: 1 row of 7, or 7 rows of 1. Seven has just two factors, and numbers like that are called prime numbers. (One small point for curious children: 1 is a special case, and it isn't called prime.)

Now you can eat the biscuits. Or at least the 7.

Multiples: skip-counting with a purpose

Multiples are the other half of the story. Start with an empty box, then add 4 biscuits at a time and say the total out loud: 4, 8, 12, 16, 20. These are the multiples of 4. They never run out, and each one divides by 4 with nothing left over.

Keeping the two apart

Here's a line worth repeating to anyone who muddles them: factors are the small numbers that fit into a number, and multiples are the bigger numbers you reach by counting. Twelve has a handful of factors. But 12 is also a multiple of 3, of 4 and of 6, so the same number can play both roles depending on who you're comparing it with.

If your child gets stuck, go back to the rows. "Does it fit in neat rows?" is a factor question. "Can I land on it by skip-counting?" is a multiple question.

Three questions, no book

Ask these over tea. Biscuits are allowed as props.

• First: Is 6 a factor or a multiple of 24? (A factor, because 24 can be shared into 6 equal groups.)
• Second: Name two multiples of 5 that are bigger than 40.
• Third: Can a number have only two factors? Give an example.

Let your child answer in their own words, and with biscuits if that helps. A slow, correct answer beats a fast, guessed one.

The chapter, in small pieces

The chapter splits this into short ideas with simple explanations and quick activities. You can see it here: Be My Multiple, I'll Be Your Factor, Class 5 Mathematics. The page also lists the quizzes and games that go with it.

If you'd like a quiz after the biscuits

KRIGYAN has short quizzes and games for Class 5 Maths chapters, plus a parent view that shows which ideas look strong and which could use another go. It's free to try right now, and we're still early enough that we'd like to hear what's confusing. Tell us your child's class and chapter, and we'll say plainly whether we cover it yet.