How to help with fractions at home using paper strips and pizza

Fractions are confusing, and that's okay. We can pretend they aren't, or we can admit that this is a brand-new kind of number and treat it that way. Until fractions arrive, numbers have counted whole things. Now a number describes a part of a thing, and the bigger bottom number makes the piece smaller. That is strange the first time you meet it.

Your child isn't bad at fractions. What usually happens is that the idea is taught with symbols before there is a picture to hang it on, and then the next lesson builds on top of it. The fix is to bring the picture back. You don't need special materials. A few strips of paper and a pizza will do.

Start with the picture, then the symbols

Ask your child to describe a fraction in words before you write it. "Three out of four equal pieces" comes first. Then 3/4.

Three things are worth getting right in the first conversations:

• The pieces must be equal. A pizza cut into one big slice and two small slices is not cut into thirds.
• The bottom number tells you how many equal pieces make the whole. The top number tells you how many you are talking about.
• A bigger bottom number means smaller pieces. One eighth of a pizza is smaller than one fourth.

If your child can say those three in their own words, they are further along than they think.

Why paper strips work

A strip of paper is a number line you can fold. Fold one in half and you can see halves. Fold it again and you have fourths, and again for eighths. Lay the strips side by side and you can see that 1/2, 2/4 and 4/8 are the same length. That is what "equivalent" means, and now they have seen it.

Children also see answers that don't make sense. If someone says 1/2 + 1/3 = 2/5, the strip shows you quickly that it can't be right, because 2/5 is less than a half.

Why pizza works

Pizza is relatable. Everyone has cut one. It gives children a story to attach the numbers to, and stories are easier to remember than rules. Cutting a real pizza, a paper plate or a drawn circle into equal pieces turns a worksheet into something familiar.

A worked example: adding 1/4 and 3/8

Say two people share a pizza that has been cut into 8 equal slices. One person eats 1/4 of the pizza and the other eats 3/8. How much pizza have they eaten in all?

The step that matters is the third one. Whatever you do to the bottom, you do to the top, so the amount stays the same.

Try this at home tonight

You need three strips of paper (cut a sheet into long strips), a pencil and, if you like, a real pizza for dinner.

• Fold the first strip in half. Open it, and colour one half.
• Fold the second strip into fourths. Colour two fourths.
• Fold the third strip into eighths. Colour four eighths.
• Line them up. Ask, "What do you notice?" Let them take their time.
• Ask, "Which is bigger, 2/3 or 3/4?" Fold two new strips, one into thirds and one into fourths, and let them compare. Fold both into twelfths if they want to count: 2/3 is 8 twelfths and 3/4 is 9 twelfths, so 3/4 is bigger.
• At dinner, if there is pizza, ask your child to cut it into equal pieces and say what fraction you each ate.

Keep it to ten minutes and stop on something they got right.

When it still doesn't click

Go back one step. If adding is hard, check comparing. If comparing is hard, check that the pieces are equal. And never give up on a child. We adapt to what they need.

Understanding fractions is not too hard. Remembering them is the challenge, so a few minutes with a strip or a quick game, spread over a few days, will do more than one long session.

Next steps

If you want to see where your child stands, the free 15-question check-in is. It has no mark and it shows what is solid and what needs practice. The free math games give extra practice.

Fractions are a topic where many children need extra time, and our Toughest Topics courses spend real time on them. We find out where your child is first, and I don't want to take your money if they don't need it.