Fractions are where many children first feel that maths stops making sense. The reason is usually that fractions are taught as symbols before they are understood as quantities. When children can see, fold, cut and share, the symbols follow naturally. Here is a path that works from the first halves to adding fractions.
Start with fair sharing
A fraction is an equal share of a whole. Cutting a sandwich into two equal parts gives halves; cutting a pizza into four equal slices gives quarters. The word “equal” matters: two unequal pieces are not halves. Fold paper strips into halves, thirds and fourths and colour one part. Our halves, thirds and fourths sheets use the same pictures.
Numerator and denominator
The bottom number, the denominator, tells how many equal parts the whole is split into. The top number, the numerator, tells how many of those parts we are talking about. Three-quarters means three of four equal parts. Practise reading and drawing fractions in a variety of shapes: circles, rectangles, groups of objects. Naming fractions is the first step.
Fractions on a number line
Fractions are numbers, and they sit on the number line between whole numbers. Draw a line from 0 to 1, mark halves and quarters, and see that one-half and two-quarters land on the same spot. This is the root of equivalent fractions. A number line also shows that a fraction like 7/4 is more than one whole. See fractions on a number line.
Comparing and equivalent fractions
A bigger denominator means smaller pieces: one-eighth is smaller than one-fourth. When denominators are the same, compare numerators. For equivalent fractions, multiply or divide top and bottom by the same number: 2/3 = 4/6. Folding paper again helps: fold a strip into thirds and then fold each third in half to get sixths. Practise with comparing fractions and equivalent fractions.
Adding and subtracting
With the same denominator, add the numerators and keep the denominator: 2/7 + 3/7 = 5/7. With different denominators, first find a common denominator, using equivalent fractions: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Do not teach “add the tops and add the bottoms”; it is the most common fraction mistake. Pictures of bars make it clear that the pieces must be the same size to be counted together.
Multiplying and dividing
Multiplying a fraction by a whole number is repeated addition: 3 × 1/4 = 3/4. Multiplying two fractions means taking a part of a part: 1/2 of 1/3 is 1/6. Dividing by a fraction asks “how many of these fit into that?”: how many halves fit into 3? Six. Only then introduce the shortcut of flipping and multiplying. Our Grade 5 fractions and decimals workbook covers all four operations.
Common mistakes to watch for
- Thinking a bigger denominator means a bigger fraction.
- Adding both numerators and denominators.
- Drawing unequal parts and calling them halves.
- Not simplifying answers; ask “can both numbers be divided by the same number?”.
Frequently asked questions
When do children start learning fractions?
Halves and quarters are introduced at ages five to seven, while operations with fractions come in the upper primary years.
Why are fractions so hard?
They represent a new kind of number, and the notation is unfamiliar. Visual models make them much easier.
Should children learn decimals or fractions first?
Fractions usually come first because they link naturally to sharing; decimals follow as another way to write fractions with denominators of ten, a hundred and so on.
