How to teach fractions

A fraction shows part of a whole that has been split into equal parts. In 3/4 the bottom number, 4, is how many equal parts the whole is divided into, and the top number, 3, is how many of those parts you have. So 3/4 means 3 of 4 equal parts.

Start with shaded shapes so part-whole is visual, then name fractions and compare ones with the same denominator. Introduce equivalent fractions with diagrams next, and only then move on to adding, subtracting and simplifying. Building the visual meaning first prevents most later misconceptions.

Fractions are introduced as early as Grade 1 with halves and quarters of shapes, and develop through Grade 6. Naming and comparing come first, equivalent fractions follow in the middle grades, and adding, subtracting, multiplying and dividing fractions build up across Grades 4 to 6.

It is a very common misconception, because with whole numbers a bigger number means more. But the denominator is how many equal parts the whole is cut into, so more parts means each part is smaller. So 1/8 is smaller than 1/4. Diagrams of the same whole cut different ways make this clear.

If the denominators are the same, compare the numerators: 3/5 is more than 2/5. If they differ, convert to a common denominator or a diagram first, because you cannot compare fifths with quarters directly. A bigger denominator means smaller parts, so more parts does not automatically mean a bigger fraction.

Equivalent fractions are different fractions that describe the same amount, such as 1/2, 2/4 and 4/8. You get one by multiplying or dividing the top and bottom by the same number. Diagrams showing the same shaded area split into different numbers of parts make the idea concrete.

Because the denominator names the size of the parts, not a quantity to be counted. Adding 1/4 and 1/4 gives 2/4, not 2/8, since you are counting two quarter-sized parts. To add fractions you need the same denominator first, then you add only the numerators.