One part is shaded. Which fraction is it?
Reading fractions
Reading fractions practice, from 3/8 of a cake to 9/4 = 2 1/4: fraction pies first, then several slices, then more than a whole and taking out the wholes.
Your child can start here straight away, with no other topic needed first; division up to 20 only comes in later, when taking out the whole ones. That step really is a division: for 11/3 a child asks how many times three goes into eleven, and without that fact there is no getting to 3 2/3.
Usually taught in Year 1–3 in England and Wales, around ages 5 to 8. Every child goes at their own pace; this is a guide, not a requirement.
The first of 7 exercises in this topic. See them all
How it fits together
The arrows point to what can be done next. Whatever sits inside a box belongs to it.
Needed first
Fractions
first this, then that belongs to
Several parts are shaded, in pies cut into as many as twelve. Which fraction is it?
Whole pies and a part one. How much is that together — 2 2/3, 1 1/5?
Count the slices and write the fraction yourself: the shaded ones on top, all of them underneath.
The same pies, counted in slices: the whole ones are cut too. The answer is more than one whole.
12/5 is how many whole pies, and how much is left? Write it as 2 2/5.
78/20 = ? ?/20. How many whole ones, and what is left? With bigger numbers now.
Why it matters
Reading comes before calculating. A fraction tells you two things at once: how many equal parts something is divided into, and how many of those parts you have. A child who sees 3/8 and straight away pictures a cake cut into eight with three slices coloured has an image they can fall back on again and again.
The exercises also go beyond a whole cake. 9/4 is more than one: two whole cakes and another quarter. Switching easily between 9/4 and 2 1/4 comes back in adding and multiplying fractions.
How to approach it
Have your child count first: how many slices does the cake have altogether? That number goes below the line, as the denominator. Then the coloured slices: they go above it, as the numerator. A child who sticks to that order won't mix up numerator and denominator.
With more than one cake, it helps to count the whole cakes first and only then look at what is left. The other way round, for 11/3: how many times does three go into eleven? Three times, with two slices left over, so 3 2/3.
When is it secure?
A round of 10 sums in one go without a mistake, within 25 seconds. That is about 2.5 seconds a sum: no more counting, just knowing.