Imaginesis: printable Year 3 Fractions maths worksheets for England (National Curriculum) — Finding a Fraction of a Number, Comparing Fractions with the Same Denominator, Finding Fractions of a Set: word problems with hints, answers and worked solutions as PDF, also as an A/B test.
Two identical chocolate bars are each cut into 6 equal parts. One plate holds 1/6 of a bar, and the second plate holds 2/6 of a bar. Which sign ( ) belongs between 1/6 and 2/6?
Hint: Since the pieces on both plates are the exact same size, look at whether 1 piece or 2 pieces of chocolate is more.
Answer: <
A baking tray holds 15 cookies. Exactly 2/3 of them have chocolate chips. How many cookies have chocolate chips?
Hint: Read the fraction carefully: what does each of its two numbers tell you?
Answer: 10
Children learn to calculate unit and non-unit fractions of an amount using small denominators, such as finding one third or three quarters of a number.
KS3.N.11 interpret fractions and percentages as operatorsKS3.R.6 understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fractionY3.F.2 recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominatorsY3.F.7 solve problems that involve all of the above.Y4.F.3 solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole numberY6.R.4 solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.
In Year 3, children learn to find both unit fractions (such as 1/3 or 1/4) and non-unit fractions (such as 2/3 or 3/4) of a discrete set of objects or a number. They connect this to sharing and grouping: dividing the starting amount into equal parts based on the denominator, and then taking the required number of parts shown by the numerator.
A typical error occurs when working with non-unit fractions. Children often successfully divide by the bottom number but forget the second step. For example, when finding 2/3 of 15, a child might correctly calculate 15 divided by 3 to get 5, but then write 5 as their final answer instead of multiplying by 2 to get 10. Some children also mix up the roles of the numbers, attempting to divide by the top number instead.
Tasks using the Find a fraction of a number template provide written practice with these steps. Children work through questions such as finding 1/4 of 24 or 3/4 of 20, drawing on their times tables to divide into equal parts and scale up the result.
Children learn to compare fractions that share the same denominator by looking at how many equal parts are selected.
Y3.F.4 recognise and show, using diagrams, equivalent fractions with small denominatorsY3.F.6 compare and order unit fractions, and fractions with the same denominators
In Year 3, children work with fractions with small denominators. They learn to recognise and show equivalent fractions using diagrams, and they practice comparing fractions that share the same denominator by checking how many parts of the whole are taken.
A frequent error occurs when children mix up how numerators and denominators work. When comparing fractions with identical denominators, some children get distracted by the shared bottom number or confuse this with unit fractions, wrongly assuming that a smaller numerator represents a larger slice.
In practice, tasks using the Compare fractions with the same denominator template present two fractions side by side, such as 2/6 and 5/6. Children compare the numerators to decide which fraction is larger, often using comparison signs to record which value is greater.
Children learn to recognise unit and non-unit fractions with small denominators as numbers and use them to find fractions of a whole set.
Y3.F.3 recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominatorsY3.F.7 solve problems that involve all of the above.
In Year 3, children build on simple halves and quarters by treating fractions as numbers in their own right. They work with unit fractions, such as 1/3 or 1/4, as well as non-unit fractions with small denominators, such as 2/3 or 3/4, applying them directly to sets of objects.
A common mistake occurs when calculating non-unit fractions of a group. A child often remembers to divide the total by the denominator to find one part, but forgets to multiply that result by the numerator. For example, when finding 2/3 of 12, they might calculate 12 divided by 3 to get 4, but stop there instead of doubling it to reach 8.
Worksheet tasks focus on finding a fraction of a set, asking questions such as finding 3/4 of 16 or 2/3 of 15. Children solve these problems by dividing the whole amount into equal groups based on the bottom number, then counting the specified number of groups to find the final total.
