fractions of amounts problem solving year 3

Fractions in Year 3 (age 7–8)

What your child will learn

Understand and count in tenths.

In Year 3, your child will learn to count in tenths. They will understand that finding a tenth is the same as dividing by ten (by dividing objects, sets of objects, and numbers into ten equal parts).

This will help them to keep seeing the connection between fractions and division. It is possible that your child will start to be introduced to decimals at this stage, too.

Find fractions of a set of objects

Your child will learn to find and write fractions of a given number of objects. For example:

Find     of 15.   First, your child can find   of 15 by dividing the total by the denominator : 15 ÷ 5 = 3.   Then, they can multiply this result by the numerator to find the correct fraction: If   of 15 is 3, then    of 15 is 3  × 2 = 6.     of 15 is therefore 6.

Your child will be able to do this with unit and non-unit fractions. They will learn that:

Use fractions as numbers

Your child will be able to do this with unit and non-unit fractions:

Show equivalent fractions using diagrams

They’ll show their understanding of equivalent fractions by drawing diagrams like this:

Your child will also learn to use objects and  fraction walls  to show equivalent fractions.

Add and subtract fractions with the same denominator

Compare and order fractions

Solve problems that involve all of the above.

Finally, your child will learn to put all this learning into practice by solving problems involving fractions.

They will be able to relate fractions to division, count in fractional steps (for example, counting up and down in tenths), compare fractions, understand  unit  and  non-unit fractions , understand equivalent fractions, find fractions of amounts, and add and subtract fractions with the same denominator.

How to help at home

There are lots of everyday ways you can help your child to understand fractions. Here are just a few ideas.

1. Make fraction snowflakes

Paper folding can be a great way to explore fractions.

Decorate a piece of paper or card and then ask your child to fold the paper into different equal parts. For example, they could fold the paper into fifths by creating five equal sections. Ask them to show you a fifth, two-fifths, three-fifths, four-fifths, and five-fifths, which they can see is equivalent to a whole.

Challenge your child by giving the paper a value and asking them to work out what the fractions would be worth. What would one fifth represent if the whole paper had a value of 10? As they fold, they may like to cut patterns into the paper to make a ‘snowflake’ and watch the pattern develop as they fold further.

2. Have fun with food

Cake, pizza, or any foods with a regular shape can help children understand what fractions are and how they work. Ask your child questions like, ‘If I cut our cake into 8 pieces, what fraction will each piece be?’

Foods that people eat lots of can help your child understand how to find fractions of amounts. For example:

‘We have 12 fish fingers in the packet. There are 4 of us. What fraction of the fish fingers can we each have? How many fish fingers would that be?’

Activity: Cupcake fractions

3. Compare fractions together

In Year 3, your child will compare  unit fractions  and fractions with the same  denominator  by saying which fraction is bigger or smaller – and explaining how they know.

4. Fraction countdown

‘Would you prefer it if I cut this cake into ten equal pieces and gave you a piece, or if I cut the cut into two equal pieces and gave you a piece?’

Print out the  Fraction Match activity sheet and cut out each fraction card. Take a selection of cards and see if your child can put them all in order, either from largest to smallest or smallest to largest. Are there any equivalent fractions? See if your child can match them up.

Activity: Fraction Match

5. Make a fraction wall

Equivalent fractions are different fractions that have the same value. In Year 3, your child will learn about equivalent fractions with small denominators using drawings and diagrams.

Why not try making a fraction wall with your child? You could investigate using the computer to make your fraction wall by creating a table and splitting each row into the equal number of parts you need. For example, to represent fifths, you would have to split the whole row into five equal parts.

Alternatively, you can download our fraction wall below.

Fraction wall

6. Adding and subtracting fractions

Try adding and subtracting fractions with the same denominator with your child. Try to do this within a whole, i.e. make sure that the sum uses numbers less than one, including the answer.

Using drawings or diagrams can help your child visualise adding and subtracting fractions. For example:

 +   =    This could be calculated using a diagram like this:     Y our child will first split the whole into five equal parts. Your child can then shade one box to represent   and two boxes to represent  . They will then be able to see that the total is  .

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Fraction Worksheets for Year 3 (age 7-8)

Children coming into Year 3 should have a sound understanding of simple fractions, especially halves, quarters and thirds.  They should have had plenty of practical experience dividing shapes and sets of objects into quarters and thirds.

There are plenty of new concepts on fractions to be understood in Year 3,but it is still important to use practical work, using shapes and objects, to help with understanding.  A key step is to begin working with tenths and recognising that tenths arise from dividing an object into ten equal parts. Later this can be developed to dividing one-digit numbers or quantities by 10. This is crucial for understanding our decimal system and understanding that a fraction such as three tenths can also be represented as a decimal (0.3) and connects to dividing 3 by 10. Counting in tenths can also help enormously with this. We have a great selection of worksheets which deal with writing tenths, counting in tenths and converting tenths to decimals.

Other fractions are also introduced, such as fifths, and equivalence between fractions is developed with the help of pictures and diagrams. This leads on to ordering fractions with the same denominator. One of the quirks of fractions, which some children find hard to understand, is that as the denominator gets larger the size of the number gets smaller (e.g. one tenth is smaller than one fifth; one twentieth is smaller than one tenth and so on). We have some excellent ordering fractions pages for Year 3 to help consolidate this concept. As well as these, some of our most popular worksheets are the sets of finding fractions of numbers, with questions such as ‘What is one sixth of 30?’ Again, the link between fractions and division needs to be constantly reinforced.

As the year progresses children will be introduced to adding and subtracting fractions, but only with the same denominator and with totals up to one whole one. Simplifying fractions is important at this stage and children should be encouraged to write fractions in their simplest form. (e.g. two sixths can be simplified to one third).

All this will lead onto much more on decimals and fractions in Year 4, including hundredths and further work on equivalence. If you child is finding the Year 3 work difficult then it is important to go back to Year 2, or even Year 1, and see what is understood and what concepts have not been fully understood.

Understand fractions and equivalent fractions

Understanding fractions and work on the importance of equivalent fractions.

Colour the correct fractions to match the sequences.

Various fraction problems.

Tricky work on equivalent fractions.

Order fractions with the same denominator.

Order simple fractions.

A little bit of revision on reading and writing fractions.

Understanding halves, quarters and thirds

Revision of work on halves, quarters and thirds.

Finding halves, quarters and thirds of numbers of bees etc..

More finding halves, quarters and thirds.

More finding halves, quarters and thirds - fun colouring.

Some tricky word problems using halves and quarters.

Ordering fractions as more than, equal to or less than a half.

Understanding tenths

Understanding tenths and counting in tenths.

Chocolate cakes to help with understanding tenths.

Colouring tenths of various shapes.

Introducing tenths by colouring one tenth; then finding six tenths, seven tenths etc of shapes. Finding out that five tenths is the same as a half.

Writing tenths in words and as a fraction.

Finding tenths of various animals.

Finding tenths of numbers of objects.

Looking at tenths as decimals and fractions.

Matching fractions and decimals. ordering fractions and decimals.

Counting on in tenths.

Estimating tenths on a number line.

Find fractions of amounts and numbers

Finding fractions of amounts.

Shading quarters, thirds or fifths of various shapes.

Finding fractions of shapes. Makes a change from numbers!

A non-unit fraction is any fraction which does not have one as a numerator.

Find fractions of pizzas.

More pizzas, this time concentrating on fifths and sixths.

Finding fractions of an allotment: equivalent fractions.

Finding fractions of numbers. Working with halves, quarters, thirds and tenths. Remember, to find one fifth, divide by 5.

More finding fractions of numbers.

Solving word problems involving fractions.

Adding and subtracting fractions

Begin to add and subtract fractions with the same denominator.

Use the bar models to help with adding fractions.

Adding fractions with visual clues.

Adding fractions with the same denominator.

More adding fractions with the same denominator.

Subtracting fractions with the same denominator.

More subtracting fractions with the same denominator.

A mixture of addition and subtraction of fractions with the same denominator.

Help for adding fractions of a number of objects.

More addition questions using objects.

Food is thew theme for this set of addition of fractions.

The statutory requirements for fractions in Year 3.

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Year 3 | Solving Fraction Problems Worksheets

In these Year 3 solving fraction problems worksheets , your learners will embark on a journey of real-world word problems, utilising their knowledge of fractions to find the answers.

In these Year 3 solving fraction problems worksheets, children are encouraged to actively apply their understanding of fractions to solve a diverse set of word problems. By engaging with various fraction problems, learners deepen their understanding of fractions and their related operations.

Our Year 3 solving fraction problems worksheets are aligned with KS2 fractions on the primary national curriculum. All of our Year 3 fractions worksheets can be used with your ideas for primary maths activities, learning resources, teaching material, visual aids, games, differentiation, display boards, homework, and lesson plans.

You may also be interested in our Year 3 Counting in Tenths Worksheets .

Explore all of our Year 3 maths worksheets .

Access this resource and thousands more for just £9.95 per year

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Year 3 Fraction Word Problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

22 February 2018

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Gareth Mottram

Great selection and good differentiation sheet. Answers would have been nice to save even more time but thanks for doing this.

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Great for my highers. Thanks.

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Fractions of an Amount 3 Lesson

This Year 3 Fractions of an Amount 3 lesson covers the prior learning of identifying non-unit fractions, before moving onto the main skill of finding non-unit fractions of an amount.

The lesson starts with a prior learning worksheet to check pupils’ understanding. The interactive lesson slides recap the prior learning before moving on to the main skill. Children can then practise further by completing the activities and can extend their learning by completing an engaging extension task.

Mathematics Year 3: (3F1c) Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators

Mathematics Year 3: (3F1b) Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

Mathematics Year 3: (3F10)  Solve problems that involve 3F1 - 3F4

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Interactive activities for children

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Lesson Slides

These lesson slides guide pupils through the prior learning of place value of identifying non-unit fractions, before moving onto the main skill of finding non-unit fractions of an amount. There are a number of questions to check pupils' understanding throughout.

Modelling PowerPoint

This powerpoint can be used to model the questions that the children will complete on the Varied Fluency and Reasoning & Problem Solving worksheets as part of this lesson.

These are the same as the lesson slides on Classroom Secrets. You can assign this as an activity for pupils to access individually in school or remotely from home.

Interactive Animation Activity

This Year 3 Fractions of an Amount Interactive Animation consists of four questions to consolidate pupils' understanding of calculating fractions of amounts.

1 Prior Learning

Video Tutorial

In this Fractions of an Amount 1 Video Tutorial, Vanessa shows pupils how to use bar models and furry creatures to find fractions of amounts. She uses key vocabulary including numerator, denominator and unit fraction.

Interactive Activity

This Year 3 Fractions of an Amount interactive game test pupils' understanding of finding unit fractions of given amounts.

2 Varied Fluency

This differentiated worksheet includes varied fluency questions for pupils to practise the main skill of this lesson.

This Fractions of an Amount Reasoning Practice interactive game checks pupils’ understanding and reasoning of finding fractions of amounts. The activity and step focus on unit fractions only.

This Year 3 Fractions of an Amount interactive game checks pupils’ understanding of finding non-unit fractions of real life contexts.

2 Reasoning & Problem Solving

This fractions of an amount 3 extension task includes a challenge activity which can be used to further pupils' understanding of the concepts taught in the fractions of an amount 3 lesson.

Mixed Practice

This worksheet includes varied fluency, reasoning and problem solving questions for pupils to practise the main skill of finding non-unit fractions of an amount.

This differentiated worksheet includes reasoning and problem solving questions to support the teaching of this step.

Discussion Problem

This worksheet includes two discussion problems which can be used in pairs or small groups to further pupils' understanding of the concepts taught in this lesson.

Challenge Activity

This Year 3 Fractions of an Amount 3 Maths Challenge is designed to check pupils' understanding of finding unit and non-unit fractions.

This differentiated worksheet includes varied fluency and reasoning and problem solving questions to support the teaching of this step.

2 Additional Activities

Consolidation Pack

These Fractions worksheets are fantastic at helping your pupils practice their reasoning and problem solving skills. This pack contains two different question types for Year 3 Spring Block 5.

Home Learning Pack

This Summer week 2 Maths pack contains varied fluency, reasoning and problem solving worksheets.

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Year 3 Fractions

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Children can use this Sports Day-themed resource to practise finding fractions of amounts for non-unit fractions. Either individually or in pairs, children solve problems about archery, the egg and spoon race, the sack race and hula hooping.

The answers for each problem are provided.

• Key Stage: Key Stage 2
• Subject: Maths
• Topic: Fractions
• Topic Group: Fractions, Decimals and Percentages
• Year(s): Year 3
• Media Type: PDF
• Resource Type: Worksheet
• Last Updated: 24/10/2023
• Resource Code: M2WAE84
• Curriculum Point(s): Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators.

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