fractions of amounts year 3 problem solving

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Published 2013 Revised 2019

Exploring Fractions

• The first group  gives you some starting points to explore with your class, which are applicable to a wide range of ages.  The tasks in this first group will build on children's current understanding of fractions and will help them get to grips with the concept of the part-whole relationship. 
• The second group of tasks  focuses on the progression of ideas associated with fractions, through a problem-solving lens.  So, the tasks in this second group are curriculum-linked but crucially also offer opportunities for learners to develop their problem-solving and reasoning skills.   

• are applicable to a range of ages;
• provide contexts in which to explore the part-whole relationship in depth;
• offer opportunities to develop conceptual understanding through talk.

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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Finding Fractions of Amounts (Year 3)

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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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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.

The statutory requirements for fractions in Year 3.

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Fractions of an Amount 3 Year 3 Fractions Resource Pack

Step 9: Fractions of an Amount 3 Year 3 Resources

Fractions of an Amount 3 Year 3 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Spring Block 5.

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What's included in the pack?

This pack includes:

• Fractions of an Amount 3 Year 3 Teaching PowerPoint.
• Fractions of an Amount 3 Year 3 Varied Fluency with answers.
• Fractions of an Amount 3 Year 3 Reasoning and Problem Solving with answers.

National Curriculum Objectives

Mathematics Year 3: (3F1b)  Recognise, find and write fractions of a discrete set of objects: unit fractions

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

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

Differentiation:

Varied Fluency Developing Questions to support finding a fraction using known division facts to find fractions of an amount in a real life context. Using denominations divisible by 2, 5 and 10 up to 5 times the denominator. Expected Questions to support finding a fraction using known division facts to find fractions of an amount in a real life context. Using denominators divisible by 2, 3, 4, 5, 8 and 10 up to 12 times the denominator. Greater Depth Questions to support finding a fraction using known division facts to find fractions of an amount in a real life context. Using denominations divisible by 2, 3, 4, 5, 8 and 10 up to 12 times the denominator and beyond using known times tables facts including some conversions and mixed measurements.

Reasoning and Problem Solving Questions 1, 4 and 7 (Problem Solving) Developing Find the cost of item(s) that amount to a given price when finding a fraction of an amount up to 5 times the denominator using denominations of 2, 5 and 10. Expected Find the item(s) that amount to a given price when finding a fraction of an amount using denominations of 2, 3, 4, 5, 8 and 10 up to 12 times the denominator. Greater Depth Find the item(s) that amount to a given price when finding a fraction of an amount using denominations of 2, 3, 4, 5, 8 and 10 up to 12 times the denominator and beyond using known times tables facts including some conversions and mixed measurements.

Questions 2, 5 and 8 (Reasoning) Developing Find the longest distance when comparing different fractions of a distance using denominations of 2, 5 and 10. Expected Find the longest distance when comparing different fractions of a distance using denominations of 2, 3, 4, 5, 8 and 10 up to 12 times the denominator. Greater Depth Find the longest distance when comparing different fractions of an amount using denominations of 2, 3, 4, 5, 8 and 10 up to 12 times the denominator and beyond using known times tables facts including some conversions and mixed measurements.

Questions 3, 6 and 9 (Reasoning) Developing Explain which statement is correct when finding a fraction of an amount up to 5 times the denominator using denominations of 2, 5 and 10. Expected Explain which statement is correct when finding a fraction of an amount up to 12 times the denominator using denominations of 2, 3, 4, 5, 8 and 10. Greater Depth Explain which statement is correct when finding a fraction of an amount using denominations of 2, 3, 4, 5, 8 and 10 up to 12 times the denominator and beyond, using known times tables facts including some conversions and mixed measurements.

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Unit and non-unit fractions worksheets (Year 3 Fractions)

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

27 January 2020

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These ready-to-use worksheets allow teachers to provide tasks to Year 3 children on the maths topic of ‘Unit and non-unit fractions’. They form part of a series of lessons on Fractions which include coverage of the objectives: • Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10 • Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators Solve problems that involve all of the above. These worksheets are available as part of the Unit and non-unit fractions lesson pack.

The worksheets are editable, giving you the option to make any changes you feel necessary with the knowledge you have about your class and school setting.

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Amazing. I am tutoring a small group of year 3 children and this resource is perfect. Thank you so much for sharing. I will definitely start to follow you on facebook.

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