fraction problem solving year 3

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3rd Grade fraction word problems

Identifying and comparing fractions word problems.

These printable worksheets have grade 3 word problems related to identifying and/or comparing fractions. They also provide practice in simplifying fractions. Both fractions and mixed numbers are used.

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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.

Today we are going to count in fractions on a number line.

Today we are going to look at the numerator of a fraction.

Today we are going to look at two tricky words we use to describe parts of a fraction.

Divvy has a question he needs help with, comparing and ordering 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 Maths Worksheets UK Hub Page

Welcome to our Year 3 Maths Worksheets area. Here you will find links to our Year 3 Math worksheets for your child will enjoy.

Come and take a look at our multiplication pages, or money flashcards. Perhaps you would prefer our telling the time worksheets, maths games or identifying 2d and 3d shapes in the geometry section?

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• This page contains links to other Math webpages where you will find a range of activities and resources.
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Year 3 Maths Learning

Here are some of the key learning objectives for the end of Year 3:

• know and use Place value up to 1000
• Compare and order numbers up to 1000
• Counting on and back in 1s, 10s and 100s from different starting points
• Position numbers on a number line up to 1000
• know addition and subtraction facts to 20
• add or subtract 1s, 10s or 100s from a 3-digit number
• subtract 2- and 3-digit numbers in columns
• solve problems using addition and subtraction
• count from 0 in multiplies of 4, 8, 50 and 100
• recall and use multiplication and division facts from the 2, 3, 4, 5, 8 and 10 times tables
• multiply 2-digit numbers by a 1-digit number
• solve problems using multiplication and division
• count up and down in tenths
• understand tenths as decimals
• recognise and use fractions as numbers
• understand and use fractions of objects or shapes
• add and subtract amounts of money
• use £ and p notation correctly
• measure, compare, add and subtract lengths, mass and volume
• measure the perimeter of simple 2D shapes
• tell the time from an analogue clock
• convert between 12- and 24-hour clock
• measure and compare times
• Identify angles including right angles
• identify acute and obtuse angles
• identify horizontal, vertical, parallel and perpendicular lines
• recognise and draw 2D and 3D shapes
• interpret and present data in bar graphs, pictograms and tables
• solve 1-step and 2-step problems using data in tables, pictograms and graphs

Please note:

Our site is mainly based around the US Elementary school math standards.

Though the links on this page are all designed primarily for students in the US, but they are also at the correct level and standard for UK students.

The main issue is that some of the spelling is different and this site uses US spelling.

Year 3 is generally equivalent to 2nd Grade in the US.

On this page you will find link to our range of math worksheets for Year 3.

Quicklinks to Year 3 ...

• Place Value Zone
• Mental Math Zone

Word Problems Zone

Fractions zone.

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Geometry Zone

Data analysis zone.

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Coronavirus Stay At Home Support

For those parents who have found themselves unexpectedly at home with the kids and need some emergency activities for them to do, we have started to develop some Maths Grab Packs for kids in the UK.

Each pack consists of at least 10 mixed math worksheets on a variety of topics to help you keep you child occupied and learning.

The idea behind them is that they can be used out-of-the-box for some quick maths activities for your child.

They are completely FREE - take a look!

• Free Maths Grabs Packs

Place Value & Number Sense Zone

Year 3 place value charts.

Here you will find a range of Free Printable Number Charts for Years 2 & 3.

These printable charts will help your child learn to read and write numbers.

Some of the charts are partially filled to help your child learn their place value.

Using these sheets will help your child to:

• learn to count in tens and ones;
• learn to read and write numbers.
• Printable Number Charts 0-99
• Hundred Number Charts (100 Squares)
• Number Grid up to 200
• Number Grid up to 300

Place Value & Counting Worksheets

Below are our selection of Place Value, Ordering and Rounding Worksheets

Using these Year 3 Maths worksheets will help your child to:

• learn to count by hundreds, tens, fives, twos and ones;
• learn their place value to Hundreds;
• order numbers to 999.
• Place Value Models and Representations
• Place Value Worksheets 3 Digits
• Math Practice - Counting by 1s 2s 5s 10s 100s

Ordering and Rounding Worksheets (3-digits)

Once your child is confident with their place value to hundreds, they can start learning about ordering and rounding numbers.

The Year 3 Maths worksheets here will help your child learn to compare numbers to 999, and round numbers to the nearest 10.

• Ordering Numbers Worksheets up to 3-Digits

Year 3 Number Line Worksheets

The following webpages involve correctly placing numbers on a number line.

Using these Year 3 maths worksheets will help your child to:

• count by 1s 2s 5s 10s 50s and 100s;
• position numbers on a number line;
• understand place value up to 3 digits.
• Number lines up to 100 (easier)
• Number Line Worksheets 3 Digits

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Year 3 Mental Maths Zone

Here you will find a range of printable mental math sheets for Year 3 to enjoy.

Each quiz tests the children on a range of math topics from number facts and mental arithmetic to geometry, fraction and measures questions.

A great way to revise topics, or use as a weekly math test or math quiz!

• Year 3 Mental Maths Worksheets Series A
• Year 3 Mental Maths Worksheets Series B

Year 3 Addition Worksheets

• learn their addition facts to 20+20
• learn how to solve addition sums where one of the addends is missing, but the total is given;
• learn to add numbers to 999 in columns.
• Number Bonds to 20
• Math Addition Facts to 20
• 2 Digit Column Addition Without Regrouping
• 2 Digit Column Addition Worksheets With Regrouping
• 3 Digit Column Addition Worksheets

Year 3 Subtraction Worksheets

The following worksheets involve using the skills of subtracting numbers, and solving subtraction problems.

• know their subtraction facts to 20;
• know how addition and subtraction are related to each other;
• learn to do 3 digit column subtraction.
• Subtraction Facts to 20 Worksheets
• Two Digit Subtraction Worksheets Without Regrouping
• 2 Digit Subtraction Worksheets With Regrouping
• 3 Digit Subtraction Worksheets

Addition & Subtraction Worksheets

You can create your own addition and subtraction worksheets with our random generator.

All you need to do is to set your number size and let the generator do the rest!

• Addition Subtraction Fact Worksheets
• Column Addition and Subtraction Worksheets

Year 3 Multiplication Worksheets

The following worksheets involve using the Year 3 Maths skills of multiplying, and solving multiplication problems.

• learn their multiplication tables up to 5 x 5;
• understand multiplication as repeated addition;
• learn how multiplication and division are related to each other.

Online Times Table Practice

• Times Tables Online Practice Zone
• Understanding Multiplication Worksheets
• Printable Times Tables - 2 Times Table sheets
• Printable Times Tables - 3 Times Table sheets
• Times Tables for kids - 4 Times Table sheets
• Times Table Math - 5 Times Table sheets
• Learning Times Tables - 8 Times Table

Multiplication Word Problems

• Year 3 Multiplication Word Problems (2nd Grade)

Randomly Generated Multiplication Worksheets

• Times Tables Worksheets (randomly generated)

2 Digit by 1 Digit Written Multiplication

• Multiplication Worksheets for 3rd Grade 2-digits by 1-digit
• Year 3 Division Worksheets

The following worksheets involve using the skills of dividing, and solving division problems.

Using these Year 3 maths worksheets will help your child learn to:

• understand division as repeated subtraction or sharing;
• understand different models of division;
• Division Facts Worksheets (randomly generated)

Here are a range of problems solving sheets for Year 3 children. Most of the sheets contain 'real-life' problems related to animal facts.

Using the sheets will help your child to:

• apply their addition, subtraction, and multiplication skills;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems.

These sheets involve solving one or two more challenging longer problems. This link opens in a new tab.

• Year 3 Maths Challenges

These sheets involve solving many 'real-life' problems involving data.

• Year 3 Math Word Problems

These sheets involve solving a range of addition word problems within 100.

• Addition Word Problems 2nd grade

These sheets involve solving a range of subtraction word problems up to 100.

• Subtraction Word Problems 2nd grade
• 2nd Grade Addition and Subtraction Word Problems

These sheets involve solving a range of multiplication problems.

• Multiplication Word Problems Year 3

Year 3 Fraction Worksheets

• understand what a half is;
• shade in half of a shape;
• find different numbers involving 'halves' on a number line;
• find half of different numbers up to 20.
• Fraction Math Worksheets - Understanding a half
• Fraction Riddles for kids (easier)

Year 3 Geometry Worksheets

At a Year 3 level, children are introduced to a wider range of 2d and 3d shapes, and start to learn to reflect, flip and rotate shapes.

They are able to classify and sort two-dimensional shapes using different criteria, and they learn the properties of three-dimensional shapes.

The following worksheets will help your child to:

• Identify and name a range of 2d and 3d shapes;
• Draw 2d shapes;
• Know some of the properties of 2d shapes.
• Year 3 Geometry Worksheets (2nd Grade)

Symmetry Worksheets

• learn how to reflect simple shapes in a horizontal or vertical mirror line;
• learn how to reflect simple shapes in 2 mirror lines.
• Symmetry Worksheets - Block Symmetry

Measurement Zone, including Time & Money

Year 3 measurement worksheets.

These sheets involve reading scales going up in ones, fives, tens and hundreds to find the length, weight or liquid capacity.

Using these sheets will help children to consolidate their counting as well as learning to read a simple scale.

• Year 3 Measurement Worksheets (2nd Grade)

Counting Money Worksheets UK - £2, £1, 50p and 20p coins

Here you will find a selection of Counting Money sheets designed to help your child count different amounts of money using UK coins up to £2.

• count a range of coins up to £5
• compare money amounts
• apply their existing skills to puzzle out clues;
• understand money terminology;
• develop their thinking skills.

The free Year 3 Money worksheets in this section are suitable for children in Years 2 and 3.

• Free Money Worksheets UK Coins up to £1
• Year 3 Money Worksheets to £5
• Money Riddles for Kids (UK coins)
• Year 3 Money Challenges

Time Worksheets

Here are our collection of clock worksheets for Year 3. These sheets cover telling the time for quarter past and quarter to times.

• read times to the nearest 5 minutes;
• convert analogue to digital times;
• adding and subtracting hours from different times.
• Clock Worksheets - Quarter Past and Quarter To
• Telling Time to 5 Minutes Worksheets
• Add and Subtract Time Worksheets

Year 3 Bar Graph Worksheets

These sheets involve reading and interpreting a range of bar graphs and picture graphs with a scale going up in ones or twos.

Draw missing bars on a bar graph to the correct height.

Use the information in a bar graph to add data into a table.

Using the link below will open the 2nd grade Math Salamanders website in a new browser window.

• Year 3 Bar Graphs (2nd Grade)

Fun Zone: Puzzles, Games and Riddles

Year 3 math games.

All children like to play Math games, and you will find a good range of 2nd Grade Math Games here for your child to play and enjoy.

The following games involve different Second Grade Math activities which you and your child can enjoy together.

• Year 3 Math Games (2nd Grade)
• Year 3 Maths Puzzles

The puzzles will help your child practice and apply their addition, subtraction and multiplication facts as well as developing their thinking and reasoning skills in a fun and engaging way.

The Number Square Puzzles page will open a new browser window which will take you to the 2nd grade math salamanders website.

Using these puzzles will help your child to:

• learn their addition facts to 20+20;
• learn and practice subtraction facts to 20;
• pratice multiplying up to 5x5;
• develop thinking and reasoning skills;
• develop perseverance.
• Number Square Puzzles
• Math Puzzles at 2nd Grade Math Salamanders

Math Salamanders Year 3 Maths Games Ebook

Our Year 3 Maths Games Ebook contains all of our fun maths games, complete with instructions and resources.

This ebooklet is available in our store, use the link below to find out more!

• Year 3 Maths Games Ebook

Help & Support

Looking for a resource which is not here.

Take a look at our 2nd Grade Math Salamanders website.

On this site you will find a wider selection of Year 3 maths worksheets and free math resources.

• 2nd Grade Math Salamanders

Other UK Maths Worksheet pages

See below for our other maths worksheets hub pages designed for children in the UK.

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Year 3 – Fractions

Welcome to Year 3 Fractions, Decimals and Percentages at Primary Maths Hub. Here you will find a growing library of outstanding resources and activities to support  Fractions, Decimals and Percentages  lessons in Year 3 and at home.  

If there’s a resource you’d like to see here, just visit our ‘Request a Resource’ page and Primary Maths Hub will create the resource and add it to the site.

Do Now Tasks / Starters

Fraction Addition Do Now Tasks

Differentiated question sets.

Fraction of a Number Question Set

Adding Fractions Question Set

Subtracting Fractions Question Set 

Adding and Subtracting Fractions Question Set 

Understanding fractions.

Strips-  Understand One Half

Strips-  Understand One Quarter

Strips-  Understand One Third

Strips-  Understand One Fifth

Understand Numerator

Understand Numerator 

Understand the Numerators of Non-Unit Fractions Reasoning 

Partition the Whole- Shaded and Unshaded 

Fractions of a number.

Find Unit Fraction of Objects

Find Unit Fraction of Shapes

Find Unit Fraction of Numbers

Fading Scaffolding Strips- Find Non-Unit Fractions of Numbers

Fading Scaffolding Strips- Find Unit Fractions of Numbers

Add fractions.

Strips-  Add Fractions with the Same Denominator

Fading Scaffolding Strips- Add Fractions with the Same Denominator

Subtract fractions.

Strips-  Subtract Fractions with the Same Denominator

Fading Scaffolding Strips- Subtract Fractions with the Same Denominator

Mixed add and subtract fractions.

Strips- Add and Subtract Fractions with the Same Denominator

Counting Forwards and Backwards in Tenths

Ordering fractions.

Fading Scaffolding Strips- Order Unit Fractions

Compare fractions.

Faded Scaffolding Strips- Compare Unit Fractions

Compare Unit Fractions

Faded Scaffolding Strips- Compare Fractions With the Same Denomintator

Decimal sequences.

Fading Scaffolding Strips- Decreasing Decimal Sequences- Missing Values

Fading Scaffolding Strips- Decreasing Decimal Sequences- Next 2 Values

Fading Scaffolding Strips- Increasing and decreasing Decimal Sequences- Missing Values

Fading Scaffolding Strips- Increasing and Decreasing Decimal Sequences- Next 2 Values

Fading Scaffolding Strips- Increasing Decimal Sequences- Missing Values

Fading Scaffolding Strips- Increasing Decimal Sequences- Next 2 Values

Equality and inequality statements.

Equality and Inequality Statement Matching- Comparing Fractions

Adding and Subtracting (Eighths)- Equality and Inequality Statement Matching 

Equality and Inequality Statement Matching- Unit Fractions of Numbers 

Understand Denominator – Reasoning

Add Fractions Reasoning 

Subtract Fractions Reasoning 

Round 2-Digit to the Nearest 10 Reasoning 

Round 3-digit to the nearest 10 reasoning , word problems and challenges.

Adding and Subtracting From the Whole Word Problems

Add and Subtract Fractions With the Same Denominator Word Problems

Steps to success.

Add Fractions- Steps to Success 

Compare Non-Unit Fractions- Steps to Success 

Compare Unit Fractions- Steps to Success 

Find a Non-Unit Fraction of an Amount- Steps to Success 

Find a Unit Fraction of an Amount- Steps to Success 

Identify Fractions on a Number Line- Steps to Success 

Order Non-Unit Fractions- Steps to Success 

Order Unit Fractions- Steps to Success 

Subtract Fractions- Steps to Success 

Understand the Numerator- Steps to Success

Understand the Whole- Steps to Success 

Resources to support fractions, decimals and percentages.

Fading Scaffolding Strips- Times Tables as Fraction

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Year 3 Fractions

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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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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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20 Word Problems For Year 3: Develop Their Problem Solving Skills Across Single and Mixed KS2 Topics

Emma Johnson

Word problems for Year 3 are an important tool for improving number fluency. The key focus in maths in Year 3 of primary school is on ensuring pupils are becoming more fluent with number facts and the concept of place value. Children are starting to develop more efficient written methods by this stage and are beginning to carry out calculations with increasingly larger whole numbers.

As children progress through school, they are exposed to a wider variety of problem solving questions covering a range of concepts. In Year 3 maths these include the four operations, fractions, measures and statistics.  

It is important that children are regularly exposed to reasoning and problem solving questions, alongside the fluency work each lesson. It is also important to remember that all children need exposure to reasoning and problem solving questions, not just the higher attaining pupils who finish quickest.

We have put together a collection of 20 word problems, aimed at Year 3 pupils.

Years 3 to 6 Rapid Reasoning (Weeks 1-6)

Download this free pack of word problems to improve your class' problem solving skills. Includes questions for Years 3 - 6.

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In Year 3, pupils focus on one-step problems, covering a range of topics across the National Curriculum. At this stage the majority of word problems pupils are tackling will have one-step, but they may also start to be introduced to simple two-step word problems. Here is a breakdown of topics that will be covered and expectations in Year 3. 

Solve number problems and practical problems involving recognising the place value of each digit of a 3-digit number; comparing and ordering numbers up to 1000 and identifying, representing and estimating numbers using different representations.

Solve problems, including missing number problems, using number facts, place value and more complex addition and subtraction word problems .

Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems

 Solve problems involving counting in tenths; recognising unit and non-unit fractions; recognising equivalent fractions and adding/ subtracting fractions with the same denominator.

Solve problems involving length, volume and mass; adding and subtracting within money word problems ; perimeter and problems involving time.

Solve-step and two-step questions (For example, ‘How many more?’ and ‘How many fewer’?) using information presented in scaled bar charts, pictograms and tables.

By Year 3, children are starting to learn how to use some of the formal written methods of addition and subtraction. It is important that the link between maths in school and maths in real-life continues to be made. Word problems are a key element in helping pupils to make this link. 

When teaching maths problems to Year 3, it’s important to think of ways to make them fun, engaging and something the children are able to relate to. This might include acting out the problem, using concrete resources and providing visual images, to bring the problems to life. 

Benefits of pairs, groups and class discussion 

Children should have plenty of opportunity to talk in pairs, groups and as a whole class, to share their understanding of what is being asked and their strategies for solving the problem. As with Key Stage One, the use of manipulatives is important and all children should have access to a range of maths resources when solving problems like this.

Pupils need to be encouraged to read word problems carefully and to make sure they understand what is being asked, before attempting to tackle the problem. This is where the use of a partner and group discussion can really help children’s understanding. Students then need to think about what they already know and how they can use this to help them answer the question. Where appropriate, pupils should also be encouraged to draw diagrams and pictures to help them solve the question.

Here is an example:

Mason needs 4 apples to make an apple pie.

If he has 28 apples. How many apple pies can he make?

How to solve:

What do you already know?

• We know 4 apples are needed to make an apple pie.
• We are told how many apples Mason has in total, so we must have to divide the total number by 4.
• In year 3, children should be building confidence with multiplication and division facts for the 4 times table, so some will be able to quickly recall these facts to solve the problem.
• Children who aren’t apple to recall quickly could use counters to represent the apples, or draw a bar model to help solve it.

How can this be drawn/represented pictorially?

We can draw a bar model or counters to represent this problem:

• To calculate how pies the 28 apples will make, we can either use or draw 28 counters and put them into groups of 4. We can see that 28 counters will make 7 groups of 4.
• Using the bar model, we can keep adding 4 to the bar until we reach 28. From the bar we can see that 7 x 4 = 28.
• 7 apple pies can be made from the 28 apple pies that Mason has.

In Year 3, pupils are exposed to a range of addition word problems , including problems involving mental addition and addition of up to 3-digits using formal written methods.

See also: Mental maths Year 3

Addition question 1

A family driving on holiday, travel 146 miles from home to the first service station.

They then drive a further 175 miles to reach their destination.

How far have they travelled altogether?

Answer (1 mark): 321 miles

146 + 175 = 321

Addition question 2

Evie is buying a bottle of drink from a vending machine. She has put in 40p. The vending machine shows she still needs to put in £1.25. 

How much is the bottle of drink?

Answer (1 mark): £1.65

125p + 40p = 165p

Addition question 3

Jamie scored 643 on his new online game.

Jared scored 468.

How many points did they score between them?

Answer (1 mark): 1111 points

643 + 468 = 1111

At Third Space Learning we often tie word problems into our one-to-one online tuition. With each programme personalised to the needs of each individual student, children are able to develop their problem solving skills, maths fluency and grow confidence in maths.

Subtraction word problems in Year 3 also need to comprise of a combination of mental calculation questions and those involving formal written subtraction up to 3-digits. Children should also be starting to estimate answers and check their calculations by using the inverse.

Subtraction question 1

Ahmed collects 374 stickers.

He needs 526 stickers to fill his sticker album.

How many more stickers does he need to collect?

Answer (1 mark): 152 stickers

526 – 374 = 152

Subtraction question 2

 A bag of carrots weigh 360g

A bag of tomatoes weighs 235g.

How much heavier is the bag of carrots?

Answer (1 mark): 125g

360 – 235 = 125

Subtraction question 3

 Ahmed buys a bag of sweets for £1.45.

He has a £2 coin. How much change will he get?

Answer (1 mark): 55p

200 – 145 or count up from £1.45 to £2

By the end of Year 3, pupils should be able to recall and use multiplication facts for the 3, 4 and 8 times table. They should also be starting to progress to using the formal written method for solving multiplication word problems involving 2 digits multiplied by a 1-digit number. 

Multiplication question 1

It costs £7 for a cinema ticket

Amber’s mum pays for Amber and her 3 friends. 

How much does she pay for all the tickets?

Answer (1 mark): £28

7 x 4 = 28 

Multiplication question 2

5 mini buses are used to take Year 3 pupils on a school trip.

Each minibus transports 15 children.

How many children go on the school trip?

Answer (1 mark): 75 children

15 x 5 = 75

Multiplication question 3

There are 24 questions on a word problems worksheet. 

A group of 8 children each complete the worksheet.

How many questions will the teacher be marking?

Answer (1 mark): 112 questions

24 x 8 = 112

In Year 3, pupils will need to learn the division facts for the 3, 4 and 8 multiplication tables. At this stage, pupils are required to learn the formal method for division, division word problems will involve mainly mental calculations.

Division question 1

6 children share 18 cookies between them. 

How many cookies does each child get?

 Answer (1 mark): 3 cookies

Division question 2

The school choir needs to travel to the concert hall.

There are 32 children in the choir and parents have been asked to help transport the children.

Each parent is able to take 4 children in their car. How many cars will be needed to get all the children to the concert?

Answer (1 mark): 8 cars

 32 ÷ 4 = 8

Division question 3

 Cakes come in packs of 4.

If Jessica needs 36 cakes for her party, how many packs does she need to buy?

Answer (1 mark): 9 packs

In Year 3 pupils are exposed to a range of fraction word problems , including questions involving counting up and down in tenths; equivalent fractions and adding/subtracting fractions with the same denominator.

Fraction question 1

Jude had 28 sweets.

He gave \frac{1}{4} of his sweets to his little sister.

How many did he have left?

Answer (1 mark): 21 sweets

\frac{1}{4} of 28 = 7

\frac{3}{4} of 28 = 21 or 28 – 7 = 21

Fraction question 2

Khalifa ate \frac{2}{8} of the chocolate bar and Abdulrahman ate \frac{3}{8} of it.

How much chocolate did they have left?

Answer (1 mark): \frac{3}{8}

\frac{2}{8} + \frac{3}{8} = \frac{5}{8} eaten

\frac{8}{8} – \frac{5}{8} = \frac{3}{8}

Fraction question 3

 Molly ate half of a pizza and Rosie ate \frac{3}{6} .

Who ate the most?

Answer (1 mark): They both ate the same amount

\frac{3}{6} is equivalent to \frac{1}{2} .

In Year 3 time word problems may be incorporated into maths problem solving. Students are expected to know time vocabulary, be able to compare time in terms of seconds, minutes and hours and know how many seconds are in a minute and minutes are in an hour. 

Time question 1

The Smith family are driving to the beach.

They leave at 9:05am and arrive at 9:50am.

How long does the journey take them?

Answer (1 mark): 45 minutes

50 – 5 = 45    or     count up from 9:05 to 9:50 = 45 

Time question 2

Holly puts her cake in the oven at 4:22pm and takes it out again at 4:47. 

How long is the cake baking for?

Answer (1 mark): 25 minutes

47 – 22 = 25    or   count up from 4:22 to 4:47

When children first move into lower Key Stage 2, word problems are predominantly one-step. As they become more confident they can be exposed to more word problems, requiring a second step or multi-step word problems .

Multi-step question 1

Oliver had 3 bags of sweets.

Each bag contained 15 sweets.

If he shared the sweets between him and 4 friends, how many sweets would they all 5 of them get?

Answer (2 marks): 9 sweets

3 x 15 = 45 

45  ÷ 5 = 9

Multi-step question 2

A teacher photocopies 95 maths worksheets and 80 English worksheets in one week.

Teachers can print a maximum of 300 worksheets per week. 

How many can the teacher print for other subjects.

Answer (2 marks): 125 worksheets

 95 + 80 = 175

300 – 175 = 125

Multi-step question 3

Three friends go trick or treating. They add all their sweets together and share them out, so they all have an equal number of sweets.

If Ben gets 34 sweets, Sophie gets 28 and Maisie gets 22 sweets. How many will they each get, once they have put them together and shared them out?

Answer (2 marks): 28 sweets each

34 + 28 + 22 = 84 sweets

84  ÷ 3 = 28

We hope that this collection of word problems for Year 3 becomes a useful resource in your Year 3 maths classroom. For more Year 3 maths resources, take a look at our library of Year 3 maths worksheets .

Third Space Learning also offers a wide array of maths and word problems resources for other year groups such as word problems for year 6 , word problems for Year 5 and word problems for year 4 . Our practice word problems cover all four operations and include more specific topics such as percentage word problems and ratio word problems .

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Fractions KS2

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

Fraction Match

A task which depends on members of the group noticing the needs of others and responding.

Bryony's Triangle

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

A4 Fraction Subtraction

This task offers opportunities to subtract fractions using A4 paper.

Matching Fractions

Can you find different ways of showing the same fraction? Try this matching game and see.

Round the Dice Decimals 2

What happens when you round these numbers to the nearest whole number?

Fractional Wall

Using the picture of the fraction wall, can you find equivalent fractions?

Would You Rather?

Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?

Round the Dice Decimals 1

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Tumbling Down

Watch this animation. What do you see? Can you explain why this happens?

Linked Chains

Can you find ways to make twenty-link chains from these smaller chains? This gives opportunities for different approaches.

Fractional Triangles

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

A4 Fraction Addition

Try adding fractions using A4 paper.

Forgot the Numbers

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

Andy's Marbles

Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.

More Fraction Bars

What fraction of the black bar are the other bars? Have a go at this challenging task!

Fractions in a Box

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Extending Fraction Bars

Can you compare these bars with each other and express their lengths as fractions of the black bar?

Route Product

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

Fraction Lengths

Can you find combinations of strips of paper which equal the length of the black strip? If the length of the black is 1, how could you write the sum of the strips?

Light Blue - Dark Blue

Investigate the successive areas of light blue in these diagrams.

Matching Fractions, Decimals and Percentages

Can you match pairs of fractions, decimals and percentages, and beat your previous scores?

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

Doughnut Percents

A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.