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28 Fraction Word Problems for Year 2 to Year 6 With Tips On Supporting Pupils’ Progress

Emma Johnson

Fraction word problems are an important piece in teaching fractions. Fractions are a key component of the National Curriculum throughout primary, with children introduced to the concept in Year 1 and continuously building upon their knowledge and understanding, through to Year 6 and beyond.

The abstract nature of fractions makes them one of the more difficult areas of maths for children to understand. It is essential that they are taught through the use of concrete resources and visual images, but also through a link to the real world. Word problems are a great way to help children develop this understanding and should be used alongside any fluency work the children do.

To help you with this, we have put together a collection of 20 word problems which can be used with children from Year 2 to Year 6.

Fraction word problems in the national curriculum

• Why are word problems important for children’s understanding of fractions?

How to teach fraction word problem solving in primary school

Fraction word problems for primary , fraction word problems for year 2, fraction word problems for year 3, fraction word problems for year 4, fraction word problems for year 5, fraction word problems for year 6, more word problems resources.

Fraction Lessons Resource Pack

Download this free pack of fraction lessons to support your students and help them to practice fractions problems.

Fractions in KS1

Pupils are first introduced to fractions in Year 1, where they begin to recognise a half and quarter of a shape or quantity. As they progress through Key Stage 1, they are introduced to a wider range of fractions.

In Year 2 pupils need to be able to recognise, find, name and write fractions \frac{1}{3}, \ \frac{1}{4}, \ \frac{2}{4} and \frac{3}{4} of lengths, shape, a set of objects or quantity.

Fractions in lower KS2

Once pupils move into Key Stage 2, there is an increased focus on fractions, with a significant period of time dedicated to developing students’ knowledge and building on previous learning from Year 3 through to Year 6.

In Year 3, pupils are taught to count in tenths; recognise, find and write fractions of a discrete set of objects; understand the term ‘unit’ and ‘non-unit’ fractions; recognise equivalent fractions, compare and order fractions and add/subtract fractions with the same denominator. At this stage, pupils also begin to solve simple problems involving fractions.

As pupils progress into Year 4, they are also introduced to the concept of decimals alongside the work on fractions. They build upon their understanding of equivalent fractions and adding/ subtracting fractions (still with the same denominator.

They also learn to count up and down in hundredths, recognise and write decimals equivalent to \frac{1}{4}, \ \frac{1}{2} and \frac{3}{4} and begin to solve problems with increasingly harder fractions.

Fractions in upper KS2

As pupils continue through the school, into upper Key Stage 2, they continue to build on their learning. They are introduced to mixed numbers and improper fractions. They are also introduced to the concept of percentages alongside fractions and decimals.

In Year 5, children build on the knowledge gained in Year 4, comparing and ordering fractions; recognising equivalent fractions; addition and subtraction of fractions (with different denominators, but multiples of the same number). Fractions appear in addition and subtraction word problems .

They are also introduced to the multiplication of fractions; converting between improper fractions and mixed numbers and the link between fractions, decimals and percentages. By Year 5 pupils will be completing more complex problems, including multi-step word problems and multiplication word problems .

In Year 6, pupils consolidate and build upon the knowledge of fractions they have gained so far. Pupils continue to add and subtract fractions (with different denominators and mixed numbers). They also develop their understanding of how to multiply fractions and begin to divide fractions by whole numbers, combining fraction and division word problems .

Pupils also continue to build upon their understanding of the equivalences between fractions, decimals and percentages and solve increasingly complex one-step, two-step and multi-step percentage word problems .

Why are word problems important for children’s understanding of fractions?

Word problems, alongside the use of concrete resources and visual images, help children to make sense of the abstract nature of fractions. 

For example, if children were presented with the question \frac{6}{8} ÷ 3, some might find this difficult to access. If children are given it as a word problem, alongside a visual image, it becomes much more accessible.

The above calculation as a word problem :

 ‘3 children shared \ \it{\frac{6}{8}} of a pizza, how much did each child get?’

Children can see and understand the concept of 3 children sharing 6 slices of pizza, compared to just seeing the written calculation.

As with all word problems, the first thing children need to do is read the question carefully and make sure they understand what is being asked. They then have to decide what calculation is needed and whether they can represent it pictorially.

Here is an example:

Ben has a bag of 48 sweets.

He gives \frac{3}{8} of his bag to his brother

How many sweets does he have left?

How to solve:

What do you already know?

• There are 48 sweets altogether. 
• The denominator is 8, so we know we need to divide the 48 by 8. This will tell us how many sweets in \frac{1}{8} .
• The numerator is 3, therefore we need to multiply the answer by 3, to tell us how many sweets are \frac{3}{8} .
• The last step of the problem is to find out how many sweets Ben has left.
• We can either calculate \frac{5}{8} , as we know Ben must have \frac{5}{8} left, or we subtract the number of sweets in \frac{3}{8} from the total of 48.

How can this be drawn/represented pictorially?

• We can draw a bar model, split into 8 sections. 
• The 48 sweets are then shared between the 8 sections (each worth \frac{1}{8} ). 
• We can see that \frac{3}{8} of the 48 sweets equals 18 sweets. 
• We can then either subtract 18 from 48, to work out how many sweets were left. 48 – 18 = 30
• Alternatively, we can calculate how many sweets are in \frac{5}{8} , which is 30.

Word problems are tied in throughout Third Space Learning’s online one-to-one tuition programmes. Tutors work with students to break down word problems and identify the operations needed to solve problems.

The following section lays out the types of fraction word problems that you can expect to see by year group in primary school. 

At Third Space Learning we incorporate word problems into our one-to-one online tutoring . With each lesson designed to suit the needs of each individual student, our tutoring programme aims to deepen mathematical understanding and confidence in maths. 

Fraction word problems are a great way to strengthen students’ conceptual understanding of fractions and grow their problem solving skills. Take a look at our article on fraction games to help with this.

• What Is A Unit Fraction: Explain For Primary School
• What Is An Improper Fraction: Explained For Primary School
• Fractions: A Comprehensive Guide
• How To Teach Fractions Key Stage 2: Maths Bootcamp
• How To Simplify Fractions: A Comprehensive Guide

Word problems in Year 2 involve recognising and naming simple fractions and beginning to understand the concept of equivalence.

Maisie was having a birthday party.

She invited 16 friends. Half of her friends were from her class and a half were from the other Year 2 class. 

How many friends did she invite from each class?

Answer: 8 friends

\frac{1}{2} of 16 = 8

Ahmed baked 12 cookies. 

He ate \frac{1}{4} of them.

How many cookies did Ahmed eat?

\frac{1}{4} of 12 = 3

Sara says ‘I ate \frac{1}{2} a pizza and my friend ate \frac{2}{4} . My friend had more than me, as she had 2 pieces’.

Is she correct? Explain why you have chosen your answer.

Answer: Sara is not correct

\frac{1}{2} is the same as \frac{2}{4}

Tom and Zeyn shared a chocolate bar.

They both had a quarter of the chocolate bar. 

How much was left?

Answer : \frac{1}{2} of the chocolate bar

\frac{2}{4} are equivalent to \frac{1}{2}

Word problems for Year 3 include proper fractions, fractions of amounts, simple equivalent fractions and adding and subtracting fractions with the same denominator. 

Sophie ate \frac{1}{4} of her chocolate bar. 

If the bar had 20 squares, how many squares did Sophie eat?

Answer : 5 squares

\frac{1}{4} of 20 = 20 ÷ 4 = 5

Hamza and Khalifa shared a pizza.

Hamza ate two fourths of the pizza and Khalifa ate one fourth.

How much pizza was left?

Answer : \frac{1}{4}

There are 24 hours in a day.

Maise worked out that she spends \frac{1}{8} of her day on Saturday, doing exercise.

How long does she spend exercising on a Saturday?

Answer: 3 hours

\frac{1}{8} of 24 hours = 24 ÷ 8 = 3

There are 30 children in the class.

\frac{2}{5} of the children are wearing jumpers.

How many children are wearing jumpers?

Answer: 12 children

\frac{1}{5} of 30 = 30 ÷ 5 = 6

\frac{2}{5} of 20 = 12

Word problems for year 4 include equivalent fractions, fractions of quantities (including non-unit fractions and adding/subtracting fractions with the same denominator. Money word problems often appear in Year 4.

Abdullah spent \frac{1}{3} of his pocket money for the month on a new game.

He receives £18 per month.

How much did he spend on the game?

Answer : £6

\frac{1}{3} of 18 = £6

Bethan had a bag of sweets.

She gave \frac{2}{7} of the bag to her mum and ate \frac{3}{7} of herself.

What fraction of the bag was left?

Answer : \frac{2}{7}

Jamal ate \frac{6}{18} of a chocolate bar.

Mason ate \frac{1}{3}

Mason said that Jamal ate more than him. Do you agree? Explain your answer.

Answer : No – they both ate the same.

\frac{1}{3} is equivalent to \frac{6}{18}

\frac{2}{7} of a piece of ribbon is 10cm.

How long is the whole piece of ribbon?

Answer: 35cm

\frac{2}{7} = 10

\frac{1}{7} = 5

\frac{7}{7} = 5 x 7 = 35

Word problems for Year 5 include more complex equivalent fractions, problems involving mixed numbers and improper fractions, adding and subtracting fractions (with different denominators) and multiplying fractions.

There are 60 pupils in Year 5.

Eden carried out a survey on favourite foods.

\frac{1}{5} of the children said pizza, \frac{2}{6} said burgers and \frac{3}{10} said hot dogs.

How many pupils did she survey altogether?

Answer: 50 pupils

\frac{1}{5} of 60 = 12

\frac{2}{6} 0f 60 = 20

\frac{3}{10} = 18

The Johnson family are driving to the zoo.

They have driven \frac{5}{9} of their journey, which is 45 miles.

How much further do they have to drive, to reach their holiday home?

Answer: 20 miles left to drive

\frac{5}{9} = 45, therefore \frac{1}{9} = 45 ÷ 9 = 5. 

\frac{5}{9} = 5 x 5 = 25 miles

\frac{9}{9} = 9 x 5 = 45 miles

45 – 25 = 20

Macy is taking part in the school maths challenge. 

She is given a word problems worksheet containing 36 questions.

Macy gets \frac{7}{9} of the questions correct.

How many does she get wrong?

Answer: 8 questions wrong

\frac{1}{9} of 36 = 4

\frac{7}{9} = 28

\frac{2}{9} = 8

Oliver and Zac are making smoothies.

They make 800 ml of smoothies.

\frac{2}{5} is made from apples, \frac{3}{7} from strawberries and the rest from orange juice.

How many ml of orange juice do they add to the apples and strawberries?

Answer: 180ml orange juice

\frac{2}{5} of 800: \frac{1}{5} = 160ml, \frac{2}{5} = 320 ml apple juice

\frac{3}{8} of 800: \frac{1}{8} = 100, \frac{3}{8} = 300 ml strawberry juice

800 – 620 = 180ml 

Word problems for year 6 include adding and subtracting fractions with different denominators and mixed numbers, multiplying fractions, dividing fractions by whole numbers and finding equivalent fractions, decimals and percentages.

Children in a Year 6 Class at Oak Tree Middle School are answering a set of ratio questions. 

There are 10 questions and 28 children completing the activity. 

If the children got \frac{6}{7} of the total number of questions correct between them. 

How many did they get wrong?

Answer: 40 questions wrong

28 x 10 = 280 questions

\frac{1}{7} of 280 = 40 

\frac{6}{7} = 40 x 6 = 240

Amber and her 5 friends are sharing 4 pizzas for her birthday party.

The pizzas are split into sixths. 

If they each eat the same amount of pizza, how many slices does each person at the party get?

Answer: 4 slices

This is a dividing fractions word problem

\frac{24}{6} ÷ 6 = \frac{4}{6}

A group of friends win a quarter of the total lottery prize for the week.

There are 4 friends and each friend shares an equal fraction of the quarter.

What fraction of the total lottery prize does each friend get?

Answer: \frac{1}{16} of the prize fund

Each friend gets \frac{1}{4} of the \frac{1}{4} prize fund

There are 30 children in the class

\frac{7}{10} of the pupils in the class are girls.

\frac{3}{7} of the girls have their ears pierced.

How many girls have their ears pierced?

Answer: 9 girls have their ears pierced

\frac{1}{10} = 3, \ \frac{7}{10} = 21 girls

\frac{1}{7} of 21 = 3. \ \frac{3}{7} = 3 x 3 = 9

Third Space Learning offers a wide range of practice word problems for all primary year groups and covering a large number of topics, including; time word problems , ratio word problems , fraction questions , addition word problems and subtraction word problems .

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Year 2 - Number

Standard 2.NS.1.4 - Identify the fraction of an object in a word problem.

Included Skills:

Number - fractions • Pupils should be taught to: - recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity - write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2.

If you notice any problems, please let us know .

Free Printable Fraction Word Problems Worksheets for 2nd Year

Fraction Word Problems: Discover a collection of free printable worksheets for Year 2 math teachers, focusing on developing students' understanding of fractions through engaging word problems.

Explore Fraction Word Problems Worksheets by Grades

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Explore printable Fraction Word Problems worksheets for 2nd Year

Fraction Word Problems worksheets for Year 2 are an essential tool for teachers to help their students develop a strong foundation in math, particularly in understanding and solving problems involving fractions. These worksheets provide a variety of engaging and challenging math word problems that are specifically designed for second-grade students. By incorporating these worksheets into their lesson plans, teachers can effectively teach the concept of fractions and their applications in real-life situations. Furthermore, these worksheets are designed to cater to different learning styles, ensuring that every student can grasp the concept of fractions and improve their overall math skills. With the help of Fraction Word Problems worksheets for Year 2, teachers can create a fun and interactive learning environment that fosters a love for math in their students.

Quizizz is an excellent platform that offers a wide range of resources for teachers, including Fraction Word Problems worksheets for Year 2, Math quizzes, and other engaging activities. This platform allows teachers to create customized quizzes and games that align with their lesson plans, making it easier for them to assess their students' understanding of various math concepts. In addition to worksheets, Quizizz also offers a variety of Math Word Problems that can be used to supplement classroom instruction and provide additional practice for students. Teachers can easily track their students' progress and identify areas where they may need extra support. By utilizing Quizizz and its vast array of resources, teachers can create a comprehensive and engaging learning experience that helps their second-grade students excel in math.

Write simple fractions and recognise equivalences

Your child will use objects to find:

• Halves by sharing equally between two groups.
• Thirds by sharing equally between three groups.
• Quarters by sharing equally between four groups.

They will also be expected to write out fractions in simple calculations. This will help them to understand the connection between fractions and division. For example:

 of 6 = 3 6 ÷ 2 = 3    of 12 = 4 12 ÷ 3 = 4

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. Exploring fractions of quantities

Try sharing objects equally to find fractions of amounts. You could do this by using things around the house – for example, grapes, buttons, beads, or pieces of dried pasta… the options are endless!

• Halves . Find 12 of the same type of object and ask your child to find half. Ask them how many are in each group and help them see that half of 12 is 6 because there are 6 objects in each group.
• Quarters . Once you’ve explored halves, you could find a quarter of the 12 objects. Show your child that you can do this by sharing the objects into four equal groups or by finding half and then half again.
• Thirds . Now see if your child can share the objects into three equal groups. How many are in each group? Try finding three quarters and then two thirds of the 12 objects.

See if your child understands that two quarters is equivalent to one half, and that four quarters is equivalent to the whole. Help them understand that finding a half is   equivalent   to dividing by 2, finding a quarter is equivalent to dividing by 4, and finding a third is equivalent to dividing by 3.

2. Fractions of shapes

If your child enjoys drawing and crafts, use paper, pens, and scissors to show them how fractions work. Together, draw simple shapes like squares, triangles, or circles. You will need to ensure they are quite even and exact – drawing around things can help with this.

Cut out the shapes and then fold them to find halves, thirds, and quarters of the shapes. Can the shape be folded into two, three, or four equal parts? There are lots of ways you can use these shapes to explore fractions. For example:

Show your child a square and ask them how they would find half of the shape. They may fold the shape in half to see if there are two equal parts. Ask them to show you one half. What shape is the half?   Investigate how many different ways a shape can be folded in half. For instance, you could fold a square diagonally to create triangular shapes. Find different ways to make a quarter of a shape or a third of a shape.

3. Writing fractions

Help your child start writing fractions using mathematical symbols. The number at the bottom is called the denominator  and the number at the top is called the numerator . The denominator tells us how many equal parts we are dividing into. The numerator tells us how many of the equal parts we are looking for.

You could play a game where children match the written fraction to an image of the fraction. For example:

4. Fractions as numbers in their own right

Your child needs to understand that a fraction is also a number in its own right. You can help your child with this concept using number lines.

You could show your child a number line as shown below. Ask them to show where a half would go on the number line. Help them to understand that a half is directly in the middle of 0 and 1.

Similarly, your child will need to be able to find a quarter, three-quarters and a third on a number line, as shown below:

5. Counting in fractional steps

Encourage your child to begin counting in halves, quarters, and thirds using objects and number lines to help. For example, cut pieces of fruit into three equal pieces and count in thirds: ⅓, ⅔, 1, 1 ⅓, 1 ⅔, and so on.

This will reinforce the idea that fractions are numbers, and will show how they can add up to more than one. Number lines and images can also represent fractions and help you count in thirds. For example:

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Fractions - Year 2 - Free Worksheets - Unit Fractions

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

9 September 2020

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This resource contains two worksheets on unit fractions for Year 2 pupils.

You may also be interested in:

Year 2 Fractions - Set of 24 Worksheets - Thirds, Unit Fractions, Non-Unit Fractions

This resource contains 24 worksheets / workbook (with answers and progress check) of mastery maths resources to support the delivery of the Year 2 Fractions - Block 4 - Spring Term White Rose (WRM) ‘small steps’ programme. These resources are for Week 9 and contain the second set of three sets of worksheets on Year 2 Fractions.

The worksheets contain tasks (concrete, pictorial and abstract) linked to the White Rose small steps with an emphasis on the mastery approach to learning advocated by the White Rose scheme and include reasoning and problem-solving tasks.

The resources focus on the following objectives and small steps:

Year 2 Maths National Curriculum Objectives

Recognise, find, name and write fractions of a length, shape, set of objects or quantity.

White Rose Small Steps

Find a third Unit fractions Non-unit fractions

Year 2 Fractions - Set 1 Halves and Quarters - Set of 24 Worksheets

Year 2 Fractions - Halves and Quarters PowerPoint Lesson

Save money and buy both the PowerPoint lesson and the worksheets in a bundle at a discounted rate:

Year 2 Fractions - PowerPoint Lesson and Worksheets

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Year 2: Fractions

New Maths Curriculum (2014): Year 2 objectives.

Pupils should use additional fractions as operators on discrete and continuous quantities by solving problems using shapes, objects and quantities. They connect unit fractions to equal sharing and grouping, to numbers when they can be calculated, and to measures, finding fractions of lengths, quantity, a set of objects or shapes. They meet 3/4 as the first example of a non-unit fraction. 

Pupils should count in fractions up to 10, starting from any number and using the 1/2 and 2/4 equivalence on the number line (e.g. 11/4, 12/4 , (or 11/2), 13/4, 2). This reinforces the concept of fractions as numbers and that they can add up to more than one. 

Recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity

Write simple fractions e.g. 1/2 of 6 = 3 and recognise the equivalence of two quarters and one half.

Year 2 | Problem Solving With Fractions Worksheets

Year 2 fractions maths mastery resources

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Aligned with the maths mastery approach, these Year 2 | Problem Solving With Fractions Worksheets  are designed to save you time whilst delivering high quality learning experiences for children.

Topic: Number – Fractions

Combine with our lesson plan, maths worksheets, activity cards and revision mat for a complete maths lesson, complete with National Curriculum links, vocabulary, TAF statements, small steps, differentiation and ready to progress criteria.

Explore our year 2 spring block 4 resources.

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Fraction Worksheets for Year 2 (age 6-7)

Children should come into Year 2 (age 6-7) being able to recognise halves and quarters and knowing that a half is one of two equal parts of an object, shape or quantity and a quarter is one of four equal parts.

In Year 2 this knowledge is developed to include recognising one third, two thirds, two quarters and three quarters of shapes, sets of objects, quantities and lengths.

Finding fractions of shapes can involve shading in or cutting out certain amounts of a shape e.g. shading two thirds of a rectangle. The important concept here is that the fractions must be of equal size.

Finding fractions of sets of objects is usually done on a practical basis e.g. take 12 bricks and sort them into three equal piles – each pile is one third of the total number of bricks. This can also be done pictorially and strengthens the link between finding fractions and division.

Finding fractions of quantities means finding a fraction of a number e.g. find a third of 6. This is a development from using shapes and objects and should only be done when children are confident with working with objects to find fractions.

A key aspect of fractions is recognising equivalence. Put simply this is the understanding that a half is equivalent to, or the same as two quarters, and that four quarters is equivalent to one whole one.

Another important aspect of work with fractions in Year 2 is counting in halves and quarters.

By the end of the year children should be familiar with terms such as part, fraction, three quarters, one third and two thirds and be able to write these fractions in both words and numbers.

Whilst we recommend that much of the fractions work in Year 2 should be practical in nature we have plenty of written material to reinforce the practical work. Why not take a look now?

Once all this has been achieved children will be ready to move onto Year 3 work when much more is done on equivalent fractions, comparing fractions and even adding and subtracting simple fractions.

Recognise and find halves.

Recognising halves and finding different ways of dividing a shape into two halves.

Recognising half of a number of objects.

Finding halves of amounts.

Draw a ring round half the creatures.

Halves, quarters and three quarters

Recognise and find halves, quarters and three quarters.

Working with quarters including finding the total number when given one quarter.

More work on quarters with a monster theme.

More work on quarters with a garden bird theme.

Recognising a quarter of a number of objects.

Finding a half and a quarter of a set of objects.

Finding one half and one quarter of a set of objects.

More finding halves and quarters of sets of objects.

Work out halves, quarters and three quarters of shapes and numbers.

Finding halves and quarters of small numbers.

Recognise and find thirds.

Find a third of small amounts.

Recognising equal parts: thirds.

Recognising a third of a number of objects.

Finding halves and introducing thirds of shapes, amounts and numbers.

Looking for thirds and quarters and finding the odd one out.

More on fractions

Finding fractions of shapes and numbers, non-unit fractions and counting in fractions.

Recognising equal and unequal parts of a whole.

Understanding simple non-unit fractions such as three quarters.

Find simple fractions of shapes and numbers

Find simple fractions of amounts. Quarters, halves and three quarters.

How many ways are there of eating a quarter of a bar of chocolate?

Estimating cutting lengths into halves, quarters and thirds plus word problems involving fractions of lengths.

Count on in quarters.

A different kind of number line: counting in quarters and halves.

Some tricky word problems which need a good knowledge of halves of small numbers!

The statutory requirements for fractions in Year 2.

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Fraction Word Problem Worksheets

Featured here is a vast collection of fraction word problems, which require learners to simplify fractions, add like and unlike fractions; subtract like and unlike fractions; multiply and divide fractions. The fraction word problems include proper fraction, improper fraction, and mixed numbers. Solve each word problem and scroll down each printable worksheet to verify your solutions using the answer key provided. Thumb through some of these word problem worksheets for free!

Represent and Simplify the Fractions: Type 1

Presented here are the fraction pdf worksheets based on real-life scenarios. Read the basic fraction word problems, write the correct fraction and reduce your answer to the simplest form.

• Download the set

Represent and Simplify the Fractions: Type 2

Before representing in fraction, children should perform addition or subtraction to solve these fraction word problems. Write your answer in the simplest form.

Adding Fractions Word Problems Worksheets

Conjure up a picture of how adding fractions plays a significant role in our day-to-day lives with the help of the real-life scenarios and circumstances presented as word problems here.

(15 Worksheets)

Subtracting Fractions Word Problems Worksheets

Crank up your skills with this set of printable worksheets on subtracting fractions word problems presenting real-world situations that involve fraction subtraction!

Multiplying Fractions Word Problems Worksheets

This set of printables is for the ardently active children! Explore the application of fraction multiplication and mixed-number multiplication in the real world with this exhilarating practice set.

Fraction Division Word Problems Worksheets

Gift children a broad view of the real-life application of dividing fractions! Let them divide fractions by whole numbers, divide 2 fractions, divide mixed numbers, and solve the word problems here.

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Fractions KS1

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

Happy Halving

Can you split each of the shapes below in half so that the two parts are exactly the same?

These pictures show squares split into halves. Can you find other ways?

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

This task provides children with the opportunity to investigate halving different shapes and check that they have made two halves.

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Year 2 Maths Worksheets UK Hub Page

Welcome to Math Salamanders Year 2 Maths Worksheets hub page.

In our Year 2 area, you will find a wide range of printable math worksheets and Maths activities for your child to enjoy.

Come and take a look at our dot-to-dot pages, or our maths games. Perhaps you would prefer our 2d shape worksheets, or learning about numbers using our number line worksheets?

Hopefully you will find something here to meet your child's maths requirements!

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Year 2 Maths Learning

Here are some of the key learning objectives for the end of Year 2:

• know and use Place value up to 100
• Compare and order numbers up to 100
• Counting on and back in 1s and 10s
• count in 2s, 5s and 10s
• Position numbers on a number line up to 1000
• use addition and subtraction facts to 20
• use related facts for addition and subtraction
• add or subtract 1 or 10 from a 2-digit number
• add and subtract 2-digit numbers
• number bonds to 100 using tens only
• add three single-digit numbers
• recognise and make equal groups
• use the x symbol to write multiplication sentences
• use arrays and pictures to represent multiplication sentences
• know multiplication facts for the 2, 5 and 10 times table
• recognise and find a half, a quarter and a third
• understand and use fraction notation
• understand the equivalence of a half and two-quarters
• count on in halves, thirds and quarters up to 10
• count in pence: 1p, 2p ,5p, 10p and 20p
• count in pounds: £1, £2, £5, £10 and £20
• find a simple total or difference between two money amounts
• find the change from simple amounts
• tell the time: o'clock, half-past, quarter-past and to
• understand and compare durations of time
• compare and measure length, mass, volume, capacity and temperature
• read a variety of scales going up in 1s, 2s, 5s and 10s
• recognise 2D and 3D shapes
• count sides and vertices on 2D shapes
• count faces, edges and vertices on 3D shapes
• sort and make patterns with 2D and 3D shapes
• describe movement and turns
• make tally charts
• draw and interpret pictograms
• understand and use block diagrams

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 2 is generally equivalent to 1st Grade in the US.

On this page you will find link to our range of math worksheets for Year 2.

Quicklinks to Year 2 ...

• Place Value Zone

Operations Zone

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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 2 Place Value Charts

Here you will find a range of Free Printable Place Value Charts for Year 2.

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

Place Value and Counting Worksheets

Here you will find a range of Year 2 Place Value Worksheets.

These Year 2 maths worksheets will help your child learn their place value, reading, writing and ordering numbers up to 100.

There are also some money worksheets involving counting in dimes and pennies to support place value learning.

• learn to order numbers to 100;
• learn to count in dimes and pennies;
• learn to read and write numbers to 100.

Year 2 Place Value Worksheets

• Place Value to 20 Worksheets
• Math Place Value Worksheets Tens and Ones
• Ordering 2-digit numbers Worksheets
• Greater than Less than Worksheets - up to 2 digit numbers
• Printable Counting Worksheets to 50
• Missing Number Chart 1-100
• Counting by 2s Worksheets
• Math Worksheets Counting by 1s 5s and 10s

Number Line Worksheets

Here is our selection of free printable number line worksheets for Year 2 pupils.

These first grade math worksheets will give your child a good grasp of place value and number sequences up to 100.

• count on and back by ones;
• position numbers to 100 on a number line.
• Number lines to 20
• Number lines to 100

Year 2 Mental Maths Zone

Here you will find a range of printable mental math sheets designed especially for Year 2 children.

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

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

• Year 2 Printable Mental Maths

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Year 2 Addition Worksheets

Here you will find a range of Free Printable Addition Worksheets to support Year 2.

The following first grade math worksheets involve adding different amounts.

• learn their addition facts to 12+12;
• learn to solve an addition fact where one of the addends is missing;
• learn to add numbers in columns up to 100.
• Number Bonds to 10 and 12
• Addition Sentences to 12
• Addition Fact Practice to 12
• Addition Facts to 20 Worksheets
• Adding tens
• Addition Word Problems
• 2 Digit Addition Without Regrouping
• 2 Digit Addition Worksheets With Regrouping
• Free Addition Worksheets (randomly generated)

Year 2 Subtraction Worksheets

Here you will find a range of Year 2 Subtraction Worksheets.

The following worksheets involve using the Math skills of subtracting.

Using these Year 2 maths worksheets will help your child to:

• learn their addition and subtraction facts to 12;
• learn to subtract 2 digit numbers.
• Subtraction Facts to 12
• Subtracting tens
• Subtraction Word Problems
• Two Digit Subtraction Worksheets Without Regrouping
• 2 Digit Subtraction Worksheets With Regrouping
• Free Subtraction Worksheets (randomly generated)

Addition & Subtraction Worksheets

If you need to mix and match addition and subtraction fact questions within the same sheet, then use this section here.

The addition and subtraction worksheets involve counting on and back with numbers to 12.

• Math Activities Addition and Subtraction to 12
• Add and Subtract 10 Worksheets
• Addition Subtraction Worksheets (randomly generated)
• Addition and Subtraction Problems

Year 2 Maths Word Problems

Here you will find a range of math word problems aimed at Year 2 level. Each problem sheet is based on an interesting theme such as parties or the seaside.

• Add and subtract with numbers to 12;
• order numbers to 100;
• solve a range of math problems.
• Maths Problems for Year 2

Longer Math Problems

• Year 2 Maths Problems (1st Grade)

Year 2 Geometry Worksheets

Here is a range of free geometry worksheets for Year 2 pupils.

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 2 Geometry Worksheets (1st Grade)

Measurement Zone, including Time & Money

Year 2 measurement worksheets.

Here is our selection of measurement worksheets for Year 2 pupils.

These sheets involve reading scales going up in ones to find the weight or liquid capacity.

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

• Year 2 Measurement Worksheets (1st Grade)

Year 2 Money Worksheets

Here you will find a range of free printable First Grade Money Worksheets.

The following worksheets involve counting different amounts of money in pennies, nickels and dimes.

• learn the names and values of the US coins;
• learn to count up different amounts of money to £1 in coins.
• Free Counting Money Worksheets UK Coins (easier)
• Free Money Worksheets UK Coins up to £1

Printable Money Resources

• Printable Money Flashcards
• Kids Counting Money Dominoes

Telling the Time Worksheets

Here is our selection of telling the time worksheets for 1st grade.

• read o'clock and half-past times;
• convert o'clock and half-past times to digital;
• draw clock hands correctly to mark out o'clock and half-past.

The year 2 maths worksheets in this section will help your child learn to tell simple times on an analogue clock.

• Telling Time Worksheets o'clock and half-past
• Clock Worksheets - Quarter Past and Quarter To

Year 2 Bar Graph Worksheets

Here is our selection of bar graphs for first graders.

These Year 2 maths worksheets involve reading and interpreting a range of bar graphs and picture graphs with a scale going up in ones.

Using these sheets will help children to understand how bar graphs work.

• Year 2 Picture/Bar Graphs (First Grade)

Fun Zone: Puzzles, Games and Riddles

Year 2 Maths Games

Here you will find a range of free printable Math games. All children like to play Math games, and you will find a good range of Maths Games at a Year 2 level here for your child to play and enjoy.

• Year 2 Maths Games (First Grade)

Year 2 Maths Puzzles

Here you will find a range of printable Year 2 level math puzzles for your child to enjoy.

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

Using these puzzles will help your child to:

• develop thinking and reasoning skills;
• develop perseverance.
• Year 2 Maths Puzzles (1st Grade)
• Dot to Dot up to 50

Math Salamanders Year 2 Maths Games Ebook

Our Year 2 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 2 Maths Games Ebook

Other UK Maths Worksheet pages

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

How to Print or Save these sheets 🖶

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Teens surprise math world with Pythagorean Theorem trigonometry proof | 60 Minutes

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Basic fractions word problems

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Care Doctor

Two Teenagers Solve a 2,000-Year-Old Math Problem

Posted: May 12, 2024 | Last updated: May 12, 2024

Over the years, many math questions have puzzled many, including one that remained unsolved for 2000 years.  

However, two teenagers managed to solve the problem after their teacher assigned it to their class, not thinking anyone would actually manage to do it.  

The 2000-Year-Old Pythagorean Theorem

The Pythagorean Theorem is a 2000-year-old theory that has been taught to countless children in schools all over the world. 

The way they have been taught is that, when squared, the two shorter sides of a triangle equal the squared longer side of the triangle. 

Proof of Pythagorean Theorem Using Trigonometry

One question that has puzzled many mathematicians for years is how the Pythagorean theorem can be proved using trigonometry.  

Many theories have been proposed about the problem over the years, but now, two teens from New Orleans have been able to refute these and solve the problem. 

The Teens Were Motivated by a $500 Cash Prize

Their teacher, Michelle Blouin Williams, offered her class a $500 cash prize if they could solve it and genuinely believed they wouldn’t be able to.  

However, she was proved wrong when the two teenagers, Calcea Johnson and Ne’Kiya Jackson, were able to solve the problem, as they were motivated by the $500 cash prize.    

Johnson and Jackson Took Two Months to Solve the Problem

It took Johnson and Jackson a total of two months to be able to solve the problem.  

The pair also worked on the problem on over 30 pieces of paper until they eventually figured it out.  

Johnson and Jackson Found Five Proofs for Trigonometry and Pythagorean Theorem

Over the years, every mathematician has looked at this problem and decided that it was impossible to solve.    

However, over a year since they first solved the problem in 2023, Johnson and Jackson have been able to find five more proofs and have also discovered a general format that could produce a further five proofs. 

Jackson and Johnson Presented Their Findings to the American Mathematical Society

Once they made their discovery, Jackson and Johnson presented their findings to the American Mathematical Society.  

In doing so, they became the first high schoolers to present their findings to the society.   

Johnson and Jackson Credited Their Teachers With Their Findings

Johnson and Jackson attended St. Mary’s Academy in New Orleans, an all-girls Catholic school.

They credited their teachers with helping them make the discovery , as they always pushed them to achieve what was previously thought to be impossible.      

Johnson and Jackson Have Contradicted Elisha Loomis

Since Johnson and Jackson have proved that there is trigonometric proof of the Pythagorean theorem, they have also contradicted Elisha Loomis’ theory. 

Elisha Loomis was a mathematician whose book, " The Pythagorean Proposition ," stated there was no trigonometric proof of the Pythagorean theorem and that if there was, it wouldn’t be correct.    

Mathematicians Thought Trigonometry Was Based on the Pythagorean Theorem

Part of Loomis’ theory was that trigonometry was based on the Pythagorean theorem.  

He said that using trigonometry to prove the Pythagorean theorem would result in going in circles, but it has since been proved wrong.      

Some Dismissed the News as Fake

Despite the proof Johnson and Jackson provided, a few people who have dismissed them solving the problem as fake.    

The girls said these people had dismissed their achievements due to them being African-American women and teenagers, with the pair saying they just wanted their achievements to be celebrated as they are.   

Johnson and Jackson Were Given the Keys to the City

Despite some people not being overly convinced by their achievement, others have given Johnson and Jackson high praise.  

So much so that they were given the keys to the city of New Orleans, a medieval tradition that means the honored persons can enter and leave a city of their own free will.    

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Teens who discovered new way to prove Pythagoras’s theorem uncover even more proofs

As high school students, Calcea Johnson and Ne’Kiya Jackson worked to find valid new proof for the 2,000-year-old theorem

Two college freshmen who, during their final year of high school, found a new way to prove Pythagoras’s theorem by using trigonometry – which mathematicians for generations thought was impossible – have since uncovered multiple more such proofs, they revealed in a national interview on Sunday.

“We found five, and then we found a general format that could potentially produce at least five additional proofs,” Calcea Johnson said on CBS’s 60 Minutes, a little more than a year after she and Ne’Kiya Jackson collaborated on an accomplishment that earned them international recognition.

Nonetheless, in comments that stunned their interviewer, Bill Whitaker, the two graduates of St Mary’s Academy in New Orleans denied seeing themselves as math geniuses and dismissed any interest in pursuing careers in mathematics.

“People might expect too much out of me if I become a mathematician,” Jackson said, shaking her head. Johnson, for her part, added: “I may take up a minor in math, but I don’t want that to be my job job.”

Sunday’s conversation on CBS’s popular Sunday evening news magazine were perhaps their most extensive, widely broadcast remarks to date on the new ground that they broke with respect to the Pythagorean theorem.

The 2,000-year-old theorem established that the sum of the squares of a right triangle’s two shorter sides equals the square of the hypotenuse – the third, longest side opposite the shape’s right angle. Countless schoolchildren taking geometry have memorized the notation summarizing the theorem: a 2 + b 2 = c 2 .

For 2,000 years, mathematicians maintained that any alleged proof of the Pythagorean theorem that was based in trigonometry would constitute a logical fallacy known as circular reason – in essence, trying to validate an idea with the idea itself.

But the bonus question on a math contest that Johnson and Jackson took home to complete during the Christmas break of their final year at St Mary’s served as the impetus for them to plot out a new way to demonstrate that one could indeed use trigonometry to prove Pythagoras’s theorem.

Their work was so compelling that the pair went to a regional meeting of the American Mathematical Society in Atlanta in March 2023 to outline their findings. At the organization’s recommendation, Jackson and Johnson have submitted their discoveries for final peer review and publication – as well as working on additional proofs while that process is pending, as 60 Minutes noted.

The 60 Minutes interview gave Johnson and Jackson occasion to reflect on the intense reaction caused by initial media reports on their innovative work at St Mary’s, a Catholic high school that has been dedicated to educating Black girls since its founding shortly after the US civil war.

Some of it was negative. Some in the math community smarted at claims in a press release issued by St Mary’s that asserted Jackson and Johnson’s research was “unprecedented”. And they flocked to social media demanding that a 2009 trigonometry-based proof for Pythagoras’s theorem get its due.

Yet a lot of the reaction to Johnson and Jackson was positive, especially as mathematicians who picked apart their work confirmed that – by all indications – they had arrived at a valid new proof, a celebration-worthy accomplishment.

Michelle Obama wrote a post on social media that linked to a story about Johnson and Jackson, adding the text: “I just love this story. … Way to go, Ne’Kiya and Calcea! I’m rooting for you and can’t wait to see what you all do next.”

They also received a commendation from Louisiana’s then governor as well as symbolic keys to the city of New Orleans .

Asked on 60 Minutes why they thought people were so impressed with what they had done, Jackson said she thought the public was surprised young Black women could author such a feat.

“I’d like to be celebrated for what it is,” Jackson said. “Like – it’s a great mathematical achievement.”

Jackson is now attending New Orleans’ Xavier University and enrolled in its pharmacy department. Meanwhile, Johnson – who graduated from St Mary’s as its valedictorian – is now an environmental engineering student at Louisiana State University in Baton Rouge.

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