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Problem Solving Resources and Worksheets

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Compare Calculations Teaching PowerPoint

These lesson slides guide pupils through the prior learning of completing multi-step addition and subtraction problems, before moving on to the main skill of comparing calculations without focusing on their answers.

Find Missing Numbers Teaching PowerPoint

These lesson slides guide pupils through the prior learning of using the inverse operation, before moving on to the main skill of finding missing numbers.

Number Line to 1,000,000 – Teaching PowerPoint

These lesson slides guide pupils through the prior learning of partitioning numbers to 1,000,000, before moving on to the main skill of using number lines to 1,000,000.

Number Line to 1,000,000 – Varied Fluency

This worksheet includes a range of varied fluency questions for pupils to practise the main skill of using number lines to 1,000,000.

Number Line to 1,000,000 – Reasoning and Problem Solving

This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of using number lines to 1,000,000.

Number Line to 1,000,000 – Extension

This worksheet includes a range of varied fluency and reasoning and problem solving questions for pupils to practise the main skill of using number lines to 1,000,000.

Number Line to 1,000,000 – Discussion Problems

This worksheet includes a discussion problem that can be used in pairs or in small groups to enable pupils to further their understanding of the concepts linked to using number lines to 1,000,000.

Mental Strategies- Discussion Problems

This worksheet includes a discussion problem that can be used in pairs or in small groups to enable pupils to further their understanding of the concepts linked to mentally calculating sums and differences.

Mental Strategies – Reasoning and Problem Solving

This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of mentally calculating sums and differences.

Mental Strategies – Extension

This worksheet includes a range of varied fluency and reasoning and problem solving questions for pupils to further extend and practise the main skill of mentally calculating sums and differences.

Mental Strategies – Varied Fluency

This worksheet includes a range of varied fluency questions for pupils to practise the main skill of mentally calculating sums and differences.

Mental Strategies Teaching Powerpoint

These lesson slides guide pupils through the prior learning of partitioning numbers to one million before moving on to the main skill of mentally calculating sums and differences.

10/100/1,000/100,000 More or Less Teaching Powerpoint

These lesson slides guide pupils through the prior learning of comparing and ordering numbers to 100,000 before moving on to the main skill of finding 10, 100, 1,000, 10,000, or 100,000 more or less than a given number.

10/100/1,000/100,000 More or Less – Reasoning and Problem Solving

This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of finding 10, 100, 1,000, 10,000, or 100,000 more or less than a given number.

10/100/1,000/100,000 More or Less – Extension

This worksheet includes a range of varied fluency and reasoning and problem solving questions for pupils to practise the main skill of finding 10, 100, 1,000, 10,000, or 100,000 more or less than a given number.

10/100/1,000/100,000 More or Less – Discussion Problems

This worksheet includes a discussion problem that can be used in pairs or in small groups to enable pupils to further their understanding of the concepts linked to finding 10, 100, 1,000, 10,000, or 100,000 more or less than a given number.

10/100/1,000/100,000 More or Less – Varied Fluency

This worksheet includes a range of varied fluency questions for pupils to practise the main skill of finding 10, 100, 1,000, 10,000, or 100,000 more or less than a given number.

Partition Numbers to 1,000,000 Teaching Powerpoint

These lesson slides guide pupils through the prior learning of finding 10, 100, 1,000, 10,000 or 100,000 more or less before moving on to the main skill of partitioning numbers up to one million. There are a number of questions to check pupils' understanding throughout.

Partition Numbers to 1,000,000 – Extension

This worksheet includes a range of varied fluency and reasoning and problem solving questions for pupils to further extend and practise the main skill of partitioning numbers up to one million.

Partition Numbers to 1,000,000 – Discussion Problems

This worksheet includes a discussion problem that can be used in pairs or in small groups to enable pupils to further their understanding of the concepts linked to partitioning numbers up to one million.

Partition Numbers to 1,000,000 – Reasoning and Problem Solving

This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of partitioning numbers up to one million.

Partition Numbers to 1,000,000 – Varied Fluency

This worksheet includes varied fluency, reasoning and problem solving questions for pupils to practise the main skill of partitioning numbers to 1,000,000.

Find Missing Numbers – Varied Fluency

This worksheet includes a range of varied fluency questions for pupils to practise the main skill of finding missing numbers.

Find Missing Numbers – Extension

This worksheet includes a range of varied fluency and reasoning and problem solving questions for pupils to further extend and practise the main skill of finding missing numbers.

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Cazoom Maths offers an outstanding range of maths worksheets for students in KS2 (Key stage 2). We are a trusted provider of maths worksheets for secondary school children and this set of maths worksheets is ideal for students at key stage 2. Our KS2 maths worksheets cover all topics in the curriculum and are perfect for use in the classroom or for additional home learning. These fun and engaging worksheets cover everything students need to know to succeed in Years 3 to 6, including addition and subtraction, multiplication and division, and number and place value, plus KS2 statistics and algebra. Our maths worksheets are used by over 50,000 teachers, parents and schools around the world and we are a Times Educational Supplement recommended resource for helping students learn mathematics.

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Reasoning and Problem Solving Questions Collection - KS1 and KS2

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

10 March 2023

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These booklets each contain over 40 reasoning and problem solving questions suitable for KS1, KS2 and KS3 classes. These are the questions that we have been putting out each day in March 2016 on Twitter in the run up to SATS.

The answers are provided with some simple notes at the back of the booklet and for some problems supplementary questions and variation has been provided.

As always we welcome any feedback on the work we are doing and the materials that we are releasing. Thank you for taking an interest in our work. The White Rose Maths Hub Team

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25 Fun Maths Problems For KS2 And KS3 (From Easy To Very Hard!)

Fun maths problems are one of the things mathematicians love about the subject; they provide an opportunity to apply mathematical knowledge, logic and problem solving skills all at once.  In this article, we’ve compiled 25 fun maths problems, each covering various topics and question types. They’re aimed at students in KS2 & KS3. We’ve categorised them as:

Maths word problems

Maths puzzles, fraction problems, multiplication and division problems, geometry problems, problem solving questions, maths puzzles are everywhere, how should teachers use these maths problems.

Teachers could make use of these maths problem solving questions in a number of ways, such as:

• embed into a relevant maths topic’s teaching.
• settling tasks at the beginning of lessons.
• break up or extend a maths worksheet.
• keep students thinking mathematically after the main lesson has finished.

Some are based on real life or historical maths problems, and some include ‘bonus’ maths questions to help to extend the problem solving fun! As you read through these problems, think about how you could adjust them to be relevant to your students or to practise different skills. 

These maths problems can also be used as introductory puzzles for maths games such as those introduced at the following links:

• KS2 maths games
• KS3 maths games

Need more support teaching reasoning, problem solving and planning for depth ? Read here for free CPD for you and your team of teachers.

1. Home on time – easy

Type: Time, Number, Addition

A cinema screening starts at 14:35. The movie lasts for 2 hours, 32 minutes after 23 minutes of adverts. It took 20 minutes to get to the cinema. What time should you tell your family that you’ll be home?

Answer: 17:50

2. A nugget of truth – mixed

Type: Times Tables, Multiplication, Multiples, Factors, Problem Solving 

Chicken nuggets come in boxes of 6, 9 or 20, so you can’t order 7 chicken nuggets. How many other impossible quantities can you find (not including fractions or decimals)?

Answer: 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37, or 43

There is actually a theorem which can be used to prove that every integer quantity greater than 43 can be ordered.

3. A pet problem – mixed

Type: Number, Problem Solving, Forming and Solving Equations, Simultaneous Equations, Algebra

Eight of my pets aren’t dogs, five aren’t rabbits, and seven aren’t cats. How many pets do I have?

Answer: 10 pets (5 rabbits, 3 cats, 2 dogs)

4. The price of things – mixed

Type: lateral thinking problem

A mouse costs £10, a bee costs £15, and a spider costs £20. How much does a duck cost? Answer: £5 (£2.50 per leg)

Looking for more word problems, solutions and explanations? Read our article on word problems for primary school.

25 Fun Maths Problems - Printable

Download a printable version of these fun maths problems together with answers and mark scheme.

5. A dicey maths challenge – easy

Type: Place value, number, addition, problem solving

Roll three dice to generate three place value digits. What’s the biggest number you can make out of these digits? What’s the smallest number you can make?

Add these two numbers together. What do you get?

Answer: In most cases, 1,089.

Bonus: Who got a different result? Why?

6. PIN problem solving – mixed

Type: Logic, problem solving, reasoning

I’ve forgotten my PIN. Six incorrect attempts locks my account: I’ve used five! Two digits are displayed after each unsuccessful attempt: “2, 0” means 2 digits from that guess are in the PIN, but 0 are in the right place.

What should my sixth attempt be?

Answer: 6347

7. So many birds – mixed

Type: Triangular Numbers, Sequences, Number, Problem Solving

On the first day of Christmas my true love gave me one gift. On the second day they gave me another pair of gifts plus a copy of what they gave me on day one. On day 3, they gave me three new gifts, plus another copy of everything they’d already given me. If they keep this up, how many gifts will I have after twelve days?

Answer: 364

Bonus: This could be calculated as 1 + (1 + 2) + (1 + 2 + 3) + … but is there an easier way? What percentage of my gifts do I receive on each day?

8. I 8 sum maths questions – mixed

Type: Number, Place Value, Addition, Problem Solving, Reasoning

Using only addition and the digit 8, can you make 1,000? You can put 8s together to make 88, for example.

Answer: 888 + 88 + 8 + 8 + 8 = 1,000 Bonus: Which other digits allow you to get 1,000 in this way?

9. Quizzical – easy

Type: Fractions, Adding Fractions, Equivalent Fractions, Fractions to Percentages

4 friends entered a maths quiz. One answered \frac{1}{5} of the maths questions, one answered \frac{1}{10} , one answered \frac{1}{4} , and the other answered \frac{4}{25} . What percentage of the questions did they answer altogether?

Answer: 71%

10. Ancient problem solving – mixed

Type: Fractions, Reasoning, Problem Solving

Ancient Egyptians only used unit fractions (like \frac{1}{2} , \frac{1}{3} or \frac{1}{4} ). For \frac{2}{3} , they’d write \frac{1}{3} + \frac{1}{3} . How might they write \frac{5}{8} ?

Answer: \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} is correct. So is \frac{1}{2} + \frac{1}{8} .

Bonus: Which solution is better? Why? Can you find any more? What if subtractions are allowed?

Learn more about unit fractions here

11. everybody wants a pizza the action – hard.

An infinite number of mathematicians buy pizza. The first wants \frac{1}{2} pizza. The second wants \frac{1}{4} pizza. The third & fourth want \frac{1}{8} and \frac{1}{16} each, and so on. How many pizzas should they order?

Answer: 1 Each successive mathematician wants a slice that is exactly half of what is left:

12. Shade it black – hard

Type: Fractions, Reasoning, Problem Solving What fraction of this image is shaded black?

Answer: \frac{1}{3}

Look at the L-shaped part made up of two white and one black squares: \frac{1}{3} of this part is shaded. Zoom in on the top-right quarter of the image, which looks exactly the same as the whole image, and use the same reasoning to find what fraction of its L-shaped portion is shaded. Imagine zooming in to do the same thing again and again…

13. Giving is receiving – easy

Type: Number, Reasoning, Problem Solving

5 people give each other a present. How many presents are given altogether?

14. Sharing is caring – mixed

I have 20 sweets. If I share them equally with my friends, there are 2 left over. If one more person joins us, there are 6 sweets left. How many friends am I with?

Answer: 6 people altogether (so 5 friends!)

15. Times tables secrets – mixed

Type: Area, 2D Shape, Rectangles

Here are 77 letters:

BYHRCGNGNEOEAAHGHGCURPUTSTSASHHSBOBOREOPEEMEMEELATPEPEFADPHLTLTUT IEEOHOHLENRYTITIIAGBMTNTNFCGEIIGIG

How many different rectangular grids could you arrange all 77 letters into?

Answer: Four: 1⨉77, 77⨉1, 11⨉7 & 7⨉11. If the letters are arranged into one of these, a message appears, reading down each column starting from the top left.

Bonus: Can you find any more integers with the same number of factors as 77? What do you notice about these factors (think about prime numbers)? Can you use this system to hide your own messages?

16. Laugh it up – hard

Type: Multiples, Lowest Common Multiple, Times Tables, Division, Time

One friend jumps every \frac{1}{3} of a minute. Another jumps every 31 seconds. When will they jump together? Answer: After 620 seconds

17. Pictures of matchstick triangles – easy

Type: 2D Shapes, Equilateral Triangles, Problem Solving, Reasoning

Look at the matchsticks arranged below. How many equilateral triangles are there?

Answer: 13 (9 small, 3 medium, 1 large)

Bonus: What if the biggest triangle only had two matchsticks on each side? What if it had four?

18. Dissecting squares – mixed

Type: Reasoning, Problem Solving

What’s the smallest number of straight lines you could draw on this grid such that each square has a line going through it?

19. Make it right – mixed

Type: Pythagoras’ theorem

This triangle does not agree with Pythagoras’ theorem. 

Adding, subtracting, multiplying or dividing each of the side lengths by the same integer can fix it. What is the integer?

Answer: 3 

8 – 3 = 5

The new side lengths are 3, 4 and 5 and  32 + 42 = 52.

20. A most regular maths question – hard

Type: Polygons, 2D Shapes, tessellation, reasoning, problem-solving, patterns

What is the regular polygon with the largest number of sides that will self-tessellate?

Answer: Hexagon.

Regular polygons tessellate if one interior angle is a factor of 360°. The interior angle of a hexagon is 120°. This is the largest factor less than 180°.

21. Pleased to meet you – easy

Type: Number Problem, Reasoning, Problem-Solving

5 people meet; each shakes everyone else’s hand once. How many handshakes take place?

Person A shakes 4 people’s hands. Person B has already shaken Person A’s hand, so only needs to shake 3 more, and so on.

Bonus: How many handshakes would there be if you did this with your class?

22. All relative – easy

Type: Number, Reasoning, Problem-Solving

When I was twelve my brother was half my age. I’m 40 now, so how old is he?

23. It’s about time – mixed

Type: Time, Reasoning, Problem-Solving

When is “8 + 10 = 6” true?

Answer: When you’re telling the time (8am + 10 hours = 6pm)

24. More than a match – mixed

Type: Reasoning, Problem-Solving, Roman Numerals, Numerical Notation

Here are three matches:

How can you add two more matches, but get eight? Answer: Put the extra two matches in a V shape to make 8 in Roman Numerals:

25. Leonhard’s graph – hard

Type: Reasoning, Problem-Solving, Logic

Leonhard’s town has seven bridges as shown below. Can you find a route around the town that crosses every bridge exactly once?

Answer: No!

This is a classic real life historical maths problem solved by mathematician Leonhard Euler (rhymes with “boiler”). The city was Konigsberg in Prussia (now Kaliningrad, Russia). Not being able to find a solution is different to proving that there aren’t any! Euler managed to do this in 1736, practically inventing graph theory in the process.

Many of these 25 maths problems are rooted in real life, from everyday occurrences to historical events. Others are just questions that might arise if you say “what if…?”. The point is that although there are many lists of such problem solving maths questions that you can make use of, with a little bit of experience and inspiration you could create your own on almost any topic – and so could your students. 

For a kick-starter on creating your own maths problems, read our article on KS3 maths problem solving .

Looking for additional support and resources at KS3? You are welcome to download any of the secondary maths resources from Third Space Learning’s resource library for free. There is a section devoted to GCSE maths revision with plenty of maths worksheets and GCSE maths questions . There are also maths tests for KS3, including a Year 7 maths test , a Year 8 maths test and a Year 9 maths test Other valuable maths practice and ideas particularly around reasoning and problem solving at secondary can be found in our KS3 and KS4 maths blog articles. Try these fun maths problems for KS2 and KS3, SSDD problems , KS3 maths games and 30 problem solving maths questions . For children who need more support, our maths intervention programmes for KS3 achieve outstanding results through a personalised one to one tuition approach.

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Learn how the programmes are aligned to maths mastery teaching or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

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All you need to know to successfully implement a mastery approach to mathematics in your primary school, at whatever stage of your journey.

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Math Problem Worksheets Word Problems Hub Page

Welcome to the Math Salamanders' Math Problem Worksheets.

Here you will find a range of different math problem sheets to help you learn to apply your math facts to solve a range of problems.

There are a range of different word problems and fun math challenges for each grade.

We also have a selection of word problems sorted by math area including fractions and ratio.

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Math Problem Worksheets

Want to apply your math fact knowledge?

Looking for some fun math problems to solve?

Want to use your knowledge to solve some 'real life' problems.

Look no further! The pages you need are below!

Here is our selection of different Math problem worksheets.

Included in this page are a range of math problem pages from 1st grade to 5th grade. There are also fraction problems, ratio problems as well as addition, subtraction, multiplication and division problems.

Many of the problem sheets use 'real life' data, so your child can learn some interesting facts while they are solving problems, and also hopefully see the point of all the math facts they have learnt at the same time.

Each problem solving sheet comes with a separate answer sheet.

Math Problems By Grade

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First Grade Math Word Problems

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

Using these sheets will help your child to:

• Add and subtract with numbers to 12;
• order numbers to 100;
• solve a range of math problems.

All the math problem sheets in this section support Elementary math benchmarks.

• Math Problems for Children 1st Grade

Longer Math Problems

• First Grade Math Problems
• 1st grade Addition Word Problems
• 1st Grade Subtraction Word Problems
• 1st Grade Addition and Subtraction Problems

Second Grade Math Word Problems

Here are a range of problems solving sheets for 2nd graders. 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.

All the 2nd grade math problem worksheets in this section support Elementary math benchmarks.

These sheets involve solving one or two more challenging longer problems.

• Second Grade Math Problems

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

• 2nd Grade Math Word Problems
• Addition Word Problems 2nd grade

These sheets involve solving a range of multiplciation problems.

• Multiplication Word Problems 2nd Grade

These sheets involve solving a range of division problems.

Using this link will open our 2nd Grade Math Salamanders website in a new browser window.

• 2nd Grade Division Worksheets

3rd Grade Math Word Problems

Here are a range of problems solving sheets for 3rd graders. Most of the sheets contain 'real-life' problems which involve real data.

• develop their knowledge of fractions;

All the 3rd grade sheets in this section support Elementary math benchmarks.

• 3rd Grade Math Problems
• Math Word Problems for kids 3rd Grade

These sheets involve solving 3-digit and 4-digit addition word problems.

• Addition Word Problems 3rd Grade (3- and 4-digits)

These sheets involve solving 3-digit and 4-digit subtraction problems.

• Subtraction Word Problems 3rd Grade
• 3rd Grade Addition and Subtraction Word Problems (3- and 4-digits)
• Multiplication Word Problem Worksheets 3rd Grade
• Division Worksheets Grade 3 Word Problems
• 4th Grade Math Problems

Here is our set of 4th grade math problems to help your child with their problem solving skills.

Each problem sheet comes complete with answers, and is available in both standard and metric units where applicable.

Many of the problems are based around 'real-life' problems and data such as the world's heaviest animals.

• apply their addition, subtraction and problem solving skills;
• solve a range of 'real life' problems;
• attempt more challenging longer problems.

Using the problems in this section will help your child develop their problem solving and reasoning skills.

• 4th Grade Math Word Problems
• Multiplication Word Problems 4th Grade
• Division Worksheets Grade 4 Word Problems
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• 5th Grade Math Word Problems

These sheets involve solving a range of ratio problems.

6th Grade Math Problems

• 6th Grade Percent Word Problems
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Math Problems By Topic

Addition problems, subtraction problems, multiplication problems, division problems.

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Fraction Problems

Percentage problems, ratio problems, finding all possibilities problems.

Here you will find a range of addtion word problems to help your child apply their addition facts.

The worksheets cover addition problems from 1st to 3rd grade.

• Addition Word Problems 2nd grade (up to 100)

Here you will find a range of subtraction word problems to help your child apply their subtraction facts.

The worksheets cover subtraction problems from 1st to 3rd grade.

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

• Subtraction Word Problems 2nd grade

Addition & Subtraction Problems

Here you will find a range of addition and subtraction word problems to help your child apply their knowledge.

• 2nd Grade Addition and Subtraction Word Problems

Here you will find a range of multiplication word problems to help your child apply their multiplication facts.

The worksheets cover multiplication problems from 2nd to 5th grade.

• Multiplication Word Problems 5th Grade

Here you will find a range of division word problems to help your child apply their division facts.

The worksheets cover division problems from 3rd to 5th grade.

Inequalities Word Problems

These sheets involve changing a word problem into an inequality.

Here you will find a range of fraction word problems to help your child apply their fraction learning.

The worksheets cover a range of fraction objectives, from adding and subtracting fractions to working out fractions of numbers. The sheets support fraction learning from 2nd grade to 5th grade.

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Here you will find a range of ratio word problems to help your child understand what a ratio is and how ratios work.

The sheets support ratio learning at a 5th grade level.

This is our finding all possibilities area where all the worksheets involve finding many different answers to the problem posed.

The sheets here encourage systematic working and logical thinking.

The problems are different in that, there is typically only one problem per sheet, but the problem may take quite a while to solve!

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This is our logic problems area where all the worksheets involve using reasoning and logical thinking skills.

The sheets here are designed to get children thinking logically and puzzling the problems out.

There are a range of different logic problems from 1st through 5th grade!

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• Equivalent Fractions Worksheet Practice And Problems For Ks2

Equivalent fractions worksheet – Practice and problems for KS2

This White Rose Maths equivalent fractions worksheet pack offers a comprehensive array of exercises and challenges. These will enhance pupils’ understanding of equivalent fractions.

Within this pack, students will encounter a diverse range of activities. These aim to reinforce pupils’ grasp of this fundamental mathematical concept.

In the first worksheet, learners are tasked with identifying fractions equivalent to those provided. They need to illustrate the equivalence of fractions such as 1/2 and 5/10 through diagrams. This fosters a visual understanding of fractional relationships.

Students also need to engage with diagrams to work out three sets of equivalent fractions, further solidifying their comprehension.

Next, the equivalent fractions worksheet prompts pupils to work out fractions equivalent to specified values, such as 1/4 and 6/20. Children need to circle the corresponding counterparts.

After this, learners need to complete a series of fractions by determining the missing numerical components. This consolidates their proficiency in fraction manipulation.

Equivalent fractions worksheet problems

In the second worksheet, pupils will work through five distinct problems. They need to identify missing values within fractional expressions.

These exercises serve to hone students’ analytical skills while reinforcing their ability to identify equivalent fractions in different contexts.

The final problem asks learners to evaluate a statement regarding equivalent fractions, requiring them to justify their response with a reasoned explanation.

The third worksheet offers a variety of activities that will help children better understand equivalent fractions.

By engaging with these equivalent fractions worksheets, students not only deepen their understanding of equivalent fractions but also develop essential problem-solving and critical thinking skills integral to their mathematical literacy.

White Rose Maths  provides high-quality, research-driven maths resources to support teaching and learning. Follow on Twitter at  @whiteroseed . Learn how to recap equivalent fractions in KS2 by getting active .

Similar resources

• Tarsia puzzle – Equivalent fractions for KS2 maths
• Place value worksheets – Free maths PDFs for KS1 and KS2
• Maths problem solving questions – KS2 lesson plan
• Bar modelling maths – Worksheets and CPD resources
• Bar model maths – Singapore-style lesson plan

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