year 6 problem solving worksheets

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Year 6 Maths Worksheets UK Hub Page

Welcome to our Year 6 Maths Worksheets area.

Here you will find a wide range of free printable Year 6 Maths Worksheets for your child to enjoy.

Come and take a look at our rounding decimal pages, or maybe some of our adding and subtracting fractions worksheets. Perhaps you are looking for some worksheets about finding angles in a triangle, or need some ratio problem worksheets to help your child learn about ratio?

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• 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 6 Maths Learning

Here are some of the key learning objectives for the end of Year 6:

• know and use Place value up to 10 million
• Counting on and back in steps of powers of 10 from any number up to 10 million
• Round numbers to any given degree of accuracy.
• Count forwards and backwards through zero with positive and negative numbers.
• Read Roman numerals to 1000 and recognise years written in Roman numerals
• solve multi-step problems using addition and subtraction in a range of contexts
• identify multiples and factors including common factors
• multiply and divide up to 4-digit numbers by up to 2 digits
• Use their knowledge of the order of operations to carry out calculations involving the four operations.
• Identify common factors, common multiples and prime numbers.
• solve problems involving addition, subtraction, multiplication and division
• simplify fractions
• compare and order fractions including mixed numbers
• add and subtract fractions with different denominators including mixed numbers
• multiply simple fractions together and simplify the answer
• divide proper fractions by whole numbers
• recall and use equivalence between simple fractions, decimals and percentages.
• Multiply and divide whole numbers and decimals up to 3dp by 10, 100 or 1000
• read, write, order and compare numbers up to 3dp
• round decimals with up to 3dp to the nearest whole
• solve problems with numbers up to 3dp
• work out percentages of different amounts
• solve problems using percentages
• use simple formulae
• express missing number problems using algebra
• find pairs of numbers that satisfy equations with two variables
• solve problems involving simple ratios
• solve problems involving similar shapes where the scale factor is known
• use, read, write and convert between standard units of measure
• measure, compare and calculate using different measures
• know that shapes with the same area can have different perimeters
• find the area of parallelograms and right triangles
• find the volume of cubes and cuboids
• convert between miles and km
• name and understand the parts of circles - radius, diameter and circumference
• draw 2D shapes accurately using dimensions and angles
• compate and classify 2D shapes by a range of properties
• find missing angles in triangles, quadrilaterals and regular shapes
• use coordinates in all 4 quadrants
• draw and translate simple shapes in all 4 quadrants
• interpret and construct pie charts and line graphs
• calculate the mean as an average

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 6 is generally equivalent to 5th Grade in the US.

On this page you will find link to our range of math worksheets for Year 6.

Quicklinks to Year 6 ...

• Place Value Zone
• Mental Math Zone

Word Problems Zone

Fractions percents ratio zone.

• Percentages Zone
• Measurement Zone

Geometry Zone

Data analysis zone.

• Fun Zone: games and puzzles

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 6 number worksheets.

Here you will find a range of Free Printable Year 6 Number Worksheets.

Using these Year 6 maths worksheets will help your child to:

• use place value with numbers up to 10 million;
• use place value with up to 3 decimal places;
• understand how to use exponents (powers) of a number;
• understand and use parentheses (brackets);
• understand and use multiples and factors;
• extend their knowledge of prime and composite (non-prime) numbers up to 100;
• know and be able to use the PEMDAS (or PEDMAS) rule.
• Place Value Worksheets to 10 million
• Place Value to 3dp
• Ordering Decimals Worksheets
• PEMDAS Rule Support Page
• PEMDAS Problems Worksheets
• Balancing Math Equations
• Roman Numerals worksheets

Ordering Large Numbers and Decimals to 3dp

The sheets in this section involve ordering lists of decimals to 3 decimal places and also large numbers up to 100 million.

There are sheets with decimals up to 10, and also sheets with numbers from -10 to 10.

• Ordering Large Numbers up to 100 million
• Ordering Decimals to 3dp

Rounding Decimals

• Rounding to the nearest tenth
• Rounding Decimal Places Sheets to 2dp
• Rounding Decimals Worksheet Challenges

Year 6 Decimal Counting Worksheets

Using these sheets will support you child to:

• count on and back by multiples of 0.1;
• fill in the missing numbers in sequences;
• count on and back into negative numbers.
• Counting By Decimals

Year 6 Mental Maths Zone

Each worksheet 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 quiz!

• Year 6 Mental Maths Tests

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Year 6 Addition Worksheets

• add decimals including tenths and hundredths mentally;
• add a columns of multi-digit numbers, including decimals.
• Decimal Addition Fact Worksheets
• 5th Grade Addition Worksheets BIG Numbers
• Decimal Column Addition Worksheets
• Money Worksheets (randomly generated)

Year 6 Subtraction Worksheets

Using these sheets will help your child to:

• subtract decimals including tenths and hundredths mentally;
• subtract multi-digit numbers, including decimals using column subtraction.
• Subtracting Decimals Worksheets (mental)
• Subtraction Worksheets up to Billions (columns)
• Column Subtraction with Decimals

Year 6 Multiplication Worksheets

• extend their knowlege of multiplication to decimals;
• use their multiplication tables to answer related facts, including decimals;
• multiply a range of decimals with up to 2 decimal places (2dp) by a whole number;
• multiply different money amounts by a whole number.
• Multiplying Decimals by 10 and 100
• Multiplication Fact Sheet Decimals
• Decimal Multiplication Worksheets to 1dp
• Decimal Multiplication Worksheets to 2dp
• Free Multiplication Worksheets (randomly generated)
• Multiply and Divide by 10 100 (decimals)
• Multiplication & Division Worksheets (randomly generated)
• Multiplication Word Problems

Division Worksheets 5th Grade

Using these Year 6 maths worksheets will help your child learn to:

• divide any whole number up to 10000 by a two digit number;
• express any division with a remainder in the form of a mixed number (a number with a fraction part).
• Long Division Worksheets (whole numbers)
• Long Division of Decimal Numbers
• Decimal Division Facts
• Division Facts Worksheets (randomly generated)

Year 6 Maths Problems

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

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

• Year 6 Math Problems (5th Grade)

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

• Year 6 Math Word Problems (5th Grade)

These sheets involve solving a range of ratio problems.

Year 6 Fraction Worksheets

Year 6 percentage worksheets, year 6 ratio worksheets.

• compare and order fractions;
• add and subtract fractions and mixed numbers;
• understand how to multiply fractions by a whole number;
• understand how to multiply two fractions together, including mixed fractions;
• understand the relationship between fractions and division;
• know how to divide fractions and mixed fractions;
• convert decimals to fractions.
• Comparing Fractions Worksheet page
• Adding Fractions Worksheets
• Adding Improper Fractions
• Subtracting Fractions Worksheets
• Adding Subtracting Fractions Worksheets
• Improper Fraction Worksheets
• Converting Decimals to Fractions Worksheets
• Fractions Decimals Percents Worksheets
• Multiplying Fractions Worksheets
• Dividing Fractions by Whole numbers
• Divide Whole numbers by Fractions
• Simplifying Fractions Worksheets
• Free Printable Fraction Riddles (harder)

Take a look at our percentage worksheets for finding the percentage of a number or money amount.

We have a range of percentage sheets from quite a basic level to much harder.

• Percentage of Numbers Worksheets
• Money Percentage Worksheets
• Percentage Word Problems

These Year 6 Ratio worksheets are a great way to introduce this concept.

We have a range of part to part ratio worksheets and slightly harder problem solving worksheets.

• Ratio Part to Part Worksheets
• Ratio and Proportion Worksheets

Year 6 Geometry Worksheets

• know how to find missing angles in a range of situations;
• learn the number of degrees in a right angle, straight line, around a point and in a triangle;
• know how to calculate the area of a triangle;
• know how to calculate the area of a range of quadrilaterals.
• learn the formulas to calculate the area of triangles and some quadrilaterals;
• write and plot coordinates in all 4 quadrants.
• (5th Grade) Geometry - Angles
• Area of Quadrilaterals
• 5th Grade Volume Worksheets
• Coordinate Worksheets (1st Quadrant)
• Coordinate Plane Worksheets (All 4 Quadrants)
• Parts of a Circle Worksheets

Measurement Zone, including Time & Money

Year 6 measurement worksheets.

Using these sheets will help your child understand how to:

• learn how to read a standard scale going up in different fractions: halves, quarters, eighths and sixteenths;
• learn how to read a metric scale going up in 0.1s, 5s, 10s, 25s, 50s & 100s;
• learn how to estimate a measurement of length, weight or liquid;
• convert temperatures in Celsius and Fahrenheit.
• (5th Grade) Measurement Worksheets

Time Puzzles - harder

Here you will find our selection of harder time puzzles.

• Time Word Problems Worksheets - Riddles (harder)

Using these sheets will help you to:

• find the mean of up to 5 numbers;
• find a missing data point when the mean is given.
• Mean Worksheets

Fun Zone: Puzzles, Games and Riddles

Year 6 maths games.

• Year 6 Math Games (5th Grade)

Year 6 Maths Puzzles

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

• Printable Math Puzzles

Math Salamanders Year 6 Maths Games Ebook

Our Year 6 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 6 Maths Games Ebook

Other UK Maths Worksheet pages

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

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Visual maths worksheets, each maths worksheet is differentiated and visual.

Year 6 Maths Worksheets

Our Year 6 Maths Worksheets provide students (aged 10-11) with an engaging and comprehensive overview of the fundamental mathematical concepts appropriate for primary school children in Year 6. The provided exercises cover all strands of mathematics, including long multiplication, short division, lowest common multiple, highest common factor, approximation, calculating areas, converting meters and comparing sizes, angle measurement and identification and many more! With our selection of Cazoom Maths PDF printable worksheets for year 6, teachers will find it easy to plan lessons around these topics while providing their pupils with the necessary support they need for success in maths class!  All resources are developed by professionals in the field and come with answer sheets, so students and parents can track their progress and teachers can pinpoint areas for revision. Our maths worksheets are used by over   50,000 teachers , parents and schools worldwide!

MATHS WORKSHEETS FOR YEAR 6 STUDENTS

Try some free sample year 6 maths worksheets

Outstanding YEAR 6 Maths Worksheets

• Separate answers are included to make marking easy and quick.
• Over 200 pages of the highest quality year 6 maths worksheets. Each worksheet is differentiated, including a progressive level of difficulty as the worksheet continues.
• Our Year 6 Maths Worksheets cover a wide range of topics, from dividing fractions, to place value, to multiplication tables, percentages, and much more. Students will be required to solve problems and use reasoning skills to answer these fun and engaging problems.
• Single user licence for parents or teachers. Separate school licences are also available.
• Single digital pdf download, with worksheets organised into high level chapters of Number, Measurement and Geometry, and further by subtopics. See below for the extensive range of sheets included.

Using Year 6 Maths Worksheets

Ever noticed how Year 6 students often have a maths worksheet tucked into their books? That’s because these sheets are a golden ticket to mastering maths! They’re like a gym for young brains, steadily building their mathematical muscles.

From practicing tricky sums over and over to getting ready for the big leagues of advanced topics, these worksheets do wonders. What’s more, they’re a teacher’s little helper, shining a light on where a student might need a bit more help. And in class? They’re the heart of group work, making maths a team sport and a problem-solving adventure.

Year 6 Maths in the real world

Now, let’s chat about why Year 6 maths feels so real-world relevant. Imagine divvying up a pizza slice with mates; that’s your fractions lesson right there. And when they’re counting their pocket money? Decimals to the rescue! Ever tried guessing if a new desk would fit in a room or tackled a DIY furniture project? That’s geometry in action.

Beyond just numbers, Year 6 maths tunes up the brain, teaching it to think logically and solve those everyday puzzles life throws our way. It’s not just about sums; it’s about gearing up for real life!

List of Topics

See below the list of topics covered. All KS1 and KS2 worksheets can be accessed here.

• Adding to a Single Digit
• Adding to a Two Digit Number
• Adding to a Three Digit Number
• Adding Three Numbers
• Number Bonds up to 20
• Number Bonds over 20

SUBTRACTION

• Single Digit Subtraction
• Two Digit Subtraction
• Three Digit Subtraction
• Working with the Difference
• Multiplication and Division worksheets
• Number and Place Value Worksheets
• Fractions, Decimals and Percentages

MEASUREMENT

• Metric Measures
• Area and Perimeter
• Properties of Shapes
• Position and Direction
• Transformations

ALGEBRA & STATISTICS

🏫 Back to School Offer 📚 - Get 25% off Premium Membership with code CAZOOM25

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35 year 6 maths questions

Practise 35 year 6 maths questions that will help your child stay on track!

Author Amber Watkins

Published February 2024

• Key takeaways
• Year 6 maths word problems help students apply mathematical concepts to real-world scenarios.
• In year 6 maths, it’s important to master fractions, decimals, and order of operations.
• Hard problems  can be simplified by drawing a picture or using a method that makes them easier to solve.

Table of contents

• Word problems
• Numbers & place value

Multiplication

If this maths page has 5 sections of maths questions  with an average of 7 questions in each section, can you guess how many problems there will be in all? That’s right, there will be a total of 35 year 6 maths questions for us to practise. Without realising it, you just solved one of our first year 6 word problems . Excellent work! Together we will review year 6 maths problems with decimals, fractions, order of operations, and rounding. We will even consider hard maths problems, like multiplying using square models and number lines. Don’t worry about getting the answers right the first time, each section includes answers if you need a sneak peek. So grab a pad and pencil and let’s begin.

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Year 6 maths word problems

Let’s begin by covering maths word problems.

Mia’s water bottle can hold 300 millilitres of water. She drinks two and a half water bottles each day. How many total millilitres of water does Mia drink each day? 

The playground is made up of four rectangular lots that are each 10 metres by 7 metres. What is the total area of the playground?

 Josh lives 2.5 kilometres away from the park. Josh rides his bike to the park and back home four days a week. How many kilometres does Josh ride his bike each week?

Since we are solving word problems, a word should always be in our answer.

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Numbers & place value

In this section, we will cover maths questions that use place values, word form to standard form, standard form to word form, and expanded form.

Place value

Which digit in the number 245 is in the hundreds place?

Which digit in the number 4,602 is in the tens place?

Which digit in the number 752 is in the ones place?

Word form to standard form

Standard form to expanded form.

4,000 + 300 + 2 = 4,302

600 + 50 + 4 = 654

20,000 + 2,000 + 300 + 60 + 5 = 22,365

In this section, we will cover year six maths questions that include comparing decimals and rounding decimals to the nearest tenth, hundredth, and thousandths place. Let’s get started.

8.9 and 8.900 are the same.

Remember if the number to the right is 5 or larger, you can borrow and become one digit larger. If the number to the right is between 0 and 4, you can’t borrow and the number remains the same.

In this section, we will review maths questionss for year six that cover the topics of adding and subtracting two and three-digit numbers using transformation, division using area models, and the order of operations.

Adding and subtracting whole numbers by transformation

A large portion of year 6 maths problems can be made easier to solve by transformation or changing numbers to make the problem simpler. Let’s practise adding and subtracting two and three-digit numbers by transformation.

How to add numbers using transformation?

When adding or subtracting numbers, look for ways to round to make the problem simpler. Don’t forget what you do to one number, you have to do the opposite to the other. This makes sure the problem stays balanced. Let’s see how this is done. What is 48 + 52? 48 + 2 = 50

52 – 2 = 50 

50 + 50 = 100.

It may be difficult to add 48 + 52 in your head, so we round 48 to 50 by adding 2. Since we added 2 to the first number, we have to make sure to subtract 2 from the second number. So now the problem is 50 plus 50, which is much easier to calculate! 

32 – 2 = 30 68 + 2 = 70 30 + 70 = 100 The answer is 100.

208 – 8 = 200 432 + 8 = 440 200 + 440 = 640 The answer is 640.

321- 1 = 320 199 + 1 = 200 320- 200 = 120 The answer is 120

Division using area models

Don’t know what an area model is? See our area model guide to help with these problems.

Using an area model find the quotient of 365 ፥ 5 =

Using an area model find the quotient of 504 ፥ 6 =

Using the area model below, find the quotient of 872 ፥ 2 =

Order of operations

Many people remember the Order of Operations with the acronym PEMDAS- “Please Excuse My Dear Aunt Sally”, with each letter representing an operation: Parentheses, Exponents, Multiply or Divide, Add or Subtract. Solve the following equations using the order of operations.

Remember that the steps Multiply or Divide can be done in any order. Also, the steps Add or Subtract can be done in any order, do the operation that comes first.

Some of the hardest maths questions involve multiplying: multiplying using square models, multiplying fractions and whole numbers using expanded form, and multiplying fractions using number lines. Let’s practise a few of each!

Multiplying using square models

Multiplying using square models is a method to help students “see” multiplication problems in a simpler way.

Multiply 42 x 35 using the square model below.

Multiply 55 x 76 using the square model below.

Multiply 98 x 42 using the square model below.

Multiplying fractions and whole numbers using expanded form

Multiply ½ x 5 using expanded form.

Multiply ⅔ x 6 using expanded form.

Multiply ⅙ x 7 using expanded form.

Multiplying fractions using a number line

For more maths practice for year 6 , our app for maths help provides year 6 maths help in a way that makes maths fun, rewards effort over being correct, and scaffolds learning. Plus, you’ll get access to a dashboard that displays your child’s participation and progression on maths topics they struggle with. Check it out today !

Parents, sign up for a DoodleMaths subscription and see your child become a maths wizard!

Word problem answer sheet

Mia drinks 750 millilitres  of water each day.

Explanation: 300 x 2 = 600. 300 / 2 = 150. 600 + 150 = 750.

280 square metres.

Explanation: The area of one lot is 10 x 7 = 70 metres. Take that area and times it by four, so 70 x 4 = 280 metres.

Josh rides 20 kilometres on his bike each week.

Explanation: Each day Josh rides 5 total kilometres: 2.5 kilometres to the park and 2.5 kilometres back home. If we multiply that number by 4 days a week, it equals 20 kilometres in all.

Writing numbers answer sheet

2 is in the hundreds place.

0 is in the tens place.

2 is in the ones place.

Division using area models answer sheet

Multiplying using square models answer sheet

Multiplying fractions and whole numbers using expanded form answer sheet

Multiplying fractions using a number line answer sheet

Explanation – First divide the number line into 6 equal parts and draw up a line up to 4/6. Then find the ½ way mark of that line you drew up to 4/6. You will now see the line is divided into three parts. So the answer would be ⅓. 

Lesson credits

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring students in maths. "Knowing that my work in maths education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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Free Printable Math Word Problems Worksheets for 6th Year

Math Word Problems: Discover a vast collection of free printable worksheets for Year 6 students, created by educators to enhance their mathematical skills and problem-solving abilities. Dive into the world of numbers with Quizizz!

Recommended Topics for you

• Addition Word Problems
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• Division Word Problems
• Mixed Operation Word Problems
• Multi-Step Word Problems
• Fraction Word Problems
• Geometry Word Problems
• Measurement Word Problems
• Time Word Problems
• Money Word Problems
• Data Word Problems
• Performance Tasks

Explore Math Word Problems Worksheets by Grades

• kindergarten

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• Social studies
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Explore printable Math Word Problems worksheets for 6th Year

Math Word Problems worksheets for Year 6 are an essential resource for teachers who want to help their students develop strong problem-solving skills and a deep understanding of mathematical concepts. These worksheets provide a variety of engaging and challenging problems that require students to apply their knowledge of math in real-world situations. With a wide range of topics covered, including fractions, decimals, percentages, and geometry, Year 6 Math Word Problems worksheets are designed to align with the Common Core State Standards and support teachers in their efforts to create a well-rounded math curriculum. By incorporating these worksheets into their lesson plans, teachers can ensure that their students are receiving the practice and reinforcement they need to excel in math.

Quizizz is an excellent platform for teachers to access a vast library of Math Word Problems worksheets for Year 6, along with other valuable resources to enhance their students' learning experience. This interactive platform offers a variety of features, such as customizable quizzes, real-time feedback, and gamification elements, to keep students engaged and motivated. In addition to Year 6 Math worksheets, Quizizz also provides resources for other subjects and grade levels, making it a one-stop-shop for teachers looking to diversify their instructional materials. By utilizing Quizizz in conjunction with Math Word Problems worksheets for Year 6, teachers can create a dynamic and effective learning environment that fosters a love for math and sets their students up for success.

The smart way to improve grades

Comprehensive & curriculum aligned, try an activity or get started for free, year 6 maths worksheets.

Get started for free to track and monitor progress.

Your child can learn, practice and test their year 6 skills (age 10 - 11) with these automatically marked, interactive year 6 maths worksheets. Towards the end of KS2, your child will need to start thinking about preparing for their year 6 maths SATs which is why we’ve created our worksheets to help your child get ready and revise everything they need to know for the year 6 maths tests. This year they'll be working towards mastering Upper Key Stage 2 (years 5 and 6) topics which they can do with our range of year 6 maths worksheets .

Year 6 maths tests & assessments

• SATs Reasoning Mathematics Paper 2 in the Style of Key Stage 2 National Tests (Practice 1) Start Test
• SATs Arithmetic Mathematics Paper 1 in the Style of Key Stage 2 National Tests (Practice 3) Start Test
• Assessment: Back-to-school (Y6) Start Test
• Assessment: End of Term 1 Start Test
• Assessment: End of Term 2 Start Test

Revise popular maths topics

• Algebra View Worksheets
• Decimals View Worksheets
• Division View Worksheets
• Fractions View Worksheets
• Percentages View Worksheets

This terms popular year 6 maths worksheets

If you're looking to give your child a bit of extra support either in the run up to their SATs or for their everyday learning, have a browse through our year 6 maths worksheets, designed and created by our own UK teachers to be approachable and engaging to complete.

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Calculate Area and Volume TRY WORKSHEET FOR FREE

Calculate Areas of Parallelograms TRY WORKSHEET FOR FREE

Calculate the Area of Parallelograms and Triangles TRY WORKSHEET FOR FREE

Calculate the Area of Triangles TRY WORKSHEET FOR FREE

Understand How to Work Out the Volume of Cubes and Cuboids TRY WORKSHEET FOR FREE

Answer Questions About 3D Shapes TRY WORKSHEET FOR FREE

Calculate and Compare the Volume of Cubes and Cuboids TRY WORKSHEET FOR FREE

Calculate and Compare Volume TRY WORKSHEET FOR FREE

Describe Linear Number Sequences TRY WORKSHEET FOR FREE

Describe Number Sequences TRY WORKSHEET FOR FREE

Evaluate Solutions when there are Two Unknowns in an Expression TRY WORKSHEET FOR FREE

Explore Equations with Two Variables TRY WORKSHEET FOR FREE

Calculate Angles TRY WORKSHEET FOR FREE

Calculate Missing Angles TRY WORKSHEET FOR FREE

Calculate the Missing Angle Round a Point TRY WORKSHEET FOR FREE

Calculate the Unknown Angle in a Triangle TRY WORKSHEET FOR FREE

Back-to-school

Assessment: Back-to-school (Y6) PREVIEW WORKSHEET

Combined Assessment

Assessment: English, Maths and Science Combined (Y6) PREVIEW WORKSHEET

Coordinates

Find Missing Coordinates to Complete a Shape TRY WORKSHEET FOR FREE

Identify Points on a Coordinate Grid TRY WORKSHEET FOR FREE

Identify Reflections on Coordinate Grids TRY WORKSHEET FOR FREE

Identify Translations on a Grid TRY WORKSHEET FOR FREE

Multiply Decimals Using Multiplication Facts TRY WORKSHEET FOR FREE

Convert Percentages to Decimals TRY WORKSHEET FOR FREE

Divide a Number with One Decimal Place by a Single-Digit Number TRY WORKSHEET FOR FREE

Divide a Number with Two Decimal Places by a Single-Digit Number TRY WORKSHEET FOR FREE

Division or Sharing

Divide Three-Digit Numbers Leaving Remainders as Decimals TRY WORKSHEET FOR FREE

Solve Problems Using Long Division TRY WORKSHEET FOR FREE

Solve Written Division Calculations TRY WORKSHEET FOR FREE

Understand How to Use Formal Long Division TRY WORKSHEET FOR FREE

End of Term 1

Assessment: End of Term 1 PREVIEW WORKSHEET

End of Term 2

Assessment: End of Term 2 PREVIEW WORKSHEET

End of Term 3

Assessment: End of Term 3 PREVIEW WORKSHEET

End of Year

Assessment: End of Year PREVIEW WORKSHEET

Estimating and Rounding

Estimate Answers to Addition Questions Using Rounding TRY WORKSHEET FOR FREE

Practise Rounding Decimals to Estimate Answers to Additions TRY WORKSHEET FOR FREE

Practise Rounding Numbers Including to One or Two Decimal Places TRY WORKSHEET FOR FREE

Round Decimals to Nearest Whole Number and Estimate Answers TRY WORKSHEET FOR FREE

Exam-Style Questions: Accurate Decimal Calculation

Dividing Decimal Numbers by 10, 100, 1000 and Multiplying by an Integer TRY WORKSHEET FOR FREE

Understand and Apply Division of Decimal Numbers to Solve Problems PREVIEW WORKSHEET

Using and Applying Decimal Numbers up to 3 Decimal Places TRY WORKSHEET FOR FREE

Exam-Style Questions: BODMAS Skills

Understand and Apply BODMAS Skills TRY WORKSHEET FOR FREE

Exam-Style Questions: Decimal Conversion

Understand and Apply the Conversion of Decimal Numbers to Percentages 1 TRY WORKSHEET FOR FREE

Understand and Apply the Conversion of Fractions to Decimal Numbers 2 TRY WORKSHEET FOR FREE

Understand and Apply the Conversion of Fractions, Decimals and Percentages 3 TRY WORKSHEET FOR FREE

Exam-Style Questions: Geometry

Understand and Apply the Conversion of Measurement Units 2 TRY WORKSHEET FOR FREE

Understand and Apply the Conversion of Metric Measurement Units TRY WORKSHEET FOR FREE

Understand and Calculate Missing Angles Using Known Angle Facts TRY WORKSHEET FOR FREE

Exam-Style Questions: Mental Maths

Use and Apply Mental Arithmetic Skills TRY WORKSHEET FOR FREE

Use and Apply Mental Arithmetic Skills 2 TRY WORKSHEET FOR FREE

Use and Apply Mental Arithmetic Skills 3 TRY WORKSHEET FOR FREE

Exam-Style Questions: Reading Timetables

Understanding Different Timetables using the 12-hour and 24-hour format TRY WORKSHEET FOR FREE

Understanding Different Timetables using the 12-hour and 24-hour format (2) TRY WORKSHEET FOR FREE

Understanding Different Timetables using the 12-hour format TRY WORKSHEET FOR FREE

Exam-Style Questions: Using Known Facts

Use and Apply Multiplication Facts to Solve Problems PREVIEW WORKSHEET

Use and Apply Multiplication Facts to Solve Problems 2 TRY WORKSHEET FOR FREE

Use and Apply Times Tables TRY WORKSHEET FOR FREE

Exam-Style Questions: Worded Problems

Understand and Apply Problem Solving Skills 1 TRY WORKSHEET FOR FREE

Understand and Apply Problem Solving Skills 2 PREVIEW WORKSHEET

Understand and Apply Problem Solving Skills 3 TRY WORKSHEET FOR FREE

Four Operations

Order Operations in Calculations Using Brackets TRY WORKSHEET FOR FREE

Order Simple Operations in Calculations TRY WORKSHEET FOR FREE

Practise Using BIDMAS to Order Operations in Calculations TRY WORKSHEET FOR FREE

Use BIDMAS to Order the Operations in Calculations TRY WORKSHEET FOR FREE

Add and Subtract Fractions with Related Denominators TRY WORKSHEET FOR FREE

Add and Subtract Fractions with Unrelated Denominators TRY WORKSHEET FOR FREE

Compare Fractions by Finding the Common Denominator TRY WORKSHEET FOR FREE

Convert Decimals to Fractions TRY WORKSHEET FOR FREE

Graphs, Tables, Charts and Data

Answer Questions From a Pie Chart TRY WORKSHEET FOR FREE

Answer Questions Using the Mean TRY WORKSHEET FOR FREE

Calculate Information from a Pie Chart TRY WORKSHEET FOR FREE

Find the Mean TRY WORKSHEET FOR FREE

Hundreds, Tens and Units

Compare Large Numbers Using Knowledge of Place Value TRY WORKSHEET FOR FREE

Arrange Integers in Ascending Order TRY WORKSHEET FOR FREE

Arrange Integers in Descending Order TRY WORKSHEET FOR FREE

Know Numbers From Ones to Millions TRY WORKSHEET FOR FREE

Measurement

Apply Accurate Conversions Between Miles and Kilometres TRY WORKSHEET FOR FREE

Convert a Range of Measures Including up to Three Decimal Places TRY WORKSHEET FOR FREE

Convert Between Measurements to Solve Problems TRY WORKSHEET FOR FREE

Convert Between Measurements with up to Three Decimal Places TRY WORKSHEET FOR FREE

Mental Maths

Add and Subtract Numbers Mentally TRY WORKSHEET FOR FREE

Calculate Without a Calculator TRY WORKSHEET FOR FREE

Calculate Without Using a Calculator TRY WORKSHEET FOR FREE

Estimate the Answer to an Addition by Rounding TRY WORKSHEET FOR FREE

Multiplication

Complete Number Grids Using Multiplication Facts TRY WORKSHEET FOR FREE

National Curriculum Objectives

Assessment: Addition, Subtraction, Multiplication and Division PREVIEW WORKSHEET

Assessment: Algebra PREVIEW WORKSHEET

Assessment: Fractions PREVIEW WORKSHEET

Assessment: Geometry - Position and Direction PREVIEW WORKSHEET

Negative Numbers

Practise Working with Negative Numbers TRY WORKSHEET FOR FREE

Solve Problems Using Negative Numbers TRY WORKSHEET FOR FREE

Understand How To Work with Negative Numbers TRY WORKSHEET FOR FREE

Use Knowledge of Negative Numbers to Solve Problems TRY WORKSHEET FOR FREE

Percentages

Calculate the Value of a Discount TRY WORKSHEET FOR FREE

Find 10% of a Number TRY WORKSHEET FOR FREE

Find Percentages of Given Amounts TRY WORKSHEET FOR FREE

Find Simple Percentages of the Given Numbers TRY WORKSHEET FOR FREE

Ratio and Proportion

Find Scale Factors and Missing Lengths Using Ratios TRY WORKSHEET FOR FREE

Calculate Simple Ratios TRY WORKSHEET FOR FREE

Convert Ratio to Proportional Scale with Mixed Units TRY WORKSHEET FOR FREE

Divide Values by a Given Ratio TRY WORKSHEET FOR FREE

SATs Maths Practice Papers

SATs Arithmetic Mathematics Paper 1 in the Style of Key Stage 2 National Tests (Practice 1) TRY WORKSHEET FOR FREE

SATs Arithmetic Mathematics Paper 1 in the Style of Key Stage 2 National Tests (Practice 2) TRY WORKSHEET FOR FREE

SATs Arithmetic Mathematics Paper 1 in the Style of Key Stage 2 National Tests (Practice 3) TRY WORKSHEET FOR FREE

SATs Mathematics Reasoning Paper 2 in the Style of the Key Stage 2 National Tests (Practice 2) PREVIEW WORKSHEET

Convert Between Units of Time TRY WORKSHEET FOR FREE

Times Tables

Calculate the Common Multiples TRY WORKSHEET FOR FREE

Develop Your Long Multiplication Skills TRY WORKSHEET FOR FREE

Develop Your Skills Multiplying Four-Digit Numbers by Two-Digit Numbers TRY WORKSHEET FOR FREE

Find the Common Multiples TRY WORKSHEET FOR FREE

19 TOPICS | 61 SUBTOPICS | 315 WORKSHEETS

Express problems algebraically.

Express Missing Number Problems Using Algebra TRY WORKSHEET FOR FREE

Find Missing Numbers Using Inverse Operations in an Algebraic Expression TRY WORKSHEET FOR FREE

Find the Missing Numbers in Equations TRY WORKSHEET FOR FREE

Find the Missing Value in an Equation TRY WORKSHEET FOR FREE

Use Algebra Formulae

Practise Using Simple Formulae TRY WORKSHEET FOR FREE

Solve Problems by Substituting Values into a Formula TRY WORKSHEET FOR FREE

Substitute Values into Simple Formulae TRY WORKSHEET FOR FREE

Know Linear Number Sequences

Find Terms and Create Expressions TRY WORKSHEET FOR FREE

Find the Rule of Linear Number Sequences TRY WORKSHEET FOR FREE

Use Equations

Find Pairs of Numbers that Fit a Simple Equation TRY WORKSHEET FOR FREE

Find Pairs of Numbers that Satisfy an Equation TRY WORKSHEET FOR FREE

Understand How to Solve Equations with Two Unknowns TRY WORKSHEET FOR FREE

Use Variables

Find the Value of an Expression by Substituting a Variable TRY WORKSHEET FOR FREE

Investigate Equations with Two Variables TRY WORKSHEET FOR FREE

Solve Equations with Two or More Variables TRY WORKSHEET FOR FREE

Identify Common Factors, Multiples and Prime Numbers

Find the Multiples TRY WORKSHEET FOR FREE

Identify Common Factors, Multiples and Prime Numbers TRY WORKSHEET FOR FREE

Perform Mental Calculations

Find the Halfway Number TRY WORKSHEET FOR FREE

Know How to Add Consecutive Numbers TRY WORKSHEET FOR FREE

Multiply to Four Digits (Long Multiplication)

Multiply a Three-Digit Number by a Two-Digit Number TRY WORKSHEET FOR FREE

Multiply Four-Digit Numbers by Two-Digit Numbers TRY WORKSHEET FOR FREE

Divide to Four Digits (Long Division)

Understand Long Division Leaving Remainders as Fractions TRY WORKSHEET FOR FREE

Carry Out Calculations Using Order of Operations

Find Three More Facts Based on the Given Fact TRY WORKSHEET FOR FREE

Practise Column Subtraction with Five-Digit Numbers TRY WORKSHEET FOR FREE

Solve Multi-Step Add/Subtract Problems

Perform Calculations Without a Calculator TRY WORKSHEET FOR FREE

Use Estimation to Check Answers

Round Decimals and Estimate the Answer to an Addition TRY WORKSHEET FOR FREE

Divide with Two Decimal Places

Halve Simple Decimals TRY WORKSHEET FOR FREE

Know Fraction-Decimal-Percentage Equivalents

Convert Percentages of a Circle into Fractions TRY WORKSHEET FOR FREE

Use Common Factors

Find HCF and LCM to Solve Problems TRY WORKSHEET FOR FREE

Practise Simplifying Fractions Using Common Factors TRY WORKSHEET FOR FREE

Practise Solving Problems Using Simplifying Fractions TRY WORKSHEET FOR FREE

Practise Using Common Factors to Simplify Fractions TRY WORKSHEET FOR FREE

Compare and Order Fractions

Find Common Denominators to Order Fractions TRY WORKSHEET FOR FREE

Identify the Larger Fraction TRY WORKSHEET FOR FREE

Practise Using Common Denominators to Order Mixed and Improper Fractions TRY WORKSHEET FOR FREE

Add/Subtract Fractions

Practise Adding and Subtracting Fractions with Mixed Numbers TRY WORKSHEET FOR FREE

Solve Problems Involving Adding and Subtracting Fractions TRY WORKSHEET FOR FREE

Multiply Proper Fractions

Multiply Fractions Including Mixed Numbers TRY WORKSHEET FOR FREE

Multiply Simple Fractions TRY WORKSHEET FOR FREE

Practise Multiplying Simple Fractions TRY WORKSHEET FOR FREE

Divide Proper Fractions

Divide Fractions by Whole Numbers TRY WORKSHEET FOR FREE

Practise Dividing Fractions TRY WORKSHEET FOR FREE

Practise Dividing Fractions by Whole Numbers TRY WORKSHEET FOR FREE

Calculate Fraction-Decimal Equivalents

Convert Fractions to Decimals Using Division TRY WORKSHEET FOR FREE

Practise Converting Decimals to Fractions TRY WORKSHEET FOR FREE

Practise Converting Fractions to Decimals Using Division TRY WORKSHEET FOR FREE

Use Three Decimal Places

Divide Decimals by 10, 100 or 1000 TRY WORKSHEET FOR FREE

Multiply Decimals by 10, 100 or 1000 TRY WORKSHEET FOR FREE

Multiply with Two Decimal Places

Multiply Decimal Numbers by One-Digit Numbers TRY WORKSHEET FOR FREE

Multiply Decimal Numbers by Whole Numbers TRY WORKSHEET FOR FREE

Multiply Simple Decimal Numbers by Whole Numbers TRY WORKSHEET FOR FREE

Solve Rounding Problems

Multiply Decimals by Rounding to Whole Numbers TRY WORKSHEET FOR FREE

Round Decimals to Nearest Whole Numbers Before Dividing TRY WORKSHEET FOR FREE

Round Decimals to Nearest Whole Numbers Before Multiplying TRY WORKSHEET FOR FREE

Solve Percentage Problems

Convert Fractions into Percentages TRY WORKSHEET FOR FREE

Find the Discount and Final Price TRY WORKSHEET FOR FREE

Solve Ratio Problems

Solve fraction/multiples problems.

Find Lowest Common Multiples to Solve Fraction Problems TRY WORKSHEET FOR FREE

Understand Unequal Sharing Using Fractions TRY WORKSHEET FOR FREE

Calculate Average/Interpret Mean

Find the Mean from Tables of Data TRY WORKSHEET FOR FREE

Find the Mean Including Negative Numbers TRY WORKSHEET FOR FREE

Use Charts and Graphs

Interpret a Line Graph on Sunflower Growth TRY WORKSHEET FOR FREE

Interpret a Travel Graph TRY WORKSHEET FOR FREE

Determine Digit Value to 10 000 000

Understand How to Order Large Numbers TRY WORKSHEET FOR FREE

Round Numbers for Accuracy

Practise Rounding Large Numbers TRY WORKSHEET FOR FREE

Round Large Numbers Including to the Nearest 1,000,000 TRY WORKSHEET FOR FREE

Round Numbers Including to One or Two Decimal Places TRY WORKSHEET FOR FREE

Use Negative Numbers

Solve number/place value problems up to 10 000 000.

Practise Reading, Writing And Ordering Numbers Up To 10,000,000 TRY WORKSHEET FOR FREE

Read, Write and Order Numbers Up To 10,000,000 TRY WORKSHEET FOR FREE

Understand Place Value Using Large Numbers TRY WORKSHEET FOR FREE

Use Place Value to Solve Problems Using Large Numbers TRY WORKSHEET FOR FREE

Solve Conversion Problems

Convert Between Measurements with up to Two Decimal Places TRY WORKSHEET FOR FREE

Solve Conversion Problems TRY WORKSHEET FOR FREE

Convert Between Standard Units

Convert Between Standard Units of Mass TRY WORKSHEET FOR FREE

Convert Decimal Units of Measure TRY WORKSHEET FOR FREE

Convert Miles/Kilometres

Convert Kilometres to Miles TRY WORKSHEET FOR FREE

Convert Miles to Kilometres TRY WORKSHEET FOR FREE

Recognise Shapes

Recognise that Shapes with the Same Area can have Different Perimeters TRY WORKSHEET FOR FREE

Recognise that Shapes with the Same Perimeter can have Different Areas TRY WORKSHEET FOR FREE

Use Area/Volume Formulae

Investigate The Formulae for Area and Volume TRY WORKSHEET FOR FREE

Recognise When to Use a Volume Formula TRY WORKSHEET FOR FREE

Recognise When to Use an Area Formula TRY WORKSHEET FOR FREE

Calculate Areas

Find the Area of a Triangle TRY WORKSHEET FOR FREE

Use Cubes/Cuboids

Calculate Cuboid Dimensions TRY WORKSHEET FOR FREE

Know 3D Shapes

Count the Faces, Vertices and Edges of 3D Shapes TRY WORKSHEET FOR FREE

Draw Dice Dots on Net Cubes TRY WORKSHEET FOR FREE

Identify the Number of Faces, Vertices and Edges of 3D Shapes TRY WORKSHEET FOR FREE

Compare Shape Properties

Recognise Descriptions of 2D and 3D Shapes TRY WORKSHEET FOR FREE

Use a Variety of Rules to Find the Missing Angle TRY WORKSHEET FOR FREE

Know Circle Parts

Calculate the Circumference of a Circle Using Pi TRY WORKSHEET FOR FREE

Explore the Relationship Between Different Parts of a Circle TRY WORKSHEET FOR FREE

Identify Parts of a Circle TRY WORKSHEET FOR FREE

Know the Parts of a Circle TRY WORKSHEET FOR FREE

Recognise/Find Angles

Find the Missing Angles TRY WORKSHEET FOR FREE

Use Coordinate Grids

Read Coordinate Grids Using all Four Quadrants TRY WORKSHEET FOR FREE

Solve Problems Using Coordinate Grids TRY WORKSHEET FOR FREE

Draw/Translate Shapes

Move Shapes on a Grid TRY WORKSHEET FOR FREE

Plot Simple Shapes on Coordinate Grids TRY WORKSHEET FOR FREE

Arithmetic Practice Papers

Reasoning practice papers.

SATs Mathematics Reasoning Paper 2 in the Style of the Key Stage 2 National Tests (Practice 3) PREVIEW WORKSHEET

SATs Mathematics Reasoning Paper 3 in the Style of Key Stage 2 National Tests (Practice 1) PREVIEW WORKSHEET

SATs Mathematics Reasoning Paper 3 in the Style of Key Stage 2 National Tests (Practice 2) PREVIEW WORKSHEET

Exam-Style Questions: Accurate Decimal Calculations

Core subjects.

Above, you'll find a list of interactive and printable year 6 maths worksheets, assessments and revision materials by topic, (including our year 6 percentages worksheets ,) which have been designed by teachers to help your child improve their understanding and comprehension of the topics taught in schools and allowing them to gain an understanding of what they'll need to know for their year 6 maths tests.

Our worksheets are perfect as year 6 maths revision for SATs - head to our SATs page for a full library of revision content across different subjects, including some SATs practice papers! If you need a boost on other subjects, you can check out our year 6 science worksheets and our year 6 English worksheets . Our year 6 maths revision worksheets are 100% aligned to the National Curriculum and can provide you visibility to your child's progress throughout the year. This is a stressful time for your child, but it’s important to be prepared which is why we’ve made maths homework, arithmetic worksheets and other revision resources to give your child the best head start possible. What’s better is that all of our worksheets are available in pdf and are printable, so you can complete them online or on paper. Try one of the below sample free year 6 maths worksheets to test your child's attainment levels - we're here to help your child succeed!

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25 Year 6 Algebra Questions And Answers: KS2 Assessment Preparation

Emma Johnson

Here are 25 Year 6 SATs algebra questions designed to cover the algebraic concepts pupils are likely to encounter in the Key Stage 2 SATs.

In addition to these questions, we look in depth at the key algebraic vocabulary children should be familiar with when tackling algebraic questions ahead of the maths SATs.  

Generally, algebra appears in the KS2 reasoning papers and not the Year 6 arithmetic questions . Usually appears less frequently in KS2 maths SATs papers than other national curriculum strands such as the four operations, place value and percentages, decimals and fractions questions . 

But, it is still essential that Year 6 pupils are confident in addressing algebraic questions for their KS2 assessments so they can develop their understanding of algebra in KS3 and at GCSE. 

Why are Year 6 algebra questions important in Key Stage 2?

Understanding basic algebraic concepts and formulas in Key Stage 2 helps to lay the foundations for more complex algebra in KS3, at GCSE and beyond. It also helps to develop children’s problem solving, critical thinking and logic. 

Often, algebra may evoke anxiety in children before they even enter year 6 — they aren’t aware that they have been engaging with basic algebraic concepts since Key Stage 1. 

For example, missing number calculations in Year 1, such as 3 + \_ = 10 are the starting blocks for algebraic expressions in Year 6, such as  x + 3 = 10 . 

As educators, it is important to make pupils aware of this relationship, helping to reduce the anxiety associated with algebra. 

Similarly to ratio questions , it helps to link algebraic concepts to real-life situations when teaching algebra in KS2 . This helps to enhance pupils’ understanding. 

Demonstrating how to apply algebra in Year 6 can help pupils independently solve problems in everyday scenarios and grasp its practical relevance. 

For instance, solving the equation 3x = 24 may initially seem quite abstract. But when asked to calculate the cost of one apple, when the cost of 3 apples is 24p, pupils can contextualise the question and make connections to this algebraic concept. 

Providing children with concrete resources, visual representations and real-life situations is vital in the teaching of algebra. This approach helps pupils break down the abstract nature of algebra and develop a conceptual understanding.

Key terminology for Year 6 SATs algebra 

Children need to have an understanding of algebra terminology in order to secure their knowledge of algebraic concepts. 

Year 6 pupils will need to have an understanding of the following key terms:

• Algebra: The use of letters and symbols to represent numbers, when we don’t know the value in an equation. For example, y + 5 = 10
• Variable : A symbol (usually a letter), used to represent an unknown or changing quantity.  For example, in the number sentence 2x + 5 = 19, \; x is the variable
• Term : A single mathematical expression separated by addition or subtraction in an algebraic expression.  For example, in 4x + 6, \; 4x and 6 are terms
• Unknown: The value you are trying to work out is shown as a letter. For example, in the number sentence 3x + 4 = 13, \; x is the unknown
• Expression: A mathematical sentence using numbers and/or variables.  For example, 3x + 7 is an expression.
• Equation: a mathematical statement or expression that contains two equal sides separated by an equals sign. For example, 2y + 4 = 12 or 2y + 4 = 3x + 3 
• Formula: Algebra uses formulas, which refer to a mathematical rule or relationship that uses letters to represent amounts which can be changed. For example, 7 + x = 10 
• One- step equation : An equation which can be solved in only one step.  For example, x + 7 = 15
• Two- step equation : An algebraic equation that takes you two steps to solve.  For example, 3x + 5 = 11
• Substitution: Replacing variables in an algebraic expression with their numerical values. For example, x + 3  = 13 is equal to 10 + 3 =13 
• Pair of unknowns: A number sentence where there are two unknown values.  For example, x + y = 12 and x is 3 times greater than y . Both x and y are unknowns. 
• Enumerate: Finding all possible answers to an algebraic problem and making a complete list of answers. For example, x + y = 5 

• Balancing equations: Performing operations on both sides of a number sentence to find the missing value. For example, where 3x +12 = 24 start by subtracting 12 from both sides of the equation. 24 - 12 = 3x = 12 12 ÷ 3 = 4 x = 4

200 arithmetic and reasoning questions for Year 6

Download 100 free arithmetic questions and 100 free reasoning questions for Year 6. Includes answers and mark scheme.

How do these Year 6 algebra questions help pupils prepare for the KS2 SATs?

These Year 6 algebra questions cover the breadth of the national curriculum. They have been designed by a math expert to cover the array of algebra SATs questions pupils may encounter in the KS2 SATs. 

All problems, including algebra word problems, are contextualised to represent real-life scenarios. This helps pupils take the abstract concept and relate it to a familiar situation. 

Practising a variety of algebra questions helps familiarise pupils with the question formats they will encounter in the KS2 SATs and develop confidence in their strategies for solving them.

Each question in the sequence becomes progressively harder, providing children with the opportunity to deepen their understanding of algebra. This also means questions will challenge those pupils who are working at greater depth. 

25 Year 6 algebra questions and answers

Year 6 algebra questions: using simple formulae.

According to the national curriculum, pupils must be able to use and apply basic mathematical formulas to solve problems. To do this, they must be familiar with simple formulas and recognise the relationship between variables. 

For example, the formula to find the area of a rectangle: Area = length x width

Question 1: using simple formulae

Calculate the value of each letter below: 4a = 12 7b = 63 9c = 27

Answer: a = 3, \; b = 9, \; c = 3

a. 12 ÷ 4 = 3

b.  63 ÷ 7 = 9

c. 27 ÷ 9 = 3

Question 2: using simple formulae

Calculate the value of the letter in the equation below:

Answer: x = 4

Question 3: using simple formulae

The formula for calculating the area of a rectangle is A = ab ( A is the area and ab are adjacent sides).

A rectangle has sides with a length of 7.2cm and a width of 3.8cm. What is the area?

Answer: 27.36 \, cm^2

Question 4: using simple formulae

The formula for converting kilometres (k) to miles (m) is: k = m \times 8÷5

Use this formula to convert 20 miles into kilometres.

Answer: 32 \, km

Question 5: using simple formulae

The formula for calculating the area of a triangle is \cfrac{1}{2} \, (b \times h)

What would be the height of a triangle with an area of 300 \, cm^2 and a base of 15 \, cm ?

Answer: 4 \, cm

 More Year 6 algebra questions: Year 6 Forming Expressions Worksheets

Year 6 algebra questions: generate and describe linear number sequences

By the end of Year 6, pupils should be able to create and articulate linear number sequences where there is a constant difference between consecutive terms. 

Pupils should also be able to create sequences where they are given the first term and a constant difference to continue expanding the sequence.

Question 6: linear number sequences

What are the next two terms in this sequence?

37, 44, 51, 58, ,

Answer: 65, 72 (+ 7)

Question 7: linear number sequences

Fill in the missing numbers in this sequence:

Answer: 98, 89, 80, 71

Question 8: linear number sequences

The formula 4n + 3 is used to generate a sequence,

Give the first 5 numbers of the sequence.

Answer: 7, 11, 15, 19, 23

Question 9: linear number sequences

Here is a linear sequence:

4, 11, 18, 25

• What is the n th term? 
• What is the 15th term?

Question 10: linear number sequences

Ben has £28 at the start of the month. He spends 30p everyday day in January. How much does he have at the end of the month?

Answer: £18.70

30 x 31 = 930 (£9.30)

£28 – £9.30 = £18.70

Year 6 algebra questions: express missing number problems algebraically 

A requirement of the national curriculum is for Year 6 pupils to be able to solve problems involving unknown values using algebraic expressions or algebraic equations. 

Children first encounter missing number problems in KS1. For example: 3 +  \_ = 10 . By the end of KS2, pupils progress to writing missing expressions and solving equations for a range of real-life problem solving scenarios.

Question 11: express missing number problems 

12 more than a number is 33. Write an expression for this, using n to represent the number:

Answer: n + 12 = 33

Question 12: linear number sequences

What needs to be added to 27 to make 59?

Show the expression and the value of n.

Answer: 27 + n = 59 \quad \;

Question 13: linear number sequences

A function machine multiplies by 4 and then adds 5. What would be the expression if x was put into the function machine?

Answer: 4x + 5

Question 14: linear number sequences

An electrician charges £15 per hour and £25 for a call out. 

What is the formula to express this calculation? (Use c for the cost and h for hour)

Answer: C = 15h + 25

Question 15: linear number sequences

A painter charges £14 per hour, but in December offers a discount of £8.

• Write a formula to express this calculation (use c for cost and h for hour)
• How much would it cost to hire the painter for 8 hours in December?

Answer: a.   C = 14h - 8

Answer: b. £104

(14 x 8)-8 = 104

Year 6 algebra questions: find pairs of numbers that satisfy an equation with two unknowns

Equations with two unknowns involve two variables which are usually represented by letters such as x and y.

Each equation expresses the relationship between the variables. Pupils should be able to identify and apply pairs of numbers to the two variables in order to solve the equation.  

Question 16: pairs of numbers for two unknown values 

Find a possible solution for the following equation:

Answer: x = 6 , \; y = 3 (other possible solutions can be given)

Question 17: pairs of numbers for two unknown values 

Find a possible solution for this equation:

Answer: a = 3, \; b = 7 (other possible solutions can be given).

Question 18: pairs of numbers for two unknown values 

x is 3 times the value of y . What are the values of x and y?

Answer: x = 27, \; y = 9

Question 19: pairs of numbers for two unknown values 

If z = 25 give one possible value of x and y?

Answer: x = 6, \; y = 3.5 (other possible answers may be given)

Question 20: pairs of numbers for two unknown values 

Mason has some 50p and 20p coins. Altogether he has £2.40.

How many of each coin could he have?

Can you find the 2 possible solutions?

Answer: 2 x 50p and 7 x 20p

Or 4 x 50p and 2 x 20p

More questions: Year 6 Finding Pairs of Values Worksheet 

Year 6 algebra questions: Enumerate possibilities of combinations of 2 variables

Enumerate possibility questions involve systematically listing and exploring various combinations of values for two variables. 

By the end of KS2, pupils should be able to methodically consider various combinations of values for two variables.

Question 21: enumerate possibilities of combinations  

The total of two numbers is 15. Both numbers are between 3 and 12.

Find all possible combinations that the two numbers could be:

Answer: 4 + 11, 5 + 10, 6 + 9, 7 + 8

Question 22: enumerate possibilities of combinations 

The difference between two numbers is 7. Both numbers are between 18 and 30.

What could the numbers be? 

Find all the possible combinations.

Answer: 30 – 23, 29 – 22, 28 – 21, 27 – 20, 26 – 19

Question 21: enumerate possibilities of combinations 

Year 6 has a maths test every week and there are 15 questions on each test.

Mason worked out he scored double in the last week of term compared to the first week of term. 

How many correct answers might Mason have scored in the first week? 

Give all the possibilities.

Answer: 1, 2, 3, 4, 5, 6 or 7

Find all the possible combinations, where x and y are whole numbers:

x < 17 and y < 27

Answer: 26 + 15, 25 + 16

Question 23: enumerate possibilities of combinations 

d is an odd number < 16 and e is a multiple of 3 < 13

What could the values of d and e be?

List all the possibilities. 

Answers: 3 x 15 + 2 x 3, 3 x 13 + 2 x 6, 3 x 11 + 2 x 9, 3 x 9 + 2 x 12

More Year 6 algebra worksheets and algebra resources 

• Year 6 Algebra and Measures Worksheet 
• Year 6 Forming and Solving One Step Equations Worksheet
• Year 6 Forming and Solving Two Step Equations Worksheet  
• Year 6 Algebra Recap  
• 15 Algebra Questions And Practice Problems (KS3 & KS4): Harder GCSE Exam Style Questions Included

While algebra does appear in Year 6 SATs questions, there are a lower percentage of algebra questions in the KS2 exams than some of the other content domains from the maths national curriculum.  Over the last 5 years, algebra questions have made up between 4\% and 9\% of the Key Stage 2 maths assessments.

Algebra is explicitly taught to children from Year 6 (age 10 and 11 ) onwards. But children are introduced to basic algebra concepts, such as missing number questions, in primary school at a much younger age.

Pupils are introduced to the concept of algebra in Year 6. According to the national curriculum, by the end of Key Stage 2, pupils should be able to:  • Use simple formulae • Generate and describe linear number sequences • Express missing number problems algebraically • Find pairs of numbers that satisfy an equation with two unknowns • Find enumerate possibilities of combinations of two variables

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Daily Maths Word Problems - Year 6 (Worksheets)

Updated:  17 Apr 2024

A set of 20 problem-solving questions suited to year 6 students.

Non-Editable:  PDF

Pages:  6 Pages

• Curriculum Curriculum:  AUS V8, VIC, AUS V9
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Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers and make estimates for these computations

Use mathematical modelling to solve practical problems, involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in te

This set of problem-solving questions has been designed to support teachers when teaching students about problem-solving in mathematics.

It provides students with the opportunity to work through 20 maths word problems, identifying the important information and how they can work it out using a variety of methods.

An answer sheet has been included.

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Daily maths problems - year 6.

A 44 slide editable PowerPoint Template for problem solving in mathematics.

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Write a review to help other teachers and parents like yourself. If you'd like to request a change to this resource, or report an error, select the corresponding tab above.

Pls tell me the answer of Millie held a two-hour cookie sale to raise money for her school. Cookies were priced at $3 each. Millie raised $48 in the first hour. At the end of the sale, Millie had raised $105. How many cookies did Millie sell in the second hour?

Hi Simba, You can find the answers on the last page of this resource. If you need assistance with anything else, please don't hesitate to get in touch!

Hello, would it be possible to have the questions related to Australia's system of measurement please e.g. miles to kilometres and Fahrenheit to Celsius Thank you!

Hi Lauren, I think the issue has been fixed now. You can download this resource again. If there is anything else I can assist you with, please don't hesitate to contact me.

Resource updates

Question 8 needed adjustments on the quantities to make the problem work. This has been updated

Fixed the answer on Question 20.

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Solving word problems Y6

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

26 December 2020

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Good range multi word problems like it thank you

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In glad it was helpful. <br /> Check our http://mathsanarchy.com<br /> Kind regards, Shirley

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This is a really useful resource to U and A skills. Thank you for sharing.

Very good resource. Re the car slide - surely each car has 4 (or 5) tyres? Therefore cost is &#163;400.

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