year 6 problem solving

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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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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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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

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Year 6 maths

IXL offers hundreds of Year 6 maths skills and games to explore and learn! Not sure where to start? Go to your personalised Recommendations wall to find a skill that looks interesting, or select a skill plan that aligns to your textbook, national curriculum, or standardised test.

A. Place values and number sense

• 1 Convert between standard and expanded form
• 2 Place values
• 3 Convert between place values
• 4 Place value word problems
• 5 Writing numbers up to one million in words: convert words to digits
• 6 Writing numbers up to one million in words: convert digits to words
• 7 Writing numbers up to ten million in words: convert words to digits
• 8 Writing numbers up to ten million in words: convert digits to words
• 9 Compare numbers up to one million
• 10 Compare numbers up to ten million
• 11 Put numbers in order: up to one million
• 12 Put numbers in order: up to ten million
• 13 Roman numerals
• 14 Rounding: up to thousands place
• 15 Rounding: up to millions place
• 16 Even or odd: arithmetic rules

B. Addition and subtraction

• 1 Add and subtract whole numbers up to millions
• 2 Add and subtract whole numbers: word problems
• 3 Complete addition and subtraction sentences
• 4 Fill in the missing digits
• 5 Choose numbers with a particular sum or difference
• 6 Properties of addition
• 7 Add using properties
• 8 Inequalities with addition and subtraction
• 9 Estimate sums and differences of whole numbers up to four digits
• 10 Estimate sums and differences of whole numbers up to six digits
• 11 Estimate sums and differences: word problems up to six digits

C. Multiplication fluency

• 1 Multiplication facts to 10
• 2 Multiplication facts up to 10: find the missing factor
• 3 Choose the multiples of a given number up to 10
• 4 Multiplication facts to 12
• 5 Multiplication facts up to 12: find the missing factor
• 6 Choose the multiples of a given number up to 12

D. Multiplication

• 1 Multiply by 1-digit numbers
• 2 Multiply by 1-digit numbers: word problems
• 3 Multiplication patterns over increasing place values
• 4 Properties of multiplication
• 5 Multiply by a multiple of ten
• 6 Estimate products
• 7 Estimate products: word problems
• 8 Use one multiplication fact to complete another
• 9 Multiply 2-digit numbers by 2-digit numbers using area models I
• 10 Multiply 2-digit numbers by 2-digit numbers using area models II
• 11 Multiply 2-digit numbers by 2-digit numbers using partial products
• 12 Multiply 2-digit numbers by 2-digit numbers: complete the missing steps
• 13 Multiply 2-digit numbers by 2-digit numbers
• 14 Multiply 2-digit numbers by 2-digit numbers: word problems
• 15 Box multiplication
• 16 Lattice multiplication
• 17 Multiply 2-digit numbers by 3-digit or 4-digit numbers: complete the missing steps
• 18 Multiply 2-digit numbers by 3-digit or 4-digit numbers
• 19 Multiply 2-digit numbers by 3-digit or 4-digit numbers: word problems
• 20 Multiply three or more numbers up to 2 digits each
• 21 Multiply three or more numbers: word problems
• 22 Choose numbers with a particular product
• 23 Multiply numbers ending in zeroes
• 24 Multiply numbers ending in zeroes: word problems
• 25 Inequalities with multiplication

E. Division fluency

• 1 Division facts to 10
• 2 Division facts to 10: word problems
• 3 Division facts to 12
• 4 Division facts to 12: word problems

F. Division

• 1 Divide by 1-digit numbers
• 2 Divide by 1-digit numbers: word problems
• 3 Division patterns over increasing place values
• 4 Estimate quotients
• 5 Estimate quotients: word problems
• 6 Estimate quotients using compatible numbers
• 7 Divide by 2-digit numbers using models
• 8 Divide by 2-digit numbers using partial quotients
• 9 Divide 2-digit and 3-digit numbers by 2-digit numbers
• 10 Divide 2-digit and 3-digit numbers by 2-digit numbers: word problems
• 11 Divide 4-digit numbers by 2-digit numbers
• 12 Divide 4-digit numbers by 2-digit numbers: word problems
• 13 Adjust quotients
• 14 Multi-step word problems: multiplicative comparison
• 15 Relate multiplication and division
• 16 Complete the division sentence: 2-digit divisors
• 17 Choose numbers with a particular quotient
• 18 Divide numbers ending in zeroes
• 19 Divide numbers ending in zeroes: word problems

G. Number theory

• 1 Divisibility rules
• 2 Divisibility rules: word problems
• 3 Identify factors
• 4 Find all the factor pairs of a number
• 5 Prime and composite numbers: up to 20
• 6 Prime and composite numbers: up to 100
• 7 Prime factorisation
• 8 Highest common factor
• 9 Lowest common multiple

H. Decimals

• 1 What decimal number is illustrated?
• 2 Model decimals and fractions
• 3 Understanding decimals expressed in words
• 4 Place values in decimal numbers
• 5 Relationship between decimal place values
• 6 Convert decimals between standard and expanded form
• 7 Equivalent decimals
• 8 Round decimals
• 9 Decimal number lines
• 10 Compare decimals on number lines
• 11 Compare decimal numbers
• 12 Put decimal numbers in order
• 13 Convert fractions to decimals
• 14 Convert mixed numbers to decimals
• 15 Convert decimals to fractions
• 16 Convert decimals to mixed numbers
• 17 Convert decimals between standard and expanded form using fractions
• 18 Compare decimals and fractions on number lines
• 19 Compare decimals and fractions
• 20 Put assorted decimals, fractions and mixed numbers in order
• 21 Number sequences involving decimals

I. Add and subtract decimals

• 1 Add decimal numbers using blocks
• 2 Add decimal numbers
• • New! Use properties to add three decimals
• 3 Subtract decimal numbers
• 4 Add and subtract decimal numbers
• • New! Use compensation to add and subtract decimals
• 5 Add and subtract decimals: word problems
• 6 Choose decimals with a particular sum or difference
• 7 Complete the decimal addition or subtraction sentence
• 8 Inequalities with decimal addition and subtraction
• 9 Estimate sums and differences of decimals

J. Multiply decimals

• 1 Estimate products of two-digit whole numbers and decimals
• 2 Estimate products of decimals
• 3 Multiply a decimal by 10, 100 or 1,000
• 4 Multiply by 0.1 or 0.01
• 5 Multiply by a power of ten with decimals: find the missing number
• 6 Multiply a decimal by a one-digit whole number using blocks
• 7 Multiply a decimal by a one-digit whole number using the distributive property
• 8 Multiply a decimal by a one-digit whole number
• 9 Multiply a decimal by a one-digit whole number: word problems
• 10 Inequalities with decimal multiplication
• 11 Multiply a decimal by a two-digit whole number using area models
• 12 Multiply a decimal by a two-digit whole number
• 13 Multiply a decimal by a one- or two-digit whole number: word problems
• 14 Multiply three or more numbers, one of which is a decimal

K. Divide decimals

• 1 Estimate decimal quotients
• 2 Divide a whole number by 10, 100 or 1,000: decimal quotients
• 3 Divide a decimal by 10, 100 or 1,000
• 4 Decimal division patterns over increasing place values
• 5 Divide two whole numbers: decimal quotients
• 6 Divide a decimal by a power of ten with decimals: find the missing number
• 7 Divide decimals using blocks: complete the equation
• 8 Divide decimals using area models: complete the equation
• 9 Divide decimals by one-digit whole numbers
• 10 Division with decimal quotients and rounding
• 11 Division with decimal quotients: word problems

L. Fractions and mixed numbers

• 1 Fractions review
• 2 Fractions of a whole: word problems
• 3 Fractions of a group: word problems
• 4 Equivalent fractions
• 5 Patterns of equivalent fractions
• 6 Write fractions in lowest terms
• 7 Lowest common denominator
• 8 Mixed numbers
• 9 Convert between improper fractions and mixed numbers
• 10 Graph and compare fractions on number lines
• 11 Compare fractions and mixed numbers
• 12 Put fractions in order
• 13 Arithmetic sequences with fractions
• 14 Geometric sequences with fractions
• 15 Round mixed numbers
• 16 Reciprocals
• 17 Relate division and fractions
• 18 Understand fractions as division: word problems
• 19 Fractions as division: decimal quotients

M. Add and subtract fractions

• 1 Decompose fractions multiple ways
• 2 Add and subtract fractions with the same denominator using number lines
• 3 Add and subtract fractions with the same denominator
• 4 Add and subtract fractions with the same denominator: word problems
• 5 Add three or more fractions with the same denominator
• 6 Add three or more fractions with the same denominator: word problems
• 7 Add and subtract mixed numbers with the same denominator
• 8 Add and subtract mixed numbers with the same denominator: word problems
• 9 Add up to 4 fractions with denominators of 10 and 100
• 10 Add fractions with different denominators using models
• 11 Add fractions with different denominators
• 12 Subtract fractions with different denominators using models
• 13 Subtract fractions with different denominators
• 14 Add and subtract fractions with different denominators
• 15 Add and subtract fractions with different denominators: word problems
• 16 Add three or more fractions with different denominators
• 17 Add three or more fractions with different denominators: word problems
• 18 Complete addition and subtraction sentences with fractions
• 19 Inequalities with addition and subtraction of fractions
• 20 Estimate sums and differences of mixed numbers
• 21 Add mixed numbers with different denominators
• 22 Subtract mixed numbers with different denominators
• 23 Add and subtract mixed numbers with different denominators
• 24 Add and subtract mixed numbers with different denominators: word problems
• 25 Complete addition and subtraction sentences with mixed numbers
• 26 Inequalities with addition and subtraction of mixed numbers

N. Multiply and divide fractions

• 1 Multiply unit fractions by whole numbers using number lines
• 2 Multiply unit fractions by whole numbers using models
• 3 Multiples of fractions
• 4 Multiply unit fractions and whole numbers: sorting
• 5 Multiply fractions by whole numbers using number lines
• 6 Multiplying fractions by whole numbers: choose the model
• 7 Multiply fractions and whole numbers: sorting
• 8 Multiply fractions by whole numbers
• 9 Multiply fractions by whole numbers: input/output tables
• 10 Fractions of a number
• 11 Fractions of a number: word problems
• 12 Scaling whole numbers by fractions: justify your answer
• 13 Scaling whole numbers by fractions
• 14 Multiply two unit fractions using models
• 15 Multiply two fractions using models
• 16 Multiply two fractions
• 17 Multiply fractions: word problems
• 18 Complete the fraction multiplication sentence I
• 19 Complete the fraction multiplication sentence II
• 20 Divide unit fractions by whole numbers using models
• 21 Divide unit fractions by whole numbers using area models
• 22 Divide unit fractions by whole numbers
• 23 Divide fractions by whole numbers

O. Integers

• 1 Understanding integers
• 2 Integers on number lines
• 3 Graph integers on horizontal and vertical number lines
• 4 Understanding opposite integers
• 5 Compare integers
• 6 Put integers in order

P. Add and subtract integers

• 1 Add integers using number lines
• 2 Subtract integers using number lines
• 3 Add and subtract integers using number lines

Q. Mixed operations

• 1 Add, subtract, multiply and divide whole numbers
• 2 Add, subtract, multiply and divide whole numbers: word problems
• 3 Write numerical expressions
• 4 Evaluate numerical expressions
• 5 Evaluate numerical expressions with brackets
• 6 Evaluate numerical expressions with brackets and square brackets
• 7 Evaluate numerical expressions with brackets in different places
• 8 Missing operators
• 9 Add, subtract, multiply and divide decimals
• 10 Add, subtract, multiply and divide decimals: word problems
• 11 Equations with mixed operations: true or false
• 12 Add, subtract, multiply and divide fractions and mixed numbers
• 13 Add, subtract and multiply fractions and mixed numbers: word problems

R. Problem solving

• 1 Make the largest possible quotient
• 2 Write numerical expressions for word problems
• 3 Multi-step addition and subtraction word problems
• 4 Multi-step word problems
• 5 Multi-step word problems involving remainders
• 6 Multi-step word problems: identify reasonable answers
• 7 Word problems with extra or missing information
• 8 Guess-and-check problems
• 9 Find the order
• 10 Use Venn diagrams to solve problems

S. Ratios and rates

• 1 Write a ratio
• 2 Write a ratio using a fraction
• 3 Write a ratio: word problems
• 4 Identify equivalent ratios
• 5 Write an equivalent ratio
• 6 Ratio tables
• 7 Unit rates
• 8 Equivalent rates
• 9 Ratios and rates: word problems
• 10 Do the ratios form a proportion?
• 11 Solve the proportion
• 12 Scale drawings: word problems

T. Percents

• 1 What percentage is illustrated?
• 2 Understanding percents: bar models
• 3 Convert fractions to percents using grid models
• 4 Convert between percents, fractions and decimals
• 5 Convert between percents, fractions and decimals: word problems
• 6 Compare percents to each other and to fractions
• 7 Compare percents and fractions: word problems
• 8 Percent of a number
• 9 Percent of a number: word problems
• 10 Compare percents of numbers
• 1 Add and subtract money amounts
• 2 Add and subtract money amounts: word problems
• 3 Multiply money amounts
• 4 Multiply money amounts: word problems
• 5 Multiply money amounts with decimals
• 6 Multiply money amounts with decimals: word problems
• 7 Divide money amounts
• 8 Divide money amounts: word problems
• 9 Divide money amounts with decimals
• 10 Divide money amounts with decimals: word problems
• 11 Price lists
• 12 Unit prices

V. Number sequences

• 1 Use a rule to complete an addition or subtraction pattern
• 2 Use a rule to complete a number pattern
• 3 Use a two-step rule to complete a number pattern
• 4 What is true about the addition pattern?
• 5 What is true about the multiplication pattern?
• 6 Complete a linear number sequence
• 7 Complete an increasing number sequence
• 8 Complete a geometric number sequence
• 9 Linear sequences: word problems
• 10 Number sequences: word problems
• 11 Number sequences: mixed review
• 12 Shape patterns

W. Coordinate plane

• 1 Describe the coordinate plane
• 2 Objects on a coordinate plane
• 3 Graph points on a coordinate plane
• 4 Coordinate planes as maps
• 5 Objects on a coordinate plane - all four quadrants
• 6 Graph points on a coordinate plane - all four quadrants
• 7 Quadrants

X. Equations and variables

• 1 Write variable expressions
• 2 Write variable expressions: word problems
• 3 Evaluate variable expressions
• 4 Properties of addition with variables
• 5 Properties of multiplication with variables
• 6 Identify equivalent expressions using bar models
• 7 Write a one-step equation from words
• 8 Model and solve one-step equations using algebra tiles
• 9 Write and solve one-step equations that represent diagrams
• 10 Solve one-step addition and subtraction equations with whole numbers
• 11 Solve one-step multiplication and division equations with whole numbers
• 12 Solve one-step equations with whole numbers
• 13 Write one-step equations: word problems
• 14 Solve one-step equations: word problems
• 15 Does (x, y) satisfy an equation?
• 16 Find a value using two-variable equations
• 17 Complete a table for a two-variable relationship
• 18 Complete a table from a graph
• 19 Graph a two-variable relationship
• 20 Write a two-variable equation

Y. Data and graphs

• 1 Read a table
• 2 Interpret pictograms
• 3 Create pictograms
• 4 Interpret line graphs
• 5 Create line graphs
• 6 Interpret bar graphs for categorical data
• 7 Create bar graphs for categorical data
• 8 Interpret double bar graphs for categorical data
• 9 Create double bar graphs for categorical data
• 10 Interpret bar graphs for grouped data
• 11 Create bar graphs for grouped data
• 12 Interpret line plots
• 13 Create line plots
• 14 Interpret frequency charts: one-step problems
• 15 Interpret frequency charts: multi-step problems
• 16 Create frequency charts
• 17 Interpret stem-and-leaf plots
• 18 Create stem-and-leaf plots
• 19 Pie charts
• 20 Pie charts and central angles
• 21 Choose the best type of graph

Z. Probability and statistics

• 1 Understanding probability
• 2 Find the probability
• 3 Find the probability as a fraction
• 4 Experimental probability
• 5 Use collected data to find probabilities and make predictions
• 6 Make predictions
• 7 Identify statistical questions
• 8 Find the mode
• 9 Find the mean
• 10 Find the median
• 11 Find the range
• 12 Mode: find the missing number
• 13 Mean: find the missing number
• 14 Median: find the missing number
• 15 Range: find the missing number
• 16 Interpret charts to find mode
• 17 Interpret charts to find mean
• 18 Interpret charts to find median
• 19 Interpret charts to find range
• 20 Identify representative, random and biased samples
• 1 Convert time units
• 2 Add and subtract mixed time units
• 3 Elapsed time
• 4 Find start and end times: word problems
• 5 Convert between 12-hour and 24-hour time
• 6 Time zones - 12-hour time
• 7 Time zones - 24-hour time
• 8 Schedules and timelines - 12-hour time
• 9 Schedules - 24-hour time
• 10 Time patterns

BB. Units of measurement

• 1 Choose the more reasonable temperature
• 2 Calculate temperature differences
• 3 Choose the appropriate metric unit of measure
• 4 Compare and convert metric units of length
• 5 Compare and convert metric units of mass
• 6 Compare and convert metric units of volume
• 7 Convert metric mixed units
• 8 Add and subtract metric mixed units
• 9 Multi-step problems with metric unit conversions
• 10 Choose the appropriate imperial unit of measure
• 11 Compare and convert imperial units of length
• 12 Compare and convert imperial units of weight
• 13 Compare and convert imperial units of volume
• 14 Imperial mixed units
• 15 Convert between miles and kilometres
• 16 Convert between metric and imperial units
• 17 Precision

CC. Two-dimensional figures

• 1 Is it a polygon?
• 2 Regular and irregular polygons
• 3 Number of sides in polygons
• 4 Interior angles of polygons
• 5 Sort polygons into Venn diagrams
• 6 Properties of polygons
• 7 Lines, line segments and rays
• 8 Parallel, perpendicular and intersecting lines
• 9 Parts of a circle
• 1 Types of angles
• 2 Measure angles with a protractor
• 3 Draw angles with a protractor
• 4 Find a missing angle - vertical angles
• 5 Find a missing angle - adjacent angles
• 6 Find a missing angle - supplementary angles
• 7 Find a missing angle - vertical, adjacent and supplementary angles
• 8 Find a missing angle - complementary angles
• 9 Find measures of complementary and supplementary angles

EE. Triangles and quadrilaterals

• 1 Classify triangles
• 2 Find missing angles in triangles
• 3 Parallel sides in quadrilaterals
• 4 Sides and angles of quadrilaterals
• 5 Identify parallelograms
• 6 Identify trapeziums
• 7 Identify rectangles
• 8 Identify rhombuses
• 9 Classify quadrilaterals
• 10 Pick all the names for a quadrilateral
• 11 Draw quadrilaterals
• 12 Graph triangles and quadrilaterals
• 13 Identify the relationships between quadrilaterals
• 14 Describe relationships among quadrilaterals
• 15 Find missing angles in quadrilaterals

FF. Symmetry and transformations

• 1 Lines of symmetry
• 2 Draw lines of symmetry
• 3 Count lines of symmetry
• 4 Rotational symmetry
• 5 Rotational symmetry: amount of rotation
• 6 Identify reflections, rotations and translations
• 7 Translations: graph the image
• 8 Reflections: graph the image
• 9 Combinations of reflections, rotations and translations
• 10 Identify congruent and similar figures
• 11 Identify similar triangles and quadrilaterals

GG. Three-dimensional figures

• 1 Identify three-dimensional figures
• 2 Count vertices, edges and faces
• 3 Which figure is being described?
• 4 Nets of three-dimensional figures
• 5 Three-dimensional figures viewed from different perspectives

HH. Geometric measurement

• 1 Find the perimeter of rectangles using formulas
• 2 Perimeter with whole number side lengths
• 3 Perimeter with decimal side lengths
• 4 Area of squares and rectangles
• 5 Understanding area of a parallelogram
• 6 Area of parallelograms
• 7 Understanding area of a triangle
• 8 Area of right triangles
• 9 Area of triangles
• 10 Area of compound figures
• 11 Area between two rectangles
• 12 Area and perimeter of figures on grids
• 13 Area and perimeter: word problems
• 14 Use area and perimeter to determine cost
• 15 Relationship between area and perimeter
• 16 Volume of figures made of unit cubes
• 17 Volume of cubes and cuboids
• 18 Relationship between volume and the area of the base: word problems
• 19 Compare volumes and dimensions of cuboids: word problems

II. Financial literacy

• 1 Identify advantages and disadvantages of payment methods
• 2 Evaluate payment methods
• 3 Reading financial records
• 4 Keeping financial records
• 5 Balance a budget
• 6 Adjust a budget

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!

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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.

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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
• Printable PDF (pdf) Sign up to Plus

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.

teaching resource

Daily maths problems - year 6.

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

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10 Comments

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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Identifying Numbers PowerPoint

A 14 page editable PowerPoint presentation to use when teaching number recognition to younger students.

Level: Year 6

Author: Leanne McMahon

Description:

According to the Australian Curriculum by the end of Year 6 students should be able to select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers. This is a skill that requires a great deal of practice and should be taught throughout the year, rather than as a designated unit. The following suggestions include a list of popular strategies for problem solving and some age-appropriate problems for students to work on.

List of Resources:

• Jo Boaler’s Weeks of inspirational Math are great sources of problems for all ages: https://www.youcubed.org/week-inspirational-math/
• NRICH is a great go-to for problem solving: https://nrich.maths.org/10334
• NCTM’s Illuminations has interactives as well as problems (Search for Problem Solving): https://illuminations.nctm.org/Default.aspx
• AAMT’s ReSolve is an Australian site that seeks to teach mathematics by inquiry: https://www.resolve.edu.au/

This activity covers the following Australian Curriculum – Mathematics Content:

• Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers  (ACMNA123)

For any  questions or queries please contact: [email protected]

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Word Problems and Reasoning for Year 6

Subject: Mathematics

Age range: 7-11

Resource type: Other

Last updated

16 December 2023

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Over 40 pages containing more than 300 reasoning and problem solving activities for Year 6 with answers - enough to last an entire year. The activities can be downloaded as PDFs or as editable Word documents.

Free samples of three of these resources are available from my shop:

https://www.tes.com/teaching-resource/decimals-reasoning-and-problem-solving-12201156

https://www.tes.com/teaching-resource/solving-length-problems-year-6-12201157

https://www.tes.com/teaching-resource/comparing-fractions-reasoning-and-problem-solving-12201154

These resources have been tried and tested with Year 6 pupils.

Problems often mirror SATs style questionning or else require pupils to explain their reasoning. These resources can be used in conjunction with White Rose schemes.

Topics covered:

Long multiplication Short division Long division Factors and multiples Order of operations Reason from known facts Equivalent fractions and simplification Improper fractions and mixed numbers Comparing fractions using a common denominator Addition and subtraction of fractions Addition and subtraction of fractions Multiplication of fractions Division of fractions Position and direction Decimals with 3 decimal places Multiplication and division of decimals by integers Converting between fractions and decimals Equivalence of fractions, decimals and percentages Finding percentages of amounts Algebraic expressions and substitutions Solving algebraic word problems Solving equations Enumerating possibilities Reasoning and problem solving with measures Solving length problems Solving measurement problems Problem solving with area and perimeter Reasoning with area and perimeter Area of triangles Volume The language of ratio Recipe problems Scale factors Proportion problems Angles

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35 SATs Maths Questions And Answers With Worked Examples: Essential Maths Reasoning Practice For Year 6 [FREE]

Anantha Anilkumar

For Year 6, the toughest of their SATs maths questions are the reasoning questions. 

No matter how good pupils’ subject knowledge is or how effective your SATs revision lessons are, the examiners always manage to come up with maths questions that can baffle and flummox even the hardiest year 6 pupil.

To mitigate against this for the SATs this year your pupils need plenty of exam practice and more specifically exam question practice to be familiar with both the types of SATs reasoning questions that can come up and the skills needed to answer them.

So to make life easy for you we’ve put together here a comprehensive collection of 35 SATs maths questions, organised by the sorts of question that pupils can expect to encounter.

All these practice SATs questions have been based on a mix of questions from past SATs papers , our own free year 6 maths SATs papers , and our collections of year 6 reasoning questions from the Rapid Reasoning resource collection. The answers are all taken from the answer sheets we provide for each test paper.

SATS 2024: STAY UP TO DATE Join our email list to stay up to date with the latest news and free resources for SATs 2024 . As usual our expert teachers will be on hand to provide one to one tuition support, revision resources, expert analysis on papers and the 2024 SATs results .

Other useful SATs revision resources

Before we get into the year 6 maths questions you might find it helpful to know that we have hundreds of other free KS2 SATs revision resources, including free SATs papers , and SATs intervention packs for those wanting to use the Year 6 SATs revision lessons we use in one to one tutoring in their own boosters.

Why the focus on maths reasoning questions for SATs? 

Ever since the new national curriculum Key Stage 2 SATs in 2016, the emphasis in the all SATs papers has been very much on SATs reasoning questions. While there is one arithmetic paper, there are two reasoning papers; and the variety, breadth and level of challenge in the reasoning paper continues to impress us.

Most Year 6 pupils find the reasoning SATs maths questions the hardest part of these maths papers. Unsurprisingly! We teach thousands of pupils every week in the run up to SATs, and teaching them maths reasoning skills at KS2 is a big part of what we do.

We even recently took the decision to restructure our SATs lessons to introduce maths reasoning questions earlier in the learning journey as the level of challenge just at the end of the lesson was too high. So we feel the Year 6 teacher’s pain!

Whatever level pupils go on to perform at in maths, maths reasoning questions and numerical reasoning tests (such as those used by grammar and private schools) are likely to be a part of the practice they require.

If you find you have children in your class with much further to catch-up than the others then we we would be happy to support them with some personalised online one to one maths tuition .

35 SATs maths questions for KS2 year 6 SATs

For the KS2 SATs tests, there are 7 types of maths reasoning question that are likely to come up:

• Single step worded problems
• Multiple step worded problems
• Problems involving measures
• Problems involving drawing
• Explanation questions
• Sequence questions
• Ordering questions

For each of these types we’ll examine an example SATs maths question from a previous SATs paper, looking at the question, the correct answer, and how to go about answering this question.

We’ll also look at further examples of each type of maths reasoning questions and answers from Third Space’s Rapid Reasoning resource, again with worked examples and an explanation of how to answer each.

Finally, at the end of this article we provide links to further Year 6 maths questions, assessments and other SATs papers that you may find useful including plenty of arithmetic practice too.

Our aim is to provide you as part of your SATs practice with a sample of the types of KS2 SATs questions pupils can expect in the reasoning papers and how to teach the reasoning and problem solving  skills they’ll need to answer them.

For more word problems like this, check out our collection of 2-step and multi-step word problems for you as well as tips on how to use the bar model to answer Year 6 word problems . For advice on how to teach children to solve problems like this, check out these maths problem solving strategies.

SATs Maths Question Type 1: Single step worded problems

The simplest type of reasoning question pupils are likely to encounter in the reasoning papers, single step problems are exactly that: pupils are asked to interpret a written question and carry out a single mathematical step to solve it.

Have a look at the question below:

Reasoning Question 1

Answer: 65p

A relatively easy question to interpret and solve – the first step is to recognise £2 and £1.35 as equivalent to 200 and 135. From here the simple mathematical step is subtraction i.e. 200-135=65.

The most crucial skill for primary school pupils in this question is a solid understanding of money as relating to place value. If this understanding is present, the mathematical step itself is quite easy.

Below are several more examples, taken from Third Space Learning’s Rapid Reasoning resources:

Reasoning Question 2

Answer : 7 hours 24 minutes

Pupils need to understand that one hour is equal to 60 minutes. From here the single mathematical step is short division: 444/60, with a remainder.

Reasoning Question 3

Answer : 48 cm 3

Pupils must calculate length by breadth by height, using the figures provided by the question.

Reasoning Question 4

Answer : 124 cm

A simple enough calculation (doubling) if pupils are aware that the diameter is twice the radius.

Reasoning Question 5

Answer : 7,590

A single, relatively simple rounding problem – pupils should recognise that ’94’ is the operative part of this figure.

SATs Maths Question Type 2: Multiple step worded problems

A more complex version of the single step worded problem, multi-step problems require pupils to interpret a written problem, but solving it then requires the use of two or three maths skills,

For example, consider this question from the 2019 KS2 maths SATs:

Reasoning Question 6

Answer: £1.85

This question encompasses three different maths skills: multiplying (and dividing) mixed numbers, addition and subtraction. Pupils can choose to work out the multiplication or division first, but must complete both before moving on.

Once these values have been worked out the next steps are relatively simple – adding the two values together, and subtracting the total from £5.

Multi-step problems are particularly valuable to include in practice tests because they require children to apply their knowledge of maths language and their reasoning skills several times across the course of a single question, usually in slightly different contexts.

More examples:

Reasoning Question 7

Answer : £5,520

There are two steps to this problem, but both are multiplications. The first is to work out how much money is made per day – 92 x £15. This sum is then multiplied by 4 – the number of days – to get to the solution.

Reasoning Question 8

Answer : 2,160 km

Another two step problem. The first step is to work out 10% of 5400 km. Then multiply this by 4 to solve 40%.

Reasoning Question 9

Answer : £43.50

There are three steps involved in solving this problem: multiplication (doubling £51 and £36 to find the cost of two adult and two child tickets), addition (putting the two costs together) and division (dividing the total by four to obtain the mean cost).

Given the number of steps involved it can be easy for pupils to make arithmetic mistakes, and the mark scheme accounts for this by allowing for one mistake – but no more.

Read more: Mean median mode

Reasoning question 10.

Answer : 11.45 kg

A two-step problem again: multiplying 3.45 kg by 4, then subtracting 2.35 kg from the total. As with the previous problem, the mark scheme again allows for at most one arithmetic error, assuming the method is correct.

Year 6 Rapid Reasoning (Weeks 1-6)

Download 6 weeks of Rapid Reasoning slides for your Year 6 pupils and help them get a head start on preparing for the SATs reasoning papers.

SATs Maths Question Type 3: Problems involving measures

As their name suggests, these questions ask pupils to solve a problem that includes one or more units of measurement.

Take a look at this question from 2018’s Reasoning Paper 3:

Reasoning Question 1 1

Answer: 40 washes

This is a two step problem; pupils must first be able to read and convert kilograms to grams (and therefore know the relationship between the two units), then divide 2600 by 65 to work out the number of washes possible.

Questions involving measures tend to be few in number in the KS2 exam papers, but they often provide an excellent way to couch key maths skills such as the four operations.

Further examples:

Reasoning Question 12

Answer : 50g

A relatively simple division problem, relying on pupils having knowledge that 200g is one fifth of a kilogram.

Reasoning Question 13

Answer : 1.1kg

Another three step problem – multiplying 500 by 4 to get the total mass of the four melons, multiplying 300 by 3 to get the total mass of the remaining three melons, and then subtracting 2000 from 900 to obtain the mass of the fourth melon.

It’s worth noting that the mark scheme allows either 1.1kg or 1,100g as acceptable answers – the units of measurement are not as important as obtaining the current figure.

Reasoning Question 14

Answer : 216cm

Interesting to note that in this problem (unlike the previous example), the units for the answer are specified – an answer given in metres will be marked as wrong, since cm is specified in the answer box. This is why we encourage pupils to keep an eye on whether units are provided in the answer box.

Reasoning Question 15

Answer : 170g

As with the melon question there are three steps involved to solve this problem: working out the mass of the four cars (4 x 80), working out the mass of the remaining three cars (3 x 50) and subtracting 150 from 320 to get the mass of the fourth car.

SATs Maths Question Type 4: Problems involving drawing

Problems involving drawing require pupils to construct an  accurate  drawing by following a set of instructions, or through reflection, translation, or scaling.   

This type of question is quite rare, but there are some notable exceptions, such as the infamous Question 21 in Paper 2 of the 2019 Reasoning SATs:

Reasoning Question 1 6

Answer: Any pair of lines that make a square of 4 units, a rectangle of 6 units, and a square of 25 units.

This question is considerably more complex than it appears, and incorporates aspects of multiplication as well as spatial awareness. One potential solution is to work out the area of the card (35), then work out the possible square numbers that will fit in (understanding that square numbers produce a square when drawn out as on a grid), and which then leave a single rectangle behind.

A lot of work for a single mark!

Some further examples:

Reasoning Question 17

Answer : Any quadrilateral made by joining the dots that has 3 acute angles e.g. an arrowhead shape.

Reasoning Question 18

Answer : An accurately drawn angle.

The mark scheme here allows some room for error – “between 34 and 36 degrees” is acceptable .

Reasoning Question 19

As with the question above, a small amount of room for error is given – “between 139 and 141 degrees”.

Reasoning Question 20

Answer : a new triangle drawn with points at (2,1), (5,1) and (2,4).

Translation can be tricky for pupils. Encourage them to look at the triangle as three points, and to translate each point separately rather than trying to move ‘the whole triangle’.

SATs Maths Question Type 5: Explanation questions

An early form of the ‘Prove X’ questions that come up in GCSEs, these problems ask children to explain a mathematical statement or error.

As an example:

Reasoning Question 21

Answer: If the distance from P to R is 800m and the distance from P to Q is (Q -> R x 4), it must be 4/5 of 800 = 640m. Therefore Olivia is wrong.

More than most problems, this type requires pupils to actively demonstrate their  reasoning skills  as well as their mathematical ones. Here pupils must articulate either in words or (where possible) numerically that they understand that Q to R is 1/5 of the total, that therefore P to Q is 4/5 of the total distance, and then calculate what this is via division and multiplication.

Further examples from TSL’s Rapid Reasoning resources:

Reasoning Question 22

Answer : No; 20/100 is the same as 20 divided by 100, which equals 0.2.

Reasoning Question 23

Answer : No; multiplication and division have the same priority, so in a problem like 40 x 6 ÷2, you would carry out the multiplication first as it occurs first.

The mark scheme notes that vague answers or any answers with a mathematical error are unacceptable.

Reasoning Question 24

Answer : No

Any explanation that provides a counter-example is acceptable e.g. “Not if the number is 1”, “Not for 0” etc.

Reasoning Question 25

Answer : Any answer that refers to the fact that there is a 5 in the hundreds place, AND a 9 in the thousands place, so that the number has to be rounded up as far as the ten-thousands place.

SATs Maths Question Type 6: Sequence questions

Another relatively simple kind of reasoning question, sequence problems involve pupils completing mathematical sequences.

Consider this example:

Reasoning Question 26

Answer:   35 , 42, 49,  56 , 63,  70

Number sequence questions, particularly those that involve linear sequences or (as in this case) times tables, come up relatively frequently in the SATs maths tests. The question’s instructions point clearly to the solution: work out what the increase between numbers is, then apply this via addition or subtraction to find the missing numbers.

Higher attaining pupils might quickly pick up that this is in fact the 7 times table and rely on their knowledge of multiplication facts to obtain the answer – this should be encouraged so long as they then check their answer in the normal method to ensure they haven’t made a mistake.

Reasoning Question 2 7

Answer(s) : 5/8 and 2 1/8 (OR 17/8)

Both answers must be correct to receive the mark. Pupils must recognise that 3/4 is the same as 6/8, so the following number must be three eighths higher.

Reasoning Question 28

Answer(s) : -19 and 9

Reasoning Question 29

Answer(s) : 128, 135 and 156.

Reasoning Question 30

Answer(s) : -10 and 22

This question can be a little tricky; pupils need to work out that the marks on the line represent increments of 4, and count backwards and forwards in 4s to obtain the missing numbers.

SATs Maths Question Type 7: Ordering questions

A slightly more complex variation of the sequence question, ordering problems require pupils to put a set of numbers, fractions or measures in the correct order.

A good example is this question from Paper 2 of the 2018 SATs:

Reasoning Question 31

Answer: 3/5, 3/4, 6/5

This question throws a stick in the wheels by including an improper fraction, but this is hardly unusual. These sorts of questions are just the place to find other ‘curveballs’ such as equivalent fractions, mixed numbers and decimals and fractions combined.

A good knowledge of the fundamentals of fractions is essential here: pupils must understand what a larger denominator means, and the significance of a fraction with a numerator greater than its denominator.

Reasoning Question 32

Answer : D,C,A,B

Encourage pupils to convert all the fractions to one denominator value to make ordering easier.

Reasoning Question 33

Answer : (descending down the ‘Place’ column) 3rd, 5th, 2nd, 4th

As with the example above, pupils should be encouraged to convert the fractions to make it easier to order them.

Reasoning Question 34

Answer : C, B, D, A

Reasoning Question 35

Answer : D, A, C, B

7 top tips for answering SATs questions

Now that we’ve covered how to answer some specific types of reasoning questions, here are some more generic tips for success in the reasoning papers. They may not all be applicable to every single question type, but will apply to at least two, usually more.

• Get pupils in the habit for any practice paper of identifying what information they’re given in a question, and what they need to know to solve the problem. This helps them start to form the steps needed to find the solution.
• Ask pupils to ‘spot the maths’ in a question – which calculations or skills do they actually need to use to solve the problem? This is useful even for arithmetic questions – it’s no surprise how often children can misread a question.
• Check the units! Especially in questions involving multiple measures, it can be easy to give the answer in the wrong one. The answer box might give a specific unit of measurement, so pupils should work to give their answer in that unit.
• In a similar vein, remind pupils to convert different units of measurement in a question into the same unit to make calculations easier e.g. kg to g.
• Encourage numerical answers where possible. Even in explanation questions demonstrating the mathematical calculation is a better explanation than trying to write it out.
• The bar model can be a useful way of visualising many different types of questions, and might make it easier to spot the ‘steps’ needed for the solution.
• Check your working out! Even if the working is ultimately irrelevant to the question, you can lose marks if it is wrong.

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