problem solving addition year 6

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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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6th Grade Addition & Subtraction Worksheets

Advanced addition and subtraction exercises.

Our grade 6 addition and subtraction worksheets focus on missing addend  & missing minuend/subtrahend problems with large numbers ; essentially providing additional computational practice problems.

Sample Grade 6 Addition & Subtraction Worksheet

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Free Year 6 Addition and Subtraction Reasoning and Problem Solving

Mix things up a little when you present your children with this Year 6 Addition and Subtraction Reasoning and Problem Solving resource.

With six reasoning and problem-solving questions to work through, children will need to use and apply their knowledge and understanding of calculations in various ways.

Ideal for independent work, this resource could be completed after whole-class teaching has taken place, or alternatively be given as additional support at home. Get downloading!

Curriculum Objectives

Solve problems involving addition, subtraction, multiplication and division

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Year 6 – Addition and Subtraction

Welcome to Year 6 Addition and Subtraction at Primary Maths Hub. Here you will find a growing library of outstanding resources and activities to support addition and subtraction lessons in Year 6 and at home.  

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

Do Now Tasks / Starters

Differentiated question sets.

Addition Question Set 

Subtraction Question Set

Column Addition to 10,000,000

Faded Scaffolding Strips Adding Numbers to 10,000,000

7-Digit Column Addition

Faded Scaffolding Strips Adding 7-Digit Numbers

Subtraction

Column Subtraction to 10,000,000

Strips Subtracting Numbers to 10,000,000

7-Digit  Column Subtraction

Faded Scaffolding Strips Subtracting 7-Digit Numbers

Faded Scaffolding Strips Subtracting 7-Digit Numbers No Regrouping

Subtract From Multiples of 100,000 to 10,000,000

Faded Scaffolding Strips Subtracting Numbers to 10,000,000

Faded Scaffolding Strips- Subtracting from Multiple of Millions

Subtract Decimal Number From a Whole Number

Mixed addition and subtraction.

Mixed Column Addition and Subtraction

Faded Scaffolding Strips Adding and Subtracting 7-Digit Numbers

Mixed 7-Digit Column Addition and Subtraction

Faded Scaffolding Strips Adding and Subtracting Numbers to 10,000,000

Strips- Adding and Subtracting Numbers to 10,000,000

Strips- Adding and Subtracting Numbers to 10,000,000 

Missing number problems.

Missing Numbers Questions to 10,000,000

Faded Scaffolding Strips Missing Number Questions to 10,000,000

Equality and inequality statements.

Equality and Inequality Statement Matching

Word problems and challenges.

Addition Challenge 1

Addition Word Problems to 10,000,000

Challenge 1

Addition and Subtraction Word Problems to 10,000,000

Subtraction Word Problems to 10,000,000

Addition to 10,000,000- Challenges

Hinge questions.

Revision- Column Addition

Revision- Column Subtraction

Revision- Mixed Column Addition and Subtraction

Resources to support addition and subtraction.

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Steps to Success

Column Addition to 10,000,000 – Steps to Success

Subtract From a Multiples of 100 – Steps to Success

Column Subtraction to 10,000,000 – Steps to Success

Subtract From a Multiples of 100 – Steps to Success 

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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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20 Word Problems For Year 6: Develop Their Problem Solving Skills Across Single and Mixed KS2 Topics

Emma Johnson

Word problems for Year 6 are an important part of the curriculum. For children to achieve success in the Year 6 SATs, in particular the more challenging reasoning element of the SATs assessments, it is essential they have the confidence to tackle a wide range of word problems.

Key to this success is regular exposure to the style and type of questions, covering the topics children could be presented with. Our collection of year 6 maths worksheets are is a great place to start.

To help child practice their problem solving skills, we have put together a collection of 20 word problems , organised by topic. This collection encompasses the types of questions children may encounter in the two reasoning papers.

All Kinds of Word Problems Four Operations

Download this free pack of word problems. With questions covering all four operations, your students will have a great opportunity to practice their problem solving skills across KS2 topics.

Place value 

Addition, subtraction, multiplication and division, fractions , ratio and proportion, why are word problems important in year 6 maths, how to teach problem solving in year 6, word problems in sats, addition word problems for year 6 , subtraction word problems for year 6, multiplication word problems for year 6, division word problems for year 6, fractions, decimals and percentage word problems for year 6, ratio word problems for year 6, mixed four operation word problems for year 6, more word problems resources, year 6 maths word problems in the national curriculum.

The National Curriculum states that children need to be able to solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into simpler steps and persevering in seeking solutions. 

By Year 6, children can expect to be tackling a range of one-step, two-step and multi-step word problems. To achieve at least the expected standard in Year 6, pupils need to demonstrate the ability to solve word problems across a range of topics.

Solving problems including ordering, rounding and negative numbers.

Solving multiplication, division and addition and subtraction word problems including one and two-step word problems and multi-step word problems in context, deciding which operations and methods to use and why.

Solving problems involving comparing, ordering and sequencing fractions; using the four operations and problems which require answers to be rounded to specified degrees of accuracy.

Solving problems involving the relative sizes of two quantities; the calculation of percentages; involving similar shapes where the scale factor is known and can be found; and unequal sharing and grouping, using knowledge of fractions and multiples.

Solving problems including time word problems and involving the calculation and conversion of units of measure, using decimal notation up to three decimal places, where appropriate.

Interpret and construct pie and line graphs and use these to solve problems.

Word problems are an essential element of the Year 6 curriculum, because they require children to apply the knowledge they have learnt to ‘real life’ situations, for example, in money word problems . They shouldn’t just be taught as stand alone topics, but should be incorporated in lessons throughout the year, to ensure children have as much exposure as possible. 

Solving word problems helps children learn the skills needed to apply their knowledge of maths beyond the classroom and into the real world.

When teaching problem solving in Year 6, children need to firstly look carefully at the key information and think about what they already know. Secondly, what is the word problem actually asking? Which calculation(s) would be required and would it help to draw/represent the problem pictorially?

Here is an example:

Ahmed is buying clothes. He buys a t-shirt for £12.99 and a pair of jeans which cost £12.26 more than the T-shirt. He pays with a £50 note. What change does Ahmed get?

How to solve:

What do you already know?

• More than means I will need to add the price of the T-shirt and jeans together.
• Decimals numbers means I need to remember to line up the decimal points in my calculations.
• Calculating change means I will need to subtract the total for the jeans and T-shirt from the original amount. 

How can this be drawn/represented pictorially?

We can draw a bar model to represent this problem:

• To calculate the cost of the jeans, we need to add £12.99 and £12.26 = £25.25
• Ahmed pays using a £50 note. 
• To calculate the change Ahmed will get, we need to subtract £25.25 from £50.
• £50 – £25.25 = £24.75

Problem solving is an important part of the preparation for the Key Stage 2 SATs, as this is the area children tend to find the most challenging. With two reasoning papers to complete, children will be expected to answer a wide range of word and number problem style questions. The best preparation for this is through regular exposure to these types of questions.

Addition word problems at Year 6 include larger 6 or 7 digit numbers, decimal numbers and problems involving finding the inverse. These can be one, two and multi-step problems

Addition question 1

A shopping centre had 124,713 visitors in January, 102,539 in February and 118,768 in March. How many shoppers visited the shopping centre from January to March?

Answer (1 mark): 346,020

Addition question 2

A shop has an offer on all T-shirts. 

Buy one T-shirt, get one for half price.

If Tom buys 2 T-shirts, how much does he pay altogether?

Answer (2 marks): £7.35

Addition question 3

The table below shows the number of visitors to the planetarium and the transport museum each day. Which day had the most visitors?

Answer (2 marks): Saturday

Subtraction word problems in Year 6 include larger 6 or 7 digit numbers, decimal numbers and problems involving finding the inverse. These can be one, two and multi-step problems

Subtraction question 1

In the Autumn term, the total number of English and maths worksheets printed by a school was 63,502. 39,756 were maths worksheets. How many worksheets were printed out for English?

Answer (1 mark): 23,746

Subtraction question 2

6 cars were weighed before being loaded onto the car transporter. 

They weight of the cars was:

What is the difference in weight between the heaviest and lightest car?

Answer (1 mark): 1043kg

Subtraction question 3

Two decimal numbers add together to make 37.53.

One number is 23.86.

What is the other number?

Answer (1 mark): 13.67

Multiplication word problems can include multiplying whole and decimal numbers by 1 and 2-digit numbers. A secure knowledge of times tables is helpful for children solving these questions confidently. 

Multiplication question 1

A box of chocolate contains 2 trays of chocolates.

There are 18 chocolates on each tray.

How many chocolates are there in 35 boxes of chocolates?

Answer (2 marks): 1260

Multiplication question 2

Zara buys 4 large boxes of cupcakes and 3 small boxes of cupcakes.

Each large box contains 28 cupcakes. Each small box contains 16 cupcakes.

How many cupcakes does Zara buy altogether?

Answer (2 marks): 160

Multiplication question 3

A cyclist cycled a route of 123.6 miles once a week for a year. How far did he cycle over the whole year?

Answer (2 marks): 6427.2

Division word problems in Year 6 can include division with whole numbers and decimal numbers, dividing by 1 and 2-digit numbers.

Division question 1

A 940ml bottle of blackcurrant makes 20 drinks.

How many millilitres of blackcurrant are in each drink?

Answer (2 marks): 47

Division question 2

Mr Jones is organising mini buses for a Year 6 school trip. Each minibus seats 12 people

120 Year 6 pupils are going on a school trip. 

There needs to be one adult for every 10 pupils

How many coaches will Mr Jones need to book?

Answer (2 marks): 12 mini buses

125 pupils will need 13 adults = 138 in total

Division question 3

A factory is packaging eggs in boxes of 12.

The factory has 878 eggs to box-up. 

How many boxes will they have, to send to the supermarket?

Answer (2 marks): 73 boxes

Decimals, percentage word problems and fraction word problems can be stand alone, or they can involve converting between. For example, in questions using measures.

Fractions, decimals and percentages question 1

By the end of the Autumn term, Chloe had used ⅔ of her maths book. If the book had 96 pages, how many pages had she used?

Answer (1 mark): 64 pages

⅓ of 96 = 32

⅔ of 96 = 64

Fractions, decimals and percentages question 2

Abdullah received £600 for his birthday. He spent 45% of him money on a VR headset. How much did the headset cost him?

Answer (1 mark): £270

Fractions, decimals and percentages question 3

Mrs Jones went to the local supermarket to buy some vegetables.

She bought:

• 1 3/10kg of potatoes
• 840.5g of apples
• 4/5kg of peaches
• 520.6g of grapes

What was the total weight of the shopping Mrs Jones bought?

Answer (1 mark):

• 1.3kg potatoes
• 0.8405kg apples
• 0.8kg peaches
• 0.520kg grapes

Ratio word problems are often linked with measures. Children should be encouraged to draw bar models to solve problems involving ratio, as these question really benefit from a visual representation.

Ratio question 1

Sam and Zeyn were making drinks for the school fair. To make the jugs of squash, they were mixing 300ml of orange squash with 1500ml of water.

If they have 900ml of orange squash

• How much water will they need altogether? 
• What will be the total volume of the squash?

Answer (2 marks):

• 4500ml of water
• 5400ml of squash

Ratio question 2

A piece of ribbon is 72cm long. It is cut into pieces in the ratio of 2:3:4.

How long is each piece of ribbon?

Answer (1 mark): 16cm:24cm:32cm

Mixed operation word problems require two or more operations to solve. Alongside the four operations, they can also include other topics, including fractions and percentages These can be two-step or multi-step questions and are worth 2 or 3 marks in SATs papers. 

Third Space Learning’s online one-to-one tutoring programmes include questions that combine skills students have learnt and test their understanding across a range of topics. Personalised to the needs of each individual student, our online tutoring programme works to identify gaps in learning, fill those gaps and reinforce students’ maths knowledge.

Mixed four operations question 1

One bank-holiday weekend, a total of 346,728 people visited a theme park.

134,235 visited on Saturday

121,689 visited on Sunday.

How many visited on bank holiday Monday?

Answer (2 marks): 90,804

Mixed four operations question 2

A pair of jeans in a shop cost £28.

In the sale, they were reduced in price by 25%.

What was the reduced price?

Answer (2 marks): £21

Mixed four operations question 3

Sophie thinks of a number.

She multiplies her number by 6.

Then she adds 10

Finally she divides by 4.

Her answer is 13. 

What was her original number?

Answer (1 mark): 7

Third Space Learning also offers a wide array of maths and word problems resources for other year groups such as word problems for Year 5 , word problems for Year 4 and word problems for Year 3

DO YOU HAVE STUDENTS WHO NEED MORE SUPPORT IN MATHS?

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Since 2013 these personalised one to one lessons have helped over 169,000 primary and secondary students become more confident, able mathematicians.

Learn how tutors develop pupils’ maths fluency or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

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• Decimals – for example, 98 ÷ 4 = 24.5
• By rounding – for example, 98 ÷ 4 = 24.5, which rounds up to 25.

Your child will be expected to interpret remainders depending on the context of the question. For example:

‘Buses can carry 30 people. There are 113 students going on the trip. How many buses will they need?’   This question is essentially asking  113 ÷ 30 = 3.77 . But because the students can’t take 0.77 of a bus to school, it is appropriate to round up to 4. The students will need 4 buses .

Perform mental calculations, including with mixed operations and large numbers

Identify common factors, common multiples, and prime numbers.

Your child will be expected to recognise common factors , common multiples, and prime numbers and use this knowledge to solve problems. For example, they could use their understanding of common factors to find equivalent fractions:

They could work out that    =   because 3 is a factor of both 12 and 15.

Solve problems involving addition, subtraction, multiplication, and division

Understand and use the order of operations.

The order of operations (sometimes called BODMAS), refers to the order operations within a calculation should be completed to get the right answer. Watch this video for an explanation:

Your child should be able to solve calculations using the order of operations, including calculations that use brackets. They should know how brackets change what the calculation means. For example:

2 + 1 × 3 = 5 (2 + 1) × 3 = 9

Use rounding to check answers and make estimates

They should be able to round answers to a specified degree of accuracy, for example, to the nearest 10, 20, 50, and so on.

Solve multi-step problems in contexts

The multi-step word problem could involve any combination of up to three operations (addition, subtraction, multiplication, and division). Your child should have a range of methods to solve these problems.

How to help at home

There are lots of ways you can help your child to understand addition and subtraction. Here are just a few ideas to support your child’s learning:

1. Play the 1 to 21 game

You can help your child practise all four operations at home by playing the 1 to 21 game.

Ask them to roll a dice five times and record each number shown on the dice on a piece of paper. For example, 1, 4, 3, 5, 3. They then need to find a way to reach an answer of 1 using any operations (addition, subtraction, multiplication, and/or division) on the numbers.

Your child can only use each number once and they have to use at least two numbers in each calculation. For example, we could get the answer of 1 by calculating 3 ÷ 3, 5 – 4, 4 – 3, and so on. Then ask your child to find a calculation with the answer of 2 using any operation, then an answer of 3 and so on until they reach 21.

You could make this game even more challenging by saying that they have to use at least three, four, or even all five numbers to make it really tricky! Print out our activity sheet to have a go:

Activity: One to twenty-one

Find ways to make all the numbers 1 to 21.

2. Play Four 4s

Play the game Four 4s to practise multiplying, dividing, adding, and taking away.

The aim is to make all the numbers from 1 to 20 using just the number 4 four times. Use a combination of operations (multiplying, dividing, adding, and taking away) to make calculations where the answers are the numbers 1 to 20.

You must use all four 4s, but you can put two together to make 44 as well as using operations.

1 = (4 ÷ 4) ÷ (4 ÷ 4) 2 = (4 × 4) ÷ (4 + 4) … and so on.

3. Try lots of different methods

Encourage your child to use their knowledge of different calculation strategies to solve problems.

For example, when solving word problems, ask your child what exactly the problem is asking them to do. Which operations will they need? Does the problem involve equal sharing, or multiplication as scaling? Sometimes it can be useful to transform word problems into mathematical symbols to make it very clear what you need to do.

Encourage your child to estimate their answer by rounding before they solve questions with a formal method. This will help them check that their answer makes sense when they come to work it out properly.

Once your child has completed a question using their preferred method, see how many different ways they can find to solve the problem. They might find it useful to explain these methods to you with drawings or symbols. Talk about which method seems the most efficient or easiest for this particular problem. You may want to challenge them to make up their own similar problem to practise some more.

4. Explore factors, multiples, primes, and composite numbers

You can help your child identify factors and factor pairs using their knowledge of times tables.

You can play a factor and multiple game with your child. Ask your child to choose an even number on a 100 square and cross it out. You then cross out a number that is either a factor or a multiple of that number. For example:

Start at 20. A factor of 20 is 4. A multiple of 4 is 40. A multiple of 40 is 80. … and so on. The game gets harder and harder as it goes on and more numbers are crossed out!

Continue to take it in turns to choose a number that is a multiple or a factor of the number that has just been crossed out by the other player. When a player cannot cross out any numbers, that player loses the game.

Your child will also need to explain why a number is prime or composite . Prime numbers are numbers that only have factors of 1 and itself. They can only be divided by 1 or themselves to get a whole number. 2, 3, 5, 7, 11, and 13 are all prime numbers. Composite numbers are numbers with more than two factors. 4, 6, 8, 9, 10, and 12 are all composite numbers.

Have more prime numbers or more composite numbers been crossed out in your game? Talk to your child about it. If you want to play another prime number game (or print out a number square), download the activity below:

Activity: Prime number lotto

Find out about prime numbers.

5. Explore square and cube numbers

Your child will need to use and understand square and cube numbers.

A square number is created by multiplying an integer (whole number) by itself. For example:

9 is a square number because it can be made by multiplying 3 by 3. 25 is a square number because it can be made by multiplying 5 by 5. 144 is a square number because it can be made by multiplying 12 by 12.

A square number can also be represented in the shape of a square. A square with 3cm by 3cm sides has an area of 9cm ². Ask your child to find some objects that are all the same size, and arrange them into a square. Notice how this makes a square number.

Cube numbers are formed by multiplying an integer (whole number) by itself three times. For example:

8 is a cube number because it can be made by multiplying 2 by 2 by 2. 27 is a cube number because it can be made by multiplying 3 by 3 by 3. 125 is a cube number because it can be made by multiplying 5 by 5 by 5.

A cube number can also be represented in the shape of a cube. You could ask your child to make a cube with building blocks or Lego. If they use blocks with sides of equal length (for example, 1cm by 1cm by 1cm), then any bigger cube they build will need to use a cube number of those blocks.

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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.

Use this resource in conjunction with the Daily Maths Problems PowerPoint : [resource:607261]

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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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Year 6 - Addition and Subtraction Reasoning Questions

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

2 November 2018

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A bank of questions from previous SATs papers including the sample tests that focus on addition and subtraction. These have all been pulled from the reasoning papers so they can be used to challenge children’s understanding or can be used as a mini-assessment of how children are with addition and subtraction.

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good material

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