y6 maths problem solving activities

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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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A perimeter/area investigation.

A good knowledge of the order of operations is needed for this problem solving task.

Find the cost of different numbers of houseplants.

Tricky addition which may need jottings to complete.

Here are sets of word problems only needing one step to solve, but it is not always obvious what calculation to carry out to reach the answer.

Here are some longer problems written in words. You need to work out more than one thing to get the answers.

Quite tricky word problems involving money, often requiring several steps to complete.

A good knowledge of metric measures is needed to complete these questions.

Questions which need an understanding of a.m., p.m., 24 hour clock, leap years as well as using graphs.

An atlas with time zones is needed for the first activity and there are line graphs on time to interpret.

When answering these problems say which operation is needed and whether it can be done mentally, on paper or with a calculator.

More on choosing the most appropriate method of calculating.

Tricky calculations working out the best and worst meal deals.

Purchasing various items from a vending machine. Tricky calculating with money.

Investigate Numbers and Patterns

Investigate numbers and patterns, including sequences.

Quick and easy way to multiply 2-digit numbers by 11 - why does it work?

Show all your calculating skills with just four fours.

A first look at triangle numbers.

More on triangle numbers.

Further investigations involving triangle numbers.

Some great patterns can be found when dividing by 9 or 11, and using square numbers.

Plenty of ideas to help with investigations and inventing similar problems.

More investigations on adding consecutive numbers, dividing by a half, writing a simple formula as well as shape patterns.

Investigate numbers and shapes; quite tricky.

Complete a variety of number sequences and say what the rule for each sequence is. Some negative number work as well.

Using a multiplication square to look for number patterns: there are certainly plenty of them! Further sequence work, including Fibonacci.

Try the Ancient Egyptian method of multiplying. Great, if you are good at adding up!

Tips and hints on how to use a calculator to ensure correct answers.

Holiday Problem Solving

A tricky selection of resources all linked to a holiday theme.

Very tricky to find the best options.

Very tricky calculations to find the best deal.

Finding the best deal is harder than it might seem!

A holiday which might cost more than it should unless there is some careful calculating.

This is complicated with special offers and percentages off making finding the cheapest deal difficult to work out.

More difficult than you might think to find the cheapest deal, including percentages.

Much trickier than it first looks, with many possible options to choose from. Some time is needed to complete this correctly.

A collection of puzzles to solve - some easy and some quite tricky. Ideal for the end of term.

Place the numbers 1 to 9 in the boxes so that each side of the triangle adds up to 20.

Replace the hexagons in the calculation with numbers: logical thinking needed.

Find the mathematical words in these anagrams.

Turn your calculator upside down to read the words!

A calculator is needed for this fun challenge.

This might not seem possible but with a little imagination it can be done.

How many moves to get all the coins on heads?

Nifty little puzzle with more than one solution.

More to do with square numbers than shapes!

Finding pairs of numbers that add up to square numbers. Tricky!

How many ways of making 15. Have you got all of them?

Can you make prime numbers by adding two square numbers?

Lots of coins and not change for £1.

Neat little code-breaker. Can you come up with others?

Logical thinking needed here.

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National Curriculum In England: Mathematics Programmes Of Study

Students are entering a new section of math that consists of algebra, geometry, decimals, and more complicated division problems. When there is not a parent or teacher around, students have access to on-demand videos for their sixth-grade mathematical lessons. Our video tutorials are taught by math teachers who go through the problem solving process.

• The key to learning math is repetition, and our math teachers go through multiple examples. 
• Math teachers show students step-by-step directions on how to solve these more complex problems.
• Students learn money, ratios, decimals, graphing, and other concepts from the 6th grade curriculum.

Teachers | Pupils | Parents

Collect 1 Mission Credit for each correct Fluency answer or solution…

Collect 3 Mission Credits for each correct iQ answer or solution…

Please use the search bar to filter and find the learning objective required.

Welcome to the Year 6 Mini-Maths homepage. Daily maths questions for Year 6 are available for every week of the year, providing free help for teachers, pupils and parents. 1000s of free tasks and activities are available to support children in their learning both in the classroom and at home. Use the search and filter box below to easily find the outcomes you require.

It is recommended that a topic is selected per week and daily maths tasks accessed using the links provided below. Use each day’s answers to help identify and guide the required support in preparation for the following day’s task. Watch your understanding, application and confidence grow throughout the week. New resources are always being added, so keep checking for updates.

More about Year 6 Maths Questions …

The Year 6 curriculum completes the Key Stage 2 maths programme of learning bringing understanding and confidence together from Year 3 through to the end of Year 6. This journey culminates in the KS2 SATs assessments where learners are able to demonstrate their progress and development in the subject.

Year 6 NUMBER …

The four operations reach a natural conclusion in Year 6 – addition, subtraction, multiplication and division involve more complex examples before introducing decimals values . Learners are looking to extend their understanding of units, tens, hundreds, thousands, etc, with the Place value of digits in decimal places, supporting the wider curriculum such as calculating decimal remainders using short division.

Year 6 SHAPE …

Learners have been developing a sound understanding of 2D shape and 3D shape allowing them to sort and classify by their properties. Being able to identify and use these properties also improves an awareness of a shape’s area and perimeter or volume .

Year 6 DATA …

Year 5 offers further coverage of tables, charts and graphs, where learners are expected to both read and interpret information in all types of graphs and charts including pie charts . Drawing graphs and charts from given data is also introduced in Year 6 maths.

All learning objectives are supported by a Home Learning pack and iQ mastery questions challenge learners’ understanding, application and confidence. The Home Learning packs provide first class opportunities for effective intervention and an ever growing library of help videos for Year 6 maths is available on the MyMiniMaths YouTube channel in support of quality learning.

Year 6 SATs …

MyMiniMaths also offers specialised support for Year 6 SATs with a programme of practice KS2 SATs papers for the arithmetic paper . Easy identification of key skills in need of further support to maximise attainment is available through the Arithmetic Target Questions .

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Year 6 Multiplication and Division - Problem-Solving Investigations

Last updated

15 April 2024

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Resources included (8)

Use short/long division in problems - Problem-Solving Investigation - Year 6

Use short/long multiplication in problems - Problem-Solving Investigation - Year 6

Solve rate and scaling problems - Problem-Solving Investigation - Year 6

Scale factor problems concerning area - Problem-Solving Investigation - Year 6

Problem-Solving Investigation: Multiples, factors & prime numbers (Year 6 Multiplication & Division)

Problem-Solving Investigation: Long multiplication problems (Year 6 Multiplication and Division)

Problem-Solving Investigation: Use short division to solve problems (Y6 Multiplication & Division)

Problem-Solving Investigation: Solve short multiplication problems (Year 6 Multiplication/Division )

These in-depth maths investigations are open-ended problem solving activities for Year 6 children.

In-depth Investigation: Magic Multiplication Squares Children complete a magic multiplication square using their knowledge of number properties and relationships. They then explore factors and multiples to create a new multiplication magic square.

In-depth Investigation: The Eights Have It Children multiply numbers starting with 9 by 9 and add single-digit numbers in a decreasing sequence. They identify and describe the patterns and start to explain them.

In-depth Investigation: Awesome Answers Using a magic square to generate 3-digit numbers, children create divisions with dividends containing specified fractions.

In-depth Investigation: Stunning Squares Children explore patterns in the squares of numbers with reversed digits to find pairs of ‘stunning squares’.

In-depth Investigation: Geometry Genius Children use what they know about how to find the areas of triangles and parallelograms to find the areas of rhombi, kites and trapezia.

In-depth Investigation: Get to the Root Children use their fluency in mental multiplication to explore the patterns of digital roots in multiplication.

In-depth Investigation: Riveting Reversals Multiply 3-digit numbers with consecutive digits by a 2-digit number; reverse the 3-digit number and repeat. Find the difference between the two answers.

In-depth Investigation: Why is it so? Children identify a pattern in the division of a total of six numbers created using the same 3 digits. They then use algebra to explain why it is so.

These investigations will develop maths meta-skills, support open-ended questioning and logical reasoning, and enable children to learn to think mathematically and articulate mathematical ideas.

These problem-solving investigations come from our Year 6 Maths Blocks . Each Hamilton maths block contains a complete set of planning and resources to teach a term’s worth of objectives for one of the National Curriculum for England’s maths areas.

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Mastery-Aligned Maths Tutoring

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FREE daily maths challenges

A new KS2 maths challenge every day. Perfect as lesson starters - no prep required!

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

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Children follow a logic to convert arrangements of dominoes to numbers, and then perform a giant addition. They then create their own domino additions and explore addition patterns. 

Children use logical thinking and number bonds to solve a mathematical puzzle involving multiplying by 10 and 100 and adding decimal numbers.

Children subtract 5-digit numbers and look for patterns in the digital roots. 

Children draw a circle and then use straight lines and angles to construct an ellipse within it.

Children complete a magic multiplication square using their knowledge of number properties and relationships. They then explore factors and multiples to create a new multiplication magic square.

Children multiply numbers starting with 9 by 9 and add single-digit numbers in a decreasing sequence. They identify and describe the patterns and start to explain them.

Using a magic square to generate 3-digit numbers, children create divisions with dividends containing specified fractions.

Children use two dice with decimal numbers to find largest and smallest possible differences, and use mathematical reasoning to calculate the probability of getting close to a specified target.

Children use systematic working to calculate the number of possibilities of making weights, and then look for patterns utilising line graphs.

Children use dominoes to create fractions. They explore sums of fractions using equivalent fractions and related denominators.

Children explore patterns in the squares of numbers with reversed digits to find pairs of ‘stunning squares’.

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