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Volume of a Cuboid Year 6 Perimeter Area and Volume Resource Pack

Step 8: Volume of a Cuboid Year 6 Spring Block 5 Resources

Volume of a Cuboid Year 6 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Spring Block 5.

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What's included in the pack?

This pack includes:

• Volume of a Cuboid Year 6 Teaching PowerPoint.
• Volume of a Cuboid Year 6 Varied Fluency with answers.
• Volume of a Cuboid Year 6 Reasoning and Problem Solving with answers.

National Curriculum Objectives

Mathematics Year 6: (6M8a) Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic metres (m3), and extending to other units [for example, mm3 and km3]

Mathematics Year 6: (6M7c)  Recognise when it is possible to use formulae for the area of shapes

Differentiation:

Varied Fluency Developing Questions to support calculating the volume of cuboids using l x w x h or area of base x height. Same metric measures used within each question; multiples of 2, 3, 5 and 10 only. Expected Questions to support calculating the volume of cuboids using l x w x h or area of base x height. Some conversion between metric measures needed (mm to cm or cm to m). Same metric measures used within each question; whole unit measurements. Greater Depth Questions to support calculating the volume of cuboids using l x w x h or area of base x height. Some conversions between metric measures needed (mm to m or m to mm); some measurements with 1 decimal place used.

Reasoning and Problem Solving Questions 1, 4 and 7 (Problem Solving) Developing Find the pair of cuboids that could be used to make a compound rectilinear shape with a given volume. Same metric measures used within each question; multiples of 2, 3, 5 and 10 only. Expected Find all the possible pairs of cuboids that could be used to make a compound rectilinear shape with a given volume. Some conversion between metric measures needed (mm to cm or cm to m). Same metric measures used within each question; whole unit measurements. Greater Depth Find all the possible pairs of cuboids that could be used to make a compound rectilinear shape with a given volume. Some conversions between metric measures needed (mm to m or m to mm); some measurements with 1 decimal place used.

Questions 2, 5 and 8 (Problem Solving) Developing Find two missing dimensions when given the volume and 2 additional clues. Differentiation as described for question 1. Expected Find two missing dimensions when given the volume and 2 additional clues. Differentiation as described for question 1. Greater Depth Find two missing dimensions when given the volume and 2 additional clues. Differentiation as described for question 1.

Questions 3, 6 and 9 (Reasoning) Developing Explain if a comparison statement about the volume of two cuboids is correct. Differentiation as described for question 1. Expected Explain if a comparison statement about the volume of two cuboids is correct. Differentiation as described for question 1. Greater Depth Explain if a comparison statement about the volume of two cuboids is correct. Differentiation as described for question 1.

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

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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.

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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)
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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

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Volume Worksheets

This humongous collection of printable volume worksheets is sure to walk middle and high school students step-by-step through a variety of exercises beginning with counting cubes, moving on to finding the volume of solid shapes such as cubes, cones, rectangular and triangular prisms and pyramids, cylinders, spheres and hemispheres, L-blocks, and mixed shapes. Brimming with learning and backed by application the PDFs offer varied levels of difficulty.

List of Volume Worksheets

Counting Cubes

• Volume of Cubes
• Volume of Rectangular Prisms
• Volume of Triangular Prisms

Volume of Mixed Prisms

• Volume of Cones
• Volume of Cylinders

Volume of Spheres and Hemispheres

• Volume of Rectangular Pyramids
• Volume of Triangular Pyramids

Volume of Mixed Pyramids

Volume of Mixed Shapes

Volume of Composite Shapes

Explore the Volume Worksheets in Detail

Work on the skill of finding volume with this batch of counting cubes worksheets. Count unit cubes to determine the volume of rectangular prisms and solid blocks, draw prisms on isometric dot paper and much more.

Volume of a Cube

Augment practice with this unit of pdf worksheets on finding the volume of a cube comprising problems presented as shapes and in the word format with side length measures involving integers, decimals and fractions.

Volume of a Rectangular Prism

This batch of volume worksheets provides a great way to learn and perfect skills in finding the volume of rectangular prisms with dimensions expressed in varied forms, find the volume of L-blocks, missing measure and more.

Volume of a Triangular Prism

Encourage students to work out the entire collection of printable worksheets on computing the volume of triangular prism using the area of the cross-section or the base and leg measures and practice unit conversions too.

Navigate through this collection of volume of mixed prism worksheets featuring triangular, rectangular, trapezoidal and polygonal prisms. Bolster practice with easy and moderate levels classified based on the number range used.

Volume of a Cone

Motivate learners to use the volume of a cone formula efficiently in the easy level, find the radius in the moderate level and convert units in the difficult level, solve for volume using slant height, and find the volume of a conical frustum too.

Volume of a Cylinder

Access our volume of a cylinder worksheets to practice finding the radius from diameter, finding the volume of cylinders with parameters in integers and decimals, find the missing parameters, solve word problems and more!

Take the hassle out of finding the volume of spheres and hemispheres with this compilation of pdf worksheets. Gain immense practice with a wide range of exercises involving integers and decimals.

Volume of a Rectangular Pyramid

This exercise is bound to help learners work on the skill of finding the volume of rectangular pyramids with dimensions expressed as integers, decimals and fractions in easy and moderate levels.

Volume of a Triangular Pyramid

Help children further their practice with this bundle of pdf worksheets on determining the volume of triangular pyramids using the measures of the base area or height and base. The problems are offered as 3D shapes and in word format in varied levels of difficulty.

Gain ample practice in finding the volume of pyramids with triangular, rectangular and polygonal base faces presented in two levels of difficulty. Apply relevant formulas to find the volume using the base area or the other dimensions provided.

Upscale practice with an enormous collection of printable worksheets on finding the volume of solid shapes like prisms, cylinders, cones, pyramids and revision exercises to revisit concepts with ease.

Learn to find the volume of composite shapes that are a combination of two or more solid 3D shapes. Begin with counting squares, find the volume of L -blocks, and compound shapes by adding or subtracting volumes of decomposed shapes.

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VOLUME AND CAPACITY WORD PROBLEMS

The units for capacity and the units for volume are closely related.

1 mL of fluid will fill a cube 1 cm x 1 cm x 1 cm.

1 cm 3 has capacity 1 mL

1 L of fluid will fill a cube 10 cm x 10 cm x 10 cm.

1000 cm 3 has capacity 1 L

1 kL of fluid will fill a cube 1 m x 1 m x 1 m.

1 m 3 has capacity 1 kL.

1 cm 3  = 1 mL

1000 cm 3  = 1 L

1 m 3  = 1 KL

Example 1 :

Calculate the capacity of the container:

Volume of the container = 30 x 10 x 20 cm 3

= 6000 cm 3 

1000 ml = 1 L

= (6000/1000) L

So, the capacity of the container is 6 L.

Example 2 :

Find the capacity in liters of a fish tank 2 m by 1 m and 50 cm.

Volume of tank = l x w x h

Substitute l = 2, w = 1 and h = 50 cm or 0.5 m.

= 2 x 1 x 0.50

So, capacity of the tank is 1 KL.

Example 3 :

A rectangular petrol tank has dimensions 50 cm by 40 cm by 25 cm. How many liters of petrol are needed to fill it?

Volume of rectangular tank  =  l x w x h.

Substitute l = 50, w = 40 and h = 25.

= 50 x 40 x 25

= 50000 cm 3

= 50000/1000

So, the capacity of the petrol tank is 50 L.

Example 4 :

A water trough has triangular cross-section as shown. Its length is 2 m.

a) the area of the triangle in cm 2

b) the volume of space in the trough in cm 3

c) the capacity of the trough in :

i) litres   ii) kilolitres.

Area of triangle :

= (1/2)  ⋅ base  ⋅ height

Base = 60 cm and height  =  50 cm

= (1/2) ⋅ 60 ⋅ 50

= 1500 cm 3

Volume of space :

=  (1/2)  ⋅   Base area x height

= (1/2)  ⋅ 1500  ⋅ 200

= 300000 cm 3

= 300000/1000

= 300 Liter

So, capacity of triangular prism is 300 liter.

1m 3  = 1 KL

1000 ml = 1 kl

So, capacity of triangular prism is 0.3 kl.

Example 5 :

Find the capacity in megaliters of a reservoir with a surface area of 1  hectare and an average depth of 2.5 meters.

1 hectare = 10000 m 2

Volume = Surface area x height

= 10000 x 2.5

= 25000 m 3

1 m 3  = 1 KL

Capacity = 25000/1000 ML

So, the capacity is 25 ML.

Example 6 :

A kidney-shaped swimming pool has surface area 15 m 2 and a constant depth of 2 meters. Find the capacity of the pool in kiloliters.

Surface area = 15 m 2  and height = 2 m

So, the capacity is  30 KL .

Example 7 :

A lake has an average depth of 6 m and a surface area of 35 ha. Find its capacity in megaliters .

35 hectare = 350000 m 2

Height = 6 m

= 350000 x 6

= 2100000  m 3

= 2100000 Kl

1 ML = 1000 KL

= 2100000/1000 ML

So, the capacity of the tank is  2100 ML.

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Find the Volume by Counting Cubes — Problem Solving (Year 6)

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This resource is suitable for the White Rose Maths Scheme of Learning, covering Spring Term Block 5 (Area, Perimeter and Volume), Step 7 (Volume — Counting Cubes).

This worksheet will help develop children's understanding of calculating the volume of cubes and cuboids using standard units. Challenge children to work out the volume of each shape in cm cubed.

This worksheet is available in different levels. Please see the drop-down menu to select another level.

This resource is also available in a handy Lesson Pack, containing a selection of brilliant worksheets for this small step.

View Lesson Pack    See all Year 6 White Rose

• Key Stage: Key Stage 2
• Subject: Maths
• Topic: White Rose Maths | Spring Term: Area, Perimeter and Volume | Small Step 7
• Topic Group: Measurement
• Year(s): Year 6
• Media Type: PDF
• Resource Type: Worksheet
• Last Updated: 24/10/2023
• Resource Code: M2WAT14624

Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm^3) and cubic metres (m^3), and extending to other units [for example, mm^3 and km^3].

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Find the Area of Any Triangle: Stretch (Year 6)

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Area of a Triangle — Activity Challenge (Year 6)

Area of a Triangle — Activity Challenge: Stretch (Year 6)

Calculating Area and Perimeter (Year 6)

Calculating Area and Perimeter: Stretch (Year 6)

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Resources tagged with: NC Yr 6

There are 51 NRICH Mathematical resources connected to NC Yr 6 , you may find related items under NC .

4 by 4 Mathdokus

Can you use the clues to complete these 4 by 4 Mathematical Sudokus?

Different Deductions

There are lots of different methods to find out what the shapes are worth - how many can you find?

Name That Triangle!

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

Number Lines in Disguise

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Price Match

Can you find pairs of differently sized windows that cost the same?

Finding 3D Stacks

Can you find a way of counting the spheres in these arrangements?

Extending Fraction Bars

Can you compare these bars with each other and express their lengths as fractions of the black bar?

More Fraction Bars

What fraction of the black bar are the other bars? Have a go at this challenging task!

Always, Sometimes or Never? Shape

Are these statements always true, sometimes true or never true?

Always, Sometimes or Never? Number

Round the Three Dice

What happens when you round these three-digit numbers to the nearest 100?

Round the Four Dice

This activity involves rounding four-digit numbers to the nearest thousand.

Use the information on these cards to draw the shape that is being described.

Dicey Perimeter, Dicey Area

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

Domino Sets

How do you know if your set of dominoes is complete?

Making Spirals

Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

Round a Hexagon

This problem shows that the external angles of an irregular hexagon add to a circle.

Have a look at this data from the RSPB 2011 Birdwatch. What can you say about the data?

So It's Times!

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

Button-up Some More

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Counting Cogs

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

Doughnut Percents

A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.

Next Size Up

The challenge for you is to make a string of six (or more!) graded cubes.

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

What can you see? What do you notice? What questions can you ask?

Treasure Hunt

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

First Connect Three

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

Factor-multiple Chains

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Fraction Fascination

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

Triangles All Around

Can you find all the different triangles on these peg boards, and find their angles?

Diagonal Sums

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Ten Hidden Squares

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

Orange Drink

A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Sponge Sections

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Factor Lines

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Would You Rather?

Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?

Plenty of Pens

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

Mystery Matrix

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

The Moons of Vuvv

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Where Are They?

Use the isometric grid paper to find the different polygons.

Rectangle Tangle

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?

Pumpkin Pie Problem

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

Quadrilaterals

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Two and Two

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Making Cuboids

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Round and Round the Circle

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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

DO YOU HAVE STUDENTS WHO NEED MORE SUPPORT IN MATHS?

Every week Third Space Learning’s specialist primary maths tutors support thousands of students across hundreds of schools with weekly online 1 to 1 maths lessons designed to plug gaps and boost progress.

Since 2013 these personalised one to one lessons have helped over 150,000 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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Mastery Maths - Year 6 Reasoning - Volume and Area - Sample

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

24 January 2019

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