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White Rose Maths Year 6: What Students Learn And The Resources To Support Them

Emma Johnson

Here we look at the White Rose Maths Year 6 scheme of learning, the topics it covers across the year and provide lots of sample questions and White Rose Maths resources for those following White Rose in Year 6.  

About White Rose Maths 

Year 6 autumn term, year 6 spring term, year 6 summer term, recommended white rose maths year 6 resources, place value year 6.

• Addition, subtraction, multiplication and division Year 6

Fractions Year 6

Fractions b year 6, converting units year 6, ratio year 6, algebra year 6, decimals year 6, fractions, decimals and percentages year 6, area, perimeter and volume year 6, read more: mean median mode, shape year 6, looking for more year 6 maths resources and guidance.

Year 6 Maths Test

Download this free Year 6 maths test to check that your class is on track with their Year 6 maths curriculum.

The White Rose Maths scheme of learning follows the national curriculum with a mastery approach to maths with a range of fluency, reasoning and problem solving elements. They also encourage concrete, pictorial and abstract representations to develop deep understanding of mathematical concepts. 

Read more: White Rose Maths

It is thought that approximately 70% of schools in the UK follow the White Rose Maths scheme and this is reflected in the thousands of young mathematicians Third Space Learning tutors every week. Our tutors are highly skilled maths and pedagogy experts, well trained in the language, representations and approach used by White Rose. They are therefore able to deliver a one to one lesson that feels familiar to students who are also used to White Rose. 

Throughout this article you’ll see example maths lesson slides and example questions from Third Space Learning’s Year 6 maths curriculum that exemplify best practice teaching to the White Rose Maths Year 6 scheme. 

We’ve also provided lots of links to White Rose Maths Year 6 resources that are suitable for use for each topic.In addition to the links provided, Third Space Learning also offers libraries for White Rose Maths Year 1 , White Rose Maths Year 2 , White Rose Maths Year 3 , White Rose Maths Year 4 , and White Rose Maths Year 5 . 

About the White Rose Maths Year 6 Scheme of Learning

The primary school White Rose Maths scheme of learning has gone through several iterations and versions up to the current version 3. The scheme of learning SOL is designed as guidance and it is not necessarily intended for each small step to take one lesson. As with all teaching, it is important that teachers adapt this SOL for their class/ pupils. 

Topics covered in Year 6 White Rose Maths scheme of learning work

The White Rose Maths Year 6 SOL outlines which topics are taught, and when, throughout the autumn, spring and summer terms of Year 6. 

The breakdown for Version 3 of the scheme of learning is as follows 

• Place value
• Addition, subtraction, multiplication and division
• Fractions A
• Fractions B
• Converting units of measurement
• Fractions, decimals and percentages
• Area, perimeter and volume
• Position and direction
• Themed projects, consolidation and problem solving

​​Third Space Learning has created several collections of White Rose Maths aligned resources for all primary year groups from early years through to Year 6. These resources can provide a different perspective on a topic and so help pupils spend the time needed to fully embed a concept.

Here is a summary of the different collections available for schools following Year 6 White Rose Maths, many of them are free resources and some are premium resources, all can be downloaded from our maths hub. Links to the topic specific versions are provided within each termly breakdown below:

Ready to go lesson slides

These ready-to-go lesson slides come in the form of editable powerpoints with related worksheets that are designed for everyday teaching. The lesson slides cover both version 2 of the White Rose scheme of learning (in blue) and version 3 of the SOL. They also include support slides that can be used to support pupils who need a little extra  pre/ post teaching to support their understanding.

Year 6 ready-to-go lesson slides

Code Crackers 

Our Code Crackers resources are aligned to the version 2 SOL. These are summative resources designed as a retrieval activity for the end of the place value block.

Maths Code Crackers Year 6

Pre and Post Diagnostic Questions 

These tests can be used before starting the place value block to assess gaps, and after teaching the place value block to identify progress. 

Diagnostic Assessments Year 6

Worked Examples

Pupils check over completed questions to identify errors (or identify correct answers). Pupils are encouraged to explain the errors they find, not just ‘mark’ work. These worked examples help to solidify understanding by getting the pupil to discuss errors and how to avoid them. 

Year 6 Worked Examples

Rapid Reasoning 

These reasoning problems go alongside our Fluent in Five resource. One question each week has a model answer so teachers can understand what the question is asking and how to solve it. 

Rapid Reasoning Year 6

All Kinds of Word Problems

Test your class’ problem solving skills with these place value word problems.

All Kinds of Word Problems Year 6

White Rose Maths Year 6 autumn term

In the autumn block, Year 6 focuses on place value; addition, subtraction, multiplication & division; fractions and converting units of measurement.

As  with all year groups, place value is the first block to be covered in the Autumn term. By Year 6, this is only a short unit of work; reading and writing numbers to 10,000,000 and exploring powers of 10.

Example year 6 place value questions

1. Write the following number in digits: twenty seven million, three hundred and forty eight thousand, five hundred and 6.

Answer: 27,348,506

2. Identify the value of each underlined digit

a) 7 3 ,640,328

b) 25, 6 04,713

c) 17,3 9 4,801

a) 3 million

Addition, subtraction , multiplication and division Year 6

Addition, subtraction, multiplication and division is the largest block of Year 6. Unlike the other year groups, the four operations are all covered in one block, rather than being separated into two separate blocks. By this stage, pupils are expected to be confident using formal written methods for addition and subtraction. Focus is on securing confidence with long multiplication and division, and applying this knowledge to solving more complex multi-step problems. Learners also build on their understanding of factors, multiples, prime, square and cube numbers.

Example year 6 addition, subtraction, multiplication and division questions

1. 196,877 ÷ 37 = 

Answer: 5,321

2. Which number is a factor of 24, but not a multiple of 8?

Answer: d) 12

Fractions in Year 6, are also split into two blocks, with both Block A and Block B being covered in the Autumn term. 

Fractions A in Year 6

Pupils continue to develop their understanding of equivalent fractions in Year  6; utilising this knowledge to be able to compare and order fractions, and add and subtract fractions and mixed numbers with different denominators.

Example year 6 fractions A questions

1. Order the following fractions from largest to smallest

\frac{1}{2}, \frac{2}{3}, \frac{9}{12}, \frac{5}{6}

Answer: \frac{5}{6}, \frac{9}{12}, \frac{2}{3}, \frac{1}{2}

2. 4\frac{3}{4} + 5\frac{4}{12}

Answer: 10\frac{1}{12}

In this second fractions block of Year 6, pupils build on the concepts introduced in Year 5; including multiplying and dividing fractions. They also continue to focus on calculating fractions of an amount

Example year 6 fractions B questions

1. 2\frac{1}{2} × 3\frac{1}{4} =

Answer: 6\frac{1}{8}

2. What is \frac{7}{8} of 336

Answer: 294

Converting units is a short topic at the end of the autumn term. In this block, pupils build on their understanding of converting metric measures and are introduced to converting between metric and imperial measures (For example, between miles and kilometres).

Example year 6 converting units questions

1. Write 7,532m as km

Answer: 7.532km

2. If 1 mile = 1.6km, how far in kilometres is 8 miles?

Answer: 12.8 miles

White Rose Maths Year 6 spring term

In the spring term term, Year 6 focuses on ratio; algebra; fractions, decimals & percentages; area, perimeter & volume and statistics

Pupils are introduced to ratio for the first time in Year 6. In this block pupils learn to use ratio language and the symbol. They also look at the connection between ratio and fractions and scale drawings.

Example year 6 ratio questions

1. Gemma is making a necklace. The ratio of purple beads to blue beads she uses is 3:1. If she uses 5 blue beads, how many purple beads does she use?

Answer: 15 purple beads

2. The ratio of counters was 4:1 (red:yellow). If there were 20 counters altogether. How many red and yellow counters were there?

Answer: 16 red and 4 yellow

Year 6 is the first time pupils are introduced to algebra. Students begin the block investigating 1-step and 2-step function machines, followed by forming expressions, formulae and equations. This progresses to solving 1-step, then 2-step equations. 

Example year 6 algebra questions

1. An x was input into the following function machine. What would be the output expression?

Answer: 2 x + 4

2. Solve the following equation: 2x + 2 = 12

Answer: x = 5

In Year 6, pupils focus on decimals in two blocks. Firstly as an independent unit, followed by a unit covering fractions, decimals and percentages. In this first block, understanding of place value within a decimal number is reinforced, followed by rounding and adding & subtracting decimals and finally building on knowledge from year 5 to multiply and divide by 10, 100 and 1000.

Example year 6 decimals questions

1. Round 3.765 to 2 decimal places

Answer: 3.77

2. Divide 32.7 by 10, 100 and 100

32.7 ÷ 10 = 3.27

32.74 ÷ 100 =0.327

32.74 ÷ 1000 =0.0327

In this block, pupils build upon the concepts learnt in Year 5; exploring and using equivalence between fractions, decimals and percentages. At this stage, students are also introduced to the concept of calculating a percentage of an amount. Initially pupils are introduced to  one-step problems, such as finding 10% of an amount. They then progress to solving multi-step problems, such as calculating 37% of an amount.

Example year 6 fractions, decimals and percentages questions

1. Write \frac{7}{25} as a decimal and a percentage

Answer: \frac{28}{100} = 0.28 = 28%

2. Use the < > or = symbol for each question below:

\frac{4}{10}   ______  45%

\frac{3}{4} ________ 70%

\frac{6}{20} ______  60%

\frac{4}{10}   < 45%

\frac{3}{4}   > 70%

\frac{6}{20} <  60%

In Year 6, pupils explore how to calculate the area of different shapes; including triangles and parallelograms. They also build on their knowledge of volume from Year 5; calculating, estimating and comparing volume of cubes and cuboids, using standard units, including cubic centimetres and cubic metres.

Example year 6 area, perimeter and volume questions

1. Calculate the volume of the cuboid below

Answer: 72cm ^{3}

2. Draw 2 different cuboids with a volume of 60cm ^{3}

Answer: 2 x 5 x 6 and 3 x 4 x 5

Statistics Year 6

In Year 6, pupils continue to focus on drawing and interpreting line graphs. They are also introduced to pie charts for the first time, learning how to interpret and construct them. Students also learn how to calculate and interpret the mean as an average.

Example year 6 statistics questions

1. A man walks up a hill. It takes him 15 minutes to reach 800m. He then stops for 10 minutes before walking back down. It takes him 10 minutes to reach the bottom of the hill. Plot the graph to show what happens.

White Rose Maths Year 6 summer term

In the summer term, Year 6 focuses on shape; position & direction, followed by themed projects, consolidation and problem solving.

Pupils build on their understanding of shape and properties of shape; drawing 2D shapes, using given dimensions. Students also learn to recognise, describe and build simple 3D shapes, including making nets. In Year 6, there is a significant focus on angles, with pupils learning how to calculate a range of angles, including: vertically opposite angles; angles in triangles, quadrilaterals and other polygons.

Example year 6 shape questions

1. Calculate the size of angle a below:

Answer: Angle a = 180°

2. A triangle has the angles: 45° and 65°. Calculate what the 3rd angle will be:

Answer: 70°

Position and direction Year 6

In Year 4 and 5, pupils learn to plot coordinates in the first quadrant. In Year 6, pupils progress to reading and plotting points in all four quadrants and solving problems with coordinates. Students also draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

Example year 6 position and direction questions

1. On the grid below, plot the following coordinates. What shape do they make?

(4,3) (-2,3) (-2, -2) (3,-2)

They make a square

• Year 6 Maths Test (Year 6 content only)
• Year 6 Maths Questions (with answers)
• Year 6 Maths Sats Papers

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Offham Primary School

Nurturing, Enquiring, Inspiring, Achieving

• The White Rose Curriculum for Maths
• Teaching and Learning
• Our Curriculum - Subject Overviews

Our Curriculum Intent for Maths

Mathematics is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

The national curriculum for mathematics aims to ensure that all pupils:

• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
• reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
• can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects. The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

Teaching and Learning of Maths (Implementation)

At Offham Primary School, children study mathematics daily covering a broad and balanced mathematical curriculum including elements of number, calculation, geometry, measures and statistics. Due to the interconnected nature of mathematics, at Offham we aim to teach maths in a cross curricular manner as well as discretely to teach the practical application of mathematical skills. We focus not only on the mathematical methods but also focus on mathematical vocabulary and to use Maths Mastery to broaden and deepen mathematical understanding.

We aim for each child to be confident in each yearly objective and develop their ability to use this knowledge to develop a greater depth understanding to solve varied fluency problems as well as problem solving and reasoning questions. 

From the 2021/22 academic year onwards, schools in England will be required to administer an online multiplication tables check (MTC) to year 4 pupils. The purpose of the MTC is to determine whether pupils can recall their times tables fluently, which is essential for future success in mathematics. It will help schools to identify pupils who have not yet mastered their times tables, so that additional support can be provided. To support the children with their multiplication practice we use ‘Times Table Rockstars’ as an online and fun learning platform which also offer resources to be used in the classroom.

White Rose Mathematics 

At Offham we are pleased to closely follow the White Rose Mathematics scheme across the school. White Rose Maths is an organisation that aims to work collaboratively with teachers across the country to improve mathematics teaching. Inspired and informed by robust, world-class research and global maths experts, the scheme aims to transform maths education and change the experience of maths forever. The white Rose approach aims to help all pupils to master mathematics.

• White Rose Maths - Information for Parents

What does it mean to  master  mathematics?

A mathematical concept or skill has been mastered when a pupil can represent it in multiple ways, has the mathematical language to communicate related ideas, and can independently apply the concept to new problems in unfamiliar situations.

Mastery is a journey and long-term goal, achieved through exploration, clarification, practice and application over time. At each stage of learning, pupils should be able to demonstrate a deep, conceptual understanding of the topic and be able to build on this over time.

This is not about just being able to memorise key facts and procedures, which tends to lead to superficial understanding that can easily be forgotten. Pupils should be able to select which mathematical approach is most effective in different scenarios.

All pupils can achieve in mathematics

A positive teacher mindset and strong subject knowledge are key to student success in mathematics. It is not the case that some pupils can do mathematics and others cannot.

No pupil should be left behind. The focus is keeping up over catching up. By making high expectations clear and emphasising the value of mathematics education, pupils are encouraged to build confidence and resilience.

Abilities are neither fixed nor innate, but can be developed through practice, support, dedication and hard work. Natural talent is just a starting point and does not determine who has more or less potential to achieve. A positive teacher mindset in maths encourages a love of learning and resilience that enables everyone to achieve.

All pupils are entitled to learn key concepts and skills

A scheme of work based around the principles of mastery really can be suitable for all. Pupils should have the opportunity to stay together and work through new content as a whole group. While mastery schemes of work may be challenging for some, the vast majority should be aiming for this standard. In extreme cases, where students have considerable learning difficulties, individual schools may want to put some alternatives in place.

It is important that high-attaining pupils fully understand key number concepts, rather than simply memorise a process. This will reap its rewards in the future at KS3, GCSE and A-level. Teachers can extend high-attaining students through depth, as opposed to acceleration onto new content.

Focus on depth

Deepen understanding before accelerating content coverage

All pupils benefit from deepening their conceptual understanding of mathematics, regardless of whether they've previously struggled or excelled. Pupils must be given time to fully understand, explore and apply ideas, rather than accelerate through new topics. This approach enables pupils to truly grasp a concept, and the challenge comes from investigating it in new, alternative and more complex ways.

Multiple representations for all

Objects, pictures, words, numbers and symbols are everywhere. The mastery approach incorporates all of these to help pupils explore and demonstrate mathematical ideas, enrich their learning experience and deepen understanding. Together, these elements help cement knowledge so pupils truly understand what they’ve learnt.

All pupils, when introduced to a key new concept, should have the opportunity to build competency in this topic by taking this approach. Pupils are encouraged to physically represent mathematical concepts. Objects and pictures are used to demonstrate and visualise abstract ideas, alongside numbers and symbols.

• Concrete  – Students should have the opportunity to use concrete objects and manipulatives to help them understand and explain what they are doing.
• Pictorial  – Students should then build on this concrete approach by using pictorial representations. These representations can then be used to reason and solve problems.
• Abstract  – With the foundations firmly laid, students should be able to move to an abstract approach using numbers and key concepts with confidence.

Fluency, reasoning and problem solving

Teaching supports the aims of the National Curriculum

Problem solving

Mathematical problem solving is at the heart of our approach. Pupils are encouraged to identify, understand and apply relevant mathematical principles and make connections between different ideas. This builds the skills needed to tackle new problems, rather than simply repeating routines without a secure understanding.

Mathematical concepts are explored in a variety of representations and problem-solving contexts to give pupils a richer and deeper learning experience. Pupils combine different concepts to solve complex problems, and apply knowledge to real-life situations.

The way pupils speak and write about mathematics transforms their learning. Mastery approaches use a carefully sequenced, structured approach to introduce and reinforce mathematical vocabulary. Pupils explain the mathematics in full sentences. They should be able to say not just what the answer is, but how they know it’s right. This is key to building mathematical language and reasoning skills.

Pupils should be able to recall and apply mathematical knowledge both rapidly and accurately.  However, it is important to stress that fluency often gets confused for just memorisation – it is far more than this. As well as fluency of facts and procedures, pupils should be able to move confidently between contexts and representations, recognise relationships and make connections in mathematics. This should help pupils develop a deep conceptual understanding of the subject. Frequent, carefully designed, intelligent practice will help them to achieve a high level of fluency.

Number at the heart

A large proportion of time is spent reinforcing number to build competency and fluency. Number is usually at the heart of any primary mastery scheme of learning, with more time devoted to this than other areas of mathematics. It is important that pupils secure these key foundations of maths before being introduced to more difficult concepts.

This increased focus on number will allow pupils to explore the concepts in more detail and secure a deeper understanding. Key number skills are fed through the rest of the scheme so that students become increasingly fluent.   

The intended impact of Maths teaching and learning at Offham

Throughout each lesson formative assessment takes place and feedback is given to the children through marking and next step tasks to ensure they are meeting the specific learning objective. Teacher’s then use this assessment to influence their planning and ensure they are providing a mathematics curriculum that will allow each child to progress. The teaching of maths is also monitored on a termly basis through book scrutinies, learning walks and lesson observations. Each term children from Year 2 and above complete a summative assessment to help them to develop their testing approach and demonstrate their understanding of the topics covered. Key Stage 1 use a combination of Headstart Assessment tests and previous SATs papers (Year 2) whilst Key Stage 2 use Headstart Assessments and previous SATs papers (Year 6.) The results from both the formative assessment and summative assessment is then used to determine children’s progress and attainment.

The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

Progression of Skills

• National Curriculum Maths Progression Primary
• Ready to progress criteria

Our School Policies for Maths

• Mathematics policy 2021-2022 (under review)
• Maths Calculation Policy 2022-2023

Unfortunately not the ones with chocolate chips.

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White Rose Problems of the Day

Every year, White Rose Maths Hub publishes a set of challenge questions each day throughout March (and bar modelling focused questions in November- Barvember). The orange problems are suitable for KS1 and the blue problems are suitable for KS2/3.

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Barvember 2019

KS1 Problem of the Day 2019

KS1 Problem of the Day 2019 with answers

KS2 Problem of the Day 2019

KS2 Problem of the Day 2019 with answers

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White Rose Maths - Year 5 - Addition and Subtraction - Problem solving and reasoning

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

1 October 2018

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A set of reasoning and problem solving worksheets to use alongside the White Rose Maths scheme. The questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included.

This set of worksheets is for Year 5, Autumn Block 2 (Addition and Subtraction), focusing on the first, second and fifth small step of adding and subtracting whole numbers with more than 4 digits and applying this knowledge to multi-step word problems. Details of how it has been differentiated can be found below: • 1 Star sheet (Working Towards Expected Level): Be able to add and subtract 3 and 4 digit whole numbers, applying this knowledge to a range of different problem solving and reasoning situations. • 2 Star sheet (Expected Level): Be able to add and subtract 4 and 5 digit whole numbers, applying this knowledge to a range of different problem solving and reasoning situations. • 3 Star sheet (Working at greater depth): Be able to add and subtract 5 and 6 digit whole numbers, applying this knowledge to a range of different problem solving and reasoning situations.

Each worksheet contains a total of 8 questions. These questions could be used as a whole, or cut up into strips of 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children.

If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated.

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White Rose Maths - Year 5 - Addition and Subtraction - Varied Fluency and Problem Solving Practice

Two sets of varied fluency and a set of problem solving and reasoning worksheets to use alongside the White Rose Maths scheme. Both sets of questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included. These sets of worksheets are for Year 5, Autumn Block 2 (Addition and Subtraction). Details of how it has been differentiated can be found below: • 1 Star sheet (Working Towards Expected Level): Be able to add and subtract 3 and 4 digit whole numbers and applying this knowledge to a range of problem solving situations, some with more than one step. • 2 Star sheet (Expected Level): Be able to add and subtract 4 and 5 digit whole numbers and applying this knowledge to a range of problem solving situations, some with more than one step. • 3 Star sheet (Working at greater depth): Be able to add and subtract 5 and 6 digit whole numbers and applying this knowledge to a range of problem solving situations, some with more than one step. The varied fluency worksheets contain a total of 8 questions, some broken down into parts (a and b) with 2 examples of each question type. This provides children with the varied fluency that White Rose aim for. These questions can be used as a quick starter and cut up so that only the first 4 questions are used, or given as more of a main activity with all 8 questions. They could also be used for partner work, depending on the ability of the children. The problem solving and reasoning worksheet contains a total of 8 questions. These questions could be used as a whole, or cut up into strips of 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children. If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated.

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