outstanding maths lesson year 6 problem solving

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Year 6 maths planning, a pathway of blocks to cover the national curriculum statutory requirements.

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See our suggested teaching order for the Curriculum for Wales and Scottish Curriculum for Excellence .

Download our Y6 SATS-style questions (button on the right) .

Subject coordinators – Staff Meetings are ready and available!

Autumn Blocks

1 pv, addition and subtraction.

• 1.  Place value in 6-digit numbers
• 2.  Place 6-digit numbers on lines and round
• 3.  Column addition and estimation
• 4.  Column subtraction and estimation
• 5.  Mental and written calculation strategies

2 Decimals and Fractions (A)

• 1.  Add or subtract decimals
• 2.  Subtract 1- and 2-place decimals
• 3.  Understand decimals with three places
• 4.  Add/subtract multiples of 0.1, 0.01, 0.001
• 1.  Generate and use simple formulae
• 2.  Solve equations with two unknowns
• 3.  Generate and continue linear sequences

4 Multiplication and Division

• 1.  Multiples, factors and prime numbers
• 2.  Solve short multiplication problems
• 3.  Use short division to solve problems
• 4.  Long multiplication problems
• 5.  Formal and informal calculation strategies

5 Decimals and Fractions (B)

• 1.  Decimals, fractions: compare, order
• 2.  Equivalent fractions: add and subtract
• 1.  2-D shapes (circles and quadrilaterals)
• 2.  Draw, translate, reflect polygons
• 3.  Draw 2-D shapes; find missing angles
• 4.  Construct 3-D shapes using nets

7 More PV, Addition, Subtraction

• 1.  Add, subtract & round 6-/7-digit numbers
• 2.  Understand/calculate negative numbers
• 3.  Strategies in mental & written calculation
• 4.  Use brackets and order of operations

8 Wellbeing

• 1.  Key skills through expressive arts Y6

Spring Blocks

1 decimals and fractions (a).

• 1.  Place value in 3-place decimals
• 2.  Add numbers with up to 3 decimal places
• 3.  Multiply/divide 2-place decimal numbers
• 1.  Conversion: metric/imperial units; line graphs
• 2.  Time intervals, timetables, 24-hour clock
• 3.  Pie-charts; find the mean of a data set

3 Multiplication and Division (A)

• 1.  Scale factor problems concerning area
• 2.  Solve rate and scaling problems

4 Decimals and Fractions (B)

• 1.  Percentages and fractions of amounts
• 2.  Multiply and divide fractions
• 3.  Ratios, proportion and percentages
• 1.  Calculate areas of different shapes
• 2.  Calculate volumes of cubes/cuboids

6 Multiplication and Division (B)

• 1.  Long division; different remainder forms
• 2.  Use short/long multiplication in problems
• 3.  Use short/long division in problems

7 Spr/Sum Revision Menu A

• 1.  Understand decimals, including negatives
• 2.  Add/subt whole numbers; solve problems
• 3.  Mental and written multiplication/division
• 4.  Mental multiplication & division; ratio
• 5.  Fractions, decimals and percentages
• 6.  Understanding and calculating fractions

8 Spr/Sum Revision Menu B

• 1.  Areas, perimeters and volume
• 2.  Shapes, angles, reflections, translations
• 3.  Bar charts, pie charts, line graphs, means
• 4.  Algebra: unknowns and linear sequences
• 5.  Problem solving

Summer Blocks

1 spr/sum revision menu a, 2 spr/sum revision menu b, 3 exploration in maths.

• 1.  Explore a million
• 2.  Number games and puzzles
• 3.  History of maths

4 Maths Around Us

• 1.  Measuring ourselves and around us
• 2.  Tessellation & other shape patterns
• 3.  Ratios in nature and art

5 Puzzles and Patterns

• 1.  Calculator patterns
• 2.  Number puzzles
• 3.  Number patterns

6 Wellbeing

7 local lockdown.

• 1.  Local Lockdown home pack - Y6 Week 1
• 2.  Local Lockdown home pack - Y6 Week 2

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

Extra Support worksheets come with guidance for a teacher or TA working with small groups. They can make a significant difference to children working below ARE. Extra support is linked to individual objectives-based units, but you can also explore a set for a whole year.

Procedural fluency is fundamental to numeracy, and Hamilton's practice worksheets are carefully differentiated for children working toward Age Related Expectations (ARE), at ARE and at greater depth. Practice is linked to individual objectives-based units, but you can also explore sets of worksheets for the whole year.

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In the Classroom

Materials, guidance and national curriculum resources

Find what you’re after, and more!

This is where the resources are to help you plan and teach great maths lessons, and to assess your pupils’ knowledge and understanding. Simply use the filter options on this page to narrow down your search. Many of the resources here are also suitable for collaborative professional development.

If you don’t find what you’re looking for in this section, you can search using by clicking on the magnifying glass at the top of the page to look across the entire website. The National Curriculum Resource Tool which was in this section has now been removed; you can find other useful contemporary classroom resources below.

Educational Phase

Resource type, exemplification of ready-to-progress criteria.

79 PowerPoints, each one focusing on one of the ready-to-progress criteria in the new DfE maths guidance for KS1 and KS2

DfE guidance on teaching maths at KS3

What the guidance consists of and how it aligns with other NCETM resources

Numberblocks support materials

Materials to support Early Years and Year 1 teachers

Curriculum prioritisation in primary maths

A term-by-term framework to support planning and teaching

Checkpoints

Diagnostic maths activities to help teachers develop their assessment of students' prior learning for KS3

KS3 key ideas exemplified

A series of 52 PowerPoints containing activities and professional development stimuli based on key ideas from the core concepts explored in the KS3 PD materials

Using mathematical representations at KS3

Guidance for some of the most useful representations for Key Stage 3 mathematics.

Algebraic Thinking

Materials for exploring algebra with KS3 students

Insights from experienced teachers

Pairs of teachers explore small sections of the mastery materials in depth

Primary ITE professional development materials

Six professional development units designed for ITE tutors to use with primary trainee teachers exploring maths

Planning to teach secondary maths

Videos and resources for teaching Key Stage 3 maths topics

Primary Assessment Materials

Questions, tasks and activities supporting teaching for mastery.

Mathematical Prompts for Deeper Thinking videos

Videos showing a teacher working with small groups of students from her Year 8 class

Progression Maps for Key Stages 1 and 2

The progression maps are structured using the topic headings as they appear in the National Curriculum

Departmental Workshops

Collaborative CPD sessions for maths departments or other groups of secondary teachers

Primary Calculation Guidance

Recommendations and effective practice teaching ideas

Primary Subject Knowledge Audit

Assess your confidence in teaching the content of the KS1 and KS2 maths curriculum

Secondary Subject Knowledge Audit

Assess your confidence in teaching the content of the KS3 maths curriculum

Secondary ITE professional development materials

Six professional development units designed for ITE tutors to use with secondary trainee maths teachers

Secondary Assessment Materials

Materials to support you and your colleagues in assessing students at KS3

Marking Guidance

Guidance documents to enable effective marking and feedback

Research study modules

Ten study modules enabling you to access, understand and engage with academic research articles

Shaping the Year 7 curriculum: building on Year 6

Ready-to-use training materials, ideal for use in planning effective curriculum transition from primary

Resources for teachers using the mastery materials

Supplementary content to support use of the Secondary Mastery PD Materials

Adapting maths teaching for the Covid-19 period

Guidance for secondary schools – updated November 2020

Training materials for DfE Mathematics guidance

A ready-to-use PowerPoint designed for whole school development, and videos to introduce the guidance

The structure of the number system

Theme 1 comprises four core concepts: place value, estimation and rounding; properties of number; ordering and comparing; simplifying and manipulating expressions, equations and formulae.

Operating on number

Theme 2 comprises two core concepts: arithmetic procedures; solving linear equations.

Multiplicative reasoning

Theme 3 comprises two core concepts: understanding multiplicative relationships; trigonometry.

Sequences and graphs

Theme 4 comprises two core concepts: sequences; graphical representations.

Statistics and probability

Theme 5 comprises three core concepts: statistical representations and measure; statistical analysis; probability.

Theme 6 comprises four core concepts: geometrical properties; perimeter, area and volume; transforming shapes; constructions.

1.1 Place value, estimation and rounding

Core concept 1.1 covers the structure of our place-value system (particularly as it relates to decimals) and rounding numbers to a required number of decimal places or significant figures.

1.2 Properties of number

Core concept 1.2 focuses on factors, multiples and primes, exploring various representations to support understanding of highest common factors and lowest common multiples.

1.3 Ordering and comparing

Core concept 1.3 covers the conversion of decimals to fractions (and vice versa), ordering positive and negative integers, fractions and decimals, and the expression of numbers in standard form.

1.4 Simplifying and manipulating expressions, equations and formulae

Core concept 1.4 concerns the generalisation of number structures, the use of algebraic symbols, and techniques for their manipulation. The rearranging of formulae is also explored.

2.1 Arithmetic procedures

Core concept 2.1 offers guidance on developing understanding of the mathematical structures that underpin standard procedures for calculation with decimals, fractions and directed numbers.

2.2 Solving linear equations

Core concept 2.2 explores how linear equations are effectively the formulation of a series of operations on unknown numbers and how solving them involves undoing these operations.

3.1 Understanding multiplicative relationships

Core concept 3.1 explores fractions, percentages, ratio and proportion (direct and inverse) as contexts in which multiplicative relationships are used.

3.2 Trigonometry

Core concept 3.2 introduces trigonometric functions through the unit circle. Ideas of similarity, scale factor and multiplicative relationships are integrated to explore problem-solving.

4.1 Sequences

Core concept 4.1 covers sequences through exploration of the mathematical structure. It also introduces the idea of the nth term of a linear sequence.

4.2 Graphical representations

Core concept 4.2 introduces x- and y-coordinates as input and output of a function. It explores linear and quadratic functions, and how linear graphs can solve simultaneous equations.

5.1 Statistical representations and measures

Core concept 5.1 covers measures of central tendency, work with grouped data and measures of spread, as well as the construction of scatter graphs and pie charts.

5.2 Statistical analysis

Core concept 5.2 explores making informed choices about which statistical analysis and representation to use for different types of data, as well as the effect on interpretation.

5.3 Probability

Core concept 5.3 introduces probability as a way to quantify, explore and explain likelihood and coincidence, and to reason about uncertainty.

6.1 Geometrical properties

Core concept 6.1 covers angle facts and the geometry of intersecting lines, similarity and congruence, and Pythagoras’ theorem.

6.2 Perimeter, area and volume

Core concept 6.2 covers how the formulae for perimeter, area and volume are derived and connected, and the importance of reasoning mathematically to solve a range of problems.

6.3 Transforming shapes

Core concept 6.3 introduces translation, rotation, reflection and enlargement. It explores the degrees of freedom available, in terms of what does and doesn’t vary for each one.

6.4 Constructions

Core concept 6.4 explores: triangles of given lengths; a perpendicular bisector of a line segment; a perpendicular to a given line through a given point; an angle bisector.

The Bar Model

A representation used to expose mathematical structure

Multiplicative Reasoning – all downloads

Links to all the downloadable folders and files in the Multiplicative Reasoning section

Year 1 curriculum map

The whole of Year 1, split into units

Year 2 curriculum map

The whole of Year 2, split into units

Year 3 curriculum map

The whole of Year 3, split into units

Year 4 curriculum map

The whole of Year 4, split into units

Year 5 curriculum map

The whole of Year 5, split into units

Year 6 curriculum map

The whole of Year 6, split into units

Previous Reception experiences and counting within 100

Unit 1 – 7 weeks

Comparison of quantities and part–whole relationships

Unit 2 – 3 weeks

Numbers 0 to 5

Unit 3 – 2 weeks

Recognise, compose, decompose and manipulate 2D and 3D shapes

Unit 4 – 3 weeks

Numbers 0 to 10

Unit 5 – 3 weeks

Additive structures

Unit 6 – 4 weeks

Addition and subtraction facts within 10

Unit 7 – 3 weeks

Numbers 10 to 100

Unit 1 – 4 weeks

Calculations within 20

Fluently add and subtract within 10.

Unit 3 – 1 week

Addition and subtraction of two-digit numbers (1)

Unit 4 – 2 weeks

Introduction to multiplication

Unit 5 – 7 weeks

Introduction to division structures

Unit 6 – 2 weeks

Unit 7 – 2 weeks

Addition and subtraction of two-digit numbers (2)

Unit 8 – 3 weeks

Unit 9 – 1 week

Unit 10 – 2 weeks

Unit 11 – 1 week

Position and direction

Unit 12 – 1 week

Multiplication and division – doubling, halving, quotitive and partitive division

Unit 13 – 3 weeks

Sense of measure – capacity, volume, mass

Unit 14 – 2 weeks

Adding and subtracting across 10

Unit 1 – 2 weeks

Numbers to 1,000

Unit 2 – 10 weeks

Right angles

Manipulating the additive relationship and securing mental calculation.

Unit 4 – 4 weeks

Column addition

Unit 5 – 2 weeks

2, 4, 8 times tables

Unit 6 – 3 weeks

Column subtraction

Unit 7 – 1 week

Review of column addition and subtraction

Unit 1 – 3 weeks

Numbers to 10,000

Unit 2 – 5 weeks

3, 6, 9 times tables

7 times table and patterns.

Unit 5 - 2 weeks

Understanding and manipulating multiplicative relationships

Unit 6 – 5 weeks

Coordinates

Decimal fractions.

Unit 1 – 5 weeks

Unit 2 – 2 weeks

Negative numbers

Short multiplication and short division.

Unit 4 – 6 weeks

Area and scaling

Unit 5 – 5 weeks

Calculating with decimal fractions

Factors, multiples and primes.

Unit 7 – 4 weeks

Unit 8 – 7 weeks

Converting units

Unit 9 - 2 weeks

Unit 10 - 3 weeks

Calculating using knowledge of structures (1)

Unit 1 – 6 weeks

Multiples of 1,000

Numbers up to 10,000,000.

Unit 3 – 4 weeks

Draw, compose and decompose shapes

Multiplication and division.

Unit 5 – 4 weeks

Area, perimeter, position and direction

Fractions and percentages.

Unit 7 – 6 weeks

Unit 8 – 1 week

Ratio and proportion

Unit 9 – 2 weeks

Calculating using knowledge of structures (2)

Unit 10 – 1 week

Solving problems with two unknowns

Unit 11 – 2 weeks

Order of operations

Mean average.

Unit 13 – 1 week

School sees better results through teaching for mastery

Embracing teaching for mastery in maths has seen pupils’ love for the subject contribute to some exceptional end of year outcomes for all year groups

Why Mastery Readiness isn't just 'mastery-lite'!

The Mastery Readiness Programme enables schools to put in place structures, systems and positive mathematical culture so they can successfully engage in teaching for mastery

Don’t abandon counters just because it’s secondary school

At Trinity Academy in Halifax all teachers are now using place value counters with students across the ability range

Teaching for mastery at secondary: is it compatible with putting students in sets?

A visit to two lessons at Tomlinscote School in Frimley, Surrey

Numberblocks – Series 1

Series 1, all episodes

Numberblocks – Series 2

Series 2, all episodes

Video material to support the implementation of the National Curriculum

Multiplication.

Lesson videos on elements of progression in multiplication across the primary school

Subtraction

Lesson videos on elements of progression in subtraction in Key Stage 2

Number Facts

Lesson videos on number facts for all four operations of addition, subtraction, multiplication and division

Number and Place Value

Lesson videos on children developing understanding and fluency with number

Lesson videos on structures of division in terms of grouping and sharing at Key Stage 1; moving into a written algorithm at Key Stage 2 and demonstration of fluency at Key Stage 3

Lesson videos addressing the ability to develop a secure understanding and calculate with fractions

Lesson videos addressing the demands of the New Curriculum to introduce formal algebra into KS2

Multiplicative Reasoning

Lesson videos on representations in terms of the bar model and double number line are used to support reasoning and problem solving

Reasoning Skills

Developing opportunities and ensuring progression in the development of reasoning skills

Gap tasks: maximising the impact of Work Groups

We visit Gorse Hill Primary School Work Group in Swindon, and find out how gap tasks are driving powerful changes in pedagogy

A Year 1 lesson on difference as a form of subtraction

A lesson from 2015/16 led by Clare Christie, maths subject leader for the Ashley Down Schools Federation in Bristol

A Year 3 lesson on multiplication

A set of video clips from 2014/15 centred on one lesson, focusing on the 6-times-table

A Year 4 lesson on place value with decimal numbers

A year 6 lesson on comparing fractions.

Comparing the value of fractions with the same denominators

A Year 6 lesson on line graphs

A lesson from 2015/16 led by James Berry, subject leader and deputy head at Chesterton Primary School in Wandsworth

Year 2 Shanghai showcase lesson

Ms Lynn, part of the the England–China exchange, leads a Year 2 lesson at Tubbenden Primary School

Year 5 Shanghai showcase lesson

Ms Dai, part of the the England–China exchange, leads a Year 5 lesson at Tubbenden Primary School

Comparison of quantities and measures

Spine 1: Number, Addition and Subtraction – Topic 1.1

Introducing 'whole' and 'parts': part–part–whole

Spine 1: Number, Addition and Subtraction – Topic 1.2

Composition of numbers: 0–5

Spine 1: Number, Addition and Subtraction – Topic 1.3

Composition of numbers: 6–10

Spine 1: Number, Addition and Subtraction – Topic 1.4

Additive structures: introduction to aggregation and partitioning

Spine 1: Number, Addition and Subtraction – Topic 1.5

Additive structures: introduction to augmentation and reduction

Spine 1: Number, Addition and Subtraction – Topic 1.6

Addition and subtraction: strategies within 10

Spine 1: Number, Addition and Subtraction – Topic 1.7

Composition of numbers: multiples of 10 up to 100

Spine 1: Number, Addition and Subtraction – Topic 1.8

Composition of numbers: 20–100

Spine 1: Number, Addition and Subtraction – Topic 1.9

Composition of numbers: 11–19

Spine 1: Number, Addition and Subtraction – Topic 1.10

Addition and subtraction: bridging 10

Spine 1: Number, Addition and Subtraction – Topic 1.11

Subtraction as difference

Spine 1: Number, Addition and Subtraction – Topic 1.12

Addition and subtraction: two-digit and single-digit numbers

Spine 1: Number, Addition and Subtraction – Topic 1.13

Addition and subtraction: two-digit numbers and multiples of ten

Spine 1: Number, Addition and Subtraction – Topic 1.14

Addition: two-digit and two-digit numbers

Spine 1: Number, Addition and Subtraction – Topic 1.15

Subtraction: two-digit and two-digit numbers

Spine 1: Number, Addition and Subtraction – Topic 1.16

Composition and calculation: 100 and bridging 100

Spine 1: Number, Addition and Subtraction – Topic 1.17

Composition and calculation: three-digit numbers

Spine 1: Number, Addition and Subtraction – Topic 1.18

Securing mental strategies: calculation up to 999

Spine 1: Number, Addition and Subtraction – Topic 1.19

Algorithms: column addition

Spine 1: Number, Addition and Subtraction – Topic 1.20

Algorithms: column subtraction

Spine 1: Number, Addition and Subtraction – Topic 1.21

Composition and calculation: 1,000 and four-digit numbers

Spine 1: Number, Addition and Subtraction – Topic 1.22

Composition and calculation: tenths

Spine 1: Number, Addition and Subtraction – Topic 1.23

Composition and calculation: hundredths and thousandths

Spine 1: Number, Addition and Subtraction – Topic 1.24

Addition and subtraction: money

Spine 1: Number, Addition and Subtraction – Topic 1.25

Composition and calculation: multiples of 1,000 up to 1,000,000

Spine 1: Number, Addition and Subtraction – Topic 1.26

Negative numbers: counting, comparing and calculating

Spine 1: Number, Addition and Subtraction – Topic 1.27

Common structures and the part–part–whole relationship

Spine 1: Number, Addition and Subtraction – Topic 1.28

Using equivalence and the compensation property to calculate

Spine 1: Number, Addition and Subtraction – Topic 1.29

Composition and calculation: numbers up to 10,000,000

Spine 1: Number, Addition and Subtraction – Topic 1.30

Numberblocks – Series 3

Series 3, all episodes

Problems with two unknowns

Spine 1: Number, Addition and Subtraction – Topic 1.31

Counting, unitising and coins

Spine 2: Multiplication and Division – Topic 2.1

Structures: multiplication representing equal groups

Spine 2: Multiplication and Division – Topic 2.2

Times tables: groups of 2 and commutativity (part 1)

Spine 2: Multiplication and Division – Topic 2.3

Times tables: groups of 10 and of 5, and factors of 0 and 1

Spine 2: Multiplication and Division – Topic 2.4

Commutativity (part 2), doubling and halving

Spine 2: Multiplication and Division – Topic 2.5

Structures: quotitive and partitive division

Spine 2: Multiplication and Division – Topic 2.6

Times tables: 2, 4 and 8, and the relationship between them

Spine 2: Multiplication and Division – Topic 2.7

Times tables: 3, 6 and 9, and the relationship between them

Spine 2: Multiplication and Division – Topic 2.8

Guidance on the teaching of fractions in Key Stage 1

Spine 3: Fractions – Topic 3.0

Preparing for fractions: the part–whole relationship

Spine 3: Fractions – Topic 3.1

Unit fractions: identifying, representing and comparing

Spine 3: Fractions – Topic 3.2

Non-unit fractions: identifying, representing and comparing

Spine 3: Fractions – Topic 3.3

Adding and subtracting within one whole

Spine 3: Fractions – Topic 3.4

Working across one whole: improper fractions and mixed numbers

Spine 3: Fractions – Topic 3.5

Multiplying whole numbers and fractions

Spine 3: Fractions – Topic 3.6

Finding equivalent fractions and simplifying fractions

Spine 3: Fractions – Topic 3.7

Common denomination: more adding and subtracting

Spine 3: Fractions – Topic 3.8

Multiplying fractions and dividing fractions by a whole number

Spine 3: Fractions – Topic 3.9

Linking fractions, decimals and percentages

Spine 3: Fractions – Topic 3.10

Times tables: 7 and patterns within/across times tables

Spine 2: Multiplication and Division – Topic 2.9

Connecting multiplication and division, and the distributive law

Spine 2: Multiplication and Division – Topic 2.10

Times tables: 11 and 12

Spine 2: Multiplication and Division – Topic 2.11

Division with remainders

Spine 2: Multiplication and Division – Topic 2.12

Calculation: multiplying and dividing by 10 or 100

Spine 2: Multiplication and Division – Topic 2.13

Multiplication: partitioning leading to short multiplication

Spine 2: Multiplication and Division – Topic 2.14

Division: partitioning leading to short division

Spine 2: Multiplication and Division – Topic 2.15

Multiplicative contexts: area and perimeter 1

Spine 2: Multiplication and Division – Topic 2.16

Structures: using measures and comparison to understand scaling

Spine 2: Multiplication and Division – Topic 2.17

Using equivalence to calculate

Spine 2: Multiplication and Division – Topic 2.18

Calculation: ×/÷ decimal fractions by whole numbers

Spine 2: Multiplication and Division – Topic 2.19

Multiplication with three factors and volume

Spine 2: Multiplication and Division – Topic 2.20

Factors, multiples, prime numbers and composite numbers

Spine 2: Multiplication and Division – Topic 2.21

Combining multiplication with addition and subtraction

Spine 2: Multiplication and Division – Topic 2.22

Multiplication strategies for larger numbers and long multiplication

Spine 2: Multiplication and Division – Topic 2.23

Division: dividing by two-digit divisors

Spine 2: Multiplication and Division – Topic 2.24

Using compensation to calculate

Spine 2: Multiplication and Division – Topic 2.25

Mean average and equal shares

Spine 2: Multiplication and Division – Topic 2.26

Scale factors, ratio and proportional reasoning

Spine 2: Multiplication and Division – Topic 2.27

Combining division with addition and subtraction

Spine 2: Multiplication and Division – Topic 2.28

Decimal place-value knowledge, multiplication and division

Spine 2: Multiplication and Division – Topic 2.29

Multiplicative contexts: area and perimeter 2

Spine 2: Multiplication and Division – Topic 2.30

Mindset: why is it so important in teaching for mastery?

Liam Colclough, a headteacher in Sheffield, is convinced that to introduce teaching for mastery effectively, a shift in mindset is required

Teaching for mastery: isn’t it just 'good teaching'?

Emma Patman, a Year 4 teacher, explains how her teaching has been transformed by her exposure to teaching for mastery pedagogy

Using a high quality textbook to support teaching for mastery

We visit the classroom of Hannah Gray, a primary teacher involved in trialling new Singapore-style textbooks, designed to support a mastery approach

Meeting the needs of all without ability setting

Removing setting from maths teaching in a three-form entry primary school

TRGs: Collaborative professional development in action

Green shoots of Teacher Research Groups (TRGs) are slowly spreading their fronds of mastery exploration across the country

How can teaching for mastery work in a mixed age class?

A group of schools in Northamptonshire have been addressing this issue, with encouraging results

Cardinality and Counting

Understanding that the cardinal value of a number refers to the quantity, or ‘howmanyness’ of things it represents

Understanding that comparing numbers involves knowing which numbers are worth more or less than each other

Composition

Understanding that one number can be made up from (composed from) two or more smaller numbers

Looking for and finding patterns helps children notice and understand mathematical relationships

Shape and Space

Understanding what happens when shapes move, or combine with other shapes, helps develop wider mathematical thinking

Comparing different aspects such as length, weight and volume, as a preliminary to using units to compare later

Teacher collaboration supports mixed-attainment classes

A London school models one possible way to make the transition

Key Stage 1 - Multiplication 1 video lessons

Video lessons on multiplication for children in Years 1 and 2

Key Stage 1 - Multiplication 2 video lessons

Key stage 1 - multiplication 3 video lessons, key stage 1 number, addition and subtraction video lessons.

Video lessons on number, addition and subtraction for children in Years 1 and 2

Lower Key Stage 2 - Fractions 1 video lessons

Video lessons on fractions for children in Years 3 and 4

Lower Key Stage 2 - Fractions 2 video lessons

Lower key stage 2 - fractions 3 video lessons, upper key stage 2 - fractions video lessons.

Video lessons on fractions for children in Years 5 and 6

Upper Key Stage 2 - Number, Addition and Subtraction video lessons

Video lessons on number, addition and subtraction for children in Years 5 and 6

Upper Key Stage 2 - Linking fractions, decimals and percentages video lessons

Video lessons on linking fractions, decimals and percentages for children in Years 5 and 6

Numberblocks at home

Resources to accompany the CBeebies Numberblocks series, designed for parents to use at home with children

What maths to teach for the rest of 2020/21

Post-16 Professional Development and Resources

Opportunities for developing teachers and maths departments and resources to support all post-16 maths teaching

Review of fractions

Fractions greater than 1.

Unit 9 – 5 weeks

Symmetry in 2D shapes

Unit 12 – 2 weeks

Unit fractions

Unit 8 – 5 weeks

Non-unit fractions

Unit 9 – 4 weeks

Parallel and perpendicular sides in polygons

Numbers 0 to 20.

Unit 8 – 4 weeks

Unitising and coin recognition

Self-audit questions for a teacher to assess confidence in the teaching of number in KS1 and KS2

Additive reasoning

Self-audit questions for a teacher to assess confidence in the teaching of additive reasoning in KS1 and KS2

Self-audit questions for a teacher to assess confidence in the teaching of multiplicative reasoning in KS1 and KS2

Self-audit questions for a teacher to assess confidence in the teaching of fractions in KS1 and KS2

Using and applying numerical structure

Theme 7 comprises two core concepts: using structure to calculate and estimate; using structure to transform and evaluate expressions.

7.1 Using structure to calculate and estimate

Core concept 7.1 focuses on understanding different representations of number and using the structure of the number system to make appropriate estimations.

7.2 Using structure to transform and evaluate expressions

Core concept 7.2 deepens understanding of fractions, indices and surds, and explores generalised expressions which underpin algebraic proof.

Proportional reasoning

Theme 8 comprises two core concepts: working with direct and inverse proportion; understanding graphical representations of proportionality.

8.1 Working with direct and inverse proportion

Core concept 8.1 focuses on students’ maturing understanding of multiplicative relationships and extending this understanding to explore proportional relationships.

8.2 Understanding graphical representations of proportionality

Core concept 8.2 focuses on multiplicative structure, particularly recognising and describing the characteristics of a multiplicative relationship from its graphical representation.

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Daily Maths Word Problems - Year 6 (Worksheets)

Updated:  17 Apr 2024

A set of 20 problem-solving questions suited to year 6 students.

Non-Editable:  PDF

Pages:  6 Pages

• Curriculum Curriculum:  AUS V8, VIC, AUS V9
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This set of problem-solving questions has been designed to support teachers when teaching students about problem-solving in mathematics.

It provides students with the opportunity to work through 20 maths word problems, identifying the important information and how they can work it out using a variety of methods.

An answer sheet has been included.

teaching resource

Daily maths problems - year 6.

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

Teach Starter Publishing

We create premium quality, downloadable teaching resources for primary/elementary school teachers that make classrooms buzz!

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Pls tell me the answer of Millie held a two-hour cookie sale to raise money for her school. Cookies were priced at $3 each. Millie raised $48 in the first hour. At the end of the sale, Millie had raised $105. How many cookies did Millie sell in the second hour?

Hi Simba, You can find the answers on the last page of this resource. If you need assistance with anything else, please don't hesitate to get in touch!

Hello, would it be possible to have the questions related to Australia's system of measurement please e.g. miles to kilometres and Fahrenheit to Celsius Thank you!

Hi Lauren, I think the issue has been fixed now. You can download this resource again. If there is anything else I can assist you with, please don't hesitate to contact me.

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Question 8 needed adjustments on the quantities to make the problem work. This has been updated

Fixed the answer on Question 20.

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Year 6 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?

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

• 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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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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Open-Ended Problem Solving - Math

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If you are looking for an end-of-the-year math assessment, then this instructional activity could be for you! Your mathematicians are assessed on their ability to solve difficult, multi-step word problems that take quite a bit of thought and mathematical acumen. The five-day process culminates by having each individual present his problem, and its solution, to the class via PowerPoint.

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Multi-step problems—all operations, multi-step problems, multi-step problems in the real world, solving two-step equations using integers (example 1), solving one-step equations: a summary, how do you solve a multi-step inequality using reverse order of operations, how do you solve a multi-step inequality, how do you solve a multi-step equation using reverse order of operations, how do you solve a multi-step equation by simplifying before solving, multi-step inequalities: summer camp.

Word problems in Year 6: challenging learners to take charge of their lesson

Word problems is one of the trickiest topics in Year 6. So why would a teacher run an experiment that challenges learners to take charge of the lesson for themselves?

As teachers, we hope we have all the answers. Mistakes and errors are usually ones we’ve come across before and it’s easy enough to guide learners back to the correct path. But what happens when you can’t find the answer? Your learners could struggle and lose confidence. Plus, you may have to admit to them, that you’re not sure what to do.

To prepare for the worst, I carried out an experiment with my Year 6 class. What if I completely left it to them to solve a maths problem?

Letting my learners take charge of the lesson

Since adopting a maths mastery approach my learners have become more independent and more engaged in their maths lessons. If I admit that I don’t know the answer, then their reaction is to take up the challenge to find the answer themselves.

It’s important for me to find ways to stretch my learners — this helps to build confidence and gives them the resilience to try and fail, and then try again.

I decided to put them to the test and challenged them to take charge of a lesson. My plan was to use the fact that I didn’t know how to reach the answer to facilitate the class discussion.

I trusted that the class’s communication skills and way of working meant that we would be able to find the answer between us. This meant no preparation. The children had full responsibility for this lesson!

The Year 6 word problems lesson

The lesson that I based my experiment on is from Maths — No Problem! 6A, Chapter 6: Word Problems, Lesson 4.

In this chapter, learners are asked to solve complex word problems using the four operations and bar model diagrams.

The first three lessons are workable, but the fourth lesson comes with a warning. It states that ‘ a traditional bar model will not be helpful and requires high-order reasoning and picture drawing ‘.

The fiendish nature of the lesson made it the perfect choice for the experiment. If this didn’t challenge my Year 6 class, nothing would!

So, did the experiment work?

It was an overwhelmingly positive experience. The class solved the problem by throwing everything in. No one went into lesson thinking it would be easy. As the children weren’t judging themselves on whether they reached the answer, they could enjoy the struggle.

The interaction was excellent; ideas jotted down, diagrams added to explain, discarded ideas crossed through. Children moved around the class comparing methods in a constant hubbub of chat!

Finding the way to the answer involved going down many wrong paths. But there may be something of use in the wrong paths. We came to realise that the answer was almost an off-shoot of the lesson. It didn’t matter as much because you were still doing maths.

They were thinking hard, working with many people, sharing ideas to spark other ideas, and tackling problems alongside the teacher on a level playing field. No one admitted to being stuck, and no one gave up. If an idea led up a cul-de-sac, then you tried another way.

Making use of journals

With the method and answer discovered, the children used their journals to write an explanation for an additional practice question. Here’s an example from one learner’s journal.

Journalling is a great way to develop higher-level thinking . In this instance, it gave the class the chance to select the relevant information and carry out the necessary calculations in groups. The journal entry also serves as a great reminder for my learners that they can persevere through tricky questions and find the answer for themselves.

The children’s engagement, communication skills, and confidence to operate a hard lesson was empowering. They had nothing to lose and all to gain by trying.

So, don’t avoid the difficult problems in lessons, see what your class comes up with. They’ll see that teachers aren’t perfect (they might suspect it already), take up the challenge, and you can share in their excitement when the answer eventually emerges.

Journalling for Mastery CPD

Would you like to use maths journalling to advance your pupils? This one-day, expert-level course will show you how. Learn from one of our friendly experts in a relaxed, face-to-face setting. 14 June in London or 28 June in Manchester.

Roger Hitchin

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Year 6 – Fractions

Welcome to Year 6 Fraction, Decimals and Percentages at Primary Maths Hub. Here you will find a growing library of outstanding resources and activities to support FDP lessons in Year 6 and at home.  

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

Do Now Tasks / Starters

Fraction Addition Do Now Tasks

Fraction Addition and Subtraction Do Now Tasks

Fraction Subtraction Do Now Tasks

Divide Fractions by Whole Numbers Do Now Tasks

Differentiated question sets.

Fraction of a Number Question Set 

Adding Fractions Question Set

Subtracting Fractions Question Set

Subtracting Mixed Numbers Question Set

Multiply Pairs of Fractions Question Set

Divide Fractions by Whole Numbers Question Set

Adding Mixed Numbers Question Set

Decimal Addition Question Set 

Decimal Subtraction Question Set

Fractions of a number.

Fraction of a Number

Faded Scaffolding Strips Fraction of a Number

Fraction of a Number- Long and Short Mult and Div

Add fractions.

Adding Fractions with Different Denominators

Faded Scaffolding Strips Add Fractions with  Different Denominators

Fading Scaffolding Strips- Add Three Fractions With Different Denominators

Adding 3 Fractions with Different Denominators

Subtract Fractions

Subtract Fractions with Different Denominators

Subtracting Fractions with Different Denominators

Subtract Fractions with Different Denominators Greater Than 1

Faded Scaffolding Strips Subtract Fractions with Different Denominators

Mixed add and subtract fractions.

Add and Subtract Fractions with Different Denominators

Add and Subtract Fractions with Different Denominators Greater Than 1

Faded Scaffolding Strips Add and Subtract Fractions with Different Denominators

Adding and Subtracting Fractions Part-Whole Model

Add and Subtract Fractions with Different Denominators 

Simplify fractions.

Fading Scaffolding Strips- Simplify Fractions

Ordering and Comparing Fractions

Faded Scaffolding Strips Compare Fractions with Different Denominators

Faded Scaffolding Strips Order Fractions with Different Denominators

Fading Scaffolding Strips- Compare Fractions With Different Denominators Greater than 1

Compare Fractions with Different Denominators

Order Fractions with Different Denominators

Equivalent fractions, multiply fractions.

Multiply Pairs of Fractions

Faded Scaffolding Strips Multiply Pairs of Fractions

Divide Fractions by Whole Numbers

Divide Fractions  by Whole Numbers

Faded Scaffolding Strips Divide Fractions by Whole Numbers

Divide Fractions by Whole Numbers 

Divide Unit Fractions by Whole Numbers

Divide mixed numbers by whole numbers.

Fading Scaffolding Strips- Divide Mixed Numbers by Whole Numbers 

Add and Subtract Mixed Numbers

Adding Mixed Numbers with Different Denominators

Subtracting Mixed Numbers with Different Denominators

Faded Scaffolding Strips Subtract Mixed Numbers with Different Denominators

Adding Mixed Numbers With Different Denominators Faded Scaffolding

Faded Scaffolding Strips Add Mixed Numbers with Different Denominators

Adding and Subtracting Fractions Greater Than 1 Part-Whole Model

Add and Subtract Mixed Numbers with Different Denominators

Convert mixed numbers and improper fractions, add decimals.

Strips- Add Decimal Numbers

Faded Scaffolding Strips Add Decimal Numbers

Add Decimal Numbers

Subtract Decimals

Strips- Subtract Decimal Numbers 

Faded Scaffolding Strips Subtract Decimal Numbers

Subtract Decimal Number From a Whole Number

Faded Scaffolding Strips Subtract Decimals From Whole

Strips- Subtract Decimal Number From Whole Number

Subtract a Decimal Number From a Whole Number 

Mixed add and subtract decimals.

Strips- Add and Subtract Decimal Numbers

Faded Scaffolding Strips- Add and Subtract Decimal Numbers 

Fading Scaffolding Strips- Find Whole From Fraction 

Faded Scaffolding Strips Complements of 1 –  Thousandths

Add and Subtract Decimal Numbers

Subtract Decimal Numbers

Multiplying decimals.

Strips- Decimal Multiplication

Multiplying Decimal Numbers by Whole Numbers- O.t x O

Multiplying Decimal Numbers by Whole Numbers- O.th x O

Multiplying Decimal Numbers by Whole Numbers- TO.t x O 

Multiplying Decimal Numbers by Whole Numbers- Mixed

Dividing decimals.

Divide a Decimal Number by 1-Digit Number

Ordering and comparing decimals.

Faded Scaffolding Strips- Compare Decimals

Compare Decimals 

Order Decimals 

Rounding decimals.

Rounding Decimal Numbers

Faded Scaffolding Strips- Round Decimal Numbers

Fdp - equality and inequality statements.

Equality and Inequality Statement Matching- Decimals 

Decimal A and S- Equality and Inequality Statement Matching

Equality and Inequality Statement Matching- Comparing Fractions 

Fractions All Operations- Equality and Inequality Statement Matching

Percentages.

Percentage of a Number- 1 Step Percentages – Decimals

Percentage of a Number- 1 Step Percentages- Whole Numbers

Percentage of a Number- Multiples of 10 – Decimals

Percentage of a Number- Multiples of 10 – Whole Numbers

Percentage of a Number- Other Percentages – Decimals

Percentage of a Number- Other Percentages- Whole Numbers

Mixed - fractions, decimals and percentages.

Mixed Fractions and Decimals Greater than 1 Part-Whole Model

Mixed Fractions and Decimals Less Than 1 Part-Whole Model 

Mixed Fractions, Decimals and Percentages Part-Whole Model 

Compare Fractions and Decimals

Order Fractions, Decimals and Percentages

Strips- Calculating Using Fraction, Decimal and Percentage Equivalence

Strips- Fraction, Decimal and Percentage Equivalence

Problem solving, challenges and word problems.

Mixed Fraction Word Problems

Add and Sub Fract with Dif Den Greater than 1 Grid Challenge

Hinge questions.

Revision- Adding and Subtracting Decimals

Steps to success.

Adding Fractions with Different Denominators- Steps to Success

Adding Mixed Numbers- Steps to Success

Comparing Fractions- Steps to Success

Divide a Fraction by a Whole Number- Steps to Success

Expressing Fractions in the Same Denominator- Steps to Success

Find a Fraction of a Number- Steps to Success

Multiply Pairs of Fractions- Steps to Success

Simplifying Fractions- Steps to Success

Subtracting Mixed Numbers- Steps to Success

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Outstanding Y3/4 Maths Money Interview Lesson

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

12 June 2024

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Looking for a maths lesson that makes learning about money a breeze? You’ve found it! This lesson is a fantastic opportunity to demonstrate your teaching prowess with activities that clearly show student progress.

Ideal for a reasoning-focused maths class, the interactive PowerPoint questions are designed to engage students across all skill levels. Rooted in the NCETM’s differentiation principles, this lesson encourages critical thinking and is outlined in the accompanying notes.

Whether you have 15 minutes or a full hour, this lesson’s flexibility has made it a hit for both interviews and Ofsted inspections.

Here’s what you’ll receive: ★ A standout lesson plan complete with mini-plenaries, tailored success criteria, and classroom management tips. ★ An interactive PowerPoint filled with thought-provoking mastery questions. ★ A double-sided worksheet featuring open-ended tasks that challenge students to consider various solutions.

Lesson objective: To master adding and subtracting money to resolve real-world problems. Success Criteria: 🌶 Confidently add various amounts of money to calculate the total. 🌶🌶 Accurately determine the correct change. 🌶🌶🌶 Skillfully apply reasoning to justify your problem-solving approach.

This lesson is perfect for observations, Ofsted visits, NQTs, and fits right into the KS2 and LKS2 curriculum for Year 4 and Year 3 classes.

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