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Maths scheme of work

The proportion of time allocated to place value, calculations and proportionality is non-negotiable. This is the minimum time required to teach these areas. This is because these areas are high value, however some of the measurement objectives could be taught between place value (numbers in context) or statistics in science lessons.

Time can be taken from measurement, geometry or statistics, if more catch up time is needed, or if the other three areas have time taken away from them.

Within the calculations area it may be that Key Stage 1 need to equally share the time or lesson between all four calculations compared to key stage two who will probably need to spend a higher proportion of time on multiplication and division. When planning over the course of a week, do not spend 5 lessons on a low value area.

Curriculum weightingKS1 KS2

Number (place value) 25% 45 sessions 10% 18 sessionsNumber addition and subtraction 15% 27 sessions 20% 36 sessionsNumber multiplication and division

15% 27 sessions 20% 36 sessions

Algebra 10% 18 sessions 10% 18 sessionsProportionality 15% 27 sessions 20% 36 sessionsMeasurement 5% 9 sessions 5% 9 sessionsGeometry- properties of shape 5% 9 sessions 5% 9 sessionsGeometry- position and direction 5% 9 sessions 5% 9 sessionsStatistics 5% 9 sessions 5% 9 sessions

Out of 39 weeks, considering 3 weeks off timetable for things like SATS, collapsed curriculum days etc… that leaves 36 weeks (180 sessions) to plan for

Year 1-5 (with the exception of Year 2)

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Autumn Spring Summer65 sessions 50 sessions 65 sessions

Years 2 and 6Autumn Spring Summer70 sessions 55 sessions 55 sessions

The scheme of work was created using: The National Curriculum (DFE 2013) statutory objectives and non-statutory guidance Missing objectives lists from Norfolk Subject Leader Network National Numeracy Strategy Framework (DFEE, 2006)

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Assessment without levels booklet (August 2016) Big Ideas White Rose Hub Teaching for Mastery Year 1-6 NCETM (2015)

Black National Curriculum statutory objectivesRed Missing and mental objectivesGreen Big Idea conceptsBlue FluencyPink ReasoningOrange Problem solving (strategies)CoEL Characteristics of Effective Learning

Curriculum

Documents used • Development matters number/shape, space, and measure• Development matters- the characteristics of effective learning• DfEE National Numeracy Strategy- Maths vocabulary• Making numbers book- 5 principles of counting• National Curriculum (year 1 programme of study)

EYFSThe 5 principles of counting

The one to one principle

The stable order

principle

The cardinal principle

The abstraction

principle

The order-irrelevance principle

Count moveable objects.Count up to 10 objects (then 20) which cannot be moved.To begin to estimate

Recite numbers in sequence forwards and backwards.Notice and extend number patterns.

Count up to 10 objects (then 20) from a larger quantity.Find the total number of items in 2

Begin to understand 0.Count actions or objects.Realise not only objects by anything can be

Estimate how many objects they can see and check by counting them.Begin counting at a given number.Count objects in different ways (e.g. circles and lines).

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numbers of objects and check by counting.Estimate how many objects they can see and check by counting them.Count objects by saying one number name for each item.

Count an irregular arrangement of objects.Understand ordinality.

groups by counting all of them.Know that numbers identify how many are in a set.

counted.Understand the conservation of number.Use coins when counting.

EYFSReading and writing numbers and symbols

Content objectives Recognise numerals and symbols.Record numbers, initially by making marks, progress to simple tally and writing numerals.Knows how to form numbers.To sequence from left to right.

Reasoning Explain the meaning of the marks they have made.Problem solving Make sense of number problems by recognising the numbers and symbols to enable them to work out the answer

to a problem.Fluency Use mathematical marks that can be understood by others.CoEL Paying attention to details.

Checking how well their activities are going and changing strategy as needed.Planning, making decisions about how to approach a task, solve a problem and reach a goal.Finding new ways to do things.

Key vocabulary(use in practical activities and discussion)

Number, zero, one, two.. (to 20 and beyond), add, take away, equals, ten, twenty, thirty (in 10s to 100), how many, estimate.

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EYFSComposition (making numbers)

Content objectives Explore composition (making numbers) and decomposition (breaking numbers down).Begin to understand 0.Understand odd and even numbers.Understand the equivalence of equals.Represent numbers in different ways (eg using different concrete and pictorial representations) and know that it is still the same amount however it looks.

Reasoning Match, group, sort, and classify.Problem solving Find the total by counting on when one group of objects is hidden.Fluency Partition numbers into 10s and 1s.

Recognise small numbers without counting.Explore teen numbers and identify that it is ten with extras (ones).

CoEL Engaging in an open-ended activity.Finding ways to solve problems.Finding new ways to do things.Making links and noticing patterns in their experience.Making predictions.Testing their ideas.Developing ideas of grouping, sequences, cause, and effect.


Tens, units, ones, zero, greater, more, larger, bigger, less, fewer, smaller, compare, order, next, between, before, after.

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EYFSComparison

Content objectives Begin to understand 0.Begin to estimate numbers of objects and check by counting.Order numbers to 10 (then 20) both ascending and descending.Separate a group of 3 or 4 objects in different ways.Understand odd and even numbers.

Reasoning Match, group, sort and classify.Problem solving Say a number which lies between 2 numbers (missing number).Fluency Begin to match numerals to numbers of objects in a set.

Understand 1 more or 1 less than a given number.Compare 2 groups or sets, saying if there is more, less, or the same.Begin to recognise the total is still the same.

CoEL Paying attention to details.Thinking of ideas.Finding ways to solve problems.Finding new ways to do things.Making links and noticing patterns in their experience.Making predictions.Testing their ideas.Developing ideas of grouping, sequences, cause, and effect.


More than, less than, the same, greater than, larger than, bigger than, smaller than, fewer than, least, most, compare, tens, units, last, between.

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EYFSCalculations

Content objectives Begin to understand 0.Understand addition to 10 (then 20).Understand subtraction to 10 (then 20).Understand 1 more and 1 less than a given number.Be able to double and half.

Reasoning Explain how they found the answer and justify their method.Record their calculations to share their ideas.

Problem solving Recognise, extend, and create 2 step (or 3 step) patterns.Find the total number of items in 2 groups by counting all of them.Explore the different pairs to make 5 and 10 (number bonds).Group objects into sets and arrays.

Fluency Relate addition to counting on (or getting larger).Relate subtracting to taking away (counting back, how many are left).Notice and extend number patterns.Recognising number patterns when counting (1s, 2s, 5s, 10s).

CoEL Engaging in an open-ended activity.Taking a risk, engaging in new experiences, and learning by trial and error.Paying attention to details.Showing belief that more effort or a different approach will pay off.Thinking of ideas.Finding ways to solve problems.Finding new ways to do things.Making links and noticing patterns in their experience.Making predictions.Testing their ideas.Developing ideas of grouping, sequences, cause and effect.Planning, making decisions about how to approach a task, solve a problem and reach a goal.Checking how well their activities are going and changing strategy as needed.Reviewing how well their approach worked.


Adding, subtracting, plus, take away, count on, count back, make, total, sum, altogether, equals, leave, distance between, same as, left over.

EYFSProportionality (fractions)

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Content objectives Be able to double, halve and share.Separate a group of 3 or 4 objects in different ways, recognising the total is still the same.

Reasoning Match, group, sort and classify.Explain what double and half means and how to find it.

Problem solving Sharing amounts between their friends in play (eg play dough cakes).Working out how many each when sharing between friends.

Fluency Finding double, half and share between groups of children.CoEL Finding ways to solve problems.

Finding new ways to do things.Making links and noticing patterns in their experience.Making predictions.Testing their ideas.Developing ideas of grouping, sequences, cause and effect.Planning, making decisions about how to approach a task, solve a problem and reach a goal.Checking how well their activities are going and changing strategy as needed.


Double, half, share, too many, not enough, fair, equal, groups, just over, just under, groups, compare.

EYFSMeasurement

Content objectives Compare the length of 2 of the same type of objects (state which is longest and shortest).Understand places that are near/close/far away.Understand language such as light, heavy, the same.Use scales to explore heavy, light, balance.Compare 2 objects by weight.Understand full, empty, and half full.Name the days of the week in order.Order and discuss the events during the school day (including morning, afternoon).

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Order events in my life.Understand new and old.Estimate and measure how many times I can __ in a length of time (10 seconds, 1 minute).Compare 2 or more time durations (quick, slower).Read the time on the clock to the hour.Order coins by their value.Recognise coins of the UK.Know the units for mass (g,kg), capacity (l,ml), and length (cm,m).Use ordinal language (1st, 2nd, 3rd).

Reasoning Sort coins by denomination and by own criteria.Explain what money is, what it is for and the different forms of money.Understand and use the language of units of time.Predict how many cups full with it take to fill a variety of containers.

Problem solving Solve money problems.Measure how many cups full with it take to fill a variety of containers.Order more than 2 objects by their weight.

Fluency Use money in play and real life situation (eg giving change/paying).Understand what money is, what it is for, and the different forms of money.Estimate and order familiar objects by length and compare them directly.Find the total of 2 coins with support.

CoEL Acting out experiences with other people.Representing their experiences in their play.Finding ways to solve problems.Finding new ways to do things.Making links and noticing patterns in their experience.Engaging in an open-ended activity.Showing particular interests.Paying attention to details.


Measure, size, compare, guess, estimate, the same, different.TimeDays of the week, morning, afternoon, evening, night, times in the day (breakfast, lunch time..), quick, slow, new, old, o'clock.CapacityDepth, size, full, empty, half full, half empty, litres, millilitres, deep, shallow, scales.MassLight, heavy, balance, grams, kilograms.

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Length/heightLength, width, height, close, near, far, centimetres, metres, long, short, tall, high, low, wide, narrow, thick, thin.MoneyCount, pair, share, count, sort, pound, coin, penny, pence, pound, price, cost, buy, sell, spend, spent, pay, change, cheap, expensive, costs more, costs less, total.

EYFSGeometry

Content objectives Recognise rectangles, squares, circles and triangles.Explore characteristics of 2D and 3D shapes.Recognise cubes, pyramids, spheres, and cones.Use familiar objects and common shapes to create and re-create patterns and build models.Describe position, direction, and movement including ½ turns and ¼ turns.

Reasoning Match, group, Sort, and classify 2D and 3D shapes.Use mathematical language to identify and describe 2D and 3D shapes.Justify why some shapes are symmetrical and some are not.

Problem solving Identify a shape based on its properties.Identify shapes which are symmetrical and which are not.Create a shape with specific properties (eg make a shape with a round face).

Fluency Recognise, extend and create a 2 (or 3) step pattern.Understand and recognise symmetry.Create symmetrical patterns.Select or identify a particular named shape.

CoEL Engaging in an open-ended activity.

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Taking a risk, engaging in new experiences and learning by trial and error.Paying attention to details.Finding ways to solve problems.Finding new ways to do things.Making links and noticing patterns in their experience.Making predictions.Testing their ideas.Developing ideas of grouping, sequences, cause and effect.Planning, making decisions about how to approach a task, solve a problem and reach a goal.Checking how well their activities are going and changing strategy as needed.Reviewing how well their approach worked.


Shape2D, 3D, solid, flat, side, edge, corner, vertex, face, flat, curved, straight, round, hollow, solid, build, draw, cube, pyramid, sphere, cone, cylinder, cuboid, circle, triangle, square, rectangle, star, diamond, semi-circle, oval, hexagon, size, bigger, larger, long side, short side, pattern, repeating pattern.Position/directionOver, under above, below, top, bottom, left, right, side, outside, inside, around, in front, behind, back, inside, next to, opposite, apart, between, close, near, far.

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EYFSStatistics

Content objectives Match, group, sort and classify.Collect information, record, interpret and explain the data collected.Organise data (eg into a pictogram) to organise, interpret and present findings.

Reasoning Using a pictogram (or data collected) to find out and explain information (eg green is the most popular because..).Problem solving Identifying which is the most/least popular.Fluency Explain their pictogram to demonstrate their interpretation and present their findings.

Carry out independent surveys to collect and interpret data (eg 'What's your favourite..?').CoEL Engaging in an open-ended activity.

Showing particular interests.Initiating activities.Finding new ways to do things.Developing ideas of grouping, sequences, cause and effect.Planning, making decisions about how to approach a task, solve a problem and reach a goal.


Collect, find out, information, record, discover, group, data, explain, most popular, least popular, the same, equal, more, less.

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Year 1The 5 principles of counting


The stable order

principle


The abstraction

principle


Count moveable objects.Count up to 10 objects (then 20) which cannot be moved.To begin to estimate numbers of objects and check by counting.Estimate how many objects they can see and check by counting them.Count objects by saying one number name for each item.

Recite numbers in sequence forwards and backwards.Notice and extend number patterns.Count and irregular arrangement of objects.Understand ordinality.

Count up to 10 objects (then 20) from a larger quantity.Find the total number of items in 2 groups by counting all of them.Know that numbers identify how many are in a set.

Begin to understand 0.Count actions or objects.Realise not only objects by anything can be counted.Understand the conservation of number.Use coins when counting.

Estimate how many objects they can see and check by counting them.Begin counting at a given number.Count objects in different ways (e.g circles and lines).

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Summer Term

Place Value (14)Addition & Subtraction (8)Multiplication & Division (8)Algebra (8)Proprotionality (9)Geometry - Shape (3)Geometry - Position (3)Measurement (3)Statistics (2)

Spring Term

Place Value (15)Addition & Subtraction (9)Multiplication & Division (9)Proportionality (8)Geometry - Shape (3)Gemonetry - Position (3)Algebra (4)Statistics (3)Measurement (3)

Autumn Term

Place Value (16)Addition & Subtraction (10)Multiplication & Division (10)Algebra (6)Proportionality (10)Geometry - Shape (3)Geometry - Postion (3)Measurement (6)Statistics (6)

Number and place valueYear 1

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Count to and across 100, forwards and backwards, beginning with 0-1, or from any given number.Count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens.Be able to, when given a number, identify one more and one less.Use the language of: equal to, more than, less than (fewer), most, leastIdentify and represent numbers using objects and pictorial representations including the number line. (Big Idea 1, Fluency, problem solving)Read and write numbers from 1-20 in numerals and words.Identify and represent numbers using objects and pictorial representations including the number line.Recognise the place value of each digit in a two-digit number (tens and ones)

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Sequence numbers from 0-100 and explain reasoning (including ordering from smallest to largest). Big idea 1, Fluency, problem solvingIdentify and explain the missing number in a sequence (numbers 0-100).Begin to identify even and odd numbers and explain understanding. (Big Idea 1, reasoning)Subitize small quantities and compare them e.g knowing that 3 still has the same value as a quantity regardless of what it looks like.(Big Idea 1 Reasoning)Look at the digits from left to right in a 2 digit number.Understand and explain the value of each digit in a 2-digit number (using apparatus to support reasoning) (Big Idea 2, reasoning)Use ordinal vocabulary e.g 1st, 2nd, 3rd.(Big Idea 1, reasoning).Count on or back in ones, twos or tenPartition small numbers, e.g. 8 + 3 = 8 + 2 + 1Partition and combine tens and onesOdd and even numbers to 20

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Flue

ncy

Demonstrate secure one to one correspondence, cardinality and conservation of numberCount on and back in ones from any start numberKnow the next and previous number in the sequenceOrder numbers from smallest to largestIdentify one more and one lessRepresent numbers conceptuallyRepresent numbers pictoriallyRepresent the same number in different wayPartition numbers in different waysRecognise positional place value e.g. the digit 2 in 21 has a value of 20Recognise additive place value e.g.21 is 20 (tens) + 1 (ones) and 10 + 10 + 1Partition two-digit numbers in different ways using tens and onesDemonstrate positional or additive place value through representing numbers pictorially or conceptually

Reas

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Use mathematical language more than, less than and equal to when comparing numbersSubitize small quantities and compare themUse counting in twos to identify even and odd numbersLink counting to ordering 1st, 2nd, 3rd…Explain the value of each digit in a two-digit numberUse positional place value to order numbers, looking at the digits from left to rightUse additive place value to partition numbers to add and subtractUse apparatus in tens and ones and pictures/marks to reason about numbers

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Fill in missing numbers in a sequence, for example on a number line or 100 square. Explain how they knowRecognise and continue patterns in a counting sequenceUse apparatus and/or diagrams to represent problems and organise thinkingUse place value to fill in missing numbers in a sequence, for example on a number line or 100 squareUse knowledge of place value (positional and additive) to solve problemsUse apparatus and/or diagrams to represent problems and organise thinking

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Year 1Addition and subtraction

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Read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs. (Big Idea 4, Reasoning)Add and subtract one-digit and two-digit numbers to 20, including zero.Represent and use number bonds and related subtraction facts within 20.

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Memorise and reason with number bonds to 5 and 10.Begin to understand that subtraction is the inverse of addition.Use the language associated with + and – (put together, add, add, altogether, total, take-away, distance between, difference between, more than, less than).Number pairs with a total of 10, e.g. 3 + 7, or what to add to a single-digit number to make 10, e.g. 3 + = 10Addition facts for totals to at least 5, e.g. 2 + 3, 4 + 3Addition doubles for all numbers to at least 10, e.g. 8 + 8Add or subtract a pair of single-digit numbers, e.g. 4 + 5, 8 – 3Add or subtract a single-digit number to or from a teens number, e.g. 13 + 5, 17 – 3Add or subtract a single-digit to or from 10 and add a multiple of 10 to a single-digit number, e.g. 10 + 7, 7 + 30Add near doubles, e.g. 6 + 7Reorder numbers when adding, e.g. put the larger number firstRead, write and interpret mathematical statements involving addition +, subtraction – and equals = signsRecall, represent and use all number bonds to and within 10, extending to 20Add and subtract one-digit and two digit numbers to 20, including 0

Flue

ncy Understand the effect of adding or subtracting zero

Add and subtract using concrete objects and/or pictorial representationsBegin to recognise addition and subtraction as inverse operations

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Reas

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gUse mathematical language of add, takeaway, subtract, difference, equalsExplain what addition and subtraction arePartition numbers in different ways to support addition and subtractionExemplify a number sentence in a variety of waysUse a variety of jottings to explain thinking

Prob

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Use objects to count out and explain the problemWork systematically and logically to solve a problemFind possibilities within a problemSolve missing number problems using concrete objects, pictorial representations and mentallyuse reasoning about addition and subtraction to solve number problemsDiscuss and solve problems in familiar practical contexts, including using quantities. Problems should include the terms: put together, add, Altogether, total, take away, distance between, difference between, more than and less than, so that pupils develop the concept of addition and subtraction and are enabled to use these operations flexibly.

Year 1Multiplication and division

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Solve one-step problems involving multiplication and division by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

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Use the mathematical language of multiplication and division (group, grouping, share, array, multiplied by, divided by, share, shared between, sets, double, half).Count in 2’s, 5’s and 10’s using a variety of resources to find a total.Know doubling facts for numbers from 1-10 and associated halving facts.Understand and explain the ’x’ as multiplication through grouping and/or the use of arrays.Partition: double and adjust, e.g. 5 + 6 = 5 + 5 + 1Doubles of all numbers to 10, e.g. double 6Count on from and back to zero in ones, twos, fives or tensUse patterns of last digits, e.g. 0 and 5 when counting in fives

Flue

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Ensure one to one correspondence skills are well developedArrange objects into equal groups and arraysFind double a number and half of an even numberCount in 2s, 5s and 10s using a variety of resources to find a totalUse number lines to count in steps of 2, 5 and 10, forwards and backRecognise division as grouping and sharingBegin to recognise multiplication and division as inverse operations, including double and half

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Begin to use the mathematical language of multiplication and division: group, grouping, share, array, multiplied by, divided by, share, shared between, sets, double, halfExplain how you can group the same quantity in different waysExplain how an answer can be reached in a number of waysUse pictures and marks to demonstrate and explain thinkingMake connections between arrays, number patterns and counting in twos, fives and tensSystematically count in 2s, 5s and 10s to find the total

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Use equal groups and share items out in play and problem solvingUse concrete objects, pictorial representations and arrays to solve one step multiplication and division problemsWork on practical problem solving activities involving equal sets or groups and conjecture about resultsThe two parts need to be equivalent in, for example, area, mass or quantity

Year 1Proportionality

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e Recognise, find and name a half as one of two equal parts of an object, shape or quantity.Recognise, find and name a quarter as one of four equal parts of an objects, shape or quantity.

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Begin to recognise ‘quarter’ when written as a fraction 14

Flue

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Recognise that a half is one of two equal parts of the whole and a quarter is one of four equal parts of a wholeUse concrete and pictorial representations to find ½ and ¼ of an object, shape or quantityFind ½ and ¼ in a number of waysRecognise and combine ½ and ¼ as parts of a whole

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Connect finding ½ and ¼ to equal sharing and grouping of objects and measuresRecognise when an object, shape or quantity is not split into ½ and ¼Identify all possible ways of finding ½ and ¼ of a shapeExplain how to show whole, half, quarter and three-quarter turns

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Children themselves move in turns, giving instructions to other children to do so, and programming robots using instructions given in whole, half, quarter and three-quarter turnsSolve simple problems involving fractions of shapes, objects and quantities

Year 1Measurement

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Compare describe and solve practical problems for:* Lengths and heights (for example long/ short, longer/shorter, tall/short, double/half).* Mass/weight (for example heavy/ light, heavier than/ lighter than).* capacity and volume (for example, full/ empty, more than, less than, half, half-full, quarter)* Time (for examples, quicker, slower, earlier, later).To measure and begin to record the following:

length and height Mass/ weight Capacity and volume, Time (hours, minutes, seconds).

Recognise and know the value of different denominations of coins and notes.Recognise and use language related to dates (including days of the week, weeks, months and years.Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.Sequence events in chronological order using language (for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon, evening).

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Recognise and use symbols for pounds (£) and pence (p)Begin to combine 1p, 2p, 5p and 10ps coins to find a total with support.Become familiar with standard measures (ruler, weighing scales and containers) and use associated vocabulary. (Big Idea 8,Fluency)Use measuring tools such as a ruler, weighing scales and containers, to record standard measures

Flue

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Move from using non-standard units including discrete (e.g. counting) and continuous (e.g. liquid) measures to using manageable common standard units.Know the names and values of the different coins and bank notesMake the same amount of money in different waysUse 10p and 1p coins as Base 10 apparatusUse the number words on coins to begin to read and write numbers from 1 to 20 in wordsThe pairs of terms: mass and weight, volume and capacity, are used interchangeably

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Describe and solve practical problems (using the correct vocabulary and reasoned argument) about: lengths and heights [e.g. long/short, Longer/shorter, tall/short, double/half] mass/weight [e.g. heavy/light, heavier than, lighter than] capacity and volume [e.g. full/empty, more than, less than, half, half full, quarter]Use pairs of terms - mass and weight, volume and capacity interchangeably and appropriatelyFind practical ways to justify and explain answersSequence events in logical orderKnow measurement is about equivalence, for example how many cubes are equivalent to the length of the table or the mass of the teddy?

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Work logically and systematically to solve a problemUse a variety of information to reach conclusionsSolve problems relating to measures, including time and moneyComplete problems with missing informationSort coins and times systematically

Year 1Geometry- properties of shape

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Recognise and name common 2D and 3D shapes including 2D shapes (for example, rectangles (including squares), circles and triangles. 3D shapes (for example, cuboids (including cubes), pyramids, spheres and cylinders)

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Sort shapes in a variety of ways and explain how shapes differ. (Big Ideas 9, Problem solving)Recognise common 2D and 3D shapes in different orientations. (Big Ideas 9, Fluency)Use mathematical language associated with shapes to describe everyday objects (sides, corners, faces, edges, straight, curved, flat, solid).Recognise, create and explain simple shape and colour patterns.

Flue

ncy Handle and name common 2D and 3D shapes, naming these and related everyday objects fluently

Know shapes have the same name whatever their orientation or sizeLink pictorial representations to concrete objectsRecognise a triangle in all its forms

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Explain how shapes differ/are the sameDescribe what is special about a particular shape

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Systematically sort shapes in a variety of waysSolve shape problems

Year 1Geometry- position and direction

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Describe position, direction and movement, including half, quarter and three quarter turns

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Use position and direction knowledge to create simple journeys (e.g programming bee-bots)Understand the mathematical terminology of clockwise and anticlockwise.

Flue

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Pupils make whole, half, quarter and three-quarter turns in both directions and connect turning clockwise with the movement on a clock face

Reas

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g Use positional language accurately, including turns

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Solve shape problemsPlan simple journeysUse a floor robot to solve problems involving position and direction

Year 1Algebra

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Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations and missing number problems, such as 7=__ - 9

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Recognise a symbol such as □ to represent a missing numberGive an example of a generalisation e.g. odd number, 2D shape, 3D shape.Recognise that 2 things and 3 things will always be 5 things, regardless of what the things areUse the equals sign as a balance, to show equivalence between two number statements and explain the equals sign, reasoning that is doesn’t simply mean “This is the answer”.

Flue

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Recognise and create repeating patterns with objects and with shapesRecognise a symbol such as □ to represent a missing numberGive an example of a generalisation e.g. odd number, 2D shape, 3D shapeUse the equals sign as a balance, to show equivalence between two number statementsGive an example of a generalisation e.g. odd number, 2D shape, 3D shape

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Recognise and describe the repeated unit in a pattern and use it to continue the patternUse counting in twos to identify even and odd numbersRecognise that 2 things and 3 things will always be 5 things regardless of what the things areRecognise that addition and subtraction are related operationsGeneralise rather than describe, e.g. they both have rather than one is blue and one is greenJustify choices in general terms

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Continue a repeating patternIdentify odd and even numbers; continue a sequence of odd or even numbersSolve missing number and shape problems

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Year 1Statistics

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NB There are no statistical National Curriculum objectives for Year 1

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Begin to construct simple pictograms, tally charts, block diagrams and simple tables to show data.Begin to ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity. (Big Idea 10, Fluency)

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Flue

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Sort according to a specified criteria e.g. odd, even, squares, pyramidsRe

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Sort using single circle, 2 circle and overlapping circle Venn diagramsSort using a simple Carroll diagram with labels such as square and not square.

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g Gather and record information to answer a question



The stable order

principle


The abstraction

principle


Count moveable objects.Count up to 10 objects (then 20) which cannot be moved.To begin to estimate numbers of objects and check by counting.Estimate how many objects

Recite numbers in sequence forwards and backwards.Notice and extend number patterns.Count and irregular arrangement of objects.Understand

Count up to 10 objects (then 20) from a larger quantity.Find the total number of items in 2 groups by counting all of them.Know that numbers

Begin to understand 0.Count actions or objects.Realise not only objects by anything can be counted.Understand the conservation of number.Use coins when


28

they can see and check by counting them.Count objects by saying one number name for each item.

ordinality. identify how many are in a set.

counting.

29

30

Autumn Term

Place Value (16)

Addition & Subtraction (10)

Multiplication & Division (10)

Algebra (6)

Proportionality (10)

Geometry - Shape (3)

Geometry - Postion (3)

Measurement (6)

Statistics (6)

Spring Term

Place Value (15)Addition & Subtraction (9)Multiplication & Division (9)Proportionality (11)Geometry - Shape (3)Algebra (4)Statistics (3)Measurement (3)

Summer Term


Number and place valueYear 2

Nat

iona

l Cur

ricu

lum

ob

ject

ives

Count in steps of 2, 3 and 5 from 0 and in 10s from any given number, forward and backwards.Compare and order numbers from 0 up to 100; use <,> and = signs.Identify, represent and estimate numbers using different representations including the number line.Read and write numbers to at least 100 in numerals and words.Identify, represent and estimate numbers using different representations including the number lineRecognise the place value of each digit in a two-digit number (tens and ones)Identify, represent and estimate numbers using different representations including the number line.Read and write numbers to at least 100 in numerals and words.Identify, represent and estimate numbers using different representations including the number lineRecognise the place value of each digit in a two-digit number (tens and ones)Use place value and number facts to solve problems.

Mis

sing

/men

tal

obje

ctiv

es

Identify and explain the missing number in a sequence (numbers 0-100).Locate any number on a hundred square and understand that each number including 10 is a multiple of ten and ones.Use the language of: equal to, more than, less than (fewer), most, least to compare numbers and their values.Recognise the place value of each digit in a three-digit number (hundreds, tens and ones)Partition: count on in tens and ones to find the total.Partition: count on or back in tens and ones to find the difference.Know odd and even numbers to 100.Count forwards and backwards in steps of different sizes.Know number bonds to 10 and 20 and related addition and subtraction facts.Describe and extend number sequences counting on or back in steps of 1, 10 or 100 from any number, recognising odd and even.Order a set of familiar numbers and position them on a number line and where appropriate a 100 square.Round a number to the nearest 10 or 100.

Flue

ncy

Compare numbers.

31

Reas

onin

gSequence numbers from 0-100 and explain reasoning.Begin to identify even and odd numbers and explain understanding. (Big Idea 1, Reasoning)Understand and explain the value of each digit in a 2-digit number, moving on to 3 digits (using apparatus to support reasoning) (Big Idea 2, Reasoning)Use mathematical language to describe, explain, convince, justify and generalise.Describe patterns and relationships involving numbers.Understand and use the vocabulary of estimation and approximation and give a sensible estimate for a number of objects.Suggest extensions by asking ‘What if…’ or ‘What could I try next…?’

Prob

lem

so

lvin

g

Present solutions to puzzles and problems in an organised way, explain decisions, methods and results in pictorial, spoken or written form using mathematical language and number sentences.Solve mathematical problems or puzzles, recognise simple patterns or relationships, generalise and predict.Choose and use appropriate number operations and ways of calculating to solve problems.Identify and record the information or calculation needed to solve a puzzle or problem.Answer questions by choosing and using suitable equipment and selecting, organising and presenting information in lists tables and simple diagrams.

Year 2Addition and subtraction

32

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Solve problems with addition and subtraction using concrete objects and pictorial representations, including those involving number, quantities and measures.Solve problems with addition and subtraction by applying their increasing knowledge of mental and written methods.Add and subtract numbers using concrete objects, pictorial representations, and mentally including a two-digit number and ones.Add and subtract numbers using concrete objects, pictorial representations, and mentally including a 2-digit number and tens.Add and subtract numbers using concrete objects, pictorial representations, and mentally including two, 2-digit numbers.Add and subtract numbers using concrete objects, pictorial representations, and mentally including adding three, one-digit numbers.Show that addition of two numbers can be done in any order (commutative law) and subtraction of one number from another cannot.

Mis

sing

/ men

tal o

bjec

tive

s

Begin to memorise and reason with number bonds to 5, 10 and 20.Understand and use the equals sign correctly as a balance of an equation.Recognise addition and subtraction facts for all numbers up to at least 10, e.g. 3 + 4, 8 – 5Know number pairs with totals to 20Know addition and subtraction facts for all numbers up to at least 10, e.g. 3 + 4, 8 – 5Know number pairs with totals to 20Use knowledge of pairs making 10Reorder numbers when addingCount in steps of 2, 3 and 5 from 0 and in 10s from any given number, forward and backwards.Read and write numbers to at least 100 in numerals and words.Recognise the place value of each digit in a two-digit number (tens and ones)Understand that subtraction is the inverse of addition and vice versa; use this to derive and record related addition and subtraction number sentencesUse partitioning to bridge through 10 and multiples of 10 when adding and subtractingUse partitioning count on in tens and ones to find the totalUse partitioning count on or back in tens and ones to find the differenceUse partitioning add a multiple of 10 and adjust by 1Use partitioning double and adjustPartition and combine multiples of tens and onesSay the number that is 1, 10 or 100 more or less than any given numberRound a number to the nearest 10 or 100Develop pencil and paper methods for additions and subtractions that cannot at this stage, be done mentally

Flue

ncy

Compare and order numbers from 0 up to 100; use <,> and = signs.Identify, represent and estimate numbers using different representations including the number line.Reorder numbers when addingUse knowledge of pairs making 10Use knowledge that addition can be done in any order (associative law)Use patterns of similar calculations

33

Reas

onin

gDescribe patterns and relationships involving numbersChoose and use appropriate number operations and ways of calculating to solve problemsPresent solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentencesUnderstand and use the vocabulary of estimation and approximation, and give a sensible estimate for a number of objectsSolve mathematical problems or puzzles, recognise simple patterns or relationships, generalise and predict. Suggest extensions by asking ‘What if…?’ or ‘What could I try next?

Prob

lem

so

lvin

g

Identify and record the information or calculation needed to solve a puzzle or problemAnswer questions by choosing and using suitable equipment and selecting, organising and presenting information in lists, tables and simple diagrams

Year 2Multiplication and division

Nat

iona

l Cur

ricu

lum

ob

ject

ives

Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers.Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (x), division (÷) and equals signs.Understand and show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot.Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods and multiplication and division facts, including problems in contexts.

34

Mis

sing

/ men

tal o

bjec

tive

sLearn and recall the 3 x table.Understand and explain the ’x’ as multiplication through grouping and/or the use of arrays.Use the mathematical language of multiplication and division (group, grouping, share, array, multiplied by, divided by, share, shared between, sets, double, half).Know doubling facts for numbers from 1-20 and associated halving facts.Know all pairs of multiples of 10 with totals up to 100, e.g. 30 + 70, or 60 + = 100Know what must be added to any two-digit number to make the next multiple of 10, e.g. 52 + = 60Partition: add a multiple of 10 and adjust by 1Partition: double and adjustKnow doubles of all numbers to 20, e.g. Double 13, and corresponding halvesKnow doubles of multiples of 10 to 50, e.g. Double 40, and corresponding halvesKnow multiplication facts for the 2, 5 and 10 times-tables, and corresponding division factsDouble any multiple of 5 up to 50, e.g. Double 35Halve any multiple of 10 up to 100, e.g. Halve 90Find half of even numbers to 40Find the total number of objects when they are organised into groups of 2, 5 or 10Partition: double the tens and ones separately, then recombineUse knowledge that halving is the inverse of doubling and that doubling is equivalent to multiplying by twoUse knowledge of multiplication facts from the 2, 5 and 10 times-tables, e.g. Recognise that there are 15 objects altogether because there are three groups of fiveKnow all pairs of multiples of 10 with totals up to 100, e.g. 30 + 70, or 60 + = 100Know what must be added to any two-digit number to make the next multiple of 10, e.g. 52 + = 60Know addition doubles for all numbers to 20, e.g. 17 + 17 and multiples of 10 to 50, e.g. 40 + 40Partition: bridge through 10 and multiples of 10 when adding and subtractingPartition and combine multiples of tens and onesPartition: double the tens and ones separately, then recombineUse knowledge of multiplication facts from the 2, 5 and 10 times-tablesRound a number to the nearest 10 or 100

Flue

ncy

Use knowledge that halving is the inverse of doubling and that doubling is equivalent to multiplying by twoUnderstand the operation of multiplication and the associated vocabulary, and that multiplication can be carried out in any order

35

Reas

onin

gDescribe patterns and relationships involving numbersChoose and use appropriate number operations and ways of calculating to solve problemsPresent solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentencesUnderstand and use the vocabulary of estimation and approximation, and give a sensible estimate for a number of objectsSolve mathematical problems or puzzles, recognise simple patterns or relationships, generalise and predict.Suggest extensions by asking ‘What if…?’ or ‘What could I try next?

Prob

lem

so

lvin

g

Identify and record the information or calculation needed to solve a puzzle or problemAnswer questions by choosing and using suitable equipment and selecting, organising and presenting information in lists, tables and simple diagramsMake sensible decisions about rounding up or down after division in the context of a problem


Nat

iona

l Cu

rric

ulu

m

obje

ctiv

e Recognise, find and write fractions13142434 of a length, shape set of objects or quantity.

Write simple fractions for 12 of 6= 3 and recognise the equivalence of 24 and 12

Mis

sing

/ m

enta

l ob

ject

ives

Understand explain that fractions involve a relationship between a whole and parts of a whole. (Big Idea, Fluency 7a)Begin to understand the vocabulary associated with fractions (numerator, denominator, whole, part-whole).Use their developing knowledge of fractions in explaining time (Big Idea 7, Problem solving).

36

Flue

ncy

Recognise the equivalence of simple fractionsRepresent fractions in different ways.

Reas

onin

g

Describe patterns and relationships involving fractionsPresent solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentencesUnderstand and use the vocabulary of estimation and approximationSolve mathematical problems or puzzles, recognise simple patterns or relationships, generalise and predict. Suggest extensions by asking ‘What if…?’ or ‘What could I try next?Investigate a general statement about simple fractionsSolve problems which involve finding all the possibilities, so that generalisations can be reached.

Prob

lem

so

lvin

g

To identify and record the information or calculation needed to solve a puzzle or problem.

Year 2Measurement

37

Nat

iona

l Cur

ricu

lum

ob

ject

ives

Choose and use appropriate standard units to estimate and measure length/ height in any direction (m/cm); mass (kg/g); temperature ºc); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels.Compare and order lengths, mass, volume/ capacity and record the results using <,> and =.Recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value.Find different combinations of coins that equal the same amount of money.Solve simple problems in a practical context involving addition and subtraction of money of the same unit including giving change.Tell and write the time to five minutes, including quarter past/ to the hour and draw the hands on a clock face to show these times.Know the number of minutes in an hour and the number of hours in a day.

Mis

sing

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enta

l ob

ject

ives

Be familiar with standard measures (ruler, weighing scales and containers) and use associated vocabulary. (Big Idea 8,fluency)Use multiplication facts to read scales (for example measuring on a weighing scale, using multiplication facts to support understanding of time intervals)Compare and sequence intervals of time.Round a number to the nearest 10 or 100

Flue

ncy

Reas

onin

g

Describe patterns and relationships involving numbersChoose and use appropriate number operations and ways of calculating to solve problemsPresent solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentencesUnderstand and use the vocabulary of estimation and approximation, and give a sensible estimate for a number of objectsSolve mathematical problems or puzzles, recognise simple patterns or relationships, generalise and predict. Suggest extensions by asking ‘What if…?’ or ‘What could i try next?

Prob

lem

so

lvin

g


38


39

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Identify and describe the properties of 2D shapes including the number of sides and line symmetry in a vertical line.Identify and describe the properties of 3D shapes including the number of edges, vertices and facesIdentify 2D shapes on the surface of 3D shapes (for example a circle on a cylinder, a triangle on a pyramid).Compare and sort common 2D and 3D shapes and everyday objects.

Mis

sin

g/

men

tal

obje

cti Read and write common 2D and 3D shape names.

Recognise a triangle in all its forms. (Big Idea 9, Fluency.)

Flue

ncy

Reas

onin

g

Describe patterns and relationships involving shapePresent solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentencesSolve mathematical problems or puzzles, recognise simple patterns or relationships, generalise and predict. Suggest extensions by asking ‘What if…?’ or ‘What could i try next?Investigate a general statement about familiar numbers or shapes

Prob

lem

so

lvin

g



40

Nat

iona

l Cu

rric

ulu

m

obje

ctiv

es

Use mathematical vocabulary to describe position, direction and movement including movement in a straight line and distinguishing between rotation as a turn and in terms of right-angles for quarter, half and three quarter turns (clockwise and anti-clockwise).

Mis

sing

/ m

enta

l ob

ject

ives

Order and arrange combinations of mathematical objects in patterns.Be able to spot, continue and generate patterns in numbers, shapes and data.Be able to recognise, verbalise and record pattern.

Flue

ncy

Reas

onin

g Describe patterns and relationships involving shapePresent solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentencesSolve mathematical problems or puzzles, recognise simple patterns or relationships, generalise and predict. Suggest extensions by asking ‘What if…?’ or ‘What could i try next?

Prob

lem

so

lvin

g Identify and record the information or calculation needed to solve a puzzle or problemAnswer questions by choosing and using suitable equipment and selecting, organising and presenting information in lists, tables and simple diagramsSolve problems which involve finding all the possibilities, so that generalisations can be reached.

Year 2Algebra

41

Nat

iona

l Cu

rric

ulu

m

obje

ctiv

e There are no statutory National Curriculum objectives for year 2 algebra, however, algebra runs throughout all other content.M

issi

ng/

men

tal

obje

ctiv

es

Understand and use the equals sign correctly as a balance of an equation.Compare and sequence intervals of time.Recall and use addition and subtraction facts to 20 fluently and derive and use related facts up to 100.

Flue

ncy

Find missing numbers using the equals sign as a balance, eg. 5 + ? = 8

Reas

onin

g

Describe patterns and relationships involving numbersPresent solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentencesUnderstand and use the vocabulary of estimation and approximation, and give a sensible estimate for a number of objectsSolve mathematical problems or puzzles, recognise simple patterns or relationships, generalise and predict. Suggest extensions by asking ‘what if…?’ or ‘what could i try next?Investigate a general statement about familiar numbers or shapesBe able to recognise, verbalise and record pattern

Prob

lem

sol

ving

Solve problems which involve finding all the possibilities, so that generalisations can be reachedIdentify and record the information or calculation needed to solve a puzzle or problemAnswer questions by choosing and using suitable equipment and selecting, organising and presenting information in lists, tables and simple diagramsRecognise and use the inverse relationship between addition and subtraction and use this to check calculations and missing number problems.Solve problems which involve finding all the possibilities, so that generalisations can be reachedRecognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.Order and arrange combinations of mathematical objects in patterns and sequences.Be able to spot, continue and generate patterns in numbers, shapes and data

Year 2Statistics

42

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Interpret and construct simple pictograms, tally charts, block diagrams and simple tables.Ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity.Ask and answer questions about total and comparing categorical data.

Mis

sing

/ m

enta

l ob

ject

ives

Use ICT where appropriate to collect and present data and draw conclusions.Sort and collect information to create a range of charts and tables including Venn and Carroll diagrams. (Big Idea 10, Fluency)

Flue

ncy

Reas

onin

g

Describe patterns and relationships involving numbersPresent solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentencesUnderstand and use the vocabulary of estimation and approximation, and give a sensible estimate for a number of objectsSolve mathematical problems or puzzles, recognise simple patterns or relationships, generalise and predict. Suggest extensions by asking ‘What if…?’ or ‘What could i try next?

Prob

lem

so

lvin

g


43



The stable order

principle


The abstraction

principle







44

45

Autumn Term

Place Value (6)



Algebra (4)




Measurement (3)

Statistics (3)

Spring Term

Place Value (6)Addition & Subtraction (7)Multiplication & Division (15)Proportionality (10)Geometry - Position (3)Algebra (5)Statistics (4)

Summer Term


Year 3

Number – place value

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Count from 0 in multiples of 4, 8, 50 and 100Identify, represent and estimate numbers using different representations.Find 10 or 100 more or less than a given number;Recognise and understand the place value of each digit in a three digit number (hundreds, tens, ones). (Big Idea 2)Compare and order numbers up to 1000 using different representations. (Big Idea 1)Read and write numbers up to 1000 in numerals and in words.Solve number problems and practical problems involving these ideas.

Mis

sing

/m

enta

l ob

ject

ives

Compare two given numbers, say which is more or less (including the use of < > =), and give a number lying between them e.g. what number is halfway between 7 and 8.Round 2 digit or 3 digit numbers to the nearest 10 or 10

Flue

ncy

(Big Idea 1 Fluency)Understand and use the vocabulary of estimation and approximation, and give a sensible estimate for a number of objects or a calculationCount forwards and backwards in steps of different sizes to 1000Understand that 847 is 8 hundreds, 4 tens and 7 ones and this gives the additive value of the whole numberUnderstand the position of 0 as a place holderUnderstand the positional place value of each digit

46

Reas

onin

g(Big Idea 1 Reasoning)Understand that in the number 847 we can find the multiplicative place value of each digit by multiplying each digit by the column it is in eg 8 x 100 = 800 to use sensible estimates and justify whyExplain and reason about patterns in number sequencesIdentify the missing number in a sequenceUse mathematical language when comparing numbersExplain and justify statements about positions of digitsConvince a friend of the value of each digit in a three-digit numberExplain why 640 is ten times bigger than 64

Prob

lem

so

lvin

g

(Big Idea 1 Problem Solving)Solve problems in context (using language such as greater, less than etc)Recognise mathematical connections between numbers and patterns of numbersDecide how to check if your conjecture is correctUse understanding of the value and position of digits to solve problemsWork systematically to find patterns in numbersUse apparatus to represent problems and organise thinking

Year 3

Number – Addition and Subtraction

47

Nat

iona

l Cur

ricu

lum

ob

ject

ives

Add and subtract numbers mentally, including: a three digit number and ones; a three-digit number and tens; a three digit number and hundreds.(Big Idea 4)Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction.Use rounding and approximation to estimate the answer to a calculation and use inverse operations to check answers. (Big Idea 4)Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

Mis

sing

/men

tal o

bjec

tive

s

Recall and use addition and subtraction facts to 20 and 100 fluently.Partition numbers to add and subtract. (Big Idea 4)Use mathematical language for addition and subtraction.Understand that addition is commutative and subtraction is not. (Big Idea 4)Use trial and improvement to make decision and justify. (Big Idea 4)Choose and use appropriate strategies for addition and subtraction depending on the numbers involved, working flexibly. (Big Idea 4)Solve problems in different ways involving number, money and measure and discuss which is the most efficient. (Big Idea 3)

Addition and subtraction facts for all numbers to 20, e.g. 9 + 8, 17 – 9, drawing on knowledge of inverse operationsSums and differences of multiples of 10, e.g. 50 + 80, 120 – 90Pairs of two-digit numbers with a total of 100, e.g. 32 + 68, or 32 + = 100Addition doubles for multiples of 10 to 100, e.g. 90 + 90Add and subtract groups of small numbers, e.g. 5 – 3 + 2Add or subtract a two-digit number to or from a multiple of 10, e.g. 50 + 38, 90 – 27Add and subtract two-digit numbers e.g. 34 + 65, 68 – 35Add near doubles, e.g. 18 + 16, 60 + 70Reorder numbers when addingIdentify pairs totalling 10 or multiples of 10Partition: add tens and ones separately, then recombinePartition: count on in tens and ones to find the totalPartition: count on or back in tens and ones to find the differencePartition: add or subtract 10 or 20 and adjustPartition: double and adjustPartition: count on or back in minutes and hours, bridging through 60 (analogue times)

48

Flue

ncy

Use different representations to solve problems.Show that the addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannotaddition and subtraction facts for all numbers to 20, e.g. 9 + 8, 17 – 9, drawing on knowledge of inverse operationsSums and differences of multiples of 10, e.g. 50 + 80, 120 – 90Derive and recall number pairs that total 100Pairs of two-digit numbers with a total of 100, e.g. 32 + 68, or 32 + = 100Addition doubles for multiples of 10 to 100, e.g. 90 + 90Adapt methods of calculation to suit the numbers allowing efficient and flexible calculationUse doubles and near doublesUse near tens and near hundredsUse jottings when neededUse known facts to work out unknown factsMentally add and subtract single digits and multiples of 10 to three digit numbersUse number bonds to calculatePartition numbers to add and subtractChoose and use appropriate strategies for addition and subtraction, depending on the numbers involved, working flexiblyUnderstand and use the fact that addition is the inverse of subtraction and vice versa

Reas

onin

g

Explain and justify statements about strategies for calculating mentallyUse the vocabulary of doubles, near doubles, tens and near tens, partitioning to reason about numbersCompare methodsUse rounding and approximation to estimate answers and make decisionsUse trial and improvement to make decisions and justifyExplain and correct mistakes within a calculationUse the mathematical language for addition and subtraction

Prob

lem

sol

ving

Use a range of strategies e.g. reorder numbers when adding, identify pairs totalling 10 or multiples of 10, partition: add tens and ones separately, then recombine, partition: count on in tens and ones to find the total, partition: count on or back in tens and ones to find the difference, partition: add or subtract 10 or 20 and adjust, partition: double and adjust, partition: count on or back in minutes and hours, bridging through 60 (analogue times)Use the 4 operations to calculate efficiently to reach a target numberRecognise there might be more than one possible solution and find themSolve problems in different ways and discuss which is the most efficient for youSolve problems involving number, money and measuresChoose and use appropriate operations and strategiesUse different representations to solve problems e.g. Bar Model

49

Year 3

Number – Multiplication and Division

Nat

iona

l Cur

ricu

lum

ob

ject

ives

Count from zero and recall and use multiplication and division facts for the 2, 3, 4, 5 and 8 and 10 multiplication tables.Calculate mathematical statements for 2 digit numbers x 1 digit numbers for multiplication and division within the multiplication tables and write them using the multiplication (x), division (÷) and equals (=) signs.Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in context.Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot.Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables.Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objectives.Write and calculate mathematical statements for multiplication and division using the multiplication tables they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods.

50

Mis

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/men

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bjec

tive

sUse the language of multiplication and division. (Big Idea 5)Divide numbers up to 2 digits using written method including division with remainders. (Big Idea 5)Represent multiplication and division facts as arrays. (Big Idea 5)Explain how multiples and factors support multiplication and division. (Big Idea 5)Use the inverse to check calculations and find a missing number. (Big Idea 5)Be able to derive all 8 facts from a fact family. (Big Idea 5)Choose and use appropriate methods and strategies. (Big Idea 5)Multiply and divide whole numbers by 10.Use doubles and near doubles (Big Idea 3)

Multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables, and corresponding division factsDoubles of multiples of 10 to 100, e.g. Double 90, and corresponding halvesMultiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables, and corresponding division factsDoubles of multiples of 10 to 100, e.g. Double 90, and corresponding halvesPartition: when doubling, double the tens and ones separately, then recombinePartition: when halving, halve the tens and ones separately, then recombineUse knowledge that halving and doubling are inverse operationsRecognise that when multiplying by 10 or 100 the digits move one or two places to the left and zero is used as a place holder

Flue

ncy

Show that the multiplication of two numbers can be done in any order (commutative) and division of one number by another cannotMultiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables, and corresponding division factsDoubles of multiples of 10 and 5 to 100, e.g. double 90, and corresponding halvesAdapt methods of calculation to suit the numbers allowing efficient and flexible calculationUse doubles and near doublesUse near tens and near hundredsUse jottings when neededCount in multiples of 2,3,4,5,8 and 10Know or quickly derive multiplication and division facts for these tablesRepresent multiplication and division facts as arraysUse inverses to check calculations and find a missing numberMultiply a two-digit by one-digit number

Reas

onin

g

Use known facts to work out unknown factsExplain and justify statements about strategies for calculating mentallyUse the vocabulary of doubles, near doubles, tens and near tens, partitioning to reason about numbersCompare methodsExplain how multiples and factors support multiplication and divisionUse the language of multiplication and divisionUse apparatus and pictures to explain thinking

51

Prob

lem

sol

ving

solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contextStrategies: partition: when doubling, double the tens and ones separately, then recombine, partition: when halving, halve the tens and ones separately, then recombine, use knowledge that halving and doubling are inverse operations, recognise that finding a unit fraction is equivalent to dividing by the denominator and use knowledge of division facts, recognise that when multiplying by 10 or 100 the digits move one or two places to the left and zero is used as a place holderUse the 4 operations to calculate efficiently to e.g. reach a target numberRecognise there might be more than one possible solution and find themSolve problems in different ways and discuss which is the most efficient for youSolve problems involving measures and money in context using multiplication and divisionChoose and use appropriate methods and strategiesBe able to derive all 8 facts in a fact family

Year 3

Algebra

Nat

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ob

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ives

Mis

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ives

Solve problems, including missing numbers problems, using number facts, place value, and more complex addition and subtraction.Solve problems, including missing numbers problems, involving multiplication and division including integer scaling.Recognise symbols and letters can represent numbers.Recognise cyclical and linear patterns

Flue

ncy

Understand and use the equal sign as the balance of an equationUse mathematical representations to notice, continue and generate patterns

52

Reas

onin

gDescribe and explain patterns, leading to predictionsGive another, and another and another exampleUse vocabulary such as repeating pattern, replace, missing (Big Idea 6)Generalise and specifyRepresent the information in a puzzle or problem using numbers, images or diagrams; use these to find a solution and present it in context, where appropriate using £.p notation or units of measure

Prob

lem

so

lvin

g

Solve problems involving equivalenceSolve missing number and shape problemsSolve problems that result in finding a generalisation

Year 3

Proportionality

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators.Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators.Count up and down in ½, 1/3, ¼ and tenths.Recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10.Recognise and show, using diagrams, equivalent fractions with small denominators.Add and subtract fractions with the same denominator within one whole.Compare and order unit fractions, and fractions with the same denominators.Solve problems that involve all of the above.

53

Mis

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/men

tal

obje

ctiv

es

Use fractions vocabulary of numerator, denominator, part whole and whole. (Big Idea 7a)Represent fractions inn different ways.Write fractions in words and numbers. (Big Idea 7a)Discuss why the smaller the denominator the larger the fraction. (Big Idea 7a)Estimate positions between whole numbers on a number line. (Big Idea 7a)Solve equivalence problems using concrete and pictorial representations. (Big Idea 7a)Use apparatus to explain addition and subtraction of fractions. (Big Idea 7b)Solve problems using fractions in real life contexts. (Big Idea 7b)Make and test conjectures about fractions. (Big Idea 7b)Find a variety of ways to make a whole. (Big Idea 7a)

Recognise that finding a unit fraction is equivalent to dividing by the denominator and use knowledge of division facts

Flue

ncy

Count in steps of ½, 1/3, ¼, 1/10Represent fractions in different waysCompare and order fractionsEstimate positions between whole numbers on a number lineWrite fractions in words and numbersAdd and subtract fractions with the same denominator

Reas

onin

g Discuss why ‘the smaller the denominator, the larger the fraction’Use apparatus to explain why might be smaller than ¼Use fractions vocabulary of numerator, denominator, part-whole and wholeUse apparatus to explain addition and subtraction of fractionsMake and test conjectures about fractions

Prob

lem

so

lvin

g Solve equivalence problems using concrete and pictorial representationsFind a variety of ways to make a wholeSolve word problems using fractions in real life contexts

54

Year 3

Measurement

Nat

iona

l Cur

ricu

lum

ob

ject

ives

Measure, compare, add and subtract: lengths (m/cm/mm).Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.Measure the perimeter of simple 2D shapes.Continue to measure using the appropriate tools and units, progressing to using a wider range of measures, including comparing and using mixed and simple equivalents of mixed units.Tell and write the time from an analogue clock, including using Roman numerals and 12-hour and 24-hour clocks.Estimate and read time with increasing accuracy to the nearest minute.Record and compare time in terms of seconds, minutes and hours.Use vocabulary such as o’clock, a.m./p.m., morning, afternoon, noon and midnight.Know the number of seconds in a minute and the number of days in each month, year and leap year.Compare durations of events (for example to calculate the time taken by particular events or tasks).Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml).Continue to measure using the appropriate tools and units, progressing to using a wider range of measures, including comparing and using mixed units (for example, 1kg and 200g) and simple equivalents of mixed units (for example, 5m = 500cm).

55

Mis

sing

/men

tal o

bjec

tive

s Estimate, measure and record different measures. (Big Idea 8)Compare and order a variety of measures. (Big Idea 8)Convince a friend why you need to measure equipment accurately. (Big Idea 8)Use multiplication facts to read scales. (Big Idea 8)Measure the perimeter of simple 2D shapes. (Big Idea 9)Describe position, direction and movement using the four compass directions to describe movement about a grid.Add and subtract amounts of money to give change, using both pound and pence in practical context. (Big Idea 8)Accurately use a range of measuring equipment. (Big Idea 8)Tell and write the time from an analogue clock including Roman Numerals from I-XII and 12 and 24 hour clocks. (Big Idea 8)Calculate time differences. (Big Idea 8)Convert quickly between mm, cm sm m, ml nd l, g and kg. (Big Idea 8)Decide on the correct equipment needed to solve a problem. (Big Idea 8)

Partition: count on or back in minutes and hours, bridging through 60 (analogue times)

Flue

ncy Convert quickly between e.g mm, cm and m, ml and l and g and kg

Accurately use a range of measuring equipmentCompare and order a variety of measuresTell the time to the minute

Reas

oni

ng

Justify and explain thinking about measures (Big Idea 8)Use the vocabulary associated with measuresConvince a friend why you need to use measuring equipment accuratelyUse multiplication facts to read scales

Prob

lem

so

lvin

g

Solve problems (in the context of measure) including missing number problems, using number facts, place value, and more complex addition and subtraction.Solve problems in real life context (Big Idea 8) Use coins and notes to find different amounts of money Solve practical problems with giving change Decide on the correct equipment needed to solve a problem Calculate time differences

56

Year 3

Geometry: Properties of Shape

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Recognise angles as a property of shape or a description of a turn.Identify right angles, acute and obtuse angles, recognise that two right angles make a half-term, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle.Identify horizontal and vertical lines and pairs of perpendicular and parallel lines.Draw 2-D shapes and make 3-D shapes using modelling materials.Recognise 3-D shapes in different orientations and describe them.

Mis

sing

/m

enta

l ob

ject

ives

Identify (name) and describe the properties of a wide range of 2D and 3D shapes.Know and use accurately the vocabulary of shape including symmetry, edges, vertices, faces, shape names, right angles, parallel and perpendicular.Solve problems in the context of shape.Justify and explain thinking in the context of shape.Conjecture which shapes tessellate and which do not.

Flue

ncy

Link shapes and pictorial representations

Reas

onin

g

Justify and explain thinking in the context of shapesKnow and use accurately the vocabulary of shape, including symmetry, edges, vertices, faces, shape names, right angel, parallel, perpendicularConvince someone that a shape has been reflected accuratelyConjecture which shapes tessellate and which do notWhat is the same and different between 2D and 3 D shapes?

57

Prob

lem

so

lvin

g

Solve problems in the context of shapeSystemically sort shapes in a variety of ways

Year 3

Geometry: Position and Direction

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Mis

sing

/ m

enta

l ob

ject

ives

Identify right angles, acute and obtuse angles, recognise that two right angles make a half-term, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle.Identify horizontal and vertical lines and pairs of perpendicular and parallel lines.Recognise angles as a measure of a turn

Flue

ncy

Reas

oni

ng

Convince someone that a shape has been reflected accurately

Prob

lem

so

lvin

g Solve problems involving position and direction

58

Year 3

Statistics

Nat

iona

l Cu

rric

ulu

m

obje

ctiv

es Interpret and present data using bar charts, pictograms and tables using ICT where appropriate and draw conclusions.Solve one step and two-step questions (for example, ‘How many more?’ and ‘How many fewer?’) using information presented in scaled bar charts and pictograms and tables.

Mis

sing

/m

enta

l ob

ject

ives

Collect and sort information to create a range of charts and tables including Venn and Carroll diagrams.Use simple scales and justify choice of scale when presenting data.Use the vocabulary associated with statistics.Collect and present data to solve a problem.Present data according to audience and purpose.

Flue

ncy

Interpret and present data using bar charts, pictograms and tablesCollect and sort information to create a range of charts and tablesUse simple scales

Reas

onin

g Use the vocabulary associated with statisticsInterpret data and draw conclusionsJustify reasons for presenting data in a particular wayJustify choice of scale

Prob

lem

so

lvin

g Solve one-step and two-step questions [for example, ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tablesFollow a line of enquiry by deciding what information is important; make and use lists, tables and graphs to organise and interpret the information

59



The stable order

principle


The abstraction

principle







60

61

Autumn Term

Place Value (6)



Algebra (4)




Measurement (3)

Statistics (3)

Spring Term


Summer Term


Year 4Number – place value

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Count in multiples of 6, 7, 9, 25 and 1000, forwards and backwards from any number (Big Idea 1)Find 1000 more or less than a given numberCount backwards through zero to include negative numbersRecognise the place value of each digit in a four digit number (thousands, hundreds, tens and ones) (Big Idea 1)Read, write, order and compare numbers and measures beyond 1000 (Big Idea 1 and 2)Identify, represent and estimate numbers using different representationsRound any number to the nearest 10, 100 or 1000Solve number and practical problems that involve all of the above and with increasingly large positive numbersRead Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value

Mis

sing

/m

enta

l ob

ject

ives

Use place value to show how to multiply and divide by 10, 100Understand that when a number is multiplied or divided by 10 or 100, its digits move one or two places to the left or the right and zero is used as a place holder (Big Idea 2)Count on or back in hundreds, tens and ones from any whole number up to 10,000Partition: add tens and ones separately, then recombinePartition: subtract tens and then ones, e.g. subtracting 27 by subtracting 20 then 7

Flue

ncy

Use knowledge of rounding, number operations and inverses to estimate and check calculations

62

Reas

onin

gSuggest a line of enquiry and the strategy needed to follow it; collect, organise and interpret selected information to find answersReport solutions to puzzles and problems, giving explanations and reasoning orally and in writing, using diagrams and symbolsRecognise and extend number sequences formed by counting on and back in steps of any size, extending beyond zero when counting backRecognise odd and even numbers and make general statements about themExplain methods and reasoning about numbers orally and in writingMake and investigate a general statement about familiar numbers or shapes by finding examples that satisfy itExplain why multiplying by 10 and multiplying again by ten is the same as multiplying by 100 (Big Idea 7b)Explain why dividing by 10 and dividing again by ten is the same as dividing by 100

Prob

lem

so

lvin

g

Solve number and practical problems that involve all of the above and with increasingly large positive numbersRepresent a puzzle or problem using number sentences, statements or diagrams; use these to solve the problem; present and interpret the solution in the context of the problemSolve one-step and two-step problems involving numbers, money or measures, including time; choose and carry out appropriate calculations, using calculator methods where appropriateSolve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions by asking ‘What if...?’

Year 4Number – addition/subtraction

63

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriateEstimate and use inverse operations to check answers to a calculationSolve addition and subtraction two-step problems in context, deciding which operations and methods to use and why (Big Idea 4)

Mis

sing

/men

tal

obje

ctiv

es

Find sums and differences of pairs of multiples of 10, 100 or 1000Find what must be added to any three-digit number to make the next multiple of 100, e.g. 521 + • = 600Add or subtract any pair of two-digit numbers, including crossing the tens and 100 boundary, e.g. 47 + 58, 91 – 35Add or subtract a near multiple of 10, e.g. 56 + 29, 86 – 38Add near doubles of 2 digit numbers e.g. 38 + 37Add or subtract two-digit or three-digit multiples of 10, e.g. 120 – 40, 140 + 150, 370 – 180Subtract by counting up from the smaller to the larger numberPartition: add or subtract a multiple of 10 and adjust, e.g. 56 + 29 = 56 + 30 – 1, or 86 – 38 = 86 – 40 + 2Use knowledge of place value and related calculations, e.g. work out 140 + 150 = 290 using 14 + 15 = 29

Flue

ncy

Use knowledge of rounding, number operations and inverses to estimate and check calculationsAdd or subtract 1, 10, 100 or 1000 to/from whole numbers, and count on or back in tens, hundreds or thousands from any whole number up to 10000Use knowledge of sums or products of odd or even numbersUnderstand commutativity and associativity in addition and subtraction (Big Idea 4)

Reas

onin

g

Use the mathematical language associated with addition and subtraction (Big Idea 4)Recognise and extend number sequences formed by counting on and back in steps of any size, extending beyond zero when counting backRecognise odd and even numbers and make general statements about themExplain methods and reasoning about numbers orally and in writingMake and investigate a general statement about familiar numbers or shapes by finding examples that satisfy it

64

Prob

lem

so

lvin

g

Suggest a line of enquiry and the strategy needed to follow it; collect, organise and interpret selected information to find answersSolve number and practical problems that involve all of the above and with increasingly large positive numbersReport solutions to puzzles and problems, giving explanations and reasoning orally and in writing, using diagrams and symbolsSolve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions by asking ‘What if...?’ (Big Idea 4)

Year 4Number – multiplication/division

65

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Recall and use multiplication and division facts for multiplication tables up to 12 x 12 (Big Idea 5)Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers (Big Idea 5)Recognise and use factor pairs and commutatively in mental calculationsMultiply two digit and three digit numbers by a one digit number using formal written layout (Big Idea 5)Solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects (Big Idea 3)

Mis

sing

/m

enta

l ob

ject

ives

Divide numbers up to three digits by a one digit number using a written method, including division with remainders (Big Idea 5)Find sums and differences of pairs of multiples of 10, 100 or 1000Partition: double and adjustMultiply a multiple of 10 to 100 by a single digit number, e.g. 40 x 3Multiply and divide numbers to 1000 by 10 and 100

Flue

ncy

Use the distributive law, e.g. 8 x 12 = (8 x 10) + (8 x 2) and associative law of multiplication, e.g. (2 x 3) x 4 = 2 x (3 x 4) (Big Idea 5)Use inverse operations to check answers to a calculationUse rounding and approximation to estimate answers and make decisionsUse place value, known and derived facts to multiply and divide mentally, e.g. use 7 x 8 = 56 to find 70 x 8 or 700 x 8Derive rapidly doubles of numbers 1 to 100, e.g. 38 + 38, and the corresponding halvesIdentify the doubles of two-digit numbers; use these to calculate doubles of multiples of 10 and 100 and derive the corresponding halvesUse related facts and doubling or halvingUse the relationship between multiplication and addition, or multiplication and divisionUse known number facts and place value to multiply or divide mentallyRecognise multiplesUse tests of divisibilityUnderstand the idea of a remainder, and when to round up or down after division

Reas

onin

g

Use the mathematical language for division and multiplicationSuggest a line of enquiry and the strategy needed to follow it; collect, organise and interpret selected information to find answersSolve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions by asking ‘What if...?’Use apparatus and pictures to explain reasoning (Big Idea 5)Prove why one multiplication calculations gives the same answer as another one (Big Idea 5)Explain how knowing one fact can help derive a related one (Big Idea 5)

66

Prob

lem

sol

ving

Suggest a line of enquiry and the strategy needed to follow it; collect, organise and interpret selected information to find answersSolve one-step and two-step multiplication and division problems involving numbers, money or measures, including timeRepresent a puzzle or problem using number sentences, statements or diagrams; use these to solve the problem; present and interpret the solution in the context of the problem (Big Idea 5)Report solutions to puzzles and problems, giving explanations and reasoning orally and in writing, using diagrams and symbolsChoose and use appropriate number operations and appropriate ways of calculating (mental, mental with jottings, written methods, calculator) to solve problems (Big Idea 4)Solve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions by asking ‘What if...?’

Year 4Algebra

67

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Mis

sing

/m

enta

l ob

ject

ives

Understand that perimeter can be expressed algebraically as 2(a+b) where a and b are the dimensions in the same unit (Big Idea 6)Partition, round and order four-digit whole numbers; use positive and negative numbers in context and position them on a number line; state inequalities using the symbols < and > (e.g. –3 > –5, –1 < +1)Recognise symbols/ letters can represent numbers

Flue

ncy

Express a rule to describe a sequence (Big Idea 6)Understand and use the equals sign as the balance of an equationUse mathematical representations to notice, continue and generate patterns (Big Idea 6)

Reas

onin

g

68

Prob

lem

so

lvin

g

Represent a puzzle or problem using number sentences, statements or diagrams; use these to solve the problem; present and interpret the solution in the context of the problemSolve multi-step problems involving equivalence and more than one missing number, such as 6 + ? = ? – 2 (Big Idea 6)Recognise and describe patterns in sequences of numbers (Big Idea 1)Solve missing term problems (Big Idea 6)Understand that perimeter can be expressed algebraically as 2(a+b) where a+b are the dimensions in the same unit (Big Idea 6)


69

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Recognise and show, using diagrams, families of common equivalent fractions (¼, ½, ¾). (Big Idea 7a)Count up and down in tenths and hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by tenSolve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole numberAdd and subtract fractions with the same denominator (Big Idea 7b)Recognise, write decimal equivalents of any number of tenths or hundredthsRecognise and write decimal equivalents to ¼, ½, ¾Find the effect of dividing a one or two digit number by 10 or 100, identifying the value of the digits in the answer as ones, tenths and hundredths (Big Idea 2, 7b)Round decimals with one decimal place to the nearest whole number (Big Idea 7a)Compare numbers with the same number of decimal places up to two decimal places (Big Idea 2)Solve simple measure and money problems involving fractions and decimals to two decimal places

Mis

sing

/m

enta

l ob

ject

ives

Compare similar shapes where the scale factor is 2 or a halfFind unit fractions and simple non-unit fractions of numbers, quantities or shapes, e.g. 1/5 of 30 plums, 3/8 of a 6 x 4 rectangle

Flue

ncy

Compare numbers with the same number of decimal places up to two decimal placesOrder a set of decimal fractions and position on a number lineUse decimal notation for tenths and hundredths and partition decimals; relate the notation to money and measurement; position one-place and two-place decimals on a number lineRecognise the equivalence between decimal and fraction forms of one half, quarters, tenths and hundredthsInterpret mixed numbers and position them on a number line (e.g. 31/2)Identify pairs of fractions that total 1Estimate a proportion (e.g. ‘About one quarter of the apples in the box are green’)

Reas

onin

g

Use the vocabulary of ratio and proportion to describe the relationship between two quantities (e.g. ‘There are 2 red beads to every 3 blue beads)Use fraction and decimal vocabulary (Big Idea 7)Apply knowledge of factors and multiples to recognise and simplify equivalent fractions (Big Idea 7a)Explain the relationship between non-unit fractions and multiplication and division of quantities (Big Idea 7b)Convert between mixed numbers and improper fractions (Big idea 7b)Convert between fractions and decimal (Big idea 7b)Solve simple problems involving ratio and proportionExplain what fractions needs to be added to any proper fraction to make a complete whole (Big Idea 7b)

70

Prob

lem

so

lvin

g

Solve problems involving finding fractions of quantities including unit fractions, e.g. 1/3 of 12 or non-unit fractions e.g. 2/3 or 12 where the answer is a whole number (Big Idea 7a)Work systematically to find families of equivalent fractions (Big Idea 7a)

Year 4Measurement

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Convert between different units of measure (Big Idea 8)Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres (Big Idea 9)Find the area of rectilinear shapes by counting squaresEstimate, compare and calculate different measures, including money in pounds and penceRead, write & convert time between analogue and digital 12 and 24 hour clocksSolve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days

71

Mis

sing

/m

enta

l ob

ject

ives

Compare and order a set of measures where conversion is neededUse multiplication and division to convert between different units of measure including: length- centimetres, millimetres, metres; money- pounds, pence; distance - kilometres, hours, minutes, seconds, year, months, weeks and days (Big Idea 8)Partition: count on or back in minutes and hours, bridging through 60 (analogue and digital times)

Flue

ncy

Use multiplication and division to convert between different units of measure including pounds to pence (Big Idea 8)Use knowledge of units to estimate mass, length and capacity in real life contexts (Big Idea 8)Read scales interpreting intervals and divisions on partially numbered scales and record readings accurately, where appropriate to the nearest tenth of a unit (Big Idea 8)Calculate time intervals from clocks and timetablesMeasure and calculate the perimeter and area of simple shapesRelate areas to arrays and multiplication and division (Big Idea 5)

Reas

onin

g

Use the vocabulary associated with measuresUse the vocabulary related to time; suggest suitable units of time to estimate or measureExplain how to find the area of a rectangle with reference to arrays (Big Idea 5)Choose appropriate equipment and units to make measurements of length, mass and capacity (Big Idea 8)Use knowledge of units to estimate mass, length and capacity in real life contexts (Big Idea 8)

Prob

lem

so

lvin

g

Work logically to order a set of measures where conversion is needed (Big Idea 8)Solve problems involving converting between different units of measure

72


Nat

iona

l Cu

rric

ulum

ob

ject

ives

Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizesIdentify acute and obtuse angles and compare and order angles up to two right angles by size (Big Idea 9)Identify lines of symmetry in 2-D shapes presented in different orientationsComplete a simple symmetric figure with respect to a specific line of symmetry

Mis

sing

/m

enta

l ob

ject

ives

Use appropriate vocabulary, including isosceles, equilateral and scalene; parallelogram, rhombus, trapezium (Big Idea 9)Identify and describe 2D shapes and their properties including angles, regular/irregular, lines of symmetry presented in different orientations (Big Idea 9)

73

Flue

ncy

Reas

onin

g

Visualise 3-D objects from 2-D drawings; make nets of common solidsMake and investigate a general statement about familiar numbers or shapes by finding examples that satisfy it

Prob

lem

so

lvin

g

Use knowledge of shape properties to solve problems (Big Idea 9)

74


Nat

iona

l Cu

rric

ulum

ob

ject

ives

Describe positions on a 2D grid as coordinates in the first quadrant (Big Idea 9)Describe movements between positions as translations of a given unit to the left/ right and up/ downPlot specified points and draw sides to complete a given polygon

Mis

sing

/m

enta

l ob

ject

ives

Compare and order angles less than 180°Recognise reflective symmetry in 2-D shapes, reflections and translations

Flue

ncy

Recognise positions and directions, and use co-ordinatesMake turns; estimate, draw and measure angles; recognise rotations

75

Reas

onin

gUse the eight compass points to describe directionDescribe and identify the position of a square on a grid of squares

Prob

lem

so

lvin

g

Solve problems involving translations

76

Year 4Statistics

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs (Big Idea 10)

Mis

sing

/m

enta

l ob

ject

ives

Read points on one axis that correspond to given measures on the other axis (Big Idea 10)Represent data as graphs and chartsComplete tables by reading graphs and charts (Big Idea 10)Use and select appropriate scales (Big Idea 10)Use Venn diagrams and Carroll diagrams to sort data and objects (Big Idea 10)

Flue

ncy

Reas

onin

g

Compare the impact of representations where scales have intervals of differing step sizeUse the language associated with probability to discuss events, including those with equally likely outcomes (Big Idea 10)

77

Prob

lem

so

lvin

g

Solve a problem by collecting, organising, representing, extracting and interpreting data in tables, graphs and chartsAnswer a question by identifying what data to collect; interpret and present discrete and continuous data using appropriate graphical methods, including tables, tally charts, pictograms, bar charts and time graphs using ICT where appropriate (Big Idea 10)organise, present, analyse and interpret the data (discrete and continuous) in tables, diagrams, tally charts, pictograms and bar charts, using ICT where appropriate


78


The stable order

principle


The abstraction

principle







79

80

Autumn Term

Place Value (6)



Algebra (4)




Measurement (3)

Statistics (3)

Spring Term


Summer Term


Year 5Number – place value

Nat

iona

l Cu

rric

ulum

ob

ject

ives

Throughout Place value Big Idea 2 ReasoningRead, write, order and compare numbers to at least 1 000 000 and determine the value of each digit. (Big Idea 1 Fluency)Count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000. (Big Idea 1 Fluency)Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero. (Big Idea 1 Problem Solving)Round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000. (Big Idea 1 Fluency, Reasoning)Solve number problems and practical problems that involve all of the above.Read Roman numerals to 1000 (M) and recognise years written in Roman numerals. (Big Idea 1 Fluency)

Mis

sing

/men

tal

obje

ctiv

es

Use knowledge of place value and related calculations, e.g. 6.3 – 4.8 using 63 – 48Use knowledge of multiplication and division facts and understanding of place value, e.g. when calculating with multiples of 10Use understanding that when a number is multiplied or divided by 10 or 100, its digits move one or two places to the left or the right relative to the decimal point, and zero is used as a place holderTo recognised and describe linear sequences including those involving fractions and decimals and find the term to term rule and express it in words.Pupils extend and apply their understanding of the number system to the decimal numbers and fractions they have met so far.Use the vocabulary on estimation and approximation. Make and justify estimate of larger numbers, and estimate simple proportions such as 1/3, 7/10

Flue

ncy

Order and compare numbersRepresent numbers in different waysIdentify the positional place value in large whole numbers and numbers up to 3 dec. placesUnderstand that in the number 63472 we can find the multiplicative place value of each digit by multiplying each digit by the column it is in e.g. 6 x 1000Recognise the additive place values of each digit so that when the individual values of each digit are added together, they total the whole number.Use rounding to estimate the results of calculationsKnow when to use a mental strategy or jottings to work out answers to calculations.Use known facts to work out unknown facts

81

Reas

onin

gComplete sequencesFind errors in sequences and explain answersExplain why digits belong in different positions in a numberShow reasoning when roundingConvince a friend of the value of each digit in integer and decimal numbersExplain why 2.85 x 100 – 285 and not 2.8500Use positional place value to reason about numbers between numbers, including decimalsUse understanding of place value to spot mistakesExplain how you know when to use a mental strategy or jottings to work out answers to calculations.Give reasons for choices of methodsExplain why one calculation strategy is more efficient than another.Make and investigate a general statement about familiar numbers by finding examples that satisfy it. Explain a generalised relationship (formula) in words

Prob

lem

so

lvin

g

Interpret negative numbers in contextSolve number problems and practical problems through a systematic and logical processChoose operations and efficient calculation strategies to solve word problemsFind multiple solutions to a problem and know when all solutions have been found or where there are an infinite number of solutions.Have a range of strategies to solve any problemRepresent problems using apparatus to organise thinking

Year 5Number- addition and subtraction

82

Nat

iona

l Cur

ricu

lum

ob

ject

ives

Add and subtract numbers mentally with increasingly large numbers. (Big Idea 3 Fluency )Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy. (Big Idea 3 Fluency )Solve addition and subtraction multi-step problems in contexts deciding which operations and methods to use and why. (Big Idea 1 Problem Solving; Big Idea 14 Fluency)

Mis

sing

/men

tal o

bjec

tive

s

Recall quickly multiplication and division facts for multiplication tables up to 12 x 12 and use these multiplication facts to multiply pairs of multiples up to 10 and 100.Addition: to reorder numbers in a calculationPartition: add hundreds, tens or ones separately, then recombineSubtract by counting up from the smaller to the larger numberAdd or subtract a multiple of 10 or 100 and adjustPartition: double and adjustSums and differences of decimals, e.g. 6.5 + 2.7, 7.8 – 1.3Doubles and halves of decimals, e.g. half of 5.6, double 3.4What must be added to any four-digit number to make the next multiple of 1000, e.g. 4087 + = 5000What must be added to a decimal with units and tenths to make the next whole number, e.g. 7.2 + = 8Add or subtract a pair or 2 digit numbers or 3 digit multiples of 10 e.g. 38 + 86, 620 – 380, 350+ 360Add or subtract a near multiple of 10 or 100 to any two-digit or three-digit number, e.g. 235 + 198Find the difference between near multiples of 100, e.g. 607 – 588, or of 1000, e.g. 6070 – 4087Add or subtract any pairs of decimal fractions each with units and tenths, e.g. 5.7 + 2.5, 6.3 – 4.8

Flue

ncy

Understand and use commutativity and associativity in addition and subtractionFind differences by counting up through next multiple of 10, 100 or 1000 e.g. calculate mentally issues such as 8,006-2,993.Identify near doubles, such as 1.5+1.6=Add several numbers, e.g. 4 or 5 single digit numbers or multiples of 10, such as 40,50 and 80.

83

Reas

onin

gExplain and correct mistakes that have been made in calculationsMake conjectures about the relationships between different calculationsGive reasons for choices of methods and strategiesUse the vocabulary of addition and subtraction

Prob

lem

so

lvin

g

Work systematically and logicallyUse information given to find missing information without promptingSolve two (or more) step problems that involve addition & subtraction.Use different representations to understand and solve problems (e.g. bar model)Follow a set of instructions to calculate a mystery number

Year 5

84

Number – multiplication and divisionN

atio

nal C

urri

culu

m

obje

ctiv

esThroughout Multiplication and Division Big Idea 2 FluencyIdentify multiples and factors, including finding all factor pairs of a number, and common factors of two numbersKnow and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbersEstablish whether a number up to 100 is prime and recall prime numbers up to 19Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbersMultiply and divide numbers mentally drawing upon known factsDivide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the contextMultiply and divide whole numbers and those involving decimals by 10, 100 and 1000

Mis

sing

/men

tal o

bjec

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Apply all of the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculationsPupils interpret non-integer answers to division by expressing results in different ways according to the context, including with remainders, as fractions, as decimals or by rounding (e.g. 98 ÷ 4 = 24 r 2 = 24 ½ = 24.5 = 25)Pupils use multiplication and division as inverses to support the introduction of ratio in Year 6, for example, by multiplying and dividing by powers of 10 in scale drawings or by multiplying or dividing by powers of 1000 in converting between units such as km and mDistributivity can be expressed as a(b + c) = ab + acThey understand the terms factor, multiple and prime, square and cube numbers and use them to construct equivalent statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 92 x 10)Pupils use and explain the = sign to indicate, equivalence, including missing number problems (for example, 13 + 24 = 12 + 25; 33 = 5 x □)Know and apply tests of divisibility by 2,4,5,10 or 100.Begin to use bracketsUse the principles of the arithmetic laws as they apply to multiplication.To reorder numbers in a multiplicationDivision facts corresponding to tables up to 10 × 10, and the related unit fractions, e.g. 7 × 9 = 63 so one-ninth of 63 is 7 and one-seventh of 63 is 9Factor pairs to 100Use knowledge of multiplication and division facts to find factor pairsFind factor pairs for numbers to 100, e.g. 30 has the factor pairs 1 × 30, 2 × 15, 3 × 10 and 5 × 6multiply or divide by 4 or 8 by repeated doubling or halvingMultiply and divide mentally using known facts

85

Flue

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Identify factors & multiples of at least 12 x 12; recognising common factors and common multiplesUse formal method to multiply and divide up to 4 digitsRecognise prime and composite numbersSolve equations with missing numbersUnderstand what letters represent in algebraic expressionsDoubling and halving starting from known facts.Use closely related facts either by multiplying by 19 or 21, multiply by 20 and adjusting.Distributive Law e.g 47x6=(40x6)+(7x6)

Reas

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Decide which operations and methods to use and whyExplain and convince others how you know a number is a prime numberJustify why adding 2 odd numbers makes an even numberConjecture answers using known factsApply to fractions, decimals and percentagesUse logic to decide how to manage remainders when dividingExplain general rules for sequences e.g. the term-to-term ruleVerbalise general rules in mathematicsGive further examples to match one or more criteriaGeneralise and express a rule to find any termUse mathematical vocabulary when generalising

Prob

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Work systematically and logicallyUse information given to find missing informationSolve problems which involve multiplication and divisionSolve problems that involve divisionExpress missing measures algebraicallySolve missing term problems in sequencesSolve multi-step problems involving equations, including with more than one missing numberWhen solving problems use apparatus to combine terms

Year 5Algebra

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To use simple formulaeTo generate and describe linear number sequencesTo express missing number problems algebraicallyTo find pairs of numbers that satisfy an equation with two unknownsTo enumerate possibilities of combinations of two variables.(Big Idea 6 Fluency, Reasoning, Problem Solving.)

Flue

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Solve equations with missing numbersUnderstand what letters represent in algebraic expressionsMake and investigate a general statement about familiar numbers by finding examples that satisfy it. Explain a generalised relationship (formula) in words

Reas

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Year 5Number: Proportionality

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Throughout Fractions Big Idea 7a,b Reasoning and Problem SolvingCompare and order fractions whose denominators are all multiples of the same numberIdentify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths Big Idea 7a, b FluencyRecognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2/5 + 4/5 = 6/5 = 1 1/5Add and subtract fractions with the same denominator and denominators that are multiples of the same number (Extend understanding to calculations that exceed 1 as a mixed number)Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams (related to scaling and problems involving simple rates)(Throughout decimals Big Idea 4 Fluency)(Throughout decimals Big Idea 7a,b Reasoning and Problem Solving)Read and write decimal numbers as fractions [for example, 0.71 = 71/100Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalentsRound decimals with two decimal places to the nearest whole number and to one decimal placeRead, write, order and compare numbers with up to three decimal placesSolve problems involving number up to three decimal places and are confident in checking the reasonableness of their answers to problems(Throughout Percentages Big Idea 7a,b Reasoning and Problem Solving)Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimalSolve problems which require knowing percentage and decimal equivalents of ½, ¼, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25.

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s Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing proportionsThey extend knowledge of fractions to thousandths and connect to decimals and measuresPupils connect equivalent fractions > 1 that simplify to integers with division and fractions > 1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractionsPupils continue to practise counting forwards and backwards in simple fractions and decimals, including bridging zero, for example on a number lineMentally add and subtract tenths, and one-digit whole numbers and tenthsAdd and subtract decimals including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 (for example 0.83 + 0.17 = 1)Pupils should go beyond the measurement and money models of decimals, for example by solving puzzles and scaling problems involving decimalsPupils should make connections between percentages, fractions and decimals (for example, 100% represents a whole quantity and 1% is 1/100, 50% is 50/100, 25% is 25/100) and relate this to finding fractions of.Multiply fractions by whole numbers

88

Flue

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Identify fractions, decimals and percentages of shapes, objects and quantities and move between themCompare and order fractions, decimals and percentages using <, >, =, ≠Add & subtract different representations of fractions (including different denominators), decimals and percentages by converting themFind missing fractions to complete calculations

Reas

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Explain why fractions, decimals and percentages can be comparedReason about which fraction of something you would preferExplain how you can add fractions, decimals and percentagesConvince others that an answer is correct by explainingExplain your solutions and convince others of your methods.

Prob

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Work systematically and logicallyUse information given to find missing informationSolve problems that involve comparing & ordering fraction, decimals and percentagesWork systematically and logicallyUse information given to find missing informationSolve problems that involve comparing & ordering fraction, decimals and percentages.Conjecture different patterns that can be seen and why when solving problemsSolve problems that involve multiplying fractions by whole numbers

Year 5Measurement

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Convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre) (Big Idea 3 Problem Solving)Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints (Big Idea 3 Problem Solving)Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metresCalculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes (Big Idea 3 Problem Solving; Big Idea 8 Problem Solving)Estimate volume [for example, using 1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water] (Big Idea 8 Problem Solving)Solve problems involving converting between units of time (for example, days to weeks, expressing the answer as weeks and days) (Big Idea 3 Problem Solving; Big Idea 8 Problem Solving)Use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling. (Big Idea 3 Problem Solving; Big Idea 8 Problem Solving.)

Mis

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Use the relations of perimeter or area to find unknown lengths. Missing measures questions such as these can be expressed algebraically, for example 4 + 2b = 20 for a rectangle of sides 2cm and b/cm and perimeter of 20cmCalculate the area from scale drawings using given measurementsUse units of time; read the time on a 24-hour digital clock and use digital 24-hour clock notation such as 19:53Partition: count on or back in minutes and hours, bridging through 60 (analogue and digital times)Tell the time using the 12-hour and 24 hour clock, both digital and analogueRead a variety of scales accurately

Flue

ncy Use apparatus to illustrate volume

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Year 5Geometry – Properties of Shape

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Identify 3-D shapes, including cubes and other cuboids, from 2-D representationsKnow angles are measured in degrees: estimate and compare acute, obtuse and reflex anglesDraw given angles, and measure them in degrees (o) (Big Idea 9 Fluency)

Identify: angles at a point and one whole turn (total 360o), angles at a point on a straight line and ½ a turn (total 180o), other multiples of 90oUse the properties of rectangles to deduce related facts and find missing lengths and angles (Big Idea 9 Fluency, Reasoning)Distinguish between regular and irregular polygons based on reasoning about equal sides and angles

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s Pupils become accurate in drawing lines with a ruler to the nearest mm, and measuring with a protractor. They use conventional markings for parallel lines and right anglesPupils use the term diagonal and make conjectures about the angles formed by diagonals and sides and other properties of quadrilaterals, for example using dynamic geometry ICT toolsPupils use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problemsClassify triangles (brackets isosceles, equilateral, scalene) using criteria such as equal sides, equal angles, lines of symmetry.Recognise reflective symmetry in regular polygons.Complete symmetrical patterns with two lines of symmetry at right angles (using squared paper or pegboard)Make shapes with increasing accuracy. Visualise 3-D shapes from 2D drawings and identify different nets from an open cube.Measure and draw angles, lines and shapes accurately using appropriate equipmentReflect shapes across horizontal, vertical & diagonal linesTranslate a shape from one place to another

Flue

ncy Find missing angles in triangles, quadrilaterals, at a point and on a line

Reas

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Explain how to calculate missing anglesJustify properties of shapes by using known facts and convince others of your findingsExplain where a shape will end up and why it ends up thereUnderstand vocabulary such as perpendicular, parallel, etc.

Prob

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g Work systematically and logicallyUse information given to find missing informationSolve problems that involve angles, shapes and/or directionSolve problems that involve reflecting & translating shapes

Year 5Geometry Position & Direction

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Identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed.

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Pupils recognise and use reflection and translation in a variety of diagrams including continuing to use a 2D grid and coordinates in the first quadrant. Reflection should be in lines that are parallel to the axesTo use coordinates in the 1st quadrant.

Flue

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Year 5Statistics

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Solve comparison, sum and difference problems using information presented in a line graphComplete, read and interpret information in tables, including timetables. (Big Idea 10 Fluency, Reasoning and Problem Solving.)

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Pupils connect their work on coordinates and scales to their interpretation of line graphsThey begin to decide which representations of data are most appropriate and whyCollect and organise information in tables and/or graphs as appropriate

Flue

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Reas

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g Prove that your findings are accurateJustify any conjectures you make using the information from the graph or table.Reason why a graph might give the results it does.Answer literal questions involving line graphs & tables, including timetables

Prob

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Interpret a variety of graphs and table to solve problemsUse logic to make up stories to fit graphs in a variety of forms


93


The stable order

principle


The abstraction

principle







94

95

Autumn Term

Place Value (6)



Algebra (6)




Measurement (3)

Statistics (3)

Spring Term

Place Value (6)Addition & Subtraction (10)Multiplication & Division (15)Proportionality (10)Algebra (9)

Summer Term

Place Value (6)Addition & Subtraction (11)Multiplication & Division (6)Algebra (4)Proprotionality (10)Geometry - Shape (4)Geometry - Position (3)Measurement (4)Statistics (2)General Revision (5)

Year 6Number - Place value

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Identify, read, write, order and compare numbers up to 10 000 000 and determine the value of each digit. (Big Idea 1)Round any whole number to a required degree of accuracy including to the nearest 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000 and including decimal numbers. (Big Idea 1)Use negative numbers in a range of contexts, and calculate intervals across zero. (Big Idea 1)Solve number and practical problems that involve all of the above. (Big Idea 1)

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Use knowledge of place value and related calculations, e.g. 680 + 430, 6.8 + 4.3, 0.68 + 0.43 can all be worked out using the related calculation 68 + 43.Use knowledge of place value and of doubles of two-digit whole numbers.Count forwards and backwards in different powers on 10. (Big Idea 2)Use place value to calculate intervals.Represent numbers in different ways.Partitioning numbers. (Big Idea 2)Know Roman numerals.Sort numbers logically and systematically. (Big Idea 1)Say and write numbers accurately. (Big Idea 1)Counting in whole number and decimal steps up to 10,000,000.Solve problems including negative numbers. (Big Idea 2)Discuss finding all numbers between 2 other numbers. (Big Idea 2)Round any whole number to the appropriate unit [cm, km, kg etc].Recognise squared [²] and cubed [³] numbers.Count forwards and backwards in different powers on 10.Count forwards and backwards in any single digit number.

96

Flue

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Understand that multiplying by 1000 is equivalent to multiplying by 10, then by 10, then by 10, or is equivalent to multiplying by 10 and then by 100.Respond quickly to written or oral questions when multiplying or dividing by 10, 100 or 1000 including missing numbers [for example 0.8 x 10 = … ].Use the correct vocabulary associated with properties of number.Partition any number – including decimals.Understand that in the number 7 328 621 we can find the multiplicative place value of each digit by multiplying each digit by the column it is in [for example 8 x 1000 = 8000].

Reas

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Comment on the effect of multiplying or dividing by 10, 100 or 1000 and how it would alter the place value of the digit.Be able to estimate and explain how you worked out the estimate, including the position of a point on a number line.Make general statements about odd or even numbers and/or give examples that match them.Determine the value of each digit and explain its value find and explain errors in sequences.Discuss finding all numbers between two other numbers.Convince someone why 0.1 is bigger than 0.09.Show in words and numbers the difference between a variety of digits within numbers.Use rounding to spot mistakes.Use understanding of place value to spot and correct mistakes.

Prob

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Sort numbers logically and systematically.Represent problems using apparatus to organise thinking.Use place value to calculate intervals.

Year 6

97

Number - Addition and SubtractionN

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esSolve addition and subtraction multi step problems in contexts, deciding which operations and methods to use and why. (Big Idea 2)Perform mental calculations, including with mixed operations and large numbers. (Big Idea 5)Identify common factors, common multiples and prime numbers.Use their knowledge of the order of operations to carry out calculations involving the four operations. (Big Idea 3)Solve problems involving addition, subtraction, multiplication and division. (Big Idea 3)Use estimation to check answers to calculations and determine in the context of a problem, an appropriate degree of accuracy. (Big Idea 3)

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Addition and subtraction facts for multiples of 10 to 1000 and decimal numbers with one decimal place, e.g. 650 + = 930, – 1.4 = 2.5What must be added to a decimal with units, tenths and hundredths to make the next whole number, e.g. 7.26 + • = 8Add or subtract pairs of decimals with units, tenths or hundredths, e.g. 0.7 + 3.38Find doubles of decimals each with units and tenths, e.g. 1.6 + 1.6Add near doubles of decimals, e.g. 2.5 + 2.6Add or subtract a decimal with units and tenths, that is nearly a whole number, e.g. 4.3 + 2.9, 6.5 – 3.8Count on or back in hundreds, tens, ones, tenths and hundredthsPartition: double and adjustPartition: add or subtract a whole number and adjust, e.g. 4.3 + 2.9 = 4.3 + 3 – 0.1, 6.5 – 3.8 = 6.5 – 4 + 0.2Partition: count on or back in minutes and hours, bridging through 60 (analogue and digital times, 12-hour and 24-hour clock)Know number bonds to 1 and powers of 10.Add and subtract whole numbers with more than 4 digits using a written method.(Big Idea 4)Use negative numbers in context and calculate intervals across zero.Find what to add to a decimal with units, 10ths and 100ths to make the next higher whole number or 10 th.Add and subtract decimals, percentages and fractions with different denominators.Recall and derive number bonds to 1 and bonds to different powers of 10.Find doubles of up to 4 digit numbers and decimals to 2 d.p.Count and work backwards and forwards.

Flue

ncy

Use the correct vocabulary associated with addition and subtraction.Understand and use all arithmetic laws (commutative, associative and distributive) for example using knowledge of inverse operations.

98

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gDecide which operations and methods to use and why.Use knowledge of the order of operations to carry out calculations involving the four operations.Use estimation and rounding to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

Prob

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Working systematically and logically to solve a problem.Find possibilities within a problem.Solve problems involving the calculation and conversion of units of measure.Use knowledge of place value and addition and subtraction facts to solve addition and subtraction problems.Recognising when to use the most efficient strategy.

Year 6Number – Multiplication and Division

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Multiply multi-digit number up to 4 digits by a 2 digit number using the formal written method of long multiplication. (Big Idea 5)Divide numbers up to 4 digits by a 2 digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions or by rounding as appropriate for the context. (Big Idea 5)Divide numbers up to 4 digits by a 2 digit number using the formal written method of short division, interpreting remainders according to context and interpreting as a fraction or a whole number. (Big Idea 5)Solve problems involving addition, subtraction, multiplication and division. (Big Idea 3)Use estimation to check answers to calculations and determine in the context of a problem, an appropriate degree of accuracy. (Big Idea 3)

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Squares to 12 × 12.Squares of the corresponding multiples of 10.Prime numbers less than 100.Multiply pairs of two-digit and single-digit numbers, e.g. 28 × 3.Divide a two-digit number by a single-digit number, e.g. 68 ÷ 4.Divide by 25 or 50, e.g. 480 ÷ 25, 3200 ÷ 50.Multiply pairs of multiples of 10 and 100, e.g. 50 × 30, 600 × 20.Divide multiples of 100 by a multiple of 10 or 100 (whole number answers), e.g. 600 ÷ 20, 800 ÷ 400, 2100 ÷ 300.Identify numbers with odd and even numbers of factors and no factor pairs other than 1 and themselves.Partition: use partitioning and the distributive law to divide tens and ones separately, e.g. 92 ÷ 4 = (80 + 12) ÷ 4 = 20 + 3 = 23.Form an equivalent calculation, e.g. to divide by 25, divide by 100, then multiply by 4; to divide by 50, divide by 100, then double.Use knowledge of the equivalence between fractions and percentages and the relationship between fractions and division.Recognise how to scale up or down using multiplication and division, e.g. if three oranges cost 24p: one orange costs 24 ÷ 3 = 8p four oranges cost 8 × 4 = 32p.Show how multiplying or dividing by 10/100/1000 alters the place value of digits. (Big Idea 5)Identify factors and multiples to at least 12x12. (Big Idea 5)Use brackets: know that they determine the order of operations, and that their contents are worked out first.Use written division methods in cases where the answer has up to two decimal places.Identify factors and multiples to at least 12 x 12.Recognise LCM and HCF.Multiply 1 digit decimals by whole numbers.Multiply 1 digit numbers with up to two decimal places by whole numbers.Divide fractions by whole numbers.Perform mental calculations including with mixed operations and large numbers.Calculate the mean average.Identify composite numbers.

100

Flue

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Understand and use all arithmetic laws (commutative, associative and distributive) for example using knowledge of inverse operations know how to double and half.Understanding the importance of the = sign.

Reas

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Decide which operations and methods to use and why.Interpret remainders as whole number remainders, fractions, or by rounding.Understand the distributive, associative and commutative law of multiplication.Use apparatus and pictures to explain thinking.Use the language of multiply and divide.

Prob

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Work systematically and logically.Solve problems that include remainders.Interpret and construct pie charts and line graphs and use these to solve problems.Solve problems involving the calculation percentages {for example of measures, and such as 15% of 360) and the use of percentages for comparison.Solve problems involving the calculation and conversion of units of measure.

101

Year 6Number – Algebra

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Use simple formulae. (Big Idea 6)Generate and describe linear number sequences. (Big Idea 6)Express missing number problems algebraically. (Big Idea 6)Find pairs of numbers that satisfy an equation with two unknowns. (Big Idea 6)Enumerate possibilities of combinations of two variables.

Mis

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Describe, extend and explain number sequences and patterns with whole numbers and decimals (Big Idea 6)Explain how number can be expressed as the nth term. (Big Idea 6)Describe, extend and explain number sequences and patterns.Generate the ‘nth’ term.

Flue

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Rearrange and simplify expressions.Show curiosity about numbers by offering comments or asking questions.

Reas

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Explain how a number can be described as nth term.Justify how sometimes a range of numbers may solve an equation and sometimes it may only have one solution.Explain the equals sign and reason that it doesn’t simply mean “This is the answer”.Recognise when it is possible to use formulae for area and volume of shapes.Use mathematical vocabulary when generalising.

102

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Use algebra to write a number sentence to a problem.Be adept at adding numbers to an equation within a number problem.Represent a real life situation in algebraic terms.Solve number and shape puzzles.Manipulate an equation to find a solution.


Nat

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Use common factors to simplify fractions; use common multiples to express fractions in the same denomination. (Big Idea 7b)Compare and order fractions, including fractions > 1Generate and describe linear number sequences (with fractions) (Big Idea 7b)Add and subtract fractions with different denominations and mixed numbers, using the concept of equivalent fractions. (Big Idea 7b)Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example 1 4 x 1 2 = 1 8 ] (Big Idea 7b)Divide proper fractions by whole numbers [for example 1/3 ÷ 2 = 1/6] (Big Idea 7b)Associate a fraction with division and calculate decimal fraction equivalents [ for example, 0.375] for a simple fraction [for example 3 8 ] (Big Idea 7a)Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts. (Big Idea 7b)Identify the value of each digit in numbers given to three decimal places and multiply numbers by 10, 100 and 1000 giving answers up to 3 decimal places (dp). (Big Idea 5)Multiply one digit numbers with up to 2dp by whole numbers. (Big Idea 5)Use written division methods in cases where the answer has up to two decimal places. (Big Idea 5)Solve problems which require answers to be rounded to specified degrees of accuracy, including decimals. (Big Idea 3)Solve problems involving the calculation of percentages [for example, of measures such as 15% of 360] and the use of percentages for comparison. (Big Idea 7a)Recall and use equivalences between simple FDP including in different contexts and comparison. (Big Idea 7a)Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.(Big Idea 7c)Solve problems involving similar shapes where the scale factor is known or can be found. (Big Idea 7c)Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples. (Big Idea 7c)

103

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sEquivalent fractions, decimals and percentages for hundredths, e.g. 35% is equivalent to 0.35 or 35/100.Double decimals with units and tenths, e.g. double 7.6, and find the corresponding halves, e.g. half of 15.2.Multiply and divide two-digit decimals such as 0.8 × 7, 4.8 ÷ 6.Find 10% or multiples of 10%, of whole numbers and quantities, e.g. 30% of 50 ml, 40% of £30, 70% of 200 g.Simplify fractions by cancelling.Scale up and down using known facts, e.g. given that three oranges cost 24p, find the cost of four oranges.Use knowledge of multiplication and division facts to identify factor pairs and numbers with only two factors.Show difference between ratio and proportion. (Big Idea 7c)Fraction of shapes. (Big Idea 7a)Convert between mixed and improper fractions.Find missing fractions to complete calculations.Counting up and down in tenths and hundredths. (Big Idea 5)Doubles of 4 digit numbers and with 2 decimal places.Reduce a fraction to its simplest form by cancelling common factors.Know common equivalents for fractions, decimals and percentages.Identify fractions of shapes, objects and quantities and move between them.Find fractions of numbers.Find percentages of numbers.Convert between mixed and improper fractions and know when it is appropriate to do so.Convert between percentages, decimals and fractions.Add & subtract fractions (with different denominators), decimals and percentages.Multiply fractions by whole numbers.Multiply fractions by fractions.Divide fractions by whole numbers.Divide fractions by fractions.Calculate ratio and proportion.

Flue

ncy Compare and order fractions, decimals and percentages using < > = ≠.

Find missing fractions to complete calculations.Recognise ratio as comparing part with part and proportion as comparing part with whole.Use apparatus to show the difference between ratio and proportion.

Reas

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Explain why fractions, decimals and percentages can be compared and how.Reason about which size of something you would prefer.Use fraction vocabulary.Explain how to compare a range of fractions, decimals and percentages.Explain how you can add fractions, decimals and percentages.Move freely between representations explaining your reasoning.Distinguish between situations with an additive change or a multiplicative change (which involves ratio).Recognise the link between ratio and proportion.

104

Prob

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Work systematically and logically.Use information given to find missing information.Solve problems that involve comparing and ordering fraction, decimals and percentages.Use information given to find missing information.Solve problems that involve comparing & ordering fraction, decimals and percentages.Solve problems that involve addition & subtraction of fractions, percentages and decimals.Solve problems that involve multiplying fractions by whole numbers.Solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts.Solve problems involving similar shapes where the scale factor is known or can be found.Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

Year 6Measurement

105

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Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate. (Big Idea 8)Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to 3dp. (Big Idea 8)Convert between miles and kilometres. (Big Idea 8)Recognise that shapes with the same areas can have different perimeters and vice versa. (Big Idea 8)Recognise when it is possible to use formulae for area and volume of shapes. (Big Idea 8)Calculate the area of parallelograms and triangles.Calculate, estimate and compare volume of cubes and cuboids using standard units, including cm3, m3 and extending to other units (mm3, km3). (Big Idea 9)Time at the beginning or end of the term for consolidation gap filling, seasonal activities, assessments etc. (Big Idea 8)

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Tell the time accurately on a 12 hour, 24 hour, digital and analogue clock. (Big Idea 8)Solve problems involving measure using decimal notation, including scale. (Big Idea 8)Use, read and interpret timetables.Use a 180° protractor accurately to measure and draw angles within 1° +/-.Convert between different units of metric measure.Calculate area and perimeter of regular irregular and composite shapes.

Flue

ncy

Understand and use approximate equivalences between metric units and common imperial units.Choose units and suitable equipment to make measurements.Read a variety of scales accurately.

Reas

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Estimate volume - for example, using 1 cm3 blocks to build cuboids (including cubes) and capacity (for example, using water) and justify estimations.Use standard units to explain how you found the volume of different cuboids.Explain how an array helps support understanding of area and perimeter.Suggest how you could measure…Suggest an imperial or metric unit to measure.

Prob

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Solve problems with rectilinear shapes where there are missing measures.Find different perimeters for shapes with the same area.Compare the area of a variety of shapes.Solve problems involving converting between units of time.Solve problems involving measure using decimal notation, including scaling.Solve ‘story’ problems involving units of time, and explain and record how the problem was solved.

106

Year 6Geometry - Properties of Shape

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Draw 2D shapes using given dimensions and angles. (Big Idea 8)Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals and regular polygons. (Big Idea 8)Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles. (Big Idea 9)

107

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Scale factor with shapes. (Big Idea 9)Use a protractor to measure and draw angles. (Big Idea 9)Identify and draw a range of nets. (Big Idea 9)Use properties such as perpendicular and parallel faces or edges.Continue to name and describe shapes.Classify quadrilaterals using criteria such as parallel sides, equal angles, equal sides.Identify, estimate, order, measure and calculate acute, obtuse, reflex and right angles.Recognise squared [²] and cubed [³] numbers.

Flue

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Move fluently between concrete and pictorial representations.

Reas

onin

g Use the correct vocabulary associated with properties of 2D and 3D shapes.Make and test conjectures and provide mathematical proof where necessary.

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Identify and draw a range of nets.Solve problems involving similar shapes where the scale factor is known or can be found.Use knowledge of the area of triangles to solve problems about the area of parallelograms.

Year 6Geometry - Position and Direction

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Describe positions on the full coordinate grid (all four quadrants). (Big Idea 9)Draw and translate simple shapes on the coordinate plane, and reflect them in the axes. (Big Idea 9)

108

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Plot positions on the full coordinate grid (all four quadrants).Sketch the position of a simple shape after a rotation of 90° or 180° about a vertex.

Flue

ncy

Use known facts to help interpret position and direction of different shapes.

Reas

onin

g Make and test conjectures and provide mathematical proof where necessary.

Prob

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lvin

g

Use knowledge of position and direction within problems on a computer program.

Year 6Statistics

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Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius. (Big Idea 9)Interpret and construct pie charts and line graphs and use these to solve problems. (Big Idea 10)Calculate the mean as an average. (Big Idea 5)

109

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Calculate and interpret the median, mode and range.Construct and interpret Venn and Carroll diagrams.Begin to draw and interpret a line graph, in which intermediate values have meaning.

Flue

ncy

Represent number in a variety of ways (concrete, pictorial & abstract).Interpret statistics in a variety of ways.

Reas

onin

g Explain what a segment in a pie chart.Make and test conjectures and provide mathematical proof where necessary.Use the correct vocabulary associated with statistics.Test a hypothesis by drawing and discussing a graphical representation where (discrete) data are grouped.

Prob

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Make a simple computer database and test hypotheses by interrogating the data in a prepared computer database, such as census data or data on road safety.

110