National Curriculum Maths

You can use some of these guidelines to help inform your planning. Take from any year-group that will be best suited to your child and your topic.

I use these key points to start a mind map for ideas, then go onto thinking about activities that we can do to address these targets.

Year 1

Number – number and place value
Pupils should be taught to:

 count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number

 count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens

 given a number, identify one more and one less

 identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least

 read and write numbers from 1 to 20 in numerals and words.

 explore the part that flowers play in the life cycle of flowering plants, including pollination, seed formation and seed dispersal.

Number – addition and subtraction

Pupils should be taught to:

 read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs

 represent and use number bonds and related subtraction facts within 20

 add and subtract one-digit and two-digit numbers to 20, including zero

 solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as  7 =    – 9.

Number – multiplication and division 
Pupils should be taught to:

 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.

Number – fractions
Pupils should be taught to:

 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 object, shape or quantity.

Measurement 
Pupils should be taught to:

 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 example, quicker, slower, earlier, later]

 measure and begin to record the following:

 lengths and heights  mass/weight  capacity and volume

 time (hours, minutes, seconds)  recognise and know the value of different denominations of coins and notes

 sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening]

 recognise and use language relating 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.

Geometry – properties of shapes 
Pupils should be taught to:

 recognise and name common 2-D and 3-D shapes, including:

 2-D shapes [for example, rectangles (including squares), circles and triangles]

 3-D shapes [for example, cuboids (including cubes), pyramids and spheres].

Geometry – position and direction 
Pupils should be taught to:

 describe position, direction and movement, including whole, half, quarter and three quarter turns.

Year 2

Number – number and place value
Pupils should be taught to:

 count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward

 recognise the place value of each digit in a two-digit number (tens, ones)

 identify, represent and estimate numbers using different representations, including the number line

 compare and order numbers from 0 up to 100; use <, > and = signs

 read and write numbers to at least 100 in numerals and in words

 use place value and number facts to solve problems.

Number – addition and subtraction 
Pupils should be taught to:

 solve problems with addition and subtraction:

 using concrete objects and pictorial representations, including those involving numbers, quantities and measures

 applying their increasing knowledge of mental and written methods

 recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

 add and subtract numbers using concrete objects, pictorial representations, and mentally, including:  a two-digit number and ones  a two-digit number and tens  two two-digit numbers  adding three one-digit numbers

 show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot

 recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.

Number – multiplication and division 
Pupils should be taught to:

 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 (×), division (÷) and equals (=) signs

 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

Number – fractions 
Pupils should be taught to:

 recognise, find, name and write fractions 3 1, 4 1, 4 2 and 4 3 of a length, shape, set of objects or quantity

 write simple fractions for example, 2 1 of 6 = 3 and recognise the equivalence of 4 2 and 2 1.

Measurement 
Pupils should be taught to:

 choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); 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 amounts of money

 solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change

 compare and sequence intervals of time

 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.

Geometry – properties of shapes 
Pupils should be taught to:

 identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line

 identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces

 identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]

 compare and sort common 2-D and 3-D shapes and everyday objects.

Geometry – position and direction
Pupils should be taught to:

 order and arrange combinations of mathematical objects in patterns and sequences

 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 anticlockwise)

Statistics 
Pupils should be taught to:

 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 totalling and comparing categorical data

Year 3

Number – number and place value 
Pupils should be taught to:

 count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number

 recognise the place value of each digit in a three-digit number (hundreds, tens, ones)

 compare and order numbers up to 1000

 identify, represent and estimate numbers using different representations

 read and write numbers up to 1000 in numerals and in words

 solve number problems and practical problems involving these ideas.

Number – addition and subtraction 
Pupils should be taught to:

 add and subtract numbers mentally, including:

 a three-digit number and ones

 a three-digit number and tens

 a three-digit number and hundreds

 add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction

 estimate the answer to a calculation and use inverse operations to check answers

 solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

Number – multiplication and division
Pupils should be taught to:

 recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables

 write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods

 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 objects.

Number – fractions 
Pupils should be taught to:

 count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10

 recognise, find and write fractions of a discrete set of objects: unit fractions and non unit fractions with small denominators

 recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators

 recognise and show, using diagrams, equivalent fractions with small denominators

 add and subtract fractions with the same denominator within one whole [for example, 
7 5 + 7 1 = 7 6]

 compare and order unit fractions, and fractions with the same denominators

 solve problems that involve all of the above.

Measurement 
Pupils should be taught to:

 measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)  measure the perimeter of simple 2-D shapes

 add and subtract amounts of money to give change, using both £ and p in practical contexts

 tell and write the time from an analogue clock, including using Roman numerals from I to XII, 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].

Geometry – properties of shapes 
Pupils should be taught to:

 draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them

 recognise angles as a property of shape or a description of a turn

 identify right angles, recognise that two right angles make a half-turn, 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.

Statistics 
Pupils should be taught to:

 interpret and present data using bar charts, pictograms and tables

 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.

Year 4

Number – number and place value 
Pupils should be taught to

 count in multiples of 6, 7, 9, 25 and 1000  find 1000 more or less than a given number

 count backwards through zero to include negative numbers

 recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)

 order and compare numbers beyond 1000

 identify, represent and estimate numbers using different representations

 round any number to the nearest 10, 100 or 1000

 solve number and practical problems that involve all of the above and with increasingly large positive numbers

 read 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.

Number – addition and subtraction 
Pupils should be taught to:

 add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate

 estimate and use inverse operations to check answers to a calculation

 solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

Number – multiplication and division 
Pupils should be taught to:

 recall multiplication and division facts for multiplication tables up to 12 × 12

 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

 recognise and use factor pairs and commutativity in mental calculations

 multiply two-digit and three-digit numbers by a one-digit number using formal written layout

 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.

Number – fractions (including decimals) 
Pupils should be taught to:

 recognise and show, using diagrams, families of common equivalent fractions

 count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.

 solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number

 add and subtract fractions with the same denominator

 recognise and write decimal equivalents of any number of tenths or hundredths

 recognise and write decimal equivalents to 4 1, 2 1, 4 3

 find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths

 round decimals with one decimal place to the nearest whole number

 compare numbers with the same number of decimal places up to two decimal places

 solve simple measure and money problems involving fractions and decimals to two decimal places

Measurement 
Pupils should be taught to:

 Convert between different units of measure [for example, kilometre to metre; hour to minute]

 measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres

 find the area of rectilinear shapes by counting squares

 estimate, compare and calculate different measures, including money in pounds and pence

 read, write and convert time between analogue and digital 12- and 24-hour clocks

 solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days.

Geometry – properties of shapes 
Pupils should be taught to:

 compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes

 identify acute and obtuse angles and compare and order angles up to two right angles by size

 identify lines of symmetry in 2-D shapes presented in different orientations

 complete a simple symmetric figure with respect to a specific line of symmetry.

Geometry – position and direction 
Pupils should be taught to:

 describe positions on a 2-D grid as coordinates in the first quadrant

 describe movements between positions as translations of a given unit to the left/right and up/down

 plot specified points and draw sides to complete a given polygon.

Statistics 
Pupils should be taught to:

 interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs.

 solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

Year 5


Number – number and place value 
Pupils should be taught to:

 read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit

 count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000

 interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero

 round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000

 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.


Number – addition and subtraction 
Pupils should be taught to:

 add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)

 add and subtract numbers mentally with increasingly large numbers

 use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy

 solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.


Number – multiplication and division 
Pupils should be taught to:

 identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers

 know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers

 establish whether a number up to 100 is prime and recall prime numbers up to 19

 multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers

 multiply and divide numbers mentally drawing upon known facts

 divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context

 multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 
 recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)

 solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes

 solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

 solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.


Number – fractions (including decimals and percentages) 
Pupils should be taught to:

 compare and order fractions whose denominators are all multiples of the same number

 identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths

 recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 5 2 + 5 4 = 5 6 = 15 1]

 add and subtract fractions with the same denominator and denominators that are multiples of the same number

 multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

 read and write decimal numbers as fractions [for example, 0.71 = 100 71 ]

 recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

 round decimals with two decimal places to the nearest whole number and to one decimal place

 read, write, order and compare numbers with up to three decimal places

 solve problems involving number up to three decimal places

 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 decimal

 solve problems which require knowing percentage and decimal equivalents of 2 1, 4 1, 
5 1, 5 2, 5 4 and those fractions with a denominator of a multiple of 10 or 25.


Measurement 
Pupils should be taught to:

 convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)

 understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints

 measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres

 calculate 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  estimate volume [for example, using 1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water]

 solve problems involving converting between units of time

 use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling.


Geometry – properties of shapes 
Pupils should be taught to:

 identify 3-D shapes, including cubes and other cuboids, from 2-D representations

 know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles

 draw given angles, and measure them in degrees (o)

 identify:  angles at a point and one whole turn (total 360o)  angles at a point on a straight line and 2 1 a turn (total 180o)  other multiples of 90o

 use the properties of rectangles to deduce related facts and find missing lengths and angles

 distinguish between regular and irregular polygons based on reasoning about equal sides and angles.


Geometry – position and direction
Pupils should be taught to:

 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.


Statistics 
Pupils should be taught to:

 solve comparison, sum and difference problems using information presented in a line graph

 complete, read and interpret information in tables, including timetables.



Year 6

Number – number and place value
Pupils should be taught to:

 read, write, order and compare numbers up to 10 000 000 and determine the value of each digit  round any whole number to a required degree of accuracy

 use negative numbers in context, and calculate intervals across zero

 solve number and practical problems that involve all of the above.

Number – addition, subtraction, multiplication and division 
Pupils should be taught to:

 multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication

 divide numbers up to 4 digits by a two-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

 divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context

 perform mental calculations, including with mixed operations and large numbers

 identify common factors, common multiples and prime numbers

 use their knowledge of the order of operations to carry out calculations involving the four operations

 solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why 
 solve problems involving addition, subtraction, multiplication and division

 use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

Number – fractions (including decimals and percentages) 
Pupils should be taught to:

 use common factors to simplify fractions; use common multiples to express fractions in the same denomination

 compare and order fractions, including fractions > 1

 add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

 multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 4 1 × 2 1 = 8 1]

 divide proper fractions by whole numbers [for example, 3 1 ÷ 2 = 6 1]

 associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 8 3]

 identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places 
 multiply one-digit numbers with up to two decimal places by whole numbers

 use written division methods in cases where the answer has up to two decimal places

 solve problems which require answers to be rounded to specified degrees of accuracy

 recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

Ratio and proportion 
Pupils should be taught to:

 solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

 solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison

 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.

Algebra 
Pupils should be taught to:

 use simple formulae

 generate and describe linear number sequences

 express missing number problems algebraically

 find pairs of numbers that satisfy an equation with two unknowns

 enumerate possibilities of combinations of two variables

Measurement 
Pupils should be taught to:

 solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate

 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 three decimal places

 convert between miles and kilometres

 recognise that shapes with the same areas can have different perimeters and vice versa

 recognise when it is possible to use formulae for area and volume of shapes

 calculate the area of parallelograms and triangles

 calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic metres (m3), and extending to other units [for example, mm3 and km3].

Geometry – properties of shapes 
Pupils should be taught to:

 draw 2-D shapes using given dimensions and angles

 recognise, describe and build simple 3-D shapes, including making nets

 compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

 illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

 recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.

Geometry – position and direction 
Pupils should be taught to:

 describe positions on the full coordinate grid (all four quadrants)

 draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

Statistics 
Pupils should be taught to:

 interpret and construct pie charts and line graphs and use these to solve problems

 calculate and interpret the mean as an average.