## Below are the target expectations, by year, for Mathematics in British schools following the National Curriculum.

YEAR ONE TARGETS |

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. |

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. |

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. |

Rrecognise, 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. |

Compare, describe and solve practical problems for lengths and heights [for example, long/short, longer/shorter, tall/short, double/half] |

Compare, describe and solve practical problems for mass/weight [for example, heavy/light, heavier than, lighter than] |

Compare, describe and solve practical problems for capacity and volume [for example, full/empty, more than, less than, half, half full, quarter] |

Compare, describe and solve practical problems for time [for example, quicker, slower, earlier, later] |

Measure and begin to record lengths and heights |

Measure and begin to record mass/weight |

Measure and begin to record capacity and volume |

Measure and begin to record 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. |

Recognise and name common 2-D and 3-D shapes, including:2-D shapes [for example, rectangles (including squares), circles and triangles] |

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

Describe position, direction and movement, including whole, half, quarter and three- quarter |

YEAR 2 TARGETS | |

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

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

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

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

5 | read and write numbers to at least 100 in numerals and in words |

6 | use place value and number facts to solve problems. |

7 | solve problems with addition and subtraction using concrete objects and pictorial representations, including those involving numbers, quantities and measures |

8 | solve problems with addition and subtraction applying their increasing knowledge of mental and written methods |

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

10 | add and subtract numbers using concrete objects, pictorial representations, and mentally, including a two-digit number and ones |

11 | add and subtract numbers using concrete objects, pictorial representations, and mentally, including a two-digit number and tens |

12 | add and subtract numbers using concrete objects, pictorial representations, and mentally, including two two-digit numbers |

13 | add and subtract numbers using concrete objects, pictorial representations, and mentally, including adding three one-digit numbers |

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

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

16 | recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers |

17 | calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs |

18 | show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot |

19 | solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts |

20 | recognise, find, name and write fractions ⅓, ¼, 2/4, ¾ of a length |

21 | recognise, find, name and write fractions ⅓, ¼, 2/4, ¾ of a shape |

22 | recognise, find, name and write fractions ⅓, ¼, 2/4, ¾ of aset of objects |

23 | recognise, find, name and write fractions ⅓, ¼, 2/4, ¾ of a quantity |

24 | choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm) to the nearest appropriate unit, using rulers |

25 | choose and use appropriate standard units to estimate and measure mass (kg/g) to the nearest appropriate unit, using scales |

26 | choose and use appropriate standard units to estimate and measure temperature (°C) to the nearest appropriate unit, using thermometers |

27 | choose and use appropriate standard units to estimate and measure capacity (Litres/ml) to the nearest appropriate unit, using measuring vessels |

28 | compare and order lengths and record the results using >, < and = |

29 | compare and order mass and record the results using >, < and = |

30 | compare and order volume/capacity and record the results using >, < and = |

31 | recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value |

32 | find different combinations of coins that equal the same amounts of money |

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

34 | compare and sequence intervals of time |

35 | 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 |

36 | know the number of minutes in an hour and the number of hours in a day |

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

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

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

40 | compare and sort common 2-D and 3-D shapes and everyday objects |

41 | order and arrange combinations of mathematical objects in patterns and sequences |

42 | 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). |

43 | interpret and construct simple pictograms, tally charts, block diagrams and simple tables |

44 | ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity |

45 | Ask and answer questions about totalling and comparing categorical data |

YEAR 3 TARGETS | |

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

2 | I can recognise the place value of each digit in a three-digit number (hundreds, tens, ones) |

3 | I can compare and order numbers up to 1000 |

4 | I can identify, represent and estimate numbers using different representations |

5 | I can read and write numbers up to 1000 in numerals and in words |

6 | I can solve number problems and practical problems involving these ideas. |

7 | I can add and subtract numbers mentally, including a three-digit number and ones |

8 | I can add and subtract numbers mentally, including a three-digit number and tens |

9 | I can add and subtract numbers mentally, including a three-digit number and hundreds |

10 | I can add and subtract numbers mentally, including adding and subtracting numbers with up to three digits, using formal written methods of columnar addition and subtraction |

11 | I can add and subtract numbers mentally, including estimate the answer to a calculation and use inverse operations to check answers |

12 | I can add and subtract numbers mentally, including solving problems include missing number problems, using number facts, place value, and more complex addition and subtraction. |

13 | I can recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables |

14 | I can 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 |

15 | I can 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. |

16 | I can 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 |

17 | I can recognise, find and write fractions of a discrete set of objects: unit fractions and non- unit fractions with small denominators |

18 | I can recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators |

19 | I can recognise and show, using diagrams, equivalent fractions with small denominators |

20 | I can add and subtract fractions with the same denominator within one whole – for example 5/7 + 1/7 = 6/7 |

21 | I can compare and order unit fractions, and fractions with the same denominators |

22 | I can solve problems that involve all of the above |

23 | I can measure, compare, add and subtract lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml) |

24 | I can measure the perimeter of simple 2-D shapes |

25 | I can add and subtract amounts of money to give change, using both £ and p in practical contexts |

26 | I can tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks |

27 | I can 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 |

28 | I can know the number of seconds in a minute and the number of days in each month, year and leap year |

29 | I can compare durations of events [for example to calculate the time taken by particular events or tasks]. |

30 | I can draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them |

31 | I can recognise angles as a property of shape or a description of a turn |

32 | I can 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 |

33 | I can identify horizontal and vertical lines and pairs of perpendicular and parallel lines. |

34 | I can interpret and present data using bar charts, pictograms and tables |

35 | I can 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 TARGETS | |

1 | I can count in multiples of 6, 7, 9, 25 and 1000 |

2 | I can find 1000 more or less than a given number |

3 | I can count backwards through zero to include negative numbers |

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

5 | I can order and compare numbers beyond 1000 |

6 | I can identify, represent and estimate numbers using different representations |

7 | I can round any number to the nearest 10, 100 or 1000 |

8 | I can solve number and practical problems that involve all of the above and with increasingly large positive numbers |

9 | I can 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 |

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

11 | I can estimate and use inverse operations to check answers to a calculation |

12 | I can solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why. |

13 | I can recall multiplication and division facts for multiplication tables up to 12 × 12 |

14 | I can 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 |

15 | I can recognise and use factor pairs and commutativity in mental calculations |

16 | I can multiply two-digit and three-digit numbers by a one-digit number using formal written layout |

17 | I can 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 |

18 | I can recognise and show, using diagrams, families of common equivalent fractions |

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

20 | I can 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 |

21 | I can add and subtract fractions with the same denominator |

22 | I can recognise and write decimal equivalents of any number of tenths or hundredths |

23 | I can recognise and write decimal equivalents to ¼, ½, ¾ |

24 | I can 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 |

25 | I can round decimals with one decimal place to the nearest whole number |

26 | I can compare numbers with the same number of decimal places up to two decimal places |

27 | I can solve simple measure and money problems involving fractions and decimals to two decimal places. |

28 | I can Convert between different units of measure [for example, kilometre to metre; hour to minute] |

29 | I can measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres |

30 | I can find the area of rectilinear shapes by counting squares |

31 | I can estimate, compare and calculate different measures, including money in pounds and pence |

32 | I can read, write and convert time between analogue and digital 12- and 24-hour clocks |

33 | I can solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days. |

34 | I can compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes |

35 | I can identify acute and obtuse angles and compare and order angles up to two right angles by size |

36 | I can identify lines of symmetry in 2-D shapes presented in different orientations |

37 | I can complete a simple symmetric figure with respect to a specific line of symmetry |

38 | I can describe positions on a 2-D grid as coordinates in the first quadrant |

39 | I can describe movements between positions as translations of a given unit to the left/right and up/down |

40 | I can plot specified points and draw sides to complete a given polygon. |

YEAR 5 TARGETS | |

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

2 | I can count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000 |

3 | I can interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero |

4 | I can round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000 |

5 | I can solve number problems and practical problems that involve all of the above |

6 | I can read Roman numerals to 1000 (M) and recognise years written in Roman numerals. |

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

8 | I can add and subtract numbers mentally with increasingly large numbers |

9 | I can use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy |

10 | I can solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why. |

11 | I can identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers |

12 | I can know and use the vocabulary of prime numbers, prime factors and composite (non- prime) numbers |

13 | I can establish whether a number up to 100 is prime and recall prime numbers up to 19 |

14 | I can 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 |

15 | I can multiply and divide numbers mentally drawing upon known facts |

16 | I can 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 |

17 | I can multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 |

18 | I can compare and order fractions whose denominators are all multiples of the same number |

19 | I can 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, 2/5 + 4/5 = 6/5 = 1 1/5] |

20 | I can add and subtract fractions with the same denominator and denominators that are multiples of the same number |

21 | I can multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams |

22 | I can read and write decimal numbers as fractions [for example. 0.71 = 71/100] |

23 | I can recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents |

24 | I can round decimals with two decimal places to the nearest whole number and to one decimal place |

25 | I can read, write, order and compare numbers with up to three decimal places |

26 | I can solve problems involving number up to three decimal places |

27 | I can 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 |

28 | I can solve 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 |

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

30 | I can understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints |

31 | I can measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres |

32 | I can calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (CM2) and square centimetres (M2) and estimate the area of irregular shapes |

33 | I can estimate volume [for example, usuing 1 cm3 blocks to build cuboids (including cubes)] for capacity [for example, using water] |

34 | I can solve problems involving converting between units of time |

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

36 | I can identify 3-D shapes, including cubes and other cuboids, from 2-D representations |

37 | I can know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles |

38 | I can draw given angles, and measure them in degrees (0) |

39 | I can identify angles at a point and one whole turn (total 360 degrees) |

40 | I can identify angles at a point on a straight line and ½ a turn (total 180 degrees) |

41 | I can identify other multiples of 90 degrees |

42 | I can use the properties of rectangles to deduce related facts and find missing lengths and angles |

43 | I can distinguish between regular and irregular polygons based on reasoning about equal sides and angles. |

44 | I can 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. |

45 | I can solve comparison, sum and difference problems using information presented in a line graph |

46 | I can complete, read and interpret information in tables, including timetables. |

YEAR 6 TARGETS | |

1 | I can read, write, order and compare numbers up to 10 000 000 and determine the value of each digit |

2 | I can round any whole number to a required degree of accuracy |

3 | I can use negative numbers in context, and calculate intervals across zero |

4 | I can solve number and practical problems that involve all of the above. |

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

6 | I can 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 |

7 | I can 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 |

8 | I can perform mental calculations, including with mixed operations and large numbers |

9 | I can identify common factors, common multiples and prime numbers |

10 | I can use their knowledge of the order of operations to carry out calculations involving the four operations |

11 | I can solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why |

12 | I can solve problems involving addition, subtraction, multiplication and division |

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

14 | I can use common factors to simplify fractions; use common multiples to express fractions in the same denomination |

15 | I can compare and order fractions, including fractions > 1 |

16 | I can add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions |

17 | I can multiply simple pairs of proper fractions, writing the answer in its simplest form [ for example, ¼ x ½ = 1/8) |

18 | I can divide proper fractions by whole numbers [for example, 1/3 / 2 = 1/6 |

19 | I can associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8 |

20 | I can 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 |

21 | I can multiply one-digit numbers with up to two decimal places by whole numbers |

22 | I can use written division methods in cases where the answer has up to two decimal places |

23 | I can solve problems which require answers to be rounded to specified degrees of accuracy |

24 | I can recall and use equivalences between simple fractions, decimals and percentages, including in different contexts. |

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

26 | I can 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 |

27 | I can convert between miles and kilometres |

28 | I can recognise that shapes with the same areas can have different perimeters and vice versa |

29 | I can recognise when it is possible to use formulae for area and volume of shapes |

30 | I can calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic meters (m3) and extending to other units (for example, mm3 and km2) |

31 | I can draw 2-D shapes using given dimensions and angles |

32 | I can recognise, describe and build simple 3-D shapes, including making nets |

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

34 | I can illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius |

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

36 | I can describe positions on the full coordinate grid (all four quadrants) |

37 | I can draw and translate simple shapes on the coordinate plane, and reflect them in the axes. |

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

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

40 | I can solve problems involving similar shapes where the scale factor is known or can be found |

41 | I can solve problems involving unequal sharing and grouping using knowledge of fractions and multiples. |

42 | I can use simple formula |

43 | I can generate and describe linear number sequences |

44 | I can express missing number problems algebraically |

45 | I can find pairs of numbers that satisfy an equation with two unknowns |

46 | I can enumerate possibilities of combinations of two variables. |