# Mathematics - Skills Progression

__Number and Place Value__

Y1 |
Pupils will learn 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. |

Y2 |
Pupils will learn 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. |

Y3 |
Pupils will learn 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, present 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. |

Y4 |
Pupils will learn 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. |

Y5 |
Pupils will learn 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. |

Y6 |
Pupils will learn 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. |

__Addition and Subtraction__

Y1 |
Pupils will learn 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. |

Y2 |
Pupils will learn 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. |

Y3 |
Pupils will learn 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. |

Y4 |
Pupils will learn 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. |

Y5 |
Pupils will learn 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. |

Y6 |
Pupils will learn 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. |

*Multiplication and Division*

Y1 |
Pupils will learn 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. |

Y2 |
Pupils will learn 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. |

Y3 |
Pupils will learn 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. |

Y4 |
Pupils will learn 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. |

Y5 |
Pupils will learn 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 (nonprime) 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. |

Y6 |
Pupils will learn 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 Mathematics 136 Statutory requirements; 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. |

__Algebra__

Y1 |
N / A |

Y2 |
N / A |

Y3 |
N / A |

Y4 |
N / A |

Y5 |
N / A |

Y6 |
Pupils will learn 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. |

__Ratio and Proportion__

Y1 |
N / A |

Y2 |
N / A |

Y3 |
N / A |

Y4 |
N / A |

Y5 |
N / A |

Y6 |
Pupils will learn 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. |

__Fractions (including Decimals and Percentages)__

Y1 |
Pupils will learn 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. |

Y2 |
Pupils will learn to: recognise, find, name and write fractions ¹/3 , ¼, ²/4 and ¾ of a length, shape, set of objects or quantity; write simple fractions for example, ½ of 6 = 3 and recognise the equivalence of ²/4 and ½. |

Y3 |
Pupils will learn 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, 5/7 + 1/7 = 6/7 ]; compare and order unit fractions, and fractions with the same denominators; solve problems that involve all of the above. |

Y4 |
Pupils will learn 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 ¼, ½, 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. |

Y5 |
Pupils will learn 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, 2/5 + 4/5 = 6/5 = 1 1/5 ]; 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 = 71/100 ]; 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 ½, ¼, 1/5 , 2/5 , 4/5 and those fractions with a denominator of a multiple of 10 or 25. |

Y6 |
Pupils will learn 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, ¼ × ½ = 1/8 ]; divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6 ]; associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8 ]; 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. |

__Measurement__

Y1 |
Pupils will learn 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. |

Y2 |
Pupils will learn 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. |

Y3 |
Pupils will learn 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]. |

Y4 |
Pupils will learn 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. |

Y5 |
Pupils will learn 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. |

Y6 |
Pupils will learn 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 [e.g. mm³ and km³]. |

__Geometry (properties of shapes)__

Y1 |
Pupils will learn 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]. |

Y2 |
Pupils will learn 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. |

Y3 |
Pupils will learn 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. |

Y4 |
Pupils will learn 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. |

Y5 |
Pupils will learn 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 ( ° ); identify: angles at a point and one whole turn (total 360°); angles at a point on a straight line and ½ a turn (total 180°); other multiples of 90°; 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. |

Y6 |
Pupils will learn 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)__

Y1 |
Pupils will learn to: describe position, direction and movement, including whole, half, quarter and three-quarter turns. |

Y2 |
Pupils will learn 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). |

Y3 |
N / A |

Y4 |
Pupils will learn 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. |

Y5 |
Pupils will learn 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. |

Y6 |
Pupils will learn 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__

Y1 |
N / A |

Y2 |
Pupils will learn 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. |

Y3 |
Pupils will learn 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 |

Y4 |
Pupils will learn 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. |

Y5 |
Pupils will learn to: solve comparison, sum and difference problems using information presented in a line graph; complete, read and interpret information in tables, including timetables. |

Y6 |
Pupils will learn to: interpret and construct pie charts and line graphs and use these to solve problems; calculate and interpret the mean as an average. |