 ## MATHEMATICS CURRICULUM

The aim of the Mathematics curriculum is to create confident mathematicians who can problem solve, apply creativity, pursue their own investigations and have an enjoyment of playing with numbers, shape and mathematical concepts.

Reception

The Reception Mathematics curriculum is based on the EYFS Development Matters.

In Reception, children learn to:

• Count reliably with numbers from 1 to 20, place them in order and say which number is one more or one less than a given number.

• Use quantities and objects to add and subtract 2 single-digit numbers and count on or back to find the answer.

• Use everyday language to talk about size, weight, capacity, position, distance, time, and money to compare quantities and objects and to solve problems.

• Recognise, create, and describe patterns.

• Explore characteristics of everyday objects and shapes and use mathematical language to describe them.

Year 1

In Year 1, children 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 2's, 5's and 10's.

• Identify 1 more and 1 less of a given number.

• 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 0.

• 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.

• Recognise, find and name a half as 1 of 2 equal parts of an object, shape or quantity.

• Recognise, find and name a quarter as 1 of 4 equal parts of an object, shape or quantity.

• Compare, describe and solve practical problems for:

• 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.

• Time - e.g. 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 - e.g. 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, being able to 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 - e.g. rectangles (including squares), circles and triangles.

• 3-D shapes - e.g. cuboids (including cubes), pyramids and spheres.

• Describe position, direction and movement, including whole, half, quarter and three-quarter turns.

Year 2

In Year 2, children learn to:

• Count in steps of 2, 3, and 5 from 0, and in 10s from any number, forward and backward.

• Recognise the place value of each digit in a two-digit number (10's and 1's).

• 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.

• 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 1's

• A two-digit number and 10's

• 2 two-digit numbers

• Show that addition of 2 numbers can be done in any order (commutative) and subtraction of 1 number from another cannot.

• Recognise and use the inverse relationship between addition and subtraction, using this to check calculations and solve missing number problems.

• 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 2 numbers can be done in any order (commutative) and division of 1 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.

• Recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity.

• Write simple fractions, for example  1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2.

• 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.

• 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 - e.g. a circle on a cylinder and a triangle on a pyramid

• Compare and sort common 2-D and 3-D shapes and everyday objects.

• 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 anti-clockwise).

• Interpret and construct simple pictograms, tally charts, block diagrams and tables.

• Ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity.

Year 3

In Year 3, children 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 3-digit number (100's, 10's, 1's).

• Compare and order numbers up to 1,000.

• Identify and estimate numbers using different representations.

• Read and write numbers up to 1,000 in numerals and in words.

• Solve number problems and practical problems involving these ideas.

• Add and subtract numbers mentally, including:

• A three-digit number and 1's

• A three-digit number and 10's

• A three-digit number and 100's

• Add and subtract numbers with up to 3 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.

• 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.

• 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 - e.g. 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.

• 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.

• 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, am/pm, 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 - e.g. to calculate the time taken by particular events or tasks.

• 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.

• Interpret and present data using bar charts, pictograms and tables.

• Solve one-step and two-step questions - e.g. ‘How many more?’ and ‘How many fewer?’, using information presented in scaled bar charts and pictograms and tables.

Year 4

In Year 4, children learn to:

• Count in multiples of 6, 7, 9, 25 and 1000 and, find 1000 more or less than a given number and recognise the place value of each digit in a four-digit number.

• Count backwards through zero to include negative numbers.

• Read, write, order and compare numbers beyond 1000.

• Round any number to the nearest 10, 100 or 1000.

• Solve number and practical problems.

• 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.

• 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.

• Recall multiplication and division facts for multiplication tables up to 12 × 12.

• Use place value, known and derived facts to multiply and divide mentally.

• Multiply two-digit and three-digit numbers by a one-digit number.

• 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.

• Recognise and write decimal equivalents of any number of tenths or hundredths.

• Recognise and write decimal equivalents.

• 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.

• Convert between different units of measure

• Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres and find the area of rectilinear shapes.

• 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.

• 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.

• 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.

• 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

In Year 5, children 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.

• Understand and use negative numbers.

• Round any number up to 1,000,000 and use this to check calculations.

• Solve number problems and practical problems.

• Read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

• 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.

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

• 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 and cubed.

• Compare and order fractions whose denominators are all multiples of the same number and identify, name and write equivalent fractions.

• Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number.

• Read and write decimal numbers as fractions.

• 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.

• 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.

• Convert between different units of measure.

• Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres.

• Calculate and compare the area of rectangles.

• Estimate volume and capacity.

• Identify 3-D shapes, including cubes and other cuboids, from 2-D representations.

• Understand, estimate and use a wide variety of different types of angles, using properties of shapes to deduce facts.

• Distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

• 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.

• Solve comparison, sum and difference problems using information presented in a line graph.

• Complete, read and interpret information in tables, including timetables.

Year 6

In Year 6, children learn to:

• Read, write, order, use and compare numbers up to 10,000,000 determining the value of each digit, rounding numbers.

• Use negative numbers in context, and calculate intervals across zero.

• Solve number and practical problems.

• Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written methods.

• Perform mental calculations, including with mixed operations and large numbers.

• Identify common factors, common multiples and prime numbers.

• Use estimation to check answers to calculations.

• Understand and calculate using fractions including simplifying, equivalence and comparing.

• Associate a fraction with division and calculate decimal fraction equivalents.

• Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers.

• Understand and use algebra to solve problems including generating and describe linear number sequences and expressing missing number problems.

• Solve problems involving the calculation and conversion of units of measure.

• Use, read, write and convert between units of measurement, converting measurements of length, mass, volume and time.

• Recognise that shapes with the same areas can have different perimeters and vice versa and recognise when it is possible to use formulae for area and volume of shapes.

• Calculate the area of parallelograms and triangles.

• 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.

• Illustrate and name parts of circles, including radius, diameter and circumference.

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

• Describe positions on the full co-ordinate grid (all four quadrants).

• Draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

• Interpret and construct pie charts and line graphs and use these to solve problems and calculate and interpret the mean as an average.

Year 7 & 8

In Year 7 & 8, children learn to:

• Understand and use place value for decimals, measures and integers of any size.

• Order positive and negative integers, decimals and fractions.

• Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation.

• Use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative.

• Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals.

• Recognise and use relationships between operations including inverse operations.

• Use integer powers and associated real roots.

• Work interchangeably with terminating decimals and their corresponding fractions.

• Define and interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.

• Interpret fractions and percentages as operators.

• Use standard units of mass, length, time, money and other measures, including with decimal quantities.

• Round numbers and measures to an appropriate degree of accuracy.

• Use approximation through rounding to estimate answers.

• Use and interpret algebraic notation.

• Substitute numerical values into formulae and expressions.

• Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors.

• Simplify and manipulate algebraic expressions to maintain equivalence.

• Understand and use standard mathematical formulae.

• Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs.

• Use algebraic methods to solve linear equations.

• Work with coordinates in all 4 quadrants.

• Recognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane.

• Interpret mathematical relationships both algebraically and graphically.

• Use linear and quadratic graphs.

• Recognise geometric and arithmetic sequences and find the nth term.

• Change freely between related standard units.

• Use scale factors, scale diagrams and maps.

• Use ratio notation, including reduction to simplest form.

• Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions.

• Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics.

• Solve problems involving direct proportion, including graphical representations.

• Use compound units such as speed, unit pricing and density to solve problems.

• Calculate and solve problems involving shapes and their angles.

• Draw, measure and label line segments shapes, their angles, proportions and use shapes in a variety of ways including translations, rotations, reflections, enlargement.

• Understand and solve problems about probability.

• Use, construct and interpret a wide variety of graphs, charts and tables.