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# Maths

 Strands EYFS Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Place Value -  Recognise some numbers of personal significance.   - Read and write numerals 1 to 20.   - Count objects to 20.   - Begin to count backwards.   - Say and select the correct numeral to represent the total number of objects counted up to 20.   - Count up to 10 objects from a larger group.   - Count an irregular arrangement of up to 20 objects.   -Estimate how many objects you can see and check by counting.   - Represent numbers using objects, including Numicon and Base 10. - Count to and across 100, forwards and backwards, from any given number.   - Count, read and write numbers to 100 in numerals.   - Represent numbers using objects and pictures eg Dienes and Numicon  - Recognise odd and even numbers. - Read and write numbers to at least 100 in numerals and in words.   - Recognise the place value of each digit in a two digit number (tens, ones)   - Identify, represent and estimate numbers, including on a number line.   - Compare and order numbers from 0 up to 100; use <, > and = signs.   - Count in tens from any number, forward and backward. - Read, write, identify, represent and estimate numbers up to 1000.   - Find 10 or 100 more or less than a given number.  - Recognise the place value of each digit in a three-digit number.  - Compare and order numbers up to 1000. - Find 1000 more or less than a given number.   - 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.  - Count backwards through zero to include negative numbers.   - Read Roman numerals to 100 (I to C). - Read, write, order and compare numbers to at least 1000000 and say the value of each digit.   - Count forwards or backwards in steps of powers of 10 from any number.   - Multiply and divide whole numbers by 10, 100 and 1000.   - Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers including through zero.  - Round any number up to 1000000 to the nearest 10, 100, 1000, 10000 and 100000  - Read Roman numerals to 1000 (M) and recognise years written in Roman numerals. - 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. Addition and Subtraction  (see calculation policy, ‘Progression in Calculation’, for detailed teaching sequences) - Use the words ‘more’ or ‘fewer’ to compare two sets of objects.  - Find the total number of objects in two groups by counting all of them.   - Say the number that is one more than a given number.   - Find one more or one less from a group of up to 20 objects.   - Begin to use the vocabulary involved in adding and subtracting.   - Add and subtract two single digit numbers, using concrete objects.   - Count on or back to find the solution to additions and subtractions within 20. - Identify the number one more or less than a given number.   - Represent and use number bonds and related subtraction facts within 20.  - Read, write and interpret mathematical statements involving addition, subtraction and equals signs.   - Add and subtract one digit numbers to 20, including 0.   - Solve one step problems and missing number problems, using concrete resources and pictures. - 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.   - Show that the addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot.   - Solve problems with addition and subtraction.  - Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems. - Add and subtract numbers with up to three digits mentally.   - Add and subtract numbers with up to three digits, using column method.   - Estimate the answer to a calculation and use inverse operations to check answers. - Add and subtract numbers mentally with increasingly large numbers.   - 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. - Add and subtract numbers mentally with increasingly large numbers.   - Add and subtract whole numbers with more than 4 digits using the column method.  - Use rounding to check answers to calculations.  - Decide which operations and methods to use and why to solve multi-step problems. - Solve addition and subtraction multi step problems in contexts, deciding which operations and methods to use and why.   - Use their knowledge of the order of operations.  - Use estimation to check answers to calculations and determine in the context of a problem, an appropriate degree of accuracy. Multiplication and Division  (see calculation policy, ‘Progression in Calculation’, for detailed teaching sequences) - Share objects out equally.   - Solve problems including doubling and halving. - Count in multiples of twos, fives and tens.   - Use grouping to solve one step multiplication and division problems using concrete resources and pictures. - Count in threes.   - Recall and use multiplication and division facts for the 2, 5 and 10 times tables.   - Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (x), division (÷) and equals (=) sign.   - Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods and multiplication and division facts.   - Show that the multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot. - Count from 0 in multiples of 4, 8, 50 and 100.   - 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 they know, including for two-digit numbers times one-digit numbers.  - Solve problems, including missing number problems, involving multiplication and division. - Count in multiples of 6, 7, 9, 25 and 1000.  - Recall and use 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.   - Divide three digit numbers by one digit numbers using short division. - Multiply and divide numbers mentally drawing upon known facts.   - Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.   - Recognise and use square numbers and cube 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 2 digit numbers.  - 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.   - Understand the use of the equals sign and be able to solve missing number problems. - Multiply multi-digit number up to 4 digits by a 2-digit number using the formal written method of long multiplication.   - Divide numbers up to 4 digits by 2-digit whole number using the formal written method of short and long division, and interpret remainders as whole number remainders, fractions, or by rounding as appropriate for the context.   - Identify common factors, common multiples and prime numbers.  - Scale quantities up and down using whole numbers. Fractions, Decimals (from Y4) and Percentages (from Y5) - Recognise, find and name a half as one of two equal parts of an object, shape or quantity. - Recognise, find, name and write fractions 1/3, ¼ , 2/4 and 3/4 of a length, shape, set of objects or quantity.   - Write simple fractions for example, ½ of 6 = 3.  - Recognise the equivalence of 2/4 and ½. - Count up and down in tenths; know the value of a tenth.   - Recognise and use fractions as numbers.  - Recognise, find and write fractions of a discrete set of objects.   - Recognise and show, using diagrams, equivalent fractions with small denominators.   - Compare and order unit fractions, and fractions with the same denominators.   - Add and subtract fractions with the same denominator within one whole. - 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.   - Add and subtract fractions with the same denominator.  - Recognise and write decimal equivalents of any number of tenths or hundredths.   - Find the effect of dividing a one or two digit number by 10 or 100, identifying the value of the digits in the answer as ones, tenths and hundredths.  - Compare numbers with the same number of decimal places up to two decimal places.   - Round decimals with one decimal place to the nearest whole number.   - Recognise and write decimal equivalents to ¼, ½ and ¾. - Compare and order fractions whose denominators are multiples of the same number.   - Identify, name and write equivalent fractions of a given fraction, represented visually.  - Recognise mixed numbers and improper fractions and convert from one form to the other.  - 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.  - Read, write, order and compare numbers with up to three decimal places.   - Round decimals with two decimal places to the nearest whole number and to one decimal place.   - Recognise the per cent symbol (%) and its meaning. - 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 denominations and mixed numbers, using the concept of equivalent fractions.   - Multiply simple pairs of proper fractions, writing the answer in its simplest form.   - Divide proper fractions by whole numbers.   - Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.  - Identify the value of each digit in numbers given to 3 decimal places and multiply numbers by 10, 100 and 1,000 giving answers up to 3 decimal places.   - Multiply one-digit numbers with up to 2 decimal places by whole numbers. Geometry - Use mathematical names for 3D and 2D shapes.   - Select a named shape.   - Describe position using terms such as ‘behind’ or ‘next to’  - Use familiar objects to create and copy patterns and build models.   - Explore characteristics of everyday objects and use mathematical language to describe them. - Recognise and name common 2-D shapes.  - Recognise and name common 3-D shapes.  - Describe position, direction and movement, including whole, half, quarter and three quarter turns. - Identify and describe the properties of 2-D shapes, including the number of sides and symmetry.  - 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.   - Compare and sort common 2-D and 3-D shapes and everyday objects.  - Use mathematical vocabulary to describe position, direction and movement including clockwise and anti-clockwise.   - Order and arrange combinations of mathematical objects in patterns and sequences. - Recognise angles as a property of shape or a description of a turn.   - Use knowledge of right angles, to estimate other angles.   - Identify horizontal and vertical lines and pairs of perpendicular and parallel lines.   - Draw 2-D shapes and make 3- D shapes using modelling materials.   - Recognise 3-D shapes in different orientations and describe them. - Identify acute and obtuse angles and compare and order angles up to two right angles by size.   - Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.   - 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.   - Plot specified points and draw sides to complete a given polygon.   - Describe movements between positions as translations of a given unit to the left/ right and up/ down. - Identify 3D shapes from 2D representations.   - 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.   - Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles.   - Draw given angles, and measure them in degrees.  - 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. - 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.  - Draw 2 -D shapes using given dimensions and angles.   - Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals and regular polygons.   - Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles. Measurement Measures  - Use everyday language to talk about size, weight, capacity and distance.   - Order a set of items by length or height.   - Order a set of items by weight or capacity.   Time  - Use everyday language related to time.   - Measure short periods of time.   Money  - Use everyday language related to money. Measures  - Measure and begin to record lengths and heights.  - Measure and begin to record mass/weight, capacity and volume.  - Compare, describe and solve practical problems for: lengths, heights, mass/ capacity and volume.  Time  - Sequence events in chronological order using appropriate language.   - 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.   - Compare, describe and solve practical problems for time [for example, quicker, slower, earlier, later]   - Measure and begin to record time (hours, minutes, seconds)   Money  - Recognise and know the value of different denominations of coins and notes. Measures  - 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).  - Compare and order: lengths, mass, volume/capacity and record the results using >, < and =.  Time  - Tell and write the time to five minutes.  - Know the number of minutes in an hour and the number of hours in a day.   Money  - 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, including giving change. Measures  - Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml).   - Measure the perimeter of simple 2D shapes.  Time  - 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.   - 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.  Money  - Add and subtract amounts of money to give change, using both £ and p in practical contexts. Measures  - Measure and calculate the perimeter of a rectilinear figure in centimetres and metres   - Convert between different units of measure.   - Find the area of rectilinear shapes by counting squares.  Time  - 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.   Money  Solve money problems involving fractions and decimals to two decimal places. Measures  - Measure and calculate the perimeter of composite rectilinear shapes in cm and m.   - Calculate and compare the area of rectangles and estimate the area of irregular shapes.  - Convert between different units of metric measure [for example, km and m; cm and m; cm and mm; g and kg; l and ml]   - Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints.  - Estimate volume and capacity.  Time  - Solve problems involving converting between units of time.  Money (included in calculations of four operations) - Use, read, write and convert between standard units of measure.  - 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 cm3 , m3 and extending to other units (mm3 , km3)  - Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius. Statistics - 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, sorting the categories by quantity and totalling. - Interpret and present data using bar charts, pictograms and tables.   - Solve one-step and two-step using information presented in scaled bar charts and pictograms and tables. - 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. - Solve comparison, sum and difference problems using information presented in a line graph.   - Complete, read and interpret information in tables including timetables. - Interpret and construct pie charts and line graphs and use these to solve problems.   - Calculate the mean as an average. Algebra - Describe simple linear number sequences.   - Solve missing number problems expressed algebraically. - 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.
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