# Maths from the National Curriculum

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1 Maths from the National Curriculum MATHS: NUMBER AND PLACE VALUE KS1 Y1 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 Y2 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. Count in 2, 3, and 5 from 0, and in tens from any number, forward, 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. KS2 Y3 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 Compare and order numbers up to 1000 Identify, represent and estimate numbers using different representations Read and write numbers up to 1000 in numerals and in words Solve number problems and practical problems involving these ideas

2 MATHS: NUMBER AND PLACE VALUE KS2 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 Read, write, order and compare numbers to at least and determine the value of each digit Count forwards or backwards in steps of 10 for any given number up to Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero Round any number up to to the nearest 10, 100, 1000, and 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. Read, write, order and compare numbers up to 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.

5 addition, mental methods, multiplication and division facts, and problems in contexts. KS2 Y3 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. Recall multiplication and division facts for multiplication tables up to 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 commutability 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 Multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects. MATHS: MULTIPICATION AND DIVISION 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 ( 2 ) and ( 3 ) Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes

6 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. 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, f 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 problems involving addition, subtraction, multiplication and division Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy NUMBER: FRACTIONS, DECIMALS and PERCENTAGES KS1 Y1 Recognise, find and name a half as 1 of 2 equal parts of an object, shape, quantity Recognise, find, name a quarter as 1 of 4 equal parts of an object, shape or quantity. Y2 Recognise, find, name and write fractions 3 1, 4 1, 4 2 and 4 3 objects or quantity of a length, shape, set of Write simple fractions for example, 1 2 of 6 = 3 and recognise equivalence of 2 4 and 1 2. KS2 Y3 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 nonunit 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

7 Compare and order unit fractions, and fractions with the same denominators Solve problems that involve all of the above. 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 1 4, 1 3 2, 4 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 Place NUMBER: FRACTIONS, DECIMALS and PERCENTAGES KS2 Compare and order fractions whose denominators are all multiples of same number Identify, name, write equivalent fractions of a given fraction, inc 1/10 and 1/100 Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number 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 = ] Recognise / use thousandths, relate them to tenths, hundredths, decimal equivalents Round decimals with 2 decimal places to nearest whole and to 1 decimal place Read, write, order and compare numbers with up to three decimal places 1, 1 2 4, 1 5, 2 5, 4 5 and those fractions with a denominator of a multiple of 10 or 25. Solve problems involving number up to three decimal places

8 Recognise the per cent symbol (%) and understand that per cent relates to number of parts per hundred, and write percentages as a fraction and as a decimal Solve problems which require knowing percentage and decimal equivalents of 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 Divide proper fractions by whole numbers [for example, = 1 6 ] 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 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. MATHS: RATIO AND PROPORTION KS1 Y1 No statutory content Y2 No statutory content KS2 Y3 No statutory content No statutory content No statutory content 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.

9 MATHS: ALGEBRA KS1 Y1 No statutory content Y2 No statutory content KS2 Y3 No statutory content No statutory content No statutory content 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. MATHS: MEASUREMENT: SHAPE KS1 Y1 Compare, describe and solve practical problems for lengths and heights [for example, long/short, longer/shorter, tall/short, double/half] Measure and begin to record lengths and heights Y2 Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm) KS2 Y3 Measure, compare, add and subtract: lengths (m/cm/mm) Measure the perimeter of simple 2-D shapes Convert between different units of measure [for example, kilometre to metre] 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 Convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre)

10 Understand and use approximate equivalences between metric units and common imperial units such as inches 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 (cm 2 ) and square metres (m 2 ) and estimate the area of irregular shapes 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 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 MATHS: MEASUREMENT: MASS, WEIGHT KS1 Y1 Compare, describe and solve practical problems for mass/weight [eg: heavy/light, heavier] Measure and begin to record mass/weight Y2 Choose and use appropriate standard units to estimate and measure mass (kg/g) Compare and order mass and record the results using >, < and = KS2 Y3 Measure, compare, add and subtract mass (kg/g) Convert between different units of measure [for example, kilometre to metre Convert between different units of metric measure (for example, gram and kilogram) Understand / use approximate equivalences between metric and imperial units 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 mass from a smaller unit of measure to a larger unit, and vice versa, using notation to up to three places

11 MATHS: MEASUREMENT: CAPACITY AND VOLUME KS1 Y1 Compare, describe and solve practical problems for capacity and volume Measure and begin to record capacity and volume Y2 Choose and use appropriate standard units to estimate and measure capacity (litres/ml) to the nearest appropriate unit, using measuring vessels Compare and order volume/capacity and record the results using >, < and = KS2 Y3 Measure, compare, add and subtract volume/capacity (l/ml) Convert between different units of measure Convert between different units of metric measure (for example, litre and millilitre) Understand and use approximate equivalences between metric units and common imperial units such as pints Estimate volume eg using 1 cm 3 blocks to build cuboids and capacity eg water 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 volume from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places Recognise when it is possible to use formulae for volume of shape Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm 3 ) and cubic metres (m 3 ), and extending to other units MATHS: MEASUREMENT: TEMPERATURE KS1 Y1 No statutory content Y2 Choose and use appropriate standard units to estimate temperature ( C) to the nearest appropriate unit using thermometers KS2 Y3-5 No statutory content Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate

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13 MATHS: MEASUREMENT: TIME KS1 Y1 Compare, describe and solve practical problems for time Measure and begin to record time (hours, minutes, seconds) Sequence events in chronological order using language [eg before and after, next] Recognise / use language relating to dates, inc days, weeks, months, 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 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. KS2 Y3 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 seconds, minutes and hours; use vocabulary eg o clock, a.m. Know the number of seconds in a minute and the number of days in each month, year and leap year Compare durations of events [eg calculate time taken by particular events]. Convert between different units of measure [for example, hour to minute 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. Solve problems involving converting between units of time Use, read, write, convert between standard units of time from a smaller unit of measure to a larger unit, using decimal to up to three decimal places.

14 MATHS: MEASUREMENT: MONEY KS1 Y1 Recognise and know the value of different denominations of coins and notes Y2 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 KS2 Y3 No statutory content Estimate, compare and calculate different measures, including money in pounds and pence Use all four operations to solve problems involving money using decimal notation, including scaling. Solve problems involving the calculation and conversion of units of money, using decimal notation up to three decimal places where appropriate MATHS: GEOMETRY: PROPERTIES OF SHAPE KS1 Y1 Recognise and name common 2-D and 3-D shapes, inc 2-D and 3-D shapes Y2 Identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line Identify and describe properties of 3-D shapes, including number of edges, vertices and faces Identify 2-D shapes on the surface of 3-D shapes [eg, circle on cylinder, triangle on pyramid) Compare and sort common 2-D and 3-D shapes and everyday objects. KS2 Y3 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.

15 MATHS: GEOMETRY: PROPERTIES OF SHAPE KS2 Compare and classify geometric shapes based on their properties and sizes Identify acute and obtuse angles and compare and order angles up to 2 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. Identify 3-D shapes, including cubes and other cuboids, from 2-D representations Know angles are measured in degrees: estimate, compare acute, obtuse and reflex Draw given angles, and measure them in degrees ( o ) Identify: angles at a point and one whole turn (total 360 o ) angles at a point on a straight line and 1 2 a turn (total 180 o ) other multiples of 90 o use properties of rectangles to deduce related facts and find missing lengths, angles distinguish between regular and irregular polygons based on reasoning about equal sides and angles. 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

16 MATHS: GEOMETRY: POSITION AND DIRECTION KS1 Y1 Describe position, direction and movement, including whole, half, quarter, threequarter turns Y2 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). KS2 Y3 No statutory content Describe positions on a 2-D grid as coordinates in the first quadrant Describe movements bet 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 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. MATHS: STATISTICS KS1 Y1 No statutory requirements Y2 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 Ask and answer questions about totalling and comparing categorical data. KS2 Y3 Interpret and present data using bar charts, pictograms and tables Solve 1 and 2step questions using info in scaled bar charts and pictograms and tables. Interpret and present discrete and continuous data using apt graphical methods, Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs. Solve comparison, sum, difference problems using info presented in line graph Complete, read and interpret information in tables, including timetables.

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

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