Mathematics
Outcomes
-
Key Stage 1
-
Year 1
-
Number
-
Number & Place Value
Pupils practise counting (1, 2, 3...), ordering (for example, first, second, third...), and to indicate a quantity (for example, 3 apples, 2 centimetres), including solving simple concrete problems, until they are fluent. Pupils begin to recognise place value in numbers beyond 20 by reading, writing, counting and comparing numbers up to 100, supported by objects and pictorial representations. They practise counting as reciting numbers and counting as enumerating objects, and counting in twos, fives and tens from different multiples to develop their recognition of patterns in the number system (for example, odd and even numbers), including varied and frequent practice through increasingly complex questions. They recognise and create repeating patterns with objects and with shapes.
-
Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number
Play Activities 183Examples
-
Count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens
Examples
-
Given a number, identify one more and one less
Examples
-
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
Examples
-
Read and write numbers from 1 to 20 in numerals and words
Examples
-
Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number
-
Addition & Subtraction
Pupils memorise and reason with number bonds to 10 and 20 in several forms (for example, 9 + 7 = 16; 16 - 7 = 9; 7 = 16 - 9). They should realise the effect of adding or subtracting zero. This establishes addition and subtraction as related operations. Pupils combine and increase numbers, counting forwards and backwards. They discuss and solve problems in familiar practical contexts, including using quantities. Problems should include the terms: put together, add, altogether, total, take away, distance between, difference between, more than and less than, so that pupils develop the concept of addition and subtraction and are enabled to use these operations flexibly.
-
Read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs
Examples
-
Represent and use number bonds and related subtraction facts within 20
Examples
-
Add and subtract one-digit and two-digit numbers to 20, including zero
Play Activities 194Examples
-
Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ? - 9
Play Activities 190Examples
-
Read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs
-
Multiplication & Division
Through grouping and sharing small quantities, pupils begin to understand: multiplication and division; doubling numbers and quantities; and finding simple fractions of objects, numbers and quantities. They make connections between arrays, number patterns, and counting in twos, fives and tens.
-
Fractions
Pupils are taught half and quarter as 'fractions of' discrete and continuous quantities by solving problems using shapes, objects and quantities. For example, they could recognise and find half a length, quantity, set of objects or shape. Pupils connect halves and quarters to the equal sharing and grouping of sets of objects and to measures, as well as recognising and combining halves and quarters as parts of a whole
-
Number & Place Value
-
Measurement
The pairs of terms: mass and weight, volume and capacity, are used interchangeably at this stage. Pupils move from using and comparing different types of quantities and measures using non-standard units, including discrete (for example, counting) and continuous (for example, liquid) measurement, to using manageable common standard units. In order to become familiar with standard measures, pupils begin to use measuring tools such as a ruler, weighing scales and containers. Pupils use the language of time, including telling the time throughout the day, first using o'clock and then half past.
-
Compare, describe and solve practical problems for:
-
Lengths and heights [for example, long/short, longer/shorter, tall/short, double/half]
Examples
-
Mass/weight [for example, heavy/light, heavier than, lighter than]
Examples
-
Capacity and volume [for example, full/empty, more than, less than, half, half full, quarter]
Examples
-
Time [for example, quicker, slower, earlier, later]
Examples
-
Lengths and heights [for example, long/short, longer/shorter, tall/short, double/half]
-
Sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening]
Examples
-
Recognise and use language relating to dates, including days of the week, weeks, months and years
Examples
-
Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times
Examples
-
Compare, describe and solve practical problems for:
-
Geometry
-
Properties of Shapes
Pupils handle common 2-D and 3-D shapes, naming these and related everyday objects fluently. They recognise these shapes in different orientations and sizes, and know that rectangles, triangles, cuboids and pyramids are not always similar to each other.Examples
-
Position & Direction
Pupils use the language of position, direction and motion, including: left and right, top, middle and bottom, on top of, in front of, above, between, around, near, close and far, up and down, forwards and backwards, inside and outside. Pupils make whole, half, quarter and three-quarter turns in both directions and connect turning clockwise with movement on a clock faceExamples
-
Properties of Shapes
-
Number
-
Year 2
-
Number
-
Number & Place Value
Using materials and a range of representations, pupils practise counting, reading, writing and comparing numbers to at least 100 and solving a variety of related problems to develop fluency. They count in multiples of three to support their later understanding of a third. As they become more confident with numbers up to 100, pupils are introduced to larger numbers to develop further their recognition of patterns within the number system and represent them in different ways, including spatial representations. Pupils should partition numbers in different ways (for example, 23 = 20 + 3 and 23 = 10 + 13) to support subtraction. They become fluent and apply their knowledge of numbers to reason with, discuss and solve problems that emphasise the value of each digit in two-digit numbers. They begin to understand zero as a place holder.
-
Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward
Examples
-
Recognise the place value of each digit in a two-digit number (tens, ones)
Examples
-
Identify, represent and estimate numbers using different representations, including the number line
Examples
-
Compare and order numbers from 0 up to 100; use <, > and = signs
Examples
-
Read and write numbers to at least 100 in numerals and in words
Examples
-
Use place value and number facts to solve problems
Examples
-
Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward
-
Addition & Subtraction
Pupils extend their understanding of the language of addition and subtraction to include sum and difference. Pupils practise addition and subtraction to 20 to become increasingly fluent in deriving facts such as using 3 + 7 = 10; 10 - 7 = 3 and 7 = 10 - 3 to calculate 30 + 70 = 100; 100 - 70 = 30 and 70 = 100 - 30. They check their calculations, including by adding to check subtraction and adding numbers in a different order to check addition (for example, 5 + 2 + 1 = 1 + 5 + 2 = 1 + 2 + 5). This establishes commutativity and associativity of addition. Recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers.
- Solve problems with addition and subtraction:
-
Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
Examples
-
Add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
-
A two-digit number and ones
Play Activities 166Examples
-
A two-digit number and tens
Examples
-
Two two-digit numbers
Examples
-
Adding three one-digit numbers
Examples
-
A two-digit number and ones
-
Show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot
Examples
-
Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems
Play Activities 222Examples
-
Multiplication & Division
Pupils use a variety of language to describe multiplication and division. Pupils are introduced to the multiplication tables. They practise to become fluent in the 2, 5 and 10 multiplication tables and connect them to each other. They connect the 10 multiplication table to place value, and the 5 multiplication table to the divisions on the clock face. They begin to use other multiplication tables and recall multiplication facts, including using related division facts to perform written and mental calculations. Pupils work with a range of materials and contexts in which multiplication and division relate to grouping and sharing discrete and continuous quantities, to arrays and to repeated addition. They begin to relate these to fractions and measures (for example, 40 ÷ 2 = 20, 20 is a half of 40). They use commutativity and inverse relations to develop multiplicative reasoning (for example, 4 x 5 = 20 and 20 ÷ 5 = 4).
-
Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
Examples
-
Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
Examples
-
Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts
Examples
-
Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
-
Fractions
Pupils use fractions as 'fractions of' discrete and continuous quantities by solving problems using shapes, objects and quantities. They connect unit fractions to equal sharing and grouping, to numbers when they can be calculated, and to measures, finding fractions of lengths, quantities, sets of objects or shapes. They meet 3/4 as the first example of a non-unit fraction. Pupils should count in fractions up to 10, starting from any number and using the 1/2 and 2/4 equivalence on the number line (for example, 1 1/4, 1 2/4 (or 1 1/2), 1 3/4, 2). This reinforces the concept of fractions as numbers and that they can add up to more than one.
-
Number & Place Value
-
Measurement
Pupils use standard units of measurement with increasing accuracy, using their knowledge of the number system. They use the appropriate language and record using standard abbreviations. Comparing measures includes simple multiples such as 'half as high'; 'twice as wide'. They become fluent in telling the time on analogue clocks and recording it. Pupils become fluent in counting and recognising coins. They read and say amounts of money confidently and use the symbols £ and p accurately, recording pounds and pence separately.
-
Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (degreesC); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels
Examples
-
Compare and order lengths, mass, volume/capacity and record the results using >, < and =
Examples
-
Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change
Examples
-
Compare and sequence intervals of time
Examples
-
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
Examples
-
Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (degreesC); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels
-
Geometry
-
Properties of Shapes
Pupils handle and name a wide variety of common 2-D and 3-D shapes including: quadrilaterals and polygons, and cuboids, prisms and cones, and identify the properties of each shape (for example, number of sides, number of faces). Pupils identify, compare and sort shapes on the basis of their properties and use vocabulary precisely, such as sides, edges, vertices and faces. Pupils read and write names for shapes that are appropriate for their word reading and spelling. Pupils draw lines and shapes using a straight edge.
-
Identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line
Examples
-
Identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
Examples
-
Identify 2-D shapes on the surface of 3-D shapes [for example, a circle on a cylinder and a triangle on a pyramid]
Examples
-
Compare and sort common 2-D and 3-D shapes and everyday objects
Examples
-
Identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line
-
Position & Direction
Pupils should work with patterns of shapes, including those in different orientations. Pupils use the concept and language of angles to describe 'turn' by applying rotations, including in practical contexts (for example, pupils themselves moving in turns, giving instructions to other pupils to do so, and programming robots using instructions given in right angles)
-
Order and arrange combinations of mathematical objects in patterns and sequences
Examples
-
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-clockw
Play Activities 106Examples
-
Order and arrange combinations of mathematical objects in patterns and sequences
-
Properties of Shapes
-
Statistics
Pupils record, interpret, collate, organise and compare information (for example, using many-to-one correspondence in pictograms with simple ratios 2, 5, 10)
-
Interpret and construct simple pictograms, tally charts, block diagrams and simple tables
Examples
-
Ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity
Examples
-
Ask and answer questions about totalling and comparing categorical data
Examples
-
Interpret and construct simple pictograms, tally charts, block diagrams and simple tables
-
Number
-
Year 1
-
Lower Key Stage 2
-
Year 3
-
Number
-
Number & Place Value
Pupils now use multiples of 2, 3, 4, 5, 8, 10, 50 and 100. They use larger numbers to at least 1000, applying partitioning related to place value using varied and increasingly complex problems, building on work in year 2 (for example, 146 = 100 + 40 and 6, 146 = 130 + 16). Using a variety of representations, including those related to measure, pupils continue to count in ones, tens and hundreds, so that they become fluent in the order and place value of numbers to 1000
-
Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number
Examples
-
Recognise the place value of each digit in a three-digit number (hundreds, tens, ones)
Examples
-
Compare and order numbers up to 1000
Examples
-
Read and write numbers up to 1000 in numerals and in words
Examples
-
Solve number problems and practical problems involving these ideas
Examples
-
Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number
-
Addition & Subtraction
Pupils practise solving varied addition and subtraction questions. For mental calculations with two-digit numbers, the answers could exceed 100. Pupils use their understanding of place value and partitioning, and practise using columnar addition and subtraction with increasingly large numbers up to three digits to become fluent (see Mathematics Appendix 1)
-
Add and subtract numbers mentally, including:
-
A three-digit number and ones
Examples
-
A three-digit number and tens
Examples
-
A three-digit number and hundreds
Examples
-
A three-digit number and ones
-
Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction
Play Activities 133Examples
-
Estimate the answer to a calculation and use inverse operations to check answers
Examples
-
Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction
Play Activities 330Examples
-
Add and subtract numbers mentally, including:
-
Multiplication & Division
Pupils continue to practise their mental recall of multiplication tables when they are calculating mathematical statements in order to improve fluency. Through doubling, they connect the 2, 4 and 8 multiplication tables. Pupils develop efficient mental methods, for example, using commutativity and associativity (for example, 4 x 12 x 5 = 4 x 5 x 12 = 20 x 12 = 240) and multiplication and division facts (for example, using 3 x 2 = 6, 6 ÷ 3 = 2 and 2 = 6 ÷ 3) to derive related facts (for example, 30 x 2 = 60, 60 ÷ 3 = 20 and 20 = 60 ÷ 3). Pupils develop reliable written methods for multiplication and division, starting with calculations of two-digit numbers by one-digit numbers and progressing to the formal written methods of short multiplication and division. Pupils solve simple problems in contexts, deciding which of the four operations to use and why. These include measuring and scaling contexts, (for example, four times as high, eight times as long etc.) and correspondence problems in which m objects are connected to n objects (for example, 3 hats and 4 coats, how many different outfits?; 12 sweets shared equally between 4 children; 4 cakes shared equally between 8 children).
-
Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
Examples
-
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
Examples
-
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
Play Activities 119Examples
-
Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
-
Fractions
Pupils connect tenths to place value, decimal measures and to division by 10. They begin to understand unit and non-unit fractions as numbers on the number line, and deduce relations between them, such as size and equivalence. They should go beyond the [0, 1] interval, including relating this to measure. Pupils understand the relation between unit fractions as operators (fractions of), and division by integers. They continue to recognise fractions in the context of parts of a whole, numbers, measurements, a shape, and unit fractions as a division of a quantity. Pupils practise adding and subtracting fractions with the same denominator through a variety of increasingly complex problems to improve fluency.
-
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
Examples
-
Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
Examples
-
Recognise and show, using diagrams, equivalent fractions with small denominators
Examples
-
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
-
Number & Place Value
-
Measurement
Pupils continue to measure using the appropriate tools and units, progressing to using a wider range of measures, including comparing and using mixed units (for example, 1 kg and 200g) and simple equivalents of mixed units (for example, 5m = 500cm). The comparison of measures includes simple scaling by integers (for example, a given quantity or measure is twice as long or five times as high) and this connects to multiplication. Pupils continue to become fluent in recognising the value of coins, by adding and subtracting amounts, including mixed units, and giving change using manageable amounts. They record £ and p separately. The decimal recording of money is introduced formally in year 4. Pupils use both analogue and digital 12-hour clocks and record their times. In this way they become fluent in and prepared for using digital 24-hour clocks in year 4.
-
Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
Examples
-
Measure the perimeter of simple 2-D shapes
Examples
-
Add and subtract amounts of money to give change, using both £ and p in practical contexts
Examples
-
Tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks
Examples
-
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
Examples
-
Know the number of seconds in a minute and the number of days in each month, year and leap year
Examples
-
Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
-
Geometry
-
Properties of Shapes
Pupils' knowledge of the properties of shapes is extended at this stage to symmetrical and non-symmetrical polygons and polyhedra. Pupils extend their use of the properties of shapes. They should be able to describe the properties of 2-D and 3-D shapes using accurate language, including lengths of lines and acute and obtuse for angles greater or lesser than a right angle. Pupils connect decimals and rounding to drawing and measuring straight lines in centimetres, in a variety of contexts.
-
Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them
Examples
-
Recognise angles as a property of shape or a description of a turn
Examples
-
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
Examples
-
Identify horizontal and vertical lines and pairs of perpendicular and parallel lines
Examples
-
Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them
-
Properties of Shapes
-
Statistics
Pupils understand and use simple scales (for example, 2, 5, 10 units per cm) in pictograms and bar charts with increasing accuracy. They continue to interpret data presented in many contexts.
-
Number
-
Year 4
-
Number
-
Number & Place Value
Using a variety of representations, including measures, pupils become fluent in the order and place value of numbers beyond 1000, including counting in tens and hundreds, and maintaining fluency in other multiples through varied and frequent practice. They begin to extend their knowledge of the number system to include the decimal numbers and fractions that they have met so far. They connect estimation and rounding numbers to the use of measuring instruments. Roman numerals should be put in their historical context so pupils understand that there have been different ways to write whole numbers and that the important concepts of zero and place value were introduced over a period of time.
-
Count in multiples of 6, 7, 9, 25 and 1000
Examples
-
Find 1000 more or less than a given number
Examples
-
Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
Examples
-
Order and compare numbers beyond 1000
Examples
-
Identify, represent and estimate numbers using different representations
Examples
-
Round any number to the nearest 10, 100 or 1000
Examples
-
Solve number and practical problems that involve all of the above and with increasingly large positive numbers
Examples
-
Count in multiples of 6, 7, 9, 25 and 1000
-
Addition & Subtraction
Pupils continue to practise both mental methods and columnar addition and subtraction with increasingly large numbers to aid fluency (see Mathematics Appendix 1).
-
Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
Play Activities 391Examples
-
Estimate and use inverse operations to check answers to a calculation
Examples
-
Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why
Examples
-
Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
-
Multiplication & Division
Pupils continue to practise recalling and using multiplication tables and related division facts to aid fluency. Pupils practise mental methods and extend this to three-digit numbers to derive facts, (for example 600 ÷ 3 = 200 can be derived from 2 x 3 = 6). Pupils practise to become fluent in the formal written method of short multiplication and short division with exact answers (see Mathematics Appendix 1). Pupils write statements about the equality of expressions (for example, use the distributive law 39 x 7 = 30 x 7 + 9 x 7 and associative law (2 x 3) x 4 = 2 x (3 x 4)). They combine their knowledge of number facts and rules of arithmetic to solve mental and written calculations for example, 2 x 6 x 5 = 10 x 6 = 60. Pupils solve two-step problems in contexts, choosing the appropriate operation, working with increasingly harder numbers. This should include correspondence questions such as the numbers of choices of a meal on a menu, or three cakes shared equally between 10 children.
-
Recall multiplication and division facts for multiplication tables up to 12 x 12
Examples
-
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
Examples
-
Recognise and use factor pairs and commutativity in mental calculations
Examples
-
Multiply two-digit and three-digit numbers by a one-digit number using formal written layout
Examples
-
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
Examples
-
Recall multiplication and division facts for multiplication tables up to 12 x 12
-
Fractions (Including Decimals)
Pupils should connect hundredths to tenths and place value and decimal measure. They extend the use of the number line to connect fractions, numbers and measures. Pupils understand the relation between non-unit fractions and multiplication and division of quantities, with particular emphasis on tenths and hundredths. Pupils make connections between fractions of a length, of a shape and as a representation of one whole or set of quantities. Pupils use factors and multiples to recognise equivalent fractions and simplify where appropriate (for example, 6/9 = 2/3 or 1/4 = 2/8). Pupils continue to practise adding and subtracting fractions with the same denominator, to become fluent through a variety of increasingly complex problems beyond one whole. Pupils are taught throughout that decimals and fractions are different ways of expressing numbers and proportions. Pupils' understanding of the number system and decimal place value is extended at this stage to tenths and then hundredths. This includes relating the decimal notation to division of whole number by 10 and later 100. They practise counting using simple fractions and decimals, both forwards and backwards. Pupils learn decimal notation and the language associated with it, including in the context of measurements. They make comparisons and order decimal amounts and quantities that are expressed to the same number of decimal places. They should be able to represent numbers with one or two decimal places in several ways, such as on number lines.
-
Recognise and show, using diagrams, families of common equivalent fractions
Examples
-
Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten
Examples
-
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
Examples
-
Add and subtract fractions with the same denominator
Examples
-
Recognise and write decimal equivalents of any number of tenths or hundredths
Examples
-
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
Examples
-
Round decimals with one decimal place to the nearest whole number
Examples
-
Compare numbers with the same number of decimal places up to two decimal places
Examples
-
Solve simple measure and money problems involving fractions and decimals to two decimal places
Examples
-
Recognise and show, using diagrams, families of common equivalent fractions
-
Number & Place Value
-
Measurement
Pupils build on their understanding of place value and decimal notation to record metric measures, including money. They use multiplication to convert from larger to smaller units. Perimeter can be expressed algebraically as 2(a + b) where a and b are the dimensions in the same unit. They relate area to arrays and multiplication.
-
Convert between different units of measure [for example, kilometre to metre; hour to minute]
Examples
-
Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres
Examples
-
Find the area of rectilinear shapes by counting squares
Examples
-
Estimate, compare and calculate different measures, including money in pounds and pence
Play Activities 125Examples
-
Read, write and convert time between analogue and digital 12- and 24-hour clocks
Examples
-
Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days
Examples
-
Convert between different units of measure [for example, kilometre to metre; hour to minute]
-
Geometry
-
Properties of Shapes
Pupils continue to classify shapes using geometrical properties, extending to classifying different triangles (for example, isosceles, equilateral, scalene) and quadrilaterals (for example, parallelogram, rhombus, trapezium). Pupils compare and order angles in preparation for using a protractor and compare lengths and angles to decide if a polygon is regular or irregular. Pupils draw symmetric patterns using a variety of media to become familiar with different orientations of lines of symmetry; and recognise line symmetry in a variety of diagrams, including where the line of symmetry does not dissect the original shape
-
Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
Examples
-
Identify acute and obtuse angles and compare and order angles up to two right angles by size
Examples
-
Identify lines of symmetry in 2-D shapes presented in different orientations
Examples
-
Complete a simple symmetric figure with respect to a specific line of symmetry
Examples
-
Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
-
Position & Direction
Pupils draw a pair of axes in one quadrant, with equal scales and integer labels. They read, write and use pairs of coordinates, for example (2, 5), including using coordinate-plotting ICT tools
-
Properties of Shapes
-
Statistics
Pupils understand and use a greater range of scales in their representations. Pupils begin to relate the graphical representation of data to recording change over time
-
Number
-
Year 3
-
Upper Key Stage 2
-
Year 5
-
Number
-
Number & Place Value
Pupils identify the place value in large whole numbers. They continue to use number in context, including measurement. Pupils extend and apply their understanding of the number system to the decimal numbers and fractions that they have met so far. They should recognise and describe linear number sequences, including those involving fractions and decimals, and find the term-to-term rule. They should recognise and describe linear number sequences (for example, 3, 3 1/2, 4, 4 1/2...), including those involving fractions and decimals, and find the term-to-term rule in words (for example, add 1/2).
-
Read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
Play Activities 189Examples
-
Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero
Examples
-
Round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000
Examples
-
Read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit
-
Addition & Subtraction
Pupils practise using the formal written methods of columnar addition and subtraction with increasingly large numbers to aid fluency (see Mathematics Appendix 1). They practise mental calculations with increasingly large numbers to aid fluency (for example, 12 462 - 2300 = 10 162)
-
Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
Play Activities 120Examples
-
Add and subtract numbers mentally with increasingly large numbers
Examples
-
Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
Examples
-
Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
-
Multiplication & Division
Pupils practise and extend their use of the formal written methods of short multiplication and short division (see Mathematics Appendix 1). They apply all the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculations. They use and understand the terms factor, multiple and prime, square and cube numbers. Pupils interpret non-integer answers to division by expressing results in different ways according to the context, including with remainders, as fractions, as decimals or by rounding (for example, 98 ÷ 4 = 98/4= 24 r 2 = 24 = 24.5 ? 25). Pupils use multiplication and division as inverses to support the introduction of ratio in year 6, for example, by multiplying and dividing by powers of 10 in scale drawings or by multiplying and dividing by powers of a 1000 in converting between units such as kilometres and metres. Distributivity can be expressed as a(b + c) = ab + ac. They understand the terms factor, multiple and prime, square and cube numbers and use them to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 92 x 10). Pupils use and explain the equals sign to indicate equivalence, including in missing number problems (for example, 13 + 24 = 12 + 25; 33 = 5 x )
-
Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers
Examples
-
Solve problems involving multiplication and division where larger numbers are used by decomposing them into their factors
Examples
-
Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
Examples
-
Establish whether a number up to 100 is prime and recall prime numbers up to 19
Examples
-
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
Examples
-
Multiply and divide numbers mentally drawing upon known facts
Examples
-
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
Play Activities 133Examples
-
Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
Examples
-
Recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)
Examples
-
Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes
Examples
-
Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
Examples
-
Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates
Examples
-
Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers
-
Fractions (Including Decimals & Percentages)
Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing proportions. They extend their knowledge of fractions to thousandths and connect to decimals and measures. Pupils connect equivalent fractions > 1 that simplify to integers with division and other fractions > 1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions. Pupils connect multiplication by a fraction to using fractions as operators (fractions of), and to division, building on work from previous years. This relates to scaling by simple fractions, including fractions > 1. Pupils practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed number. Pupils continue to practise counting forwards and backwards in simple fractions. Pupils continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities. Pupils extend counting from year 4, using decimals and fractions including bridging zero, for example on a number line. Pupils say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and are confident in checking the reasonableness of their answers to problems. They mentally add and subtract tenths, and one-digit whole numbers and tenths. They practise adding and subtracting decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 (for example, 0.83 + 0.17 = 1). Pupils should go beyond the measurement and money models of decimals, for example, by solving puzzles involving decimals. Pupils should make connections between percentages, fractions and decimals (for example, 100% represents a whole quantity and 1% is 1/100, 50% is 50/100, 25% is 25/100) and relate this to finding 'fractions of'.
-
Compare and order fractions whose denominators are all multiples of the same number
Examples
-
Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
Play Activities 140Examples
-
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]
Examples
-
Add and subtract fractions with the same denominator and denominators that are multiples of the same number
Examples
-
Read and write decimal numbers as fractions [for example, 0.71 = 71/100]
Examples
-
Round decimals with two decimal places to the nearest whole number and to one decimal place
Examples
-
Read, write, order and compare numbers with up to three decimal places
Examples
-
Solve problems involving number up to three decimal places
Play Activities 431Examples
-
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
Examples
-
Solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25
Examples
-
Compare and order fractions whose denominators are all multiples of the same number
-
Number & Place Value
-
Measurement
Pupils use their knowledge of place value and multiplication and division to convert between standard units. Pupils calculate the perimeter of rectangles and related composite shapes, including using the relations of perimeter or area to find unknown lengths. Missing measures questions such as these can be expressed algebraically, for example 4 + 2b = 20 for a rectangle of sides 2 cm and b cm and perimeter of 20cm. Pupils calculate the area from scale drawings using given measurements. Pupils use all four operations in problems involving time and money, including conversions (for example, days to weeks, expressing the answer as weeks and days).
-
Convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)
Examples
-
Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
Examples
-
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
Examples
-
Estimate volume [for example, using 1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water]
Examples
-
Solve problems involving converting between units of time
Examples
-
Use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling
Play Activities 166Examples
-
Convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)
-
Geometry
-
Properties of Shapes
Pupils become accurate in drawing lines with a ruler to the nearest millimetre, and measuring with a protractor. They use conventional markings for parallel lines and right angles. Pupils use the term diagonal and make conjectures about the angles formed between sides, and between diagonals and parallel sides, and other properties of quadrilaterals, for example using dynamic geometry ICT tools. Pupils use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems
-
Identify 3-D shapes, including cubes and other cuboids, from 2-D representations
Examples
-
Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
Examples
- Identify:
-
Use the properties of rectangles to deduce related facts and find missing lengths and angles
Examples
-
Identify 3-D shapes, including cubes and other cuboids, from 2-D representations
-
Position & Direction
Pupils recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2-D grid and coordinates in the first quadrant. Reflection should be in lines that are parallel to the axes
-
Properties of Shapes
-
Statistics
Pupils connect their work on coordinates and scales to their interpretation of time graphs. They begin to decide which representations of data are most appropriate and why
-
Number
-
Year 6
-
Number
-
Number & Place Value
Pupils use the whole number system, including saying, reading and writing numbers accurately
-
Addition, Subtraction, Multiplication & Division
Pupils practise addition, subtraction, multiplication and division for larger numbers, using the formal written methods of columnar addition and subtraction, short and long multiplication, and short and long division (see Mathematics Appendix 1). They undertake mental calculations with increasingly large numbers and more complex calculations. Pupils continue to use all the multiplication tables to calculate mathematical statements in order to maintain their fluency. Pupils round answers to a specified degree of accuracy, for example, to the nearest 10, 20, 50 etc., but not to a specified number of significant figures. Pupils explore the order of operations using brackets; for example, 2 + 1 x 3 = 5 and (2 + 1) x 3 = 9. Common factors can be related to finding equivalent fractions
-
Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
Examples
-
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
Examples
-
Perform mental calculations, including with mixed operations and large numbers
Examples
-
Identify common factors, common multiples and prime numbers
Examples
-
Use their knowledge of the order of operations to carry out calculations involving the four operations
Examples
-
Solve problems involving addition, subtraction, multiplication and division
Play Activities 241Examples
-
Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
Examples
-
Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
-
Fractions (Including Decimals & Percentages)
Pupils should practise, use and understand the addition and subtraction of fractions with different denominators by identifying equivalent fractions with the same denominator. They should start with fractions where the denominator of one fraction is a multiple of the other (for example, 1/2 + 1/8 = 5/8) and progress to varied and increasingly complex problems. Pupils should use a variety of images to support their understanding of multiplication with fractions. This follows earlier work about fractions as operators (fractions of), as numbers, and as equal parts of objects, for example as parts of a rectangle. Pupils use their understanding of the relationship between unit fractions and division to work backwards by multiplying a quantity that represents a unit fraction to find the whole quantity (for example, if 1/4 of a length is 36cm, then the whole length is 36 x 4 = 144cm). They practise calculations with simple fractions and decimal fraction equivalents to aid fluency, including listing equivalent fractions to identify fractions with common denominators. Pupils can explore and make conjectures about converting a simple fraction to a decimal fraction (for example, 3 ÷ 8 = 0.375). For simple fractions with recurring decimal equivalents, pupils learn about rounding the decimal to three decimal places, or other appropriate approximations depending on the context. Pupils multiply and divide numbers with up to two decimal places by one-digit and two-digit whole numbers. Pupils multiply decimals by whole numbers, starting with the simplest cases, such as 0.4 x 2 = 0.8, and in practical contexts, such as measures and money. Pupils are introduced to the division of decimal numbers by one-digit whole number, initially, in practical contexts involving measures and money. They recognise division calculations as the inverse of multiplication. Pupils also develop their skills of rounding and estimating as a means of predicting and checking the order of magnitude of their answers to decimal calculations. This includes rounding answers to a specified degree of accuracy and checking the reasonableness of their answers.
-
Compare and order fractions, including fractions >> 1
Examples
-
Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
Examples
-
Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4 x 1/2 = 1/8]
Examples
-
Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8]
Examples
-
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
Examples
-
Multiply one-digit numbers with up to two decimal places by whole numbers
Examples
-
Solve problems which require answers to be rounded to specified degrees of accuracy
Examples
-
Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts
Examples
-
Compare and order fractions, including fractions >> 1
-
Number & Place Value
-
Ratio & Proportion
Pupils recognise proportionality in contexts when the relations between quantities are in the same ratio (for example, similar shapes and recipes). Pupils link percentages or 360degrees to calculating angles of pie charts. Pupils should consolidate their understanding of ratio when comparing quantities, sizes and scale drawings by solving a variety of problems. They might use the notation a:b to record their work. Pupils solve problems involving unequal quantities, for example, 'for every egg you need three spoonfuls of flour', '3/5 of the class are boys'. These problems are the foundation for later formal approaches to ratio and proportion
-
Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
Examples
-
Solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison
Examples
-
Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
Examples
-
Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
-
Algebra
Pupils should be introduced to the use of symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as: missing numbers, lengths, coordinates and angles, formulae in mathematics and science, equivalent expressions (for example, a + b = b + a), generalisations of number patterns, number puzzles (for example, what two numbers can add up to)
-
Use simple formulae
Examples
-
Generate and describe linear number sequences
Examples
-
Express missing number problems algebraically
Examples
-
Use simple formulae
-
Measurement
Pupils connect conversion (for example, from kilometres to miles) to a graphical representation as preparation for understanding linear/proportional graphs. They know approximate conversions and are able to tell if an answer is sensible. Using the number line, pupils use, add and subtract positive and negative integers for measures such as temperature. They relate the area of rectangles to parallelograms and triangles, for example, by dissection, and calculate their areas, understanding and using the formulae (in words or symbols) to do this. Pupils could be introduced to compound units for speed, such as miles per hour, and apply their knowledge in science or other subjects as appropriate.
-
Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate
Examples
-
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
Examples
-
Recognise that shapes with the same areas can have different perimeters and vice versa
Examples
-
Recognise when it is possible to use formulae for area and volume of shapes
Examples
-
Calculate the area of parallelograms and triangles
Examples
-
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 [for example, mm3 and km3]
Examples
-
Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate
-
Geometry
-
Properties of Shapes
Pupils draw shapes and nets accurately, using measuring tools and conventional markings and labels for lines and angles. Pupils describe the properties of shapes and explain how unknown angles and lengths can be derived from known measurements. These relationships might be expressed algebraically for example, d = 2 x r; a = 180 - (b + c)
-
Recognise, describe and build simple 3-D shapes, including making nets
Examples
-
Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
Examples
-
Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles
Examples
-
Recognise, describe and build simple 3-D shapes, including making nets
-
Position & Direction
Pupils draw and label a pair of axes in all four quadrants with equal scaling. This extends their knowledge of one quadrant to all four quadrants, including the use of negative numbers. Pupils draw and label rectangles (including squares), parallelograms and rhombuses, specified by coordinates in the four quadrants, predicting missing coordinates using the properties of shapes. These might be expressed algebraically for example, translating vertex (a, b) to (a - 2, b + 3); (a, b) and (a + d, b + d) being opposite vertices of a square of side d.
-
Properties of Shapes
-
Statistics
Pupils connect their work on angles, fractions and percentages to the interpretation of pie charts. Pupils both encounter and draw graphs relating two variables, arising from their own enquiry and in other subjects. They should connect conversion from kilometres to miles in measurement to its graphical representation. Pupils know when it is appropriate to find the mean of a data set
-
Number
-
Year 5
-
Key Stage 3
- Working Mathematically
-
Subject Content
-
Number
-
Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ?, <, >, ?, ?
Examples
-
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 and the unique factorisation propert
Examples
-
Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
Play Activities 232Examples
-
Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
Examples
-
Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations
Examples
-
Interpret and compare numbers in standard form A x 10n 1?A< 10, where n is a positive or negative integer or zero
Examples
-
Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8)
Examples
-
Define percentage as 'number of parts per hundred', interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and w
Examples
-
Interpret fractions and percentages as operators
Play Activities 121Examples
-
Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]
Examples
-
Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a< x?b
Examples
-
Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ?, <, >, ?, ?
-
Algebra
-
Use and interpret algebraic notation, including:
-
Ab in place of a x b
Examples
-
3y in place of y + y + y and 3 x y
Examples
-
A2 in place of a x a, a3 in place of a x a x a; a2b in place of a x a x b
Examples
-
A/b in place of a ÷ b
Examples
-
Brackets
Examples
-
Ab in place of a x b
-
Substitute numerical values into formulae and expressions, including scientific formulae
Examples
-
Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
Examples
-
Simplify and manipulate algebraic expressions to maintain equivalence by:
-
Collecting like terms
Examples
-
Multiplying a single term over a bracket
Examples
-
Taking out common factors
Examples
-
Expanding products of two or more binomials
Examples
-
Collecting like terms
-
Understand and use standard mathematical formulae; rearrange formulae to change the subject
Examples
-
Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs
Examples
-
Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
Examples
-
Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
Examples
-
Interpret mathematical relationships both algebraically and graphically
Examples
-
Reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically
Examples
-
Use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations
Examples
-
Find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs
Examples
-
Generate terms of a sequence from either a term-to-term or a position-to-term rule
Examples
-
Recognise arithmetic sequences and find the nth term
Examples
-
Recognise geometric sequences and appreciate other sequences that arise
Examples
-
Use and interpret algebraic notation, including:
-
Ratio, Proportion & Change
-
Use scale factors, scale diagrams and maps
Examples
-
Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
Examples
-
Use ratio notation, including reduction to simplest form
Examples
-
Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
Play Activities 110Examples
-
Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
Examples
-
Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
Examples
-
Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
Examples
-
Solve problems involving direct and inverse proportion, including graphical and algebraic representations
Examples
-
Use compound units such as speed, unit pricing and density to solve problems
Examples
-
Use scale factors, scale diagrams and maps
-
Geometry & Measures
-
Derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)
Examples
-
Calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
Examples
-
Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
Examples
-
Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
Examples
-
Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
Examples
-
Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
Examples
-
Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
Examples
-
Understand and use the relationship between parallel lines and alternate and corresponding angles
Examples
-
Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons
Examples
-
Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras' Theorem, and use known results to obtain simple proofs
Examples
-
Use Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
Examples
-
Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D
Examples
-
Interpret mathematical relationships both algebraically and geometrically
Examples
-
Derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)
-
Probability
-
Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale
Play Activities 116Examples
-
Understand that the probabilities of all possible outcomes sum to 1
Examples
-
Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale
-
Statistics
-
Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range,
Examples
-
Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
Examples
-
Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs
Examples
-
Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range,
-
Number