Core learning in mathematics: links tothe 1999 Framework for teaching mathematicsA blue box on the right shows that there is no equivalent in the new objectives. A blue box on the left shows that there is no equivalent in the 1999 objectives.
A pink box shows that the equivalent objective was in a different year group in the 1999 Framework.
Foundation Stage
Using and applying mathematics2006 objectives 1999 Framework and Supplement of examples• Use developing mathematical ideas
and methods to solve practical problems
• Use developing mathematical ideas and methods to solve practical problems involving counting and comparing in a real or role play context.
Reception18, 20
• Match sets of objects to numerals that represent the number of objects
• Recognise numerals 1 to 9, then 0 and 10, then beyond 10.
Reception9
.• Sort objects, making choices and justifying decisions
• Sort and match objects, pictures or children themselves, justifying the decisions made.
Reception19
• Sort coins, including the £1 and £2 coins, and use them in role play to pay and give change.
Reception21
• Talk about, recognise and recreate simple patterns
• Talk about, recognise and recreate simple patterns, e.g. simple repeating or symmetrical patterns.
Reception18
• Describe solutions to practical problems, drawing on experience, talking about their own ideas, methods and choices
• Solve simple problems or puzzles in a practical context, and respond to 'What could we try next?'
Reception18
Counting and understanding number2006 objectives 1999 Framework and Supplement of examples• Say and use the number names in
order in familiar contexts• Say and use the number names in
order In familiar contexts such as number rhymes, songs, stories, counting games and activities.
Reception2
• Continue the count forwards or backwards from a given number.
Reception2, 3
• Know that numbers identify how many objects are in a set
• Count reliably up to 10 everyday objects
• Count reliably up to 10 everyday objects (first to 5, then 10, then beyond).
Measuring2006 objectives 1999 Framework and Supplement of examples• Use language such as ‘greater’,
‘smaller’, ‘heavier’ or ‘lighter’ to compare quantities
• Use language such as more or less, longer or shorter, heavier or lighter to compare two quantities, then more than two, by making direct comparisons of lengths or masses, and by filling and emptying containers.
Reception1922
• Use everyday language related to time; order and sequence familiar events
• Begin to understand and use the vocabulary of time; sequence familiar events.
Reception23
• Begin to know the days of the week in order.
Reception23
Handling data2006 objectives 1999 Framework and Supplement of examples• Sort familiar objects and count how
many objects share a particular property, presenting results using pictures, drawings or numerals
• Sort and match objects, pictures or children themselves, justifying the decisions made.
• Count reliably up to 10 everyday objects.
• Begin to record numbers, initially by making marks, progressing to simple tallying and writing numerals.
Reception194, 510
Year 1
Using and applying mathematics2006 objectives 1999 Framework and Supplement of examples• Solve problems involving counting,
adding, subtracting, doubling or halving in the context of numbers, measures or money, e.g. to ‘pay’ and ‘give change’
• Use mental strategies to solve simple problems set in ‘real life’, money or measurement contexts, using counting, addition, subtraction, halving or doubling.
• Recognise coins of different values. Find totals and change from up to 20p. Work out how to pay an exact sum using smaller coins
Year 166, 68
• Describe a problem using numbers, practical materials and diagrams; use these to solve the problem and set the solution back in the original context
• Choose and use appropriate number operations and mental strategies to solve problems.
• Use the +, – and = signs to record mental calculations in a number sentence.
Year 16024, 28
• Answer a question by selecting and using suitable equipment, and sorting information, shapes or objects; display results using tables and pictures
• Solve a given problem by sorting, classifying and organising information in simple ways. Discuss and explain results.
• Describe simple patterns and relationships involving numbers or shapes; decide whether examples satisfy given conditions
• Solve simple mathematical problems or puzzles; recognise and predict from simple patterns and relationships. Suggest extensions by asking ‘What if…?’ or ‘What could I try next?’
• Investigate a general statement about familiar numbers or shapes by finding examples that satisfy it.
Year 162, 64
• Describe ways of solving puzzles and problems, explaining choices and decisions orally or using pictures
• Explain methods and reasoning orally.
Year 164
Counting and understanding number2006 objectives 1999 Framework and Supplement of examples• Count reliably at least 20 objects,
recognising that when rearranged the number of objects stays the same; estimate a number of objects that can be checked by counting
• Count reliably at least 20 objects.• Give a sensible estimate of a
number of objects that can be checked by counting (e.g. up to about 30 objects).
Year 12, 4, 616
• Understand and use the vocabulary of comparing and ordering numbers, including ordinal numbers to at least 20.
Year 110
• Compare and order numbers, using the related vocabulary; use the equals (=) sign
• Order numbers to at least 20, and position them on a number track.
• Use the = sign to represent equality.• Compare two familiar numbers, say
which is more or less, and give a number which lies between them.
Year 110, 14
• Read and write numerals from 0 to 20, then beyond; use knowledge of place value to position these numbers on a number track and number line
• Read and write numerals from 0 to at least 20.
• Begin to partition two-digit numbers into a multiple of 10 and ones
Year 18
• Say the number that is one more or less than any given number and ten more or less for multiples of ten
• Within the range 0 to 30, say the number that is 1 or 10 more or less than any given number.
Year 112
• Use the vocabulary of halves and quarters in context
• Read the time to the hour or half hour on analogue clocks.
• Fold shapes in half.• Make whole turns and half turns.
Year 178, 82, 88
• Begin to recognise and find one half and one quarter of shapes and small numbers of objects.
• Begin to recognise that two halves or four quarters make one whole and that two quarters and one half are equivalent.
Knowing and using number facts2006 objectives 1999 Framework and Supplement of examples• Derive and recall all pairs of
numbers with a total of 10 and addition facts for totals to at least 5; work out the corresponding subtraction facts
• Know by heart all pairs of numbers with a total of 10 (e.g. 3 + 7), addition facts for all totals to at least 5, and the corresponding subtraction facts.
Year 130
• Count on or back in ones, twos, fives and tens and use this knowledge to derive the multiples of 2, 5 and 10 to the tenth multiple
• Count on and back in ones from any small number, and in tens from and back to zero;count on in twos from zero, then one; begin to recognise odd or even numbers to about 20 as ‘every other number’;count in steps of 5 from zero to 20 or more, then back again.
Year 14, 6
• Begin to recognise two-digit multiples of 2, 5 or 10.
Year 27
• Recall the doubles of all numbers to at least 10
• Know by heart doubles of all numbers to 10 and the corresponding halves.
Year 253
Calculating2006 objectives 1999 Framework and Supplement of examples• Relate addition to counting on;
recognise that addition can be done in any order; use practical and informal written methods to support the addition of a one-digit number or a multiple of 10 to a one-digit or two-digit number
• Use mental calculation strategies –several objectives, including:use known number facts and place value to add a pair of numbers.
• Begin to recognise that addition can be done in any order.
Year 132, 34, 36, 38, 40
• Understand subtraction as ‘take away’ and find a ‘difference’ by counting up; use practical and informal written methods to support the subtraction of a one-digit number from a one-digit or two-digit number and a multiple of 10 from a two-digit number
• Understand subtraction as ‘take away’ or ‘difference’.
• Use mental calculation strategies –several objectives, including:use known number facts and place value to subtract a pair of numbers.
Year 12832, 34, 36, 38, 40
• Use the vocabulary related to addition and subtraction and symbols to describe and record addition and subtraction number sentences
• Begin to use the +, – and = signs to record mental calculations in a number sentence, and to recognise the use of symbols such as to stand for an unknown number.
Year 124, 28
• Solve practical problems that involve combining groups of 2, 5 or 10, or sharing into equal groups
• Understand multiplication as repeated addition, and division as sharing.
Understanding shape2006 objectives 1999 Framework and Supplement of examples• Visualise and name common 2-D
shapes and 3-D solids and describe their features; use them to make patterns, pictures and models
• Describe features of familiar 3-D and 2-D shapes, including the cube, cuboid, sphere, cylinder, cone…, circle, triangle, square, rectangle, …, referring to properties such as the shapes of flat faces, or the number of faces or corners, or the number and types of sides.
• Make and describe models, patterns and pictures
• Fold shapes in half, then make them into symmetrical patterns.
• Use shapes to make, describe and continue repeating patterns.
Year 1808288
• Identify objects that turn about a point (e.g. scissors) or about a line (e.g. a door); recognise and make whole, half and quarter turns
• Talk about things that turn; make whole turns and half turns.
• Recognise quarter turns.
Years 1, 288, 89
• Visualise and use everyday language to describe the position of objects and direction and distance when moving them, e.g. when placing or moving objects on a games board
• Use everyday language to describe position, direction and movement.
Year 186, 88
Measuring2006 objectives 1999 Framework and Supplement of examples• Estimate, measure, weigh and
compare objects choosing and using suitable uniform non-standard or standard units and measuring instruments, e.g. a lever balance, metre stick or measuring jug
• Compare two lengths, masses or capacities by direct comparison; extend to more than two.
• Measure using uniform non-standard units (e.g. straws, wooden cubes, plastic weights, yogurt pots), or standard units (e.g. metre sticks, litre jugs).
• Suggest suitable units and measuring equipment to estimate or measure; record estimates and measurements as ‘about 3 beakers full’ or ‘about as heavy as 20 cubes’.
Year 17274, 76
• Use vocabulary related to time; order days of the week and months; read the time to the hour and half hour
• Understand and use the vocabulary related to time. Order familiar events in time. Know the days of the week and the seasons of the year.
• Read the time to the hour or half hour on analogue clocks.
Handling data2006 objectives 1999 Framework and Supplement of examples• Answer a question by recording
information in lists and tables; present outcomes using practical resources, pictures, block graphs or pictograms
• Use diagrams to sort objects into groups according to a given criterion; suggest a different criterion for grouping the same objects
• Solve a given problem by sorting, classifying and organising information in simple ways, such as:– using objects or pictures;– in a list or simple table.Discuss and explain results.
Year 190, 92
• Solve a given problem by sorting, classifying and organising information in:– a pictogram;– a block graph.
Year 291, 93
Year 2
Using and applying mathematics2006 objectives 1999 Framework and Supplement of examples• Solve problems involving addition,
subtraction, multiplication or division in contexts of numbers, measures or pounds and pence
• Use mental addition and subtraction, and simple multiplication and division, to solve simple word problems involving numbers in ‘real life’, money or measures, using one or two steps.
• Recognise all coins; begin to use £.p notation for money (e.g. know that £4.65 indicates £4 and 65p). Find totals, give change; work out which coins to pay.
Year 267, 69
• Identify and record the information or calculation needed to solve a puzzle or problem; carry out the steps or calculations and check the solution in the context of the problem
• Use the +, –, ×, ÷ and = signs to record mental calculations in a number sentence, and recognise the use of a symbol such as to stand for an unknown number.
• Choose and use appropriate operations and efficient calculation strategies (e.g. mental, mental with jottings) to solve problems.
• Check results of calculations, e.g. repeat addition in a different order, check with an equivalent calculation.
Year 225, 29,47, 496159
• Follow a line of enquiry; answer questions by choosing and using suitable equipment and selecting, organising and presenting information in lists, tables and simple diagrams
• Solve a given problem by sorting, classifying and organising information in simple ways. Discuss and explain results.
• Describe patterns and relationships involving numbers or shapes, make predictions and test these with examples
• Solve mathematical problems or puzzles, recognise simple patterns and relationships, generalise and predict. Suggest extensions by asking ‘What if…?’ or ‘What could I try next?’
• Investigate a general statement about familiar numbers or shapes by finding examples that satisfy it.
Year 263, 65
• Present solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentences
• Explain how a problem was solved orally and, where appropriate, in writing.
Year 265
Counting and understanding number2006 objectives 1999 Framework and Supplement of examples
• Read and write two- and three-digit numbers in figures and words; describe and extend number sequences and recognise odd and even numbers
• Read and write whole numbers to at least 100 in figures and words.
• Describe and extend simple number sequences; recognise odd and even numbers to at least 30.
Year 293, 5, 7
• Count up to 100 objects by grouping them and counting in tens, fives or twos; explain what each digit in a two-digit number represents, including numbers where 0 is a place holder; partition two-digit numbers in different ways, including into multiples of ten and one
• Count reliably up to 100 objects by grouping them, e.g. in tens, then in fives or twos.
• Know what each digit in a two-digit number represents, including 0 as a place holder; partition two-digit numbers into a multiple of ten and ones (TU).
Year 239, 13
• Order two-digit numbers and position them on a number line; use the greater than (>), less than (<) signs
• Order whole numbers to at least 100, and position them on a number line and 100 square.
Year 213, 15
• Use symbols correctly, including less than (<), greater than (>), equals (=).
Year 48
• Estimate a number of objects and round two-digit numbers to the nearest 10
• Give a sensible estimate of at least 50 objects.
• Round numbers less than 100 to the nearest 10.
Year 217, 19
• Find one half, one quarter and three quarters of shapes and sets of objects
• Begin to recognise and find one half and one quarter of shapes and small numbers of objects.
• Begin to recognise that two halves or four quarters make one whole and that two quarters and one half are equivalent.
Knowing and using number facts2006 objectives 1999 Framework and Supplement of examples• Derive and recall all addition and
subtraction facts for each number to at least 10, all pairs with totals to 20 and all pairs of multiples of 10 with totals up to 100
• Know by heart:all addition and subtraction facts for each number to at least 10; all pairs of numbers with a total of 20 (e.g. 13 + 7, 6 + 14); all pairs of multiples of 10 with a total of 100 (e.g. 30 + 70).
Year 231
• Understand that halving is the inverse of doubling and derive and recall doubles of all numbers to 20, and the corresponding halves
• Derive quickly doubles of all whole numbers to at least 20 (e.g. 17 × 2), and the corresponding halves (e.g. 36 ÷ 2).
Year 353
• Derive and recall multiplication facts for the 2, 5 and 10 times-tables and the related division facts; recognise multiples of 2, 5 and 10
• Know by heart multiplication facts for the 2 and 10 times-tables; begin to know multiplication facts for the 5 times-table. Derive quickly the corresponding division facts.
Year 253
• Know by heart multiplication facts for the 5 times-table.
Year 353
• Use knowledge of number facts and operations to estimate and check answers to calculations
• Check results of calculations by repeating addition in a different order, or with an equivalent calculation.
Year 259
Calculating2006 objectives 1999 Framework and Supplement of examples• Add or subtract mentally a single-
digit number or a multiple of 10 to or from any two-digit number; use practical and informal written methods to add and subtract two-digit numbers
• Use mental calculation strategies –several objectives, including:use known number facts and place value to add/subtract mentally;partition, then recombine;bridge through 10 or 20, then adjust;find a small difference by counting up from the smaller to the larger number.
• Extend understanding of the operations of addition and subtraction.
• Understand that more than two numbers can be added. Begin to add three single-digit numbers mentally.
Year 233–4125, 2927
• Understand that subtraction is the inverse of addition and vice versa and use this to derive and record related addition and subtraction number sentences
• Understand that subtraction is the inverse of addition (subtraction reverses addition).
• State the subtraction corresponding to a given addition, and vice versa.
• Represent repeated addition and arrays as multiplication, and sharing and repeated subtraction (grouping) as division; use practical and informal written methods and related vocabulary to support multiplication and division, including calculations with remainders
• Understand the operation of multiplication as repeated addition or as describing an array, and begin to understand division as grouping (repeated subtraction) or sharing.
• Use known number facts and place value to carry out mentally simple multiplications and divisions.
Year 247, 4957
• Begin to find remainders after simple division.
• Round up or down after division, depending on the context.
Year 351
• Use the symbols +, –, ×, ÷ and = to record and interpret number sentences involving all four operations; calculate the value of an unknown in a number sentence, e.g. 30 – = 24, ÷ 2 = 6
• Use the +, –, ×, ÷ and = signs to record mental calculations in a number sentence, and recognise the use of a symbol such as to stand for an unknown number.
Year 225, 2947, 49
Understanding shape2006 objectives 1999 Framework and Supplement of examples• Visualise common 2-D shapes and
3-D solids; identify shapes from pictures of them in different positions and orientations; sort, make and describe shapes, referring to their properties
• Use the mathematical names for common 3-D and 2-D shapes, including the pyramid, cylinder, pentagon, hexagon, octagon.
• Relate solid shapes to pictures of them.
• Sort shapes and describe some of their features, such as the number of sides and corners, symmetry.
• Make and describe shapes, pictures and patterns, e.g. using solid shapes, pinboard and elastic bands, squared paper, a programmable robot, …
Year 281, 83
• Identify reflective symmetry in patterns and 2-D shapes and draw lines of symmetry in shapes
• Begin to recognise line symmetry. Year 285
• Follow and give instructions involving position, direction and movement
• Use mathematical vocabulary to describe position, direction and movement, e.g. describe, place, tick, draw or visualise objects in given positions.
• Give instructions for moving along a route in straight lines and round right-angled corners, e.g. to pass through a simple maze.
Year 287, 89
• Recognise and use whole, half and quarter turns, both clockwise and anti-clockwise; know that a right angle represents a quarter turn
• Recognise whole, half and quarter turns, to the left or right, clockwise or anti-clockwise; know that a right angle is a measure of a quarter turn, and recognise right angles in squares and rectangles.
Measuring2006 objectives 1999 Framework and Supplement of examples• Estimate, compare and measure
lengths, weights and capacities, choosing and using standard units (m, cm, kg, litre) and suitable measuring instruments
• Estimate, measure and compare lengths, masses and capacities, using standard units (m, cm, kg, litre).
• Suggest suitable units and equipment for such measurements.
Year 273, 75
• Read the numbered divisions on a scale, and interpret the divisions between them, e.g. on a scale from 0 to 25 with intervals of 1 shown but only the divisions 0, 5, 10, 15 and 20 numbered; use a ruler to draw and measure lines to the nearest centimetre
• Read a simple scale to the nearest labelled division, including using a ruler to draw and measure lines to the nearest centimetre, recording estimates and measurements as ‘3 and a bit metres long’ or ‘about 8 centimetres’ or ‘nearly 3 kilograms heavy’.
Year 277
• Read scales to the nearest division (labelled or unlabelled).
Year 377
• Use units of time (seconds, minutes, hours, days) and know the relationships between them; read the time to the quarter hour; identify time intervals, including those that cross the hour
• Use units of time and know the relationships between them (second, minute, hour, day, week).
• Read the time to the quarter hour on an analogue clock and 12-hour digital clock; understand the notation 7:30.
• Solve word problems involving measures.
• Suggest suitable units to estimate or measure time.
Year 27971
Handling data2006 objectives 1999 Framework and Supplement of examples• Answer a question by collecting and
recording data in lists and tables; represent the data as block graphs or pictograms to show results; use ICT to organise and present data
• Solve a given problem by sorting, classifying and organising information in simple ways, such as:– in a list or simple table;– in a pictogram;– in a block graph.Discuss and explain results.
Year 291, 93
• Use lists, tables and diagrams to sort objects; explain choices using appropriate language, including not
Using and applying mathematics2006 objectives 1999 Framework and Supplement of examples• Solve one- and two-step problems
involving numbers, money or measures, including time, choosing and carrying out appropriate calculations
• Represent the information in a puzzle or problem using numbers, images or diagrams; use these to find a solution and present it in context, where appropriate using £.p notation or units of measure
• Solve word problems involving numbers in ‘real life’, money and measures, using one or more steps, including finding totals and giving change, and working out which coins to pay. Explain how the problem was solved.
• Choose and use appropriate operations (including multiplication and division) to solve word problems, and appropriate ways of calculating: mental, mental with jottings, pencil and paper.
• Recognise all coins and notes. Understand and use £.p notation (for example, know that £3.06 is £3 and 6p).
Year 367, 69, 7161
• Follow a line of enquiry by deciding what information is important; make and use lists, tables and graphs to organise and interpret the information
• Solve a given problem by organising and interpreting numerical data in simple lists, tables and graphs.
Year 391, 93
• Identify patterns and relationships involving numbers or shapes, and use these to solve problems
• Solve mathematical problems or puzzles, recognise simple patterns and relationships, generalise and predict. Suggest extensions by asking ‘What if…?’
• Describe and extend number sequences.
• Investigate a general statement about familiar numbers or shapes by finding examples that satisfy it.
Year 363, 653, 5, 7
• Describe and explain methods, choices and solutions to puzzles and problems, orally and in writing, using pictures and diagrams
• Explain methods and reasoning orally and, where appropriate, in writing.
65
Counting and understanding number2006 objectives 1999 Framework and Supplement of examples• Read, write and order whole
numbers to at least 1000 and position them on a number line; count on from and back to zero in single-digit steps or multiples of 10
• Read and write whole numbers to at least 1000 in figures and words.
• Order whole numbers to at least 1000, and position them on a number line.
Year 311, 13, 15
• Partition three-digit numbers into multiples of one hundred, ten and one in different ways
• Know what each digit represents, and partition three-digit numbers into a multiple of 100, a multiple of ten and ones (HTU).
• Round two- or three-digit numbers to the nearest 10 or 100 and give estimates for their sums and differences
• Round any two-digit number to the nearest 10 and any three-digit number to the nearest 100.
Year 319
• Round any positive integer less than 1000 to the nearest 10 or 100.
Year 410, 12
• Read and write proper fractions, e.g. 37, 910, interpreting the denominator as the parts of a whole and the numerator as the number of parts; identify and estimate fractions of shapes; use diagrams to compare fractions and establish equivalents
• Recognise unit fractions such as 12, 13, 14, 15, 110, … and use them to find fractions of shapes and numbers.
• Begin to recognise simple fractions that are several parts of a whole, such as 34, 23 or 310.
• Compare familiar fractions, e.g. know that on the number line one half lies between one quarter and three quarters.
• Begin to recognise simple equivalent fractions, e.g. five tenths and one half, five fifths and one whole.
• Estimate a simple fraction.
Year 321, 23
Knowing and using number facts2006 objectives 1999 Framework and Supplement of examples• Derive and recall all addition and
subtraction facts for each number to 20, sums and differences of multiples of 10 and number pairs that total 100
• Know by heart:all addition and subtraction facts for each number to 20;all pairs of multiples of 100 with a total of 1000 (e.g. 300 + 700);all pairs of multiples of 5 with a total of 100 (e.g. 35 + 65).
Year 331
• Derive quickly all number pairs that total 100 (e.g. 62 + 38, 75 + 25, 40 + 60).
Year 438
• Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and the corresponding division facts; recognise multiples of 2, 5 or 10 up to 1000
• Know by heart multiplication facts for the 2, 5 and 10 times-tables; begin to know the 3 and 4 times-tables. Derive quickly corresponding division facts.
• Recognise two-digit and three-digit multiples of 2, 5 or 10, and three-digit multiples of 50 and 100.
Year 3537
• Know by heart: multiplication facts for 2, 3, 4, 5 and 10 times-tables.
• Begin to know multiplication facts for the 6 times-tables.
• Derive quickly corresponding division facts.
Year 458
• Use knowledge of number operations and corresponding inverses, including doubling and halving, to estimate and check calculations
• Check subtraction with addition, halving with doubling and division with multiplication.
• Repeat addition or multiplication in a different order.
Calculating2006 objectives 1999 Framework and Supplement of examples• Add or subtract mentally
combinations of one- and two-digit numbers
• Use mental calculation strategies –several objectives, including:use known number facts and place value to add/subtract mentally;add and subtract mentally a ‘near multiple of 10’;add mentally three or four small numbers;find a difference by counting up.
Year 337, 39, 4133, 35
• Develop and use written methods to record, support or explain addition and subtraction of two- and three-digit numbers
• Use informal pencil and paper methods to support, record or explain HTU ± TU, HTU ± HTU.
• Begin to use column addition and subtraction for HTU ± TU where the calculation cannot easily be done mentally.
Year 343, 45
• Multiply one- and two-digit numbers by 10 or 100, and describe the effect
• Multiply mentally by 10/100 by shifting the digits one/two places to the left.
Year 355
• Use practical and informal written methods to support multiplication and division of two-digit numbers (e.g. 13 × 3, 30 ÷ 4); round remainders up or down, depending on the context
• Use known number facts and place value to carry out mentally simple multiplications and divisions.
• Begin to find remainders after simple division; round up or down after division, depending on the context.
Year 351, 57
• Understand that division is the inverse of multiplication and vice versa and use to derive and record related multiplication and division number sentences
• Recognise that division is the inverse of multiplication, and that halving is the inverse of doubling.
• Say or write a division statement corresponding to a given multiplication statement.
Year 34955
• Find unit fractions of numbers and quantities, e.g. ½, ⅓, ¼ and 16 of 12 litres
• Recognise unit fractions such as 12, 13, 14, 1/5, 110, … and use them to find fractions of shapes and numbers.
Understanding shape2006 objectives 1999 Framework and Supplement of examples• Relate 2-D shapes and 3-D solids to
drawings of them; describe, visualise, classify, draw and make the shapes
• Relate solid shapes to pictures of them.
• Classify and describe 3-D and 2-D shapes, including the hemisphere, prism, semi-circle, quadrilateral… referring to properties such as reflective symmetry, the number or shapes of faces, the number of sides/edges and vertices, whether sides/edges are the same length, whether or not angles are right angles…
• Make and describe shapes and patterns, e.g. explore the different shapes that can be made from four cubes.
Year 381, 83
• Draw and complete shapes with reflective symmetry and draw the reflection of a shape in a mirror line along one side
• Identify and sketch lines of symmetry in simple shapes, and recognise shapes with no lines of symmetry.
• Sketch the reflection of a simple shape in a mirror line along one edge.
Year 385
• Read and record the vocabulary of position, direction and movement, using the four compass directions to describe movement about a grid
• Read and begin to write the vocabulary related to position, direction and movement, e.g. describe and find the position of a square on a grid of squares with the rows and columns labelled.
• Recognise and use the four compass directions N, S, E, W.
Year 387
• Use a set-square to draw right angles and to identify right angles in 2-D shapes; compare angles with a right angle; recognise that a straight line is equivalent to two right angles
• Identify right angles in 2-D shapes and the environment.
• Recognise that a straight line is equivalent to two right angles.
• Compare angles with a right angle.
Year 389
Measuring2006 objectives 1999 Framework and Supplement of examples• Know the relationships between
kilometres and metres, metres and centimetres, kilograms and grams, litres and millilitres; choose and use appropriate units to estimate, measure and record measurements
• Measure and compare using standard units (km, m, cm, kg, g, l, ml)
• Know the relationships between kilometres and metres, metres and centimetres, kilograms and grams, litres and millilitres.
• Begin to use decimal notation for metres and centimetres.
• Suggest suitable units and measuring equipment to estimate or measure length, mass or capacity.
• Read, to the nearest division and half-division, scales that are numbered or partially numbered; use the information to measure and draw to a suitable degree of accuracy
• Read scales to the nearest division (labelled or unlabelled); record estimates and measurements to the nearest whole or half unit (e.g. ‘about 3.5 kg’), or in mixed units (e.g. ‘3 m and 20 cm’).
• Use a ruler to draw and measure lines to the nearest half centimetre
Year 377
• Read the time on a 12-hour digital clock and to the nearest five minutes on an analogue clock; calculate time intervals and find start or end times for a given time interval
• Read the time to 5 minutes on an analogue clock and 12-hour digital clock; use the notation 9:40.
• Solve word problems involving measures.
Year 37971
• Read the time to the nearest minute from a 12-hour digital clock.
Year 498, 100
Handling data2006 objectives 1999 Framework and Supplement of examples• Answer a question by collecting,
organising and interpreting data; use tally charts, frequency tables, pictograms and bar charts to represent results and illustrate observations; use ICT to create a simple bar chart
• Use Venn diagrams or Carroll diagrams to sort data and objects using more than one criterion
• Solve a given problem by organising and interpreting numerical data in simple lists, tables and graphs, e.g.– simple frequency tables;– pictograms;– bar charts;– Venn and Carroll diagrams (one
criterion).
Year 391, 93
• Solve a given problem by organising and interpreting numerical data in Venn and Carroll diagrams (two criteria).
Using and applying mathematics2006 objectives 1999 Framework and Supplement of examples• Solve one- and two-step problems
involving numbers, money or measures, including time; choose and carry out appropriate calculations, using calculator methods where appropriate
• Represent a puzzle or problem using number sentences, statements or diagrams; use these to solve the problem; present and interpret the solution in the context of the problem
• Use all four operations to solve word problems involving numbers in ‘real life’, money and measures (including time), using one or more steps, including converting pounds to pence and metres to centimetres and vice versa.
• Choose and use appropriate number operations and appropriate ways of calculating (mental, mental with jottings, pencil and paper) to solve problems.
• Round up or down after division, depending on the context.
Year 482, 84, 86, 88, 1007456
• Choose appropriate ways of calculating: calculator.
Year 575
• Suggest a line of enquiry and the strategy needed to follow it; collect, organise and interpret selected information to find answers
• Solve a problem by collecting quickly, organising, representing and interpreting data in tables, charts, graphs and diagrams, including those generated by a computer.
Year 4114, 116
• Identify and use patterns, relationships and properties of numbers or shapes; investigate a statement involving numbers and test it with examples
• Solve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions by asking ‘What if…?’
• Recognise and extend number sequences.
• Make and investigate a general statement about familiar numbers or shapes by finding examples that satisfy it.
Year 47816, 1880
• Report solutions to puzzles and problems, giving explanations and reasoning orally and in writing, using diagrams and symbols
• Explain methods and reasoning about numbers orally and in writing.
Year 476
Counting and understanding number2006 objectives 1999 Framework and Supplement of examples• Recognise and continue number
sequences formed by counting on or back in steps of constant size
• Recognise and extend number sequences formed by counting in steps of constant size, extending beyond zero when counting back.
Year 416
• Partition, round and order four-digit whole numbers; use positive and negative numbers in context and position them on a number line; state inequalities using the symbols < and >, e.g. –3 > –5, –1 < +1
• Recognise negative numbers in context (e.g. on a number line, on a temperature scale).
• Use symbols correctly, including less than (<), greater than (>), equals (=).
• Use decimal notation for tenths and hundredths and partition decimals; relate the notation to money and measurement; position one- and two-place decimals on a number line
• Understand decimal notation and place value for tenths and hundredths, and use it in context, e.g. order amounts of money; convert a sum of money such as £13.25 to pence, or a length such as 125 cm to metres; round a sum of money to the nearest pound.
Year 428
• Order a set of numbers or measurements with one or two decimal places.
Year 529
• Recognise the equivalence between decimal and fraction forms of one half, quarters, tenths and hundredths
• Recognise the equivalence between the decimal and fraction forms of tenths and hundredths (e.g. 710 = 0.7, 27100 = 0.27).
Year 531
• Use diagrams to identify equivalent fractions, e.g. 68 and 34, or 70100 and 710; interpret mixed numbers and position them on a number line, e.g. 312
• Begin to relate fractions to division and find simple fractions such as 12, 13, 14, 15, 110, … of numbers.
• Find fractions such as 23, 34, 35, 710, … of shapes.
• Recognise the equivalence of simple fractions
• Order a set of fractions such as 2, 234, 134, 212, 112, and position them on a number line.
Year 422, 24
• Use the vocabulary of ratio and proportion to describe the relationship between two quantities, e.g. there are 2 red beads to every 3 blue beads, or 2 beads in every 5 beads are red; estimate a proportion, e.g. ‘about one quarter of the apples in the box are green’
• Begin to use ideas of simple proportion: for example, ‘one for every …’ and ‘one in every …’.
Year 426
• Solve simple problems using ideas of ratio and proportion (‘one for every…’ and ‘one in every…’).
Year 527
Knowing and using number facts2006 objectives 1999 Framework and Supplement of examples• Use knowledge of addition and
subtraction facts and place value to derive sums and differences of pairs of multiples of 10, 100 or 1000
• Derive quickly all pairs of multiples of 50 with a total of 1000 (e.g. 850 + 150).
• Add three two-digit multiples of 10, such as 40 + 70 + 50.
• Use known number facts and place value to add or subtract mentally.
Year 4384244, 46
• Use known number facts and place value for mental addition and subtraction (e.g. 470 + 380, 810 – 380).
Year 545, 47
• Identify the doubles of two-digit numbers; use to calculate doubles of multiples of 10 and 100 and derive the corresponding halves
• Derive quickly doubles of all whole numbers to 50, multiples of 10 to 500 and multiples of 100 to 5000, and the corresponding halves.
• Derive and recall multiplication facts up to 10 × 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple
• Know by heart all multiplication facts up to 10 × 10; derive quickly corresponding division facts.
• Recognise multiples of 6, 7, 8, 9, up to the 10th multiple.
Year 55919
• Recognise multiples of 2, 3, 4, 5 and 10, up to the tenth multiple.
Year 418
• Use knowledge of rounding, number operations and inverses to estimate and check calculations
• Check results of calculations. Year 472
• Identify pairs of fractions that total 1 • Identify two simple fractions with a total of 1 (e.g. 310 and 710).
Year 422
Calculating2006 objectives 1999 Framework and Supplement of examples• Add or subtract mentally pairs of
two-digit whole numbers, e.g. 47 + 58, 91 – 35
• Use known number facts and place value to add or subtract mentally, including any pair of two-digit whole numbers.
Year 440, 42,44, 46
• Refine and use efficient written methods to add and subtract two- and three-digit whole numbers and £.p
Develop and refine written methods for:column addition and subtraction of two whole numbers less than 1000, and addition of more than two such numbers;money calculations (e.g. £7.85 ± £3.49).
Year 448, 50
• Multiply and divide numbers to 1000 by 10 and then 100 (whole number answers), understanding the effect; relate to scaling up or down
• Multiply or divide any integer up to 1000 by 10 (whole-number answers), and understand the effect; begin to multiply by 100.
Year 46
• Develop and use written methods to record, support and explain multiplication and division of two-digit numbers by a one-digit number, including division with remainders, e.g. 15 × 9, 98 ÷ 6
• Develop and refine written methods for TU × U, TU ÷ U.
• Find remainders after division; divide a whole number of pounds by 2, 4, 5 or 10 to give £.p; round up or down after division, depending on the context.
Year 466, 6856
• Find fractions of numbers, quantities or shapes, e.g. 15 of 30 plums, 38 of a 6 by 4 rectangle
• Begin to relate fractions to division and find simple fractions such as 12, 13, 14, 15, 110, … of numbers or quantities.
• Find fractions such as 23, 34, 35, 710, … of shapes.
Year 424
• Use a calculator to carry out one- and two-step calculations involving all four operations; recognise negative numbers in the display, correct mistaken entries and interpret the display correctly in the context of money
• Develop calculator skills and use a calculator effectively.
Understanding shape2006 objectives 1999 Framework and Supplement of examples• Draw polygons and classify them by
identifying their properties, including their line symmetry
• Classify polygons using criteria such as number of right angles, whether or not they are regular, symmetry properties.
• Make shapes, e.g. construct polygons by paper folding or using pinboard, and discuss properties such as lines of symmetry.
Year 4102, 104
• Visualise 3-D objects from 2-D drawings and make nets of common solids
• Visualise 3-D shapes from 2-D drawings and identify simple nets of solid shapes.
Year 4104
• Recognise horizontal and vertical lines; use the eight compass points to describe direction; describe and identify the position of a square on a grid of squares
• Recognise simple examples of horizontal and vertical lines.
• Use the eight compass directions N, S, E, W, NE, NW, SE, SW.
• Recognise positions and directions: for example, describe and find the position of a point on a grid of squares where the lines are numbered.
Year 4108
• Know that angles are measured in degrees and that one whole turn is 360°; draw, compare and order angles less than 180°
• Begin to know that angles are measured in degrees and that one whole turn is 360° or 4 right angles; a quarter turn is 90° or one right angle; half a right angle is 45°; start to order a set of angles less than 180°.
Year 4110
Measuring2006 objectives 1999 Framework and Supplement of examples• Choose and use standard metric
units and their abbreviations when estimating, measuring and recording length, weight and capacity; know the meaning of kilo, centi and milli and, where appropriate, use decimal notation to record measurements, e.g. 1.3 m or 0.6 kg
• Use, read and write standard metric units (km, m, cm, mm, kg, g, l, ml), including their abbreviations, and imperial units (mile, pint).
• Know and use the relationships between familiar units of length, mass and capacity.
• Know the equivalent of one half, one quarter, three quarters and one tenth of 1 km, 1 m, 1 kg, 1 litre in m, cm, g, ml.
• Suggest suitable units and measuring equipment to estimate or measure length, mass or capacity.
Year 49092, 94
• Interpret intervals and divisions on partially numbered scales and record readings accurately, where appropriate to the nearest tenth of a unit
• Record estimates and readings from scales to a suitable degree of accuracy.
• Draw rectangles and measure and calculate their perimeters, find the area of rectilinear shapes drawn on a square grid by counting squares
• Measure and calculate the perimeter and area of rectangles and other simple shapes, using counting methods and standard units (cm, cm2).
Year 496
• Read time to the nearest minute; use am, pm and 12-hour clock notation; choose units of time to measure time intervals; calculate time intervals from clocks and timetables
• Use am and pm and the notation 9:53.
• Read simple timetables.• Solve word problems involving time.
Year 498, 10088
Handling data2006 objectives 1999 Framework and Supplement of examples• Answer a question by identifying
what data to collect; organise, present, analyse and interpret the data in tables, diagrams, tally charts, pictograms and bar charts, using ICT where appropriate
• Compare the impact of representations where scales have intervals of differing step size
• Solve a problem by collecting quickly, organising, representing and interpreting data in tables, charts, graphs and diagrams, including those generated by a computer, e.g.– tally charts and frequency tables;– pictograms – symbol representing
2, 5, 10 or 20 units;– bar charts – intervals labelled in
2s, 5s, 10s or 20s;– Venn and Carroll diagrams (two
Using and applying mathematics2006 objectives 1999 Framework and Supplement of examples• Solve one- and two-step problems
involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use
• Represent a problem by identifying and recording the calculations needed to solve it; find possible solutions and confirm them in the context of the problem
• Use all four operations to solve simple word problems involving numbers and quantities based on ‘real life’, money and measures (including time), using one or more steps, including finding simple percentages.
• Choose and use appropriate number operations to solve problems, and appropriate ways of calculating: mental, mental with jottings, written methods, calculator.
• Round up or down after division, depending on the context.
Year 583, 85,87, 89, 1017557
• Plan and pursue an enquiry; present evidence by collecting, organising and interpreting information; suggest extensions to the enquiry
• Solve a problem by representing and interpreting data in tables, charts, graphs and diagrams, including those generated by a computer.
Year 5113–117
• Explore patterns, properties and relationships and propose a general statement involving numbers or shapes; identify examples for which the statement is true or false
• Solve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions asking ‘What if…?’
• Recognise and extend number sequences.
• Make and investigate a general statement about familiar numbers or shapes by finding examples that satisfy it; explain a generalised relationship (formula) in words.
Year 57917, 19, 2181
• Explain reasoning using diagrams, graphs and text; refine ways of recording using images and symbols
• Explain methods and reasoning, orally and in writing.
Year 577
Counting and understanding number2006 objectives 1999 Framework and Supplement of examples• Count from any given number in
whole number and decimal steps, extending beyond zero when counting backwards; relate the numbers to their position on a number line
• Recognise and extend number sequences formed by counting from any number in steps of constant size, extending beyond zero when counting back, e.g. count on in steps of 25 to 1000, and then back; count on or back in steps of 0.1, 0.2, 0.3, …
• Explain what each digit represents in whole numbers and decimals with up to two places, and partition, round and order these numbers
• Read and write whole numbers in figures and words, and know what each digit represents.
• Know what each digit represents in a number with up to two decimal places.
Year 5329
• Express a smaller whole number as a fraction of a larger one, e.g. recognise that 5 out of 8 is 58; find equivalent fractions, e.g. 710 = 1420, or 1910 = 1910; relate fractions to their decimal representations
• Relate fractions to their decimal representations: that is, recognise the equivalence between the decimal and fraction forms of one half, one quarter, three quarters… and tenths and hundredths (e.g. 710 = 0.7, 27100 = 0.27).
• Recognise when two simple fractions are equivalent, including relating hundredths to tenths (e.g. 70100 = 710).
• Change an improper fraction to a mixed number (e.g. change 1310 to 1310).
Year 53123
• Understand percentage as the number of parts in every 100 and express tenths and hundredths as percentages
• Begin to understand percentage as the number of parts in every 100.
• Express one half, one quarter, three quarters, and tenths and hundredths, as percentages (e.g. know that 34 = 75%).
Year 533
• Use sequences to scale numbers up or down; solve problems involving proportions of quantities, e.g. decrease quantities in a recipe designed to feed six people
• Solve problems involving ratio and proportion.
Year 627
Knowing and using number facts2006 objectives 1999 Framework and Supplement of examples• Use knowledge of place value and
addition and subtraction of two-digit numbers to derive sums and differences, doubles and halves of decimals, e.g. 6.5 ± 2.7, halve 5.6, double 0.34
• Derive quickly pairs of decimals that total 1 (e.g. 0.2 + 0.8) or 10 (e.g. 6.2 + 3.8).
• Use known number facts and place value for mental addition and subtraction (e.g. 7.4 + 9.8, 9.2 – 8.6).
Year 53945, 47
• Derive quickly doubles of two-digit decimals (e.g. 3.8 × 2, 0.76 × 2), and the corresponding halves.
Year 659
• Recall quickly multiplication facts up to 10 × 10, use to multiply pairs of multiples of 10 and 100 and derive quickly corresponding division facts
• Know by heart all multiplication facts up to 10 × 10; derive quickly division facts.
• Use known facts and place value to multiply and divide mentally.
Year 55965
• Identify pairs of factors of two-digit whole numbers and find common multiples, e.g. for 6 and 9
• Find all the pairs of factors of any number up to 100.
• Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations
• Check results of calculations. Year 573
Calculating2006 objectives 1999 Framework and Supplement of examples• Extend mental methods for whole-
number calculations, e.g. to multiply a two-digit by one-digit number (e.g. 12 × 9), to multiply by 25 (e.g. 16 × 25), to subtract one near multiple of 1000 from another (e.g. 6070 – 4097)
• Use mental calculation strategies –several objectives, including:partitioning;find a difference by counting up (e.g. 5003 – 4996);se related facts, e.g. to multiply by 25, multiply by 100 then divide by 4.
Year 541, 4361, 63, 65
• Use efficient written methods to add and subtract whole numbers and decimals with up to two places
• Extend written methods to:addition of more than two integers; addition or subtraction of a pair of decimal fractions (e.g. £29.78 + £53.34).
Year 549, 51
• Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000
• Multiply and divide decimals by 10 or 100 and integers by 1000 explain the effect.
Year 67
• Refine and use efficient written methods to multiply and divide HTU × U, TU × TU, U.t × U, and HTU ÷ U
• Extend written methods to HTU or U.t by U; long multiplication of TU by TU; HTU by U (integer remainder).
Year 567, 69
• Find fractions using division, e.g. 1100
of 5 kg, and percentages of numbers and quantities, e.g. 10%, 5% and 15% of £80
• Relate fractions to division, and use division to find simple fractions, including tenths and hundredths, of numbers and quantities (e.g. 34 of 12, 110 of 50, 1100 of £3).
• Find simple percentages of small whole-number quantities (e.g. 25% of £8).
Year 52533
• Use a calculator to solve problems, including those involving decimals or fractions, e.g. to find 34 of 150 g; interpret the display correctly in the context of measurement
• Develop calculator skills and use a calculator effectively.
Year 571
Understanding shape2006 objectives 1999 Framework and Supplement of examples• Identify, visualise and describe
properties of rectangles, triangles, regular polygons and 3-D solids; use knowledge of properties to draw 2-D shapes and identify and draw nets of 3-D shapes
• Recognise properties of rectangles; classify triangles (isosceles, equilateral, scalene), using criteria such as equal sides, equal angles, lines of symmetry.
• Make shapes with increasing accuracy; visualise 3-D shapes from 2-D drawings; identify different nets for an open cube.
• Read and plot co-ordinates in the first quadrant; recognise parallel and perpendicular lines in grids and shapes; use a set-square and ruler to draw shapes with perpendicular or parallel sides
• Read and plot co-ordinates in the first quadrant.
• Recognise perpendicular and parallel lines.
Year 5109
• Complete patterns with up to two lines of symmetry and draw the position of a shape after a reflection or translation
• Recognise reflective symmetry in regular polygons, e.g. know that a square has four lines of symmetry and an equilateral triangle has three.
• Complete symmetrical patterns with two lines of symmetry at right angles (using squared paper or pegboard).
• Recognise where a shape will be after reflection in a mirror line parallel to one side (sides not all parallel or perpendicular to the mirror line).
• Recognise where a shape will be after a translation.
Year 5107
• Estimate, draw and measure acute and obtuse angles using an angle measurer or protractor to a suitable degree of accuracy; calculate angles in a straight line
• Understand and use angle measure in degrees; identify, estimate and order acute and obtuse angles.
• Use a protractor to measure and draw acute and obtuse angles to the nearest 5°.
• Calculate angles in a straight line.
Year 5111
Measuring2006 objectives 1999 Framework and Supplement of examples• Read, choose, use and record
standard metric units to estimate and measure length, weight and capacity to a suitable degree of accuracy, e.g. the nearest centimetre; convert larger to smaller units using decimals to one place, e.g. change 2.6 kg to 2600 g
• Use, read and write standard metric units (km, m, cm, mm, kg, g, l, ml), including their abbreviations, and relationships between them. Convert larger to smaller units (e.g. km to m, m to cm or mm, kg to g, l to ml).
• Suggest suitable units and measuring equipment to estimate or measure length, mass or capacity.
Year 59193
• Interpret a reading that lies between two unnumbered divisions on a scale
• Record estimates and readings from scales to a suitable degree of accuracy.
Year 595
• Draw and measure lines to the nearest millimetre; measure and calculate the perimeter of regular and irregular polygons; use the formula for the area of a rectangle to calculate its area
• Measure and draw lines to the nearest millimetre.
• Measure and calculate perimeters of rectangles and regular polygons.
• Understand area measured in square centimetres (cm2); use the formula for the area of a rectangle.
Year 597
• Read timetables and time using 24-hour clock notation; use a calendar to calculate time intervals
• Read the time on a 24-hour digital clock and use 24-hour clock notation, such as 19:53. Use timetables.
Handling data2006 objectives 1999 Framework and Supplement of examples• Describe the occurrence of familiar
events using the language of chance or likelihood
• Discuss the chance or likelihood of particular events.
Year 5113
• Answer a set of related questions by collecting, selecting and organising relevant data; draw conclusions, using ICT to present features, and identify further questions to ask
• Construct frequency tables, pictograms and bar and line graphs to represent the frequencies of events and changes over time
• Solve a problem by representing and interpreting data in tables, charts, graphs and diagrams, including those generated by a computer, e.g. bar line charts, vertical axis labelled in 2s, 5s, 10s, 20s or 100s, first where intermediate points have no meaning (e.g. scores on a dice rolled 50 times), then where they may have meaning (e.g. room temperature over time).
Using and applying mathematics2006 objectives 1999 Framework and Supplement of examples• Solve multi-step problems, and
problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use
• Tabulate systematically the information in a problem or puzzle; identify and record the steps or calculations needed to solve it, using symbols where appropriate; interpret solutions in the original context and check their accuracy
• Identify and use appropriate operations (including combinations of operations) to solve word problems involving numbers and quantities based on ‘real life’, money or measures (including time), using one or more steps; explain methods and reasoning.
• Choose and use appropriate number operations to solve problems, and appropriate ways of calculating: mental, mental with jottings, written methods, calculator.
• Round up or down after division, depending on the context.
Year 683, 8587, 89, 1017557
• Suggest, plan and develop lines of enquiry; collect, organise and represent information, interpret results and review methods; identify and answer related questions
• Solve a problem by representing, extracting and interpreting data in tables, graphs, charts and diagrams, including those generated by a computer.
Year 6115, 117
• Represent and interpret sequences, patterns and relationships involving numbers and shapes; suggest and test hypotheses; construct and use simple expressions and formulae in words then symbols, e.g. the cost of c pens at 15 pence each is 15c pence
• Solve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions asking ‘What if…?’
• Recognise and extend number sequences.
• Make and investigate a general statement about familiar numbers or shapes by finding examples that satisfy it; develop from explaining a generalised relationship in words to expressing it in a formula using letters as symbols (e.g. the cost of n articles at 15p each).
Year 67917, 19, 2181
• Explain reasoning and conclusions, using words, symbols or diagrams as appropriate
• Explain methods and reasoning, orally and in writing.
Year 677
Counting and understanding number2006 objectives 1999 Framework and Supplement of examples• Find the difference between a
positive and a negative integer, or two negative integers, in context
• Find the difference between a positive and a negative integer, or two negative integers, in a context such as temperature or the number line
• Use decimal notation for tenths, hundredths and thousandths, partition, round and order decimals with up to three places, and position them on the number line
• Know what each digit represents in a number with up to three decimal places.
• Order numbers or measurements with up to three decimal places.
• Consolidate rounding an integer to the nearest 10, 100 or 1000.
• Round a number with two decimal places to the nearest tenth or to the nearest whole number.
Year 629Year 61331
• Round whole numbers to the nearest 10, 100 or 1000, and decimals to the nearest whole number or one decimal place.
Year 742, 44
• Express a larger whole number as a fraction of a smaller one e. g. recognise that 8 slices of a 5-slice pizza represents 85 or 1 35 pizzas; simplify fractions by cancelling common factors; order a set of fractions by converting them to fractions with a common denominator
• Reduce a fraction to its simplest form by cancelling common factors in the numerator and denominator.
• Order fractions such as 23, 34 and 56 by converting them to fractions with a common denominator, and position them on a number line.
Year 623
• Express one quantity as a percentage of another, e.g. express £400 as a percentage of £1000; find equivalent percentages, decimals and fractions
• Understand percentage as the number of parts in every hundred. Find simple percentages of whole number quantities.
• Recognise the equivalence between the decimal and fraction forms of one half, one quarter, three quarters, one eighth… and tenths, hundredths and thousandths.
• Express simple fractions such as one half, one quarter, three quarters, one third, two thirds…, and tenths and hundredths, as percentages (e.g. know that 13 = 3313%).
Year 63133
• Solve simple problems involving direct proportion by scaling quantities up or down
• Use the vocabulary of estimation and approximation.
• Solve simple problems involving ratio and proportion.
Year 61127
Knowing and using number facts2006 objectives 1999 Framework and Supplement of examples• Use knowledge of place value and
multiplication facts to 10 × 10 to derive related multiplication and division facts involving decimal numbers, e.g. 0.8 × 7, 4.8 ÷ 6
• Use mental calculation strategies –several objectives, including:partition;use factors;use known number facts and place value to consolidate mental multiplication and division.
• Use knowledge of multiplication facts to derive quickly squares of numbers to 12 × 12 and the corresponding squares of multiples of 10
• Recognise squares of numbers to at least 12 × 12.
• Derive quickly squares of multiples of 10 (e.g. 60 × 60).
Year 62159
• Recognise that prime numbers have only two factors and identify prime numbers less than 100; find the prime factors of two-digit numbers
• Recognise prime numbers; factorise numbers to 100 into prime factors.
Year 621
• Use approximations, inverse operations and tests of divisibility to estimate and check results
• Check results of calculations.• Know and apply simple tests of
divisibility.
Year 67319
Calculating2006 objectives 1999 Framework and Supplement of examples• Calculate mentally with integers and
decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U
• Use known number facts and place value to consolidate mental addition/subtraction (e.g. 9.2 – 8.6, 7.4 + 9.8).
• Use known number facts and place value to consolidate mental multiplication and division.
Year 645, 4765
• Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two- and three-digit integers by a two-digit integer
• Extend written methods to column addition and subtraction of numbers involving decimals.
• Extend written methods to short multiplication of numbers involving decimals; short division of numbers involving decimals.
• Express a quotient as a fraction or as a decimal rounded to one decimal place.
Year 649, 5167, 6957
• Relate fractions to multiplication and division, e.g. 6 ÷ 2 = 12 of 6 = 6 × 12; express a quotient as a fraction or decimal, e.g. 67 ÷ 5 = 13.4 or 1325; find fractions and percentages of whole-number quantities, e.g. 58 of 96, 65% of £260
• Find fractions, including tenths and hundredths, of numbers or quantities (e.g. 58 of 32, 710 of 40, 9100 of 400 cm).
• Find simple percentages of small whole-number quantities (e.g. find 10% of £500, then 20%, 40% and 80% by doubling).
Year 62533
• Use a calculator to solve problems involving multi-step calculations
• Develop calculator skills and use a calculator effectively.
Year 671
Understanding shape2006 objectives 1999 Framework and Supplement of examples• Describe, identify and visualise
parallel and perpendicular edges or faces and use these properties to classify 2-D shapes and 3-D solids
• Describe and visualise properties of solid shapes such as parallel or perpendicular faces or edges.
• Classify quadrilaterals, using criteria such as parallel sides, equal angles, equal sides, …
• Make and draw shapes with increasing accuracy and apply knowledge of their properties
• Make shapes with increasing accuracy.
Year 6105
• Visualise and draw on grids of different types where a shape will be after reflection, after translations or after rotation through 90° or 180° about its centre or one of its vertices
• Recognise where a shape will be after reflection, or after two translations.
• Recognise where a shape will be after a rotation through 90° about one of its vertices.
Year 6107111
• Use coordinates in the first quadrant to draw and locate shapes
• Read and plot coordinates. Year 6109
• Estimate angles, and use a protractor to measure and draw them, on their own and in shapes; calculate angles in a triangle or around a point
• Estimate angles; use a protractor to measure and draw acute and obtuse angles to the nearest degree.
• Check that the sum of the angles of a triangle is 180°: e.g. by measuring or paper folding.
• Calculate angles in a triangle or around a point.
Year 6111
Measuring2006 objectives 1999 Framework and Supplement of examples• Select and use standard metric units
of measure and convert between units using decimals to two places, e.g. change 2.75 litres to 2750 ml, or vice versa
• Use, read and write standard metric units (km, m, cm, mm, kg, g, l, ml, cl), including their abbreviations, and relationships between them. Convert smaller to larger units (e.g. m to km, cm or mm to m, g to kg, ml to l) and vice versa.
• Suggest suitable units and measuring equipment to estimate or measure length, mass or capacity.
Year 69193
• Read and interpret scales on a range of measuring instruments, recognising that the measurement made is approximate and recording results to a required degree of accuracy; compare readings on different scales, e.g. when using different instruments
• Record estimates and readings from scales to a suitable degree of accuracy.
Year 695
• Calculate the perimeter and area of rectilinear shapes; estimate the area of an irregular shape by counting squares
• Calculate the perimeter and area of simple compound shapes that can be split into rectangles.
Year 697
Handling data2006 objectives 1999 Framework and Supplement of examples• Describe and predict outcomes from
data using the language of chance or likelihood
• Use the language associated with probability to discuss events, including those with equally likely outcomes.
• Solve problems by collecting, selecting, processing, presenting and interpreting data, using ICT where appropriate; draw conclusions and identify further questions to ask
• Construct and interpret frequency tables, bar charts with grouped discrete data, and line graphs; interpret pie charts
• Solve a problem by representing, extracting and interpreting data in tables, graphs, charts and diagrams, including those generated by a computer, e.g.– line graphs (e.g. for distance/time,
for a multiplication table, a conversion graph, a graph of pairs of numbers adding to 8);
– frequency tables and bar charts with grouped discrete data (e.g. test marks 0–5, 6–10, 11–15, …).
Year 6115, 117
• Describe and interpret results and solutions to problems using the mode, range, median and mean
• Find the mode and range of a set of data; begin to find the median and mean of a set of data.
Using and applying mathematics2006 objectives KS2/KS3 Frameworks and Supplements of
examples• Solve problems by breaking down
complex calculations into simpler steps, choose and use operations and calculation strategies appropriate to the numbers and context; try alternative approaches to overcome difficulties; present, interpret and compare solutions
• Solve word problems in a range of contexts: number, algebra, shape, space and measures, and handling data; compare and evaluate solutions.
Year 72–24
• Represent information or unknown numbers in a problem, e.g. in a table, formula or equation; explain solutions in the context of the problem
• Represent problems mathematically, making correct use of symbols, words, diagrams, tables and graphs.
• Use simple formulae from mathematics and other subjects.
• Construct and solve simple linear equations.
• Present and interpret solutions in the context of the original problem.
Year 726138–142122–12430
• Develop and evaluate lines of enquiry; identify, collect, organise and analyse relevant information; decide how best to represent conclusions and what further questions to ask
• Identify the necessary information to solve a problem.
• Interpret diagrams and graphs, and draw simple conclusions.
• Present and interpret solutions in the context of the original problem.
• Suggest extensions to problems.
Year 72626830138–142
• Generate sequences and describe the general term; use letters and symbols to represent unknown numbers or variables; represent simple relationships as graphs
• Generate sequences from practical contexts and describe the general term in simple cases.
• Use letter symbols to represent unknown numbers or variables.
• Suggest extensions to problems by asking 'What if...?'; begin to generalise and to understand the significance of a counter-example.
Year 7154, 156112138–142
• Explain and justify reasoning and conclusions, using notation, symbols and diagrams; find a counter-example to disprove a conjecture; use step-by-step deductions to solve problems
• Solve geometrical problems, using step-by-step deduction and explaining reasoning with diagrams and text.
• Explain and justify methods and conclusions, orally and in writing.
Counting and understanding number2006 objectives KS2/KS3 Frameworks and Supplements of
examples• Compare and order integers and
decimals in different contexts• Compare and order decimals in
different contexts; know that when comparing measurements they must be in the same units.
• Order a set of positive and negative integers.
Year 740Year 615
• Order a set of fractions by converting them to decimals
• Order fractions and position them on a number line.
Year 623
• Recognise approximate proportions of a whole and use fractions and percentages to describe and compare them, e.g. when interpreting pie charts
• Use percentages to compare simple proportions.
Year 774
• Use ratio notation, reduce a ratio to its simplest form and divide a quantity into two parts in a given ratio; solve simple problems involving ratio and direct proportion, e.g. identify the quantities needed to make a fruit drink by mixing water and juice in a given ratio
• Understand the relationship between ratio and proportion; use direct proportion in simple contexts; use ratio notation, reduce a ratio to its simplest form and divide a quantity into two parts in a given ratio.
Year 778, 80
Knowing and using number facts2006 objectives KS2/KS3 Frameworks and Supplements of
examples• Consolidate rapid recall of number
facts, including multiplication facts to 10 × 10 and the associated division facts
• Consolidate the rapid recall of number facts, including multiplication facts to 10 x 10, and the associated division facts.
Year 788, 100
• Recognise the square roots of perfect squares to 12 × 12
• Recognise the first few triangular numbers, squares of numbers to at least 12 × 12 and the corresponding roots.
Year 756, 58
• Recognise and use multiples, factors, divisors, common factors, highest common factors and lowest common multiples in simple cases
• Recognise multiples up to 10 × 10. Know and apply simple tests of divisibility. Find simple common multiples.
• Factorise numbers to 100 into prime factors.
• Recognise and use multiples, factors (divisors), common factor, highest common factor and lowest common multiple in simple cases, and primes (less than 100); use simple tests of divisibility.
KS2: Year 6
19, 21KS3: Year
752, 54
• Make and justify estimates and approximations of calculations
• Make and justify estimates and approximations of calculations.
Calculating2006 objectives KS2/KS3 Frameworks and Supplements of
examples• Understand how the commutative,
associative and distributive laws, and the relationships between operations, including inverse operations, can be used to calculate more efficiently; use the order of operations, including brackets
• Know and use the order of operations, including brackets
Year 786
• Consolidate and extend mental methods of calculation to include decimals, fractions and percentages
• Consolidate and extend mental methods of calculation to include decimals, fractions and percentages.
Year 792, 94, 9698, 100
• Use standard column procedures to add and subtract integers and decimals, and to multiply two- and three-digit integers by a one- or two-digit integer; extend division to dividing three-digit integers by a two-digit integer
• Use standard column procedures to add and subtract whole numbers and decimals.
• Multiply and divide three-digit by two-digit whole numbers; extend to multiplying and dividing decimals with one or two places by single-digit whole numbers.
Year 7104106
• Calculate percentage increases or decreases and fractions of quantities and measurements (integer answers)
• Calculate simple percentages.• Calculate simple fractions of
quantities and measurements (whole-number answers).
Year 770,7266, 68
• Use bracket keys and the memory of a calculator to carry out calculations with more than one step; use the square root key
• Know and use the order of operations, including brackets.
• Carry out calculations with more than one step using brackets and the memory; use the square root and sign change keys.
• Enter numbers and interpret the display in different contexts (decimals, percentages, money, metric measures).
Year 786108
Understanding shape2006 objectives KS2/KS3 Frameworks and Supplements of
examples• Use correctly the vocabulary,
notation and labelling conventions for lines, angles and shapes
• Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes.
Year 7178
• Extend knowledge of properties of triangles and quadrilaterals and use these to visualise and solve problems, explaining reasoning with diagrams
• Begin to identify and use angle, side and symmetry properties of triangles and quadrilaterals; solve geometrical problems involving these properties, using step-by-step deduction and explaining reasoning with diagrams and text.
Year 7184, 186, 188
• Know the sum of angles at a point, on a straight line and in a triangle, and recognise vertically opposite angles
• Know the sum of angles at a point, on a straight line and in a triangle, and recognise vertically opposite angles.
• Use all four quadrants to find coordinates of points determined by geometric information
• Read and plot co-ordinates in all four quadrants.
• Use conventions and notation for 2-D coordinates in all four quadrants; find coordinates of points determined by geometric information.
Year 6109KS3: Year
7218
• Identify all the symmetries of 2-D shapes; transform images using ICT
• Recognise and visualise the transformation and symmetry of a 2-D shape:– reflection in given mirror lines,
and line symmetry;– rotation about a given point, and
rotation symmetry;– translation;explore these transformations and symmetries using ICT.
Year 7202–212
• Construct a triangle given two sides and the included angle
• Use a ruler and protractor to construct a triangle given two sides and the included angle.
Year 7222
Measuring2006 objectives KS2/KS3 Frameworks and Supplements of
examples• Convert between related metric units
using decimals to three places, e.g. convert 1375 mm to 1.375 m, or vice versa
• Convert one metric unit to another (e.g. grams to kilograms).
Year 7230
• Solve problems by measuring, estimating and calculating; measure and calculate using imperial units still in everyday use; know their approximate metric values
• Know imperial units (mile, pint, gallon, lb, oz); know rough equivalents of lb and kg, oz and g, miles and km, litres and pints or gallons.
Year 691
• Calculate the area of right-angled triangles given the lengths of the two perpendicular sides, and the volume and surface area of cubes and cuboids
• Know and use the formula for the area of a rectangle; calculate the perimeter and area of shapes made from rectangles.
• Calculate the surface area of cubes and cuboids.
Year 7234, 236238, 240
Handling data2006 objectives KS2/KS3 Frameworks and Supplements of
examples• Understand and use the probability
scale from 0 to 1, find and justify probabilities based on equally likely outcomes in simple contexts
• Understand and use the probability scale from 0 to 1; find and justify probabilities based on equally likely outcomes in simple contexts.
• Explore hypotheses by planning surveys or experiments to collect small sets of discrete or continuous data; select, process, present and interpret the data, using ICT where appropriate; identify ways to extend the survey or experiments
• Construct, interpret and compare graphs and diagrams that represent data, e.g. compare proportions in two pie charts that represent different totals
• Plan how to collect and organise small sets of data.
• Collect small sets of data from surveys and experiments.
• Construct, on paper and using ICT, graphs and diagrams to represent data; use ICT to generate pie charts.
• Interpret and discuss results.
Year 7252, 254262, 264268, 270
• Write a short report of a statistical enquiry and illustrate with appropriate diagrams, graphs and charts, using ICT as appropriate; justify the choice of what is presented
• Write a short report of a statistical enquiry and illustrate with appropriate diagrams, graphs and charts, using ICT as appropriate; justify the choice of what is presented.
