Framework review Core learning in mathematics: links to the 1999 Framework for teaching mathematics

A 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 mathematics 2006 objectives 1999 Framework and Supplement of examples • Use developing mathematical ideas • Use developing mathematical ideas Reception and methods to solve practical and methods to solve practical 18, 20 problems problems involving counting and comparing in a real or role play context. • Match sets of objects to numerals • Recognise numerals 1 to 9, then 0 Reception that represent the number of objects and 10, then beyond 10. 9 .• Sort objects, making choices and • Sort and match objects, pictures or Reception justifying decisions children themselves, justifying the 19 decisions made. • Sort coins, including the £1 and £2 Reception coins, and use them in role play to 21 pay and give change. • Talk about, recognise and recreate • Talk about, recognise and recreate Reception simple patterns simple patterns, e.g. simple 18 repeating or symmetrical patterns. • Describe solutions to practical • Solve simple problems or puzzles in Reception problems, drawing on experience, a practical context, and respond to 18 talking about their own ideas, 'What could we try next?' methods and choices

Counting and understanding number 2006 objectives 1999 Framework and Supplement of examples • Say and use the number names in • Say and use the number names in Reception order in familiar contexts order In familiar contexts such as 2 number rhymes, songs, stories, counting games and activities. • Continue the count forwards or Reception backwards from a given number. 2, 3 • Know that numbers identify how many objects are in a set • Count reliably up to 10 everyday • Count reliably up to 10 everyday Reception objects objects (first to 5, then 10, then 4 beyond).

1 | Framework review © Crown copyright 2006 Framework review • Count reliably in other contexts, Reception such as clapping sounds or hopping 4, 5, 6 movements. • Recognise small numbers without counting. • Begin to recognise 'none' and 'zero' in stories, rhymes and when counting. • Estimate how many objects they can • Estimate a number in the range that Reception see and check by counting can be counted reliably, then check 8 by counting. • Make simple estimates and Reception predictions, e.g. of the number of 19 cubes that will fit in a box or strides across the room. • Count aloud in ones, twos or tens • Count in tens. Reception • Count in twos. 7 • Use language such as ‘more’ or • Use language such as more or less, Reception ‘less’ to compare two numbers greater or smaller, to compare two 11, 12 numbers and say which is more or less. • Say a number which lies between Reception two given numbers 12 • Use ordinal numbers in different • Begin to understand and use ordinal Reception contexts numbers in different contexts. 13 • Recognise numerals 1 to 9 • Recognise numerals 1 to 9, then 0 Reception and 10, then beyond 10. 9 • Order a given set of numbers: for Reception example, the set of numbers 1 to 6 12 in random order.

Knowing and using number facts 2006 objectives 1999 Framework and Supplement of examples • Observe number relationships and • Talk about, recognise and recreate Reception patterns in the environment and use simple patterns. 18 these to derive facts • Find one more or one less than a • Find one more or one less than a Reception number from 1 to 10 number from 1 to 10. 10 • Select two groups of objects to • Select two groups of objects to make Reception make a given total of objects a given total. 16 • Separate (partition) a given number Reception of objects into two groups. 16

2 | Framework review © Crown copyright 2006 Framework review Calculating 2006 objectives 1999 Framework and Supplement of examples • Begin to relate addition to combining • Begin to relate addition to combining Reception two groups of objects and two groups of objects, counting all 14 subtraction to ‘taking away’ the objects. 16, 17 • In practical activities and discussion • Begin to relate subtraction to 'taking begin to use the vocabulary involved away' and counting how many are in adding and subtracting left. • Begin to relate addition to counting Reception on. 14 • Find a total by counting on when one group of objects is hidden. • Count repeated groups of the same • Count in tens. Reception size • Count in twos. 7 • Share objects into equal groups and • Begin to understand division as Year 2 count how many in each group grouping (repeated subtraction) or 49 sharing

Understanding shape 2006 objectives 1999 Framework and Supplement of examples • Use familiar objects and common • Talk about, recognise and recreate Reception shapes to create and recreate patterns, e.g. simple repeating or 25, 26 patterns and build models symmetrical patterns in the environment • Use a variety of shapes to make models, pictures and patterns, and describe them. • Use language such as ‘circle’ or • Use language such as circle or Reception ‘bigger’ to describe the shape and bigger to describe the shape and 24, 25 size of solids and flat shapes size of solids and flat shapes. • Begin to name solids such as a Reception cube, cone, sphere and flat shapes 26 such as a circle, triangle, square, rectangle. • Put sets of objects in order of size. Reception 24 • Use everyday words to describe • Use everyday words to describe Reception position position 27 • Use everyday words to describe Reception direction and movement, e.g. follow 27 and give instructions in physical activities.

3 | Framework review © Crown copyright 2006 Framework review Measuring 2006 objectives 1999 Framework and Supplement of examples • Use language such as ‘greater’, • Use language such as more or less, Reception ‘smaller’, ‘heavier’ or ‘lighter’ to longer or shorter, heavier or lighter 19 compare quantities to compare two quantities, then more than two, by making direct 22 comparisons of lengths or masses, and by filling and emptying containers. • Use everyday language related to • Begin to understand and use the Reception time; order and sequence familiar vocabulary of time; sequence 23 events familiar events. • Begin to know the days of the week Reception in order. 23

Handling data 2006 objectives 1999 Framework and Supplement of examples • Sort familiar objects and count how • Sort and match objects, pictures or Reception many objects share a particular children themselves, justifying the 19 property, presenting results using decisions made. 4, 5 pictures, drawings or numerals • Count reliably up to 10 everyday objects. 10 • Begin to record numbers, initially by making marks, progressing to simple tallying and writing numerals.

Year 1

Using and applying mathematics 2006 objectives 1999 Framework and Supplement of examples • Solve problems involving counting, • Use mental strategies to solve Year 1 adding, subtracting, doubling or simple problems set in ‘real life’, 66, 68 halving in the context of numbers, money or measurement contexts, measures or money, e.g. to ‘pay’ using counting, addition, subtraction, and ‘give change’ 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 • Describe a problem using numbers, • Choose and use appropriate number Year 1 practical materials and diagrams; operations and mental strategies to 60 use these to solve the problem and solve problems. 24, 28 set the solution back in the original • Use the +, – and = signs to record context mental calculations in a number sentence. • Answer a question by selecting and • Solve a given problem by sorting, Year 1 using suitable equipment, and classifying and organising 90, 92 sorting information, shapes or information in simple ways. Discuss objects; display results using tables and explain results. and pictures

4 | Framework review © Crown copyright 2006 Framework review • Describe simple patterns and • Solve simple mathematical problems Year 1 relationships involving numbers or or puzzles; recognise and predict 62, 64 shapes; decide whether examples from simple patterns and satisfy given conditions 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. • Describe ways of solving puzzles • Explain methods and reasoning Year 1 and problems, explaining choices orally. 64 and decisions orally or using pictures

Counting and understanding number 2006 objectives 1999 Framework and Supplement of examples • Count reliably at least 20 objects, • Count reliably at least 20 objects. Year 1 recognising that when rearranged • Give a sensible estimate of a 2, 4, 6 the number of objects stays the number of objects that can be 16 same; estimate a number of objects checked by counting (e.g. up to that can be checked by counting about 30 objects). • Understand and use the vocabulary Year 1 of comparing and ordering numbers, 10 including ordinal numbers to at least 20. • Compare and order numbers, using • Order numbers to at least 20, and Year 1 the related vocabulary; use the position them on a number track. 10, 14 equals (=) sign • Use the = sign to represent equality. • Compare two familiar numbers, say which is more or less, and give a number which lies between them.

• Read and write numerals from 0 to • Read and write numerals from 0 to Year 1 20, then beyond; use knowledge of at least 20. 8 place value to position these • Begin to partition two-digit numbers numbers on a number track and into a multiple of 10 and ones number line • Say the number that is one more or • Within the range 0 to 30, say the Year 1 less than any given number and ten number that is 1 or 10 more or less 12 more or less for multiples of ten than any given number. • Use the vocabulary of halves and • Read the time to the hour or half Year 1 quarters in context hour on analogue clocks. 78, 82, 88 • Fold shapes in half. • Make whole turns and half turns. • Begin to recognise and find one half Year 2 and one quarter of shapes and small 21, 23 numbers of objects. • Begin to recognise that two halves or four quarters make one whole and that two quarters and one half are equivalent.

5 | Framework review © Crown copyright 2006 Framework review Knowing and using number facts 2006 objectives 1999 Framework and Supplement of examples • Derive and recall all pairs of • Know by heart all pairs of numbers Year 1 numbers with a total of 10 and with a total of 10 (e.g. 3 + 7), 30 addition facts for totals to at least 5; addition facts for all totals to at least work out the corresponding 5, and the corresponding subtraction subtraction facts facts. • Count on or back in ones, twos, fives • Count on and back in ones from any Year 1 and tens and use this knowledge to small number, and in tens from and 4, 6 derive the multiples of 2, 5 and 10 to back to zero; the tenth multiple 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. • Begin to recognise two-digit Year 2 multiples of 2, 5 or 10. 7 • Recall the doubles of all numbers to • Know by heart doubles of all Year 2 at least 10 numbers to 10 and the 53 corresponding halves.

Calculating 2006 objectives 1999 Framework and Supplement of examples • Relate addition to counting on; • Use mental calculation strategies – Year 1 recognise that addition can be done several objectives, including: 32, 34, 36, in any order; use practical and use known number facts and place 38, 40 informal written methods to support value to add a pair of numbers. the addition of a one-digit number or a multiple of 10 to a one-digit or two- • Begin to recognise that addition can digit number be done in any order. • Understand subtraction as ‘take • Understand subtraction as ‘take Year 1 away’ and find a ‘difference’ by away’ or ‘difference’. 28 counting up; use practical and • Use mental calculation strategies – 32, 34, 36, informal written methods to support several objectives, including: the subtraction of a one-digit number 38, 40 from a one-digit or two-digit number use known number facts and place and a multiple of 10 from a two-digit value to subtract a pair of numbers. number • Use the vocabulary related to • Begin to use the +, – and = signs to Year 1 addition and subtraction and record mental calculations in a 24, 28 symbols to describe and record number sentence, and to recognise addition and subtraction number the use of symbols such as  to sentences stand for an unknown number. • Solve practical problems that involve • Understand multiplication as Year 2 combining groups of 2, 5 or 10, or repeated addition, and division as 47, 49 sharing into equal groups sharing.

6 | Framework review © Crown copyright 2006 Framework review Understanding shape 2006 objectives 1999 Framework and Supplement of examples • Visualise and name common 2-D • Describe features of familiar 3-D and Year 1 shapes and 3-D solids and describe 2-D shapes, including the cube, 80 their features; use them to make cuboid, sphere, cylinder, cone…, patterns, pictures and models circle, triangle, square, rectangle, …, 82 referring to properties such as the 88 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. • Identify objects that turn about a • Talk about things that turn; make Years 1, 2 point (e.g. scissors) or about a line whole turns and half turns. 88, 89 (e.g. a door); recognise and make • Recognise quarter turns. whole, half and quarter turns • Visualise and use everyday • Use everyday language to describe Year 1 language to describe the position of position, direction and movement. 86, 88 objects and direction and distance when moving them, e.g. when placing or moving objects on a games board

Measuring 2006 objectives 1999 Framework and Supplement of examples • Estimate, measure, weigh and • Compare two lengths, masses or Year 1 compare objects choosing and using capacities by direct comparison; 72 suitable uniform non-standard or extend to more than two. 74, 76 standard units and measuring • Measure using uniform non- instruments, e.g. a lever balance, standard units (e.g. straws, wooden metre stick or measuring jug 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’. • Use vocabulary related to time; • Understand and use the vocabulary Year 1 order days of the week and months; related to time. Order familiar events 78 read the time to the hour and half in time. Know the days of the week hour and the seasons of the year. • Read the time to the hour or half hour on analogue clocks. • Order the months of the year. Year 2 79

7 | Framework review © Crown copyright 2006 Framework review Handling data 2006 objectives 1999 Framework and Supplement of examples • Answer a question by recording • Solve a given problem by sorting, Year 1 information in lists and tables; classifying and organising 90, 92 present outcomes using practical information in simple ways, such as: resources, pictures, block graphs or – using objects or pictures; pictograms – in a list or simple table. • Use diagrams to sort objects into Discuss and explain results. groups according to a given criterion; suggest a different criterion • Solve a given problem by sorting, Year 2 for grouping the same objects classifying and organising 91, 93 information in: – a pictogram; – a block graph.

Year 2

Using and applying mathematics 2006 objectives 1999 Framework and Supplement of examples • Solve problems involving addition, • Use mental addition and subtraction, Year 2 subtraction, multiplication or division and simple multiplication and 67, 69 in contexts of numbers, measures or division, to solve simple word pounds and pence 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. • Identify and record the information or • Use the +, –, ×, ÷ and = signs to Year 2 calculation needed to solve a puzzle record mental calculations in a 25, 29, or problem; carry out the steps or number sentence, and recognise the 47, 49 calculations and check the solution use of a symbol such as  to stand in the context of the problem for an unknown number. 61 • Choose and use appropriate 59 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. • Follow a line of enquiry; answer • Solve a given problem by sorting, Year 2 questions by choosing and using classifying and organising 91, 93 suitable equipment and selecting, information in simple ways. Discuss organising and presenting and explain results. information in lists, tables and simple diagrams

8 | Framework review © Crown copyright 2006 Framework review • Describe patterns and relationships • Solve mathematical problems or Year 2 involving numbers or shapes, make puzzles, recognise simple patterns 63, 65 predictions and test these with and relationships, generalise and examples 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. • Present solutions to puzzles and • Explain how a problem was solved Year 2 problems in an organised way; orally and, where appropriate, in 65 explain decisions, methods and writing. results in pictorial, spoken or written form, using mathematical language and number sentences

Counting and understanding number

2006 objectives 1999 Framework and Supplement of examples • Read and write two- and three-digit • Read and write whole numbers to at Year 2 numbers in figures and words; least 100 in figures and words. 9 describe and extend number • Describe and extend simple number 3, 5, 7 sequences and recognise odd and sequences; recognise odd and even even numbers numbers to at least 30. • Count up to 100 objects by grouping • Count reliably up to 100 objects by Year 2 them and counting in tens, fives or grouping them, e.g. in tens, then in 3 twos; explain what each digit in a fives or twos. 9, 13 two-digit number represents, • Know what each digit in a two-digit including numbers where 0 is a number represents, including 0 as a place holder; partition two-digit place holder; partition two-digit numbers in different ways, including numbers into a multiple of ten and into multiples of ten and one ones (TU). • Order two-digit numbers and • Order whole numbers to at least Year 2 position them on a number line; use 100, and position them on a number 13, 15 the greater than (>), less than (<) line and 100 square. signs • Use symbols correctly, including less Year 4 than (<), greater than (>), equals (=). 8 • Estimate a number of objects and • Give a sensible estimate of at least Year 2 round two-digit numbers to the 50 objects. 17, 19 nearest 10 • Round numbers less than 100 to the nearest 10. • Find one half, one quarter and three • Begin to recognise and find one half Year 2 quarters of shapes and sets of and one quarter of shapes and small 21, 23 objects numbers of objects. • Begin to recognise that two halves or four quarters make one whole and that two quarters and one half are equivalent.

9 | Framework review © Crown copyright 2006 Framework review Knowing and using number facts 2006 objectives 1999 Framework and Supplement of examples • Derive and recall all addition and • Know by heart: Year 2 subtraction facts for each number to all addition and subtraction facts for 31 at least 10, all pairs with totals to 20 each number to at least 10; and all pairs of multiples of 10 with totals up to 100 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). • Understand that halving is the • Derive quickly doubles of all whole Year 3 inverse of doubling and derive and numbers to at least 20 (e.g. 17 × 2), 53 recall doubles of all numbers to 20, and the corresponding halves (e.g. and the corresponding halves 36 ÷ 2). • Derive and recall multiplication facts • Know by heart multiplication facts for Year 2 for the 2, 5 and 10 times-tables and the 2 and 10 times-tables; begin to 53 the related division facts; recognise know multiplication facts for the 5 multiples of 2, 5 and 10 times-table. Derive quickly the corresponding division facts. • Know by heart multiplication facts for Year 3 the 5 times-table. 53 • Use knowledge of number facts and • Check results of calculations by Year 2 operations to estimate and check repeating addition in a different 59 answers to calculations order, or with an equivalent calculation.

Calculating 2006 objectives 1999 Framework and Supplement of examples • Add or subtract mentally a single- • Use mental calculation strategies – Year 2 digit number or a multiple of 10 to or several objectives, including: 33–41 from any two-digit number; use use known number facts and place 25, 29 practical and informal written value to add/subtract mentally; methods to add and subtract two- 27 digit numbers 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. • Understand that subtraction is the • Understand that subtraction is the Year 2 inverse of addition and vice versa inverse of addition (subtraction 25, 29 and use this to derive and record reverses addition). 35 related addition and subtraction • State the subtraction corresponding number sentences to a given addition, and vice versa.

10 | Framework review © Crown copyright 2006 Framework review • Represent repeated addition and • Understand the operation of Year 2 arrays as multiplication, and sharing multiplication as repeated addition or 47, 49 and repeated subtraction (grouping) as describing an array, and begin to as division; use practical and understand division as grouping 57 informal written methods and related (repeated subtraction) or sharing. vocabulary to support multiplication • Use known number facts and place and division, including calculations value to carry out mentally simple with remainders multiplications and divisions. • Begin to find remainders after simple Year 3 division. 51 • Round up or down after division, depending on the context. • Use the symbols +, –, ×, ÷ and = to • Use the +, –, ×, ÷ and = signs to Year 2 record and interpret number record mental calculations in a 25, 29 sentences involving all four number sentence, and recognise the operations; calculate the value of an use of a symbol such as  to stand 47, 49 unknown in a number sentence, e.g. for an unknown number. 30 –  = 24,  ÷ 2 = 6

Understanding shape 2006 objectives 1999 Framework and Supplement of examples • Visualise common 2-D shapes and • Use the mathematical names for Year 2 3-D solids; identify shapes from common 3-D and 2-D shapes, 81, 83 pictures of them in different positions including the pyramid, cylinder, and orientations; sort, make and pentagon, hexagon, octagon. describe shapes, referring to their • Relate solid shapes to pictures of properties 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, … • Identify reflective symmetry in • Begin to recognise line symmetry. Year 2 patterns and 2-D shapes and draw 85 lines of symmetry in shapes • Follow and give instructions • Use mathematical vocabulary to Year 2 involving position, direction and describe position, direction and 87, 89 movement 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. • Recognise and use whole, half and • Recognise whole, half and quarter Year 2 quarter turns, both clockwise and turns, to the left or right, clockwise or 89 anti-clockwise; know that a right anti-clockwise; know that a right angle represents a quarter turn angle is a measure of a quarter turn, and recognise right angles in squares and rectangles.

11 | Framework review © Crown copyright 2006 Framework review Measuring 2006 objectives 1999 Framework and Supplement of examples • Estimate, compare and measure • Estimate, measure and compare Year 2 lengths, weights and capacities, lengths, masses and capacities, 73, 75 choosing and using standard units using standard units (m, cm, kg, (m, cm, kg, litre) and suitable litre). measuring instruments • Suggest suitable units and equipment for such measurements. • Read the numbered divisions on a • Read a simple scale to the nearest Year 2 scale, and interpret the divisions labelled division, including using a 77 between them, e.g. on a scale from ruler to draw and measure lines to 0 to 25 with intervals of 1 shown but the nearest centimetre, recording only the divisions 0, 5, 10, 15 and 20 estimates and measurements as ‘3 numbered; use a ruler to draw and and a bit metres long’ or ‘about 8 measure lines to the nearest centimetres’ or ‘nearly 3 kilograms centimetre heavy’. • Read scales to the nearest division Year 3 (labelled or unlabelled). 77 • Use units of time (seconds, minutes, • Use units of time and know the Year 2 hours, days) and know the relationships between them (second, 79 relationships between them; read minute, hour, day, week). 71 the time to the quarter hour; identify • Read the time to the quarter hour on time intervals, including those that an analogue clock and 12-hour cross the hour digital clock; understand the notation 7:30. • Solve word problems involving measures. • Suggest suitable units to estimate or measure time.

Handling data 2006 objectives 1999 Framework and Supplement of examples • Answer a question by collecting and • Solve a given problem by sorting, Year 2 recording data in lists and tables; classifying and organising 91, 93 represent the data as block graphs information in simple ways, such as: or pictograms to show results; use – in a list or simple table; ICT to organise and present data – in a pictogram; • Use lists, tables and diagrams to – in a block graph. sort objects; explain choices using Discuss and explain results. appropriate language, including not

12 | Framework review © Crown copyright 2006 Framework review Year 3

Using and applying mathematics 2006 objectives 1999 Framework and Supplement of examples • Solve one- and two-step problems • Solve word problems involving Year 3 involving numbers, money or numbers in ‘real life’, money and 67, 69, 71 measures, including time, choosing measures, using one or more steps, and carrying out appropriate including finding totals and giving 61 calculations change, and working out which coins • Represent the information in a to pay. Explain how the problem was puzzle or problem using numbers, solved. images or diagrams; use these to • Choose and use appropriate find a solution and present it in operations (including multiplication context, where appropriate using £.p and division) to solve word notation or units of measure 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). • Follow a line of enquiry by deciding • Solve a given problem by organising Year 3 what information is important; make and interpreting numerical data in 91, 93 and use lists, tables and graphs to simple lists, tables and graphs. organise and interpret the information • Identify patterns and relationships • Solve mathematical problems or Year 3 involving numbers or shapes, and puzzles, recognise simple patterns 63, 65 use these to solve problems and relationships, generalise and predict. Suggest extensions by 3, 5, 7 asking ‘What if…?’ • Describe and extend number sequences. • Investigate a general statement about familiar numbers or shapes by finding examples that satisfy it. • Describe and explain methods, • Explain methods and reasoning 65 choices and solutions to puzzles and orally and, where appropriate, in problems, orally and in writing, using writing. pictures and diagrams

Counting and understanding number 2006 objectives 1999 Framework and Supplement of examples • Read, write and order whole • Read and write whole numbers to at Year 3 numbers to at least 1000 and least 1000 in figures and words. 11, 13, 15 position them on a number line; • Order whole numbers to at least count on from and back to zero in 1000, and position them on a single-digit steps or multiples of 10 number line. • Partition three-digit numbers into • Know what each digit represents, Year 3 multiples of one hundred, ten and and partition three-digit numbers into 9 one in different ways a multiple of 100, a multiple of ten and ones (HTU).

13 | Framework review © Crown copyright 2006 Framework review • Round two- or three-digit numbers to • Round any two-digit number to the Year 3 the nearest 10 or 100 and give nearest 10 and any three-digit 19 estimates for their sums and number to the nearest 100. differences • Round any positive integer less than Year 4 1000 to the nearest 10 or 100. 10, 12

1 • Read and write proper fractions, e.g. • Recognise unit fractions such as 2, Year 3 3 9 1 1 1 1 7, 10, interpreting the denominator 3, 4, 5, 10, … and use them to find 21, 23 as the parts of a whole and the fractions of shapes and numbers. numerator as the number of parts; • Begin to recognise simple fractions identify and estimate fractions of that are several parts of a whole, shapes; use diagrams to compare 3 2 3 such as 4, 3 or 10. fractions and establish equivalents • 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.

Knowing and using number facts 2006 objectives 1999 Framework and Supplement of examples • Derive and recall all addition and • Know by heart: Year 3 subtraction facts for each number to all addition and subtraction facts for 31 20, sums and differences of each number to 20; multiples of 10 and number pairs all pairs of multiples of 100 with a that total 100 total of 1000 (e.g. 300 + 700); all pairs of multiples of 5 with a total of 100 (e.g. 35 + 65). • Derive quickly all number pairs that Year 4 total 100 (e.g. 62 + 38, 75 + 25, 40 + 38 60). • Derive and recall multiplication facts • Know by heart multiplication facts for Year 3 for the 2, 3, 4, 5, 6 and 10 times- the 2, 5 and 10 times-tables; begin 53 tables and the corresponding to know the 3 and 4 times-tables. division facts; recognise multiples of Derive quickly corresponding 7 2, 5 or 10 up to 1000 division facts. • Recognise two-digit and three-digit multiples of 2, 5 or 10, and three- digit multiples of 50 and 100. • Know by heart: multiplication facts Year 4 for 2, 3, 4, 5 and 10 times-tables. 58 • Begin to know multiplication facts for the 6 times-tables. • Derive quickly corresponding division facts. • Use knowledge of number • Check subtraction with addition, Year 3 operations and corresponding halving with doubling and division 59 inverses, including doubling and with multiplication. halving, to estimate and check • Repeat addition or multiplication in a calculations different order. • Check with an equivalent calculation.

14 | Framework review © Crown copyright 2006 Framework review Calculating 2006 objectives 1999 Framework and Supplement of examples • Add or subtract mentally • Use mental calculation strategies – Year 3 combinations of one- and two-digit several objectives, including: 37, 39, 41 numbers use known number facts and place 33, 35 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. • Develop and use written methods to • Use informal pencil and paper Year 3 record, support or explain addition methods to support, record or 43, 45 and subtraction of two- and three- explain HTU ± TU, HTU ± HTU. digit numbers • Begin to use column addition and subtraction for HTU ± TU where the calculation cannot easily be done mentally. • Multiply one- and two-digit numbers • Multiply mentally by 10/100 by Year 3 by 10 or 100, and describe the effect shifting the digits one/two places to 55 the left. • Use practical and informal written • Use known number facts and place Year 3 methods to support multiplication value to carry out mentally simple 51, 57 and division of two-digit numbers multiplications and divisions. (e.g. 13 × 3, 30 ÷ 4); round • Begin to find remainders after simple remainders up or down, depending division; round up or down after on the context division, depending on the context. • Understand that division is the • Recognise that division is the Year 3 inverse of multiplication and vice inverse of multiplication, and that 49 versa and use to derive and record halving is the inverse of doubling. 55 related multiplication and division • Say or write a division statement number sentences corresponding to a given multiplication statement.

1 • Find unit fractions of numbers and • Recognise unit fractions such as 2, Year 3 1 1 1 1 1 quantities, e.g. ½, ⅓, ¼ and 6 of 12 3, 4, /5, 10, … and use them to 21, 23 litres find fractions of shapes and numbers.

15 | Framework review © Crown copyright 2006 Framework review Understanding shape 2006 objectives 1999 Framework and Supplement of examples • Relate 2-D shapes and 3-D solids to • Relate solid shapes to pictures of Year 3 drawings of them; describe, them. 81, 83 visualise, classify, draw and make • Classify and describe 3-D and 2-D the shapes 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. • Draw and complete shapes with • Identify and sketch lines of Year 3 reflective symmetry and draw the symmetry in simple shapes, and 85 reflection of a shape in a mirror line recognise shapes with no lines of along one side symmetry. • Sketch the reflection of a simple shape in a mirror line along one edge. • Read and record the vocabulary of • Read and begin to write the Year 3 position, direction and movement, vocabulary related to position, 87 using the four compass directions to direction and movement, e.g. describe movement about a grid 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. • Use a set-square to draw right • Identify right angles in 2-D shapes Year 3 angles and to identify right angles in and the environment. 89 2-D shapes; compare angles with a • Recognise that a straight line is right angle; recognise that a straight equivalent to two right angles. line is equivalent to two right angles • Compare angles with a right angle.

Measuring 2006 objectives 1999 Framework and Supplement of examples • Know the relationships between • Measure and compare using Year 3 kilometres and metres, metres and standard units (km, m, cm, kg, g, l, 73, 75 centimetres, kilograms and grams, ml) litres and millilitres; choose and use • Know the relationships between appropriate units to estimate, kilometres and metres, metres and measure and record measurements 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.

16 | Framework review © Crown copyright 2006 Framework review • Read, to the nearest division and • Read scales to the nearest division Year 3 half-division, scales that are (labelled or unlabelled); record 77 numbered or partially numbered; estimates and measurements to the use the information to measure and nearest whole or half unit (e.g. draw to a suitable degree of ‘about 3.5 kg’), or in mixed units accuracy (e.g. ‘3 m and 20 cm’). • Use a ruler to draw and measure lines to the nearest half centimetre • Read the time on a 12-hour digital • Read the time to 5 minutes on an Year 3 clock and to the nearest five minutes analogue clock and 12-hour digital 79 on an analogue clock; calculate time clock; use the notation 9:40. 71 intervals and find start or end times • Solve word problems involving for a given time interval measures. • Read the time to the nearest minute Year 4 from a 12-hour digital clock. 98, 100

Handling data 2006 objectives 1999 Framework and Supplement of examples • Answer a question by collecting, • Solve a given problem by organising Year 3 organising and interpreting data; use and interpreting numerical data in 91, 93 tally charts, frequency tables, simple lists, tables and graphs, e.g. pictograms and bar charts to – simple frequency tables; represent results and illustrate – pictograms; observations; use ICT to create a – bar charts; simple bar chart – Venn and Carroll diagrams (one • Use Venn diagrams or Carroll criterion). diagrams to sort data and objects • Solve a given problem by organising Year 4 using more than one criterion and interpreting numerical data in 116 Venn and Carroll diagrams (two criteria).

17 | Framework review © Crown copyright 2006 Framework review

Year 4

Using and applying mathematics 2006 objectives 1999 Framework and Supplement of examples • Solve one- and two-step problems • Use all four operations to solve word Year 4 involving numbers, money or problems involving numbers in ‘real 82, 84, measures, including time; choose life’, money and measures (including 86, 88, 100 and carry out appropriate time), using one or more steps, calculations, using calculator including converting pounds to 74 methods where appropriate pence and metres to centimetres 56 • Represent a puzzle or problem and vice versa. using number sentences, • Choose and use appropriate number statements or diagrams; use these operations and appropriate ways of to solve the problem; present and calculating (mental, mental with interpret the solution in the context jottings, pencil and paper) to solve of the problem problems. • Round up or down after division, depending on the context. • Choose appropriate ways of Year 5 calculating: calculator. 75 • Suggest a line of enquiry and the • Solve a problem by collecting Year 4 strategy needed to follow it; collect, quickly, organising, representing and 114, 116 organise and interpret selected interpreting data in tables, charts, information to find answers graphs and diagrams, including those generated by a computer. • Identify and use patterns, • Solve mathematical problems or Year 4 relationships and properties of puzzles, recognise and explain 78 numbers or shapes; investigate a patterns and relationships, statement involving numbers and generalise and predict. Suggest 16, 18 test it with examples extensions by asking ‘What if…?’ 80 • Recognise and extend number sequences. • Make and investigate a general statement about familiar numbers or shapes by finding examples that satisfy it. • Report solutions to puzzles and • Explain methods and reasoning Year 4 problems, giving explanations and about numbers orally and in writing. 76 reasoning orally and in writing, using diagrams and symbols

Counting and understanding number 2006 objectives 1999 Framework and Supplement of examples • Recognise and continue number • Recognise and extend number Year 4 sequences formed by counting on or sequences formed by counting in 16 back in steps of constant size steps of constant size, extending beyond zero when counting back.

18 | Framework review © Crown copyright 2006 Framework review • Partition, round and order four-digit • Recognise negative numbers in Year 4 whole numbers; use positive and context (e.g. on a number line, on a 14 negative numbers in context and temperature scale). 8 position them on a number line; • Use symbols correctly, including less state inequalities using the symbols than (<), greater than (>), equals (=). < and >, e.g. –3 > –5, –1 < +1 • Use decimal notation for tenths and • Understand decimal notation and Year 4 hundredths and partition decimals; place value for tenths and 28 relate the notation to money and hundredths, and use it in context, measurement; position one- and e.g. order amounts of money; two-place decimals on a number line 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. • Order a set of numbers or Year 5 measurements with one or two 29 decimal places. • Recognise the equivalence between • Recognise the equivalence between Year 5 decimal and fraction forms of one the decimal and fraction forms of 31 7 half, quarters, tenths and hundredths tenths and hundredths (e.g. 10 = 27 0.7, 100 = 0.27). • Use diagrams to identify equivalent • Begin to relate fractions to division Year 4 6 3 70 1 fractions, e.g. 8 and 4, or 100 and and find simple fractions such as 2, 22, 24 7 1 1 1 1 10; interpret mixed numbers and 3, 4, 5, 10, … of numbers.

position them on a number line, e.g. 2 3 3 7 1 • Find fractions such as 3, 4, 5, 10, 3 2 … of shapes. • Recognise the equivalence of simple fractions • Order a set of fractions such as 2, 3 3 1 1 2 4, 1 4, 2 2, 1 2, and position them on a number line. • Use the vocabulary of ratio and • Begin to use ideas of simple Year 4 proportion to describe the proportion: for example, ‘one for 26 relationship between two quantities, every …’ and ‘one in every …’. e.g. there are 2 red beads to every 3 • Solve simple problems using ideas Year 5 blue beads, or 2 beads in every 5 of ratio and proportion (‘one for 27 beads are red; estimate a every…’ and ‘one in every…’). proportion, e.g. ‘about one quarter of the apples in the box are green’

Knowing and using number facts 2006 objectives 1999 Framework and Supplement of examples • Use knowledge of addition and • Derive quickly all pairs of multiples Year 4 subtraction facts and place value to of 50 with a total of 1000 (e.g. 850 + 38 derive sums and differences of pairs 150). 42 of multiples of 10, 100 or 1000 • Add three two-digit multiples of 10, such as 40 + 70 + 50. 44, 46 • Use known number facts and place value to add or subtract mentally. • Use known number facts and place Year 5 value for mental addition and 45, 47 subtraction (e.g. 470 + 380, 810 – 380).

19 | Framework review © Crown copyright 2006 Framework review • Identify the doubles of two-digit • Derive quickly doubles of all whole Year 4 numbers; use to calculate doubles of numbers to 50, multiples of 10 to 58 multiples of 10 and 100 and derive 500 and multiples of 100 to 5000, the corresponding halves and the corresponding halves. • Derive and recall multiplication facts • Know by heart all multiplication facts Year 5 up to 10 × 10, the corresponding up to 10 × 10; derive quickly 59 division facts and multiples of corresponding division facts. 19 numbers to 10 up to the tenth • Recognise multiples of 6, 7, 8, 9, up multiple to the 10th multiple. • Recognise multiples of 2, 3, 4, 5 and Year 4 10, up to the tenth multiple. 18 • Use knowledge of rounding, number • Check results of calculations. Year 4 operations and inverses to estimate 72 and check calculations • Identify pairs of fractions that total 1 • Identify two simple fractions with a Year 4 3 7 total of 1 (e.g. 10 and 10). 22

Calculating 2006 objectives 1999 Framework and Supplement of examples • Add or subtract mentally pairs of • Use known number facts and place Year 4 two-digit whole numbers, e.g. 47 + value to add or subtract mentally, 40, 42, 58, including any pair of two-digit whole 44, 46 91 – 35 numbers. • Refine and use efficient written Develop and refine written methods Year 4 methods to add and subtract two- for: 48, 50 and three-digit whole numbers and column addition and subtraction of £.p two whole numbers less than 1000, and addition of more than two such numbers; money calculations (e.g. £7.85 ± £3.49). • Multiply and divide numbers to 1000 • Multiply or divide any integer up to Year 4 by 10 and then 100 (whole number 1000 by 10 (whole-number 6 answers), understanding the effect; answers), and understand the effect; relate to scaling up or down begin to multiply by 100. • Develop and use written methods to • Develop and refine written methods Year 4 record, support and explain for TU × U, TU ÷ U. 66, 68 multiplication and division of two- • Find remainders after division; divide 56 digit numbers by a one-digit number, a whole number of pounds by 2, 4, 5 including division with remainders, or 10 to give £.p; round up or down e.g. 15 × 9, 98 ÷ 6 after division, depending on the context. • Find fractions of numbers, quantities • Begin to relate fractions to division Year 4 1 3 1 or shapes, e.g. 5 of 30 plums, 8 of and find simple fractions such as 2, 24 1 1 1 1 a 6 by 4 rectangle 3, 4, 5, 10, … of numbers or quantities.

2 3 3 7 • Find fractions such as 3, 4, 5, 10, … of shapes.

20 | Framework review © Crown copyright 2006 Framework review • Use a calculator to carry out one- • Develop calculator skills and use a Year 5 and two-step calculations involving calculator effectively. 71 all four operations; recognise negative numbers in the display, correct mistaken entries and interpret the display correctly in the context of money

Understanding shape 2006 objectives 1999 Framework and Supplement of examples • Draw polygons and classify them by • Classify polygons using criteria such Year 4 identifying their properties, including as number of right angles, whether 102, 104 their line symmetry 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. • Visualise 3-D objects from 2-D • Visualise 3-D shapes from 2-D Year 4 drawings and make nets of common drawings and identify simple nets of 104 solids solid shapes. • Recognise horizontal and vertical • Recognise simple examples of Year 4 lines; use the eight compass points horizontal and vertical lines. 108 to describe direction; describe and • Use the eight compass directions N, identify the position of a square on a S, E, W, NE, NW, SE, SW. grid of squares • Recognise positions and directions: for example, describe and find the position of a point on a grid of squares where the lines are numbered. • Know that angles are measured in • Begin to know that angles are Year 4 degrees and that one whole turn is measured in degrees and that one 110 360°; draw, compare and order whole turn is 360° or 4 right angles; angles less than 180° 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°.

Measuring 2006 objectives 1999 Framework and Supplement of examples • Choose and use standard metric • Use, read and write standard metric Year 4 units and their abbreviations when units (km, m, cm, mm, kg, g, l, ml), 90 estimating, measuring and recording including their abbreviations, and length, weight and capacity; know imperial units (mile, pint). 92, 94 the meaning of kilo, centi and milli • Know and use the relationships and, where appropriate, use decimal between familiar units of length, notation to record measurements, mass and capacity. e.g. 1.3 m or 0.6 kg • 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.

21 | Framework review © Crown copyright 2006 Framework review • Interpret intervals and divisions on • Record estimates and readings from Year 4 partially numbered scales and scales to a suitable degree of 94 record readings accurately, where accuracy. appropriate to the nearest tenth of a unit • Draw rectangles and measure and • Measure and calculate the perimeter Year 4 calculate their perimeters, find the and area of rectangles and other 96 area of rectilinear shapes drawn on simple shapes, using counting a square grid by counting squares methods and standard units (cm, cm2). • Read time to the nearest minute; • Use am and pm and the notation Year 4 use am, pm and 12-hour clock 9:53. 98, 100 notation; choose units of time to • Read simple timetables. measure time intervals; calculate 88 time intervals from clocks and • Solve word problems involving time. timetables

Handling data 2006 objectives 1999 Framework and Supplement of examples • Answer a question by identifying • Solve a problem by collecting Year 4 what data to collect; organise, quickly, organising, representing and 114, 116 present, analyse and interpret the interpreting data in tables, charts, data in tables, diagrams, tally charts, graphs and diagrams, including pictograms and bar charts, using those generated by a computer, e.g. ICT where appropriate – tally charts and frequency tables; • Compare the impact of – pictograms – symbol representing representations where scales have 2, 5, 10 or 20 units; intervals of differing step size – bar charts – intervals labelled in 2s, 5s, 10s or 20s; – Venn and Carroll diagrams (two criteria).

22 | Framework review © Crown copyright 2006 Framework review

Year 5

Using and applying mathematics 2006 objectives 1999 Framework and Supplement of examples • Solve one- and two-step problems • Use all four operations to solve Year 5 involving whole numbers and simple word problems involving 83, 85, decimals and all four operations, numbers and quantities based on 87, 89, 101 choosing and using appropriate ‘real life’, money and measures calculation strategies, including (including time), using one or more 75 calculator use steps, including finding simple 57 • Represent a problem by identifying percentages. and recording the calculations • Choose and use appropriate number needed to solve it; find possible operations to solve problems, and solutions and confirm them in the appropriate ways of calculating: context of the problem mental, mental with jottings, written methods, calculator. • Round up or down after division, depending on the context. • Plan and pursue an enquiry; present • Solve a problem by representing Year 5 evidence by collecting, organising and interpreting data in tables, 113–117 and interpreting information; suggest charts, graphs and diagrams, extensions to the enquiry including those generated by a computer. • Explore patterns, properties and • Solve mathematical problems or Year 5 relationships and propose a general puzzles, recognise and explain 79 statement involving numbers or patterns and relationships, shapes; identify examples for which generalise and predict. Suggest 17, 19, 21 the statement is true or false extensions asking ‘What if…?’ 81 • 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. • Explain reasoning using diagrams, • Explain methods and reasoning, Year 5 graphs and text; refine ways of orally and in writing. 77 recording using images and symbols

Counting and understanding number 2006 objectives 1999 Framework and Supplement of examples • Count from any given number in • Recognise and extend number Year 5 whole number and decimal steps, sequences formed by counting from 17 extending beyond zero when any number in steps of constant counting backwards; relate the size, extending beyond zero when numbers to their position on a counting back, e.g. count on in steps number line of 25 to 1000, and then back; count on or back in steps of 0.1, 0.2, 0.3, …

23 | Framework review © Crown copyright 2006 Framework review • Explain what each digit represents in • Read and write whole numbers in Year 5 whole numbers and decimals with figures and words, and know what 3 up to two places, and partition, each digit represents. 29 round and order these numbers • Know what each digit represents in a number with up to two decimal places. • Express a smaller whole number as • Relate fractions to their decimal Year 5 a fraction of a larger one, e.g. representations: that is, recognise 31 5 recognise that 5 out of 8 is 8; find the equivalence between the 7 14 23 equivalent fractions, e.g. 10 = 20, or decimal and fraction forms of one 19 9 10 = 1 10; relate fractions to their half, one quarter, three quarters… 7 decimal representations and tenths and hundredths (e.g. 10 27 = 0.7, 100 = 0.27). • Recognise when two simple fractions are equivalent, including relating hundredths to tenths (e.g. 70 7 100 = 10). • Change an improper fraction to a 13 mixed number (e.g. change 10 to 3 1 10). • Understand percentage as the • Begin to understand percentage as Year 5 number of parts in every 100 and the number of parts in every 100. 33 express tenths and hundredths as • Express one half, one quarter, three percentages quarters, and tenths and hundredths, as percentages (e.g. 3 know that 4 = 75%). • Use sequences to scale numbers up • Solve problems involving ratio and Year 6 or down; solve problems involving proportion. 27 proportions of quantities, e.g. decrease quantities in a recipe designed to feed six people

Knowing and using number facts 2006 objectives 1999 Framework and Supplement of examples • Use knowledge of place value and • Derive quickly pairs of decimals that Year 5 addition and subtraction of two-digit total 1 (e.g. 0.2 + 0.8) or 10 (e.g. 6.2 39 numbers to derive sums and + 3.8). 45, 47 differences, doubles and halves of • Use known number facts and place decimals, e.g. 6.5 ± 2.7, halve 5.6, value for mental addition and double 0.34 subtraction (e.g. 7.4 + 9.8, 9.2 – 8.6). • Derive quickly doubles of two-digit Year 6 decimals (e.g. 3.8 × 2, 0.76 × 2), and 59 the corresponding halves. • Recall quickly multiplication facts up • Know by heart all multiplication facts Year 5 to 10 × 10, use to multiply pairs of up to 10 × 10; derive quickly division 59 multiples of 10 and 100 and derive facts. 65 quickly corresponding division facts • Use known facts and place value to multiply and divide mentally. • Identify pairs of factors of two-digit • Find all the pairs of factors of any Year 5 whole numbers and find common number up to 100. 21 multiples, e.g. for 6 and 9

24 | Framework review © Crown copyright 2006 Framework review • Use knowledge of rounding, place • Check results of calculations. Year 5 value, number facts and inverse 73 operations to estimate and check calculations

Calculating 2006 objectives 1999 Framework and Supplement of examples • Extend mental methods for whole- • Use mental calculation strategies – Year 5 number calculations, e.g. to multiply several objectives, including: 41, 43 a two-digit by one-digit number (e.g. partitioning; 12 × 9), to multiply by 25 (e.g. 16 × 61, 63, 65 25), to subtract one near multiple of find a difference by counting up (e.g. 1000 from another (e.g. 5003 – 4996); 6070 – 4097) se related facts, e.g. to multiply by 25, multiply by 100 then divide by 4. • Use efficient written methods to add • Extend written methods to: Year 5 and subtract whole numbers and addition of more than two integers; 49, 51 decimals with up to two places addition or subtraction of a pair of decimal fractions (e.g. £29.78 + £53.34). • Use understanding of place value to • Multiply and divide decimals by 10 or Year 6 multiply and divide whole numbers 100 and integers by 1000 explain 7 and decimals by 10, 100 or 1000 the effect. • Refine and use efficient written • Extend written methods to HTU or Year 5 methods to multiply and divide U.t by U; long multiplication of TU by 67, 69 HTU × U, TU × TU, U.t × U, and TU; HTU by U (integer remainder). HTU ÷ U

1 • Find fractions using division, e.g. 100 • Relate fractions to division, and use Year 5

of 5 kg, and percentages of numbers division to find simple fractions, 25 and quantities, e.g. 10%, 5% and including tenths and hundredths, of 3 33 15% of £80 numbers and quantities (e.g. 4 of 1 1 12, 10 of 50, 100 of £3). • Find simple percentages of small whole-number quantities (e.g. 25% of £8). • Use a calculator to solve problems, • Develop calculator skills and use a Year 5 including those involving decimals or calculator effectively. 71 3 fractions, e.g. to find 4 of 150 g; interpret the display correctly in the context of measurement

Understanding shape 2006 objectives 1999 Framework and Supplement of examples • Identify, visualise and describe • Recognise properties of rectangles; Year 5 properties of rectangles, triangles, classify triangles (isosceles, 103, 105 regular polygons and 3-D solids; use equilateral, scalene), using criteria knowledge of properties to draw 2-D such as equal sides, equal angles, shapes and identify and draw nets of lines of symmetry. 3-D shapes • Make shapes with increasing accuracy; visualise 3-D shapes from 2-D drawings; identify different nets for an open cube. • Identify different nets for a closed Year 6 cube. 105

25 | Framework review © Crown copyright 2006 Framework review • Read and plot co-ordinates in the • Read and plot co-ordinates in the Year 5 first quadrant; recognise parallel and first quadrant. 109 perpendicular lines in grids and • Recognise perpendicular and shapes; use a set-square and ruler parallel lines. to draw shapes with perpendicular or parallel sides • Complete patterns with up to two • Recognise reflective symmetry in Year 5 lines of symmetry and draw the regular polygons, e.g. know that a 107 position of a shape after a reflection square has four lines of symmetry or translation 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. • Estimate, draw and measure acute • Understand and use angle measure Year 5 and obtuse angles using an angle in degrees; identify, estimate and 111 measurer or protractor to a suitable order acute and obtuse angles. degree of accuracy; calculate angles • Use a protractor to measure and in a straight line draw acute and obtuse angles to the nearest 5°. • Calculate angles in a straight line.

Measuring 2006 objectives 1999 Framework and Supplement of examples • Read, choose, use and record • Use, read and write standard metric Year 5 standard metric units to estimate units (km, m, cm, mm, kg, g, l, ml), 91 and measure length, weight and including their abbreviations, and capacity to a suitable degree of relationships between them. Convert 93 accuracy, e.g. the nearest larger to smaller units (e.g. km to m, centimetre; convert larger to smaller m to cm or mm, kg to g, l to ml). units using decimals to one place, • Suggest suitable units and e.g. change 2.6 kg to 2600 g measuring equipment to estimate or measure length, mass or capacity. • Interpret a reading that lies between • Record estimates and readings from Year 5 two unnumbered divisions on a scales to a suitable degree of 95 scale accuracy. • Draw and measure lines to the • Measure and draw lines to the Year 5 nearest millimetre; measure and nearest millimetre. 97 calculate the perimeter of regular • Measure and calculate perimeters of and irregular polygons; use the rectangles and regular polygons. formula for the area of a rectangle to calculate its area • Understand area measured in square centimetres (cm2); use the formula for the area of a rectangle. • Read timetables and time using 24- • Read the time on a 24-hour digital Year 5 hour clock notation; use a calendar clock and use 24-hour clock 99 to calculate time intervals notation, such as 19:53. Use timetables. 89 • Solve word problems involving time.

26 | Framework review © Crown copyright 2006 Framework review • Use a calendar. Year 4 100

Handling data 2006 objectives 1999 Framework and Supplement of examples • Describe the occurrence of familiar • Discuss the chance or likelihood of Year 5 events using the language of chance particular events. 113 or likelihood • Answer a set of related questions by • Solve a problem by representing Year 5 collecting, selecting and organising and interpreting data in tables, 115 relevant data; draw conclusions, charts, graphs and diagrams, using ICT to present features, and including those generated by a identify further questions to ask computer, e.g. bar line charts, • Construct frequency tables, vertical axis labelled in 2s, 5s, 10s, pictograms and bar and line graphs 20s or 100s, first where intermediate to represent the frequencies of points have no meaning (e.g. scores events and changes over time on a dice rolled 50 times), then where they may have meaning (e.g. room temperature over time). • Find and interpret the mode of a set • Find the mode of a set of data. Year 5 of data 117

27 | Framework review © Crown copyright 2006 Framework review

Year 6

Using and applying mathematics 2006 objectives 1999 Framework and Supplement of examples • Solve multi-step problems, and • Identify and use appropriate Year 6 problems involving fractions, operations (including combinations 83, 85 decimals and percentages; choose of operations) to solve word 87, 89, 101 and use appropriate calculation problems involving numbers and strategies at each stage, including quantities based on ‘real life’, money 75 calculator use or measures (including time), using 57 • Tabulate systematically the one or more steps; explain methods information in a problem or puzzle; and reasoning. identify and record the steps or • Choose and use appropriate number calculations needed to solve it, using operations to solve problems, and symbols where appropriate; interpret appropriate ways of calculating: solutions in the original context and mental, mental with jottings, written check their accuracy methods, calculator. • Round up or down after division, depending on the context. • Suggest, plan and develop lines of • Solve a problem by representing, Year 6 enquiry; collect, organise and extracting and interpreting data in 115, 117 represent information, interpret tables, graphs, charts and diagrams, results and review methods; identify including those generated by a and answer related questions computer. • Represent and interpret sequences, • Solve mathematical problems or Year 6 patterns and relationships involving puzzles, recognise and explain 79 numbers and shapes; suggest and patterns and relationships, test hypotheses; construct and use generalise and predict. Suggest 17, 19, 21 simple expressions and formulae in extensions asking ‘What if…?’ 81 words then symbols, e.g. the cost of c pens at 15 pence each is 15c • Recognise and extend number pence 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). • Explain reasoning and conclusions, • Explain methods and reasoning, Year 6 using words, symbols or diagrams orally and in writing. 77 as appropriate

Counting and understanding number 2006 objectives 1999 Framework and Supplement of examples • Find the difference between a • Find the difference between a Year 6 positive and a negative integer, or positive and a negative integer, or 15 two negative integers, in context two negative integers, in a context such as temperature or the number line

28 | Framework review © Crown copyright 2006 Framework review • Use decimal notation for tenths, • Know what each digit represents in a Year 6 hundredths and thousandths, number with up to three decimal 29 partition, round and order decimals places. Year 6 with up to three places, and position • Order numbers or measurements them on the number line with up to three decimal places. 13 • Consolidate rounding an integer to 31 the nearest 10, 100 or 1000. • Round a number with two decimal places to the nearest tenth or to the nearest whole number. • Round whole numbers to the Year 7 nearest 10, 100 or 1000, and 42, 44 decimals to the nearest whole number or one decimal place. • Express a larger whole number as • Reduce a fraction to its simplest Year 6 a fraction of a smaller one e. g. form by cancelling common factors 23 recognise that 8 slices of a 5-slice in the numerator and denominator. 8 3 pizza represents 5 or 1 5 pizzas; 2 3 5 • Order fractions such as 3, 4 and 6 simplify fractions by cancelling by converting them to fractions with common factors; order a set of a common denominator, and fractions by converting them to position them on a number line. fractions with a common denominator • Express one quantity as a • Understand percentage as the Year 6 percentage of another, e.g. express number of parts in every hundred. 31 £400 as a percentage of £1000; find Find simple percentages of whole equivalent percentages, decimals number quantities. 33 and fractions • 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 1 1 (e.g. know that 3 = 33 3%). • Solve simple problems involving • Use the vocabulary of estimation Year 6 direct proportion by scaling and approximation. 11 quantities up or down • Solve simple problems involving 27 ratio and proportion.

Knowing and using number facts 2006 objectives 1999 Framework and Supplement of examples • Use knowledge of place value and • Use mental calculation strategies – Year 6 multiplication facts to 10 × 10 to several objectives, including: 61, 63, 65 derive related multiplication and partition; division facts involving decimal numbers, e.g. 0.8 × 7, 4.8 ÷ 6 use factors; use known number facts and place value to consolidate mental multiplication and division.

29 | Framework review © Crown copyright 2006 Framework review • Use knowledge of multiplication • Recognise squares of numbers to at Year 6 facts to derive quickly squares of least 12 × 12. 21 numbers to 12 × 12 and the • Derive quickly squares of multiples 59 corresponding squares of multiples of 10 (e.g. 60 × 60). of 10 • Recognise that prime numbers have • Recognise prime numbers; factorise Year 6 only two factors and identify prime numbers to 100 into prime factors. 21 numbers less than 100; find the prime factors of two-digit numbers • Use approximations, inverse • Check results of calculations. Year 6 operations and tests of divisibility to • Know and apply simple tests of 73 estimate and check results divisibility. 19

Calculating 2006 objectives 1999 Framework and Supplement of examples • Calculate mentally with integers and • Use known number facts and place Year 6 decimals: U.t ± U.t, TU × U, TU ÷ U, value to consolidate mental 45, 47 U.t × U, U.t ÷ U addition/subtraction (e.g. 9.2 – 8.6, 7.4 + 9.8). 65 • Use known number facts and place value to consolidate mental multiplication and division. • Use efficient written methods to add • Extend written methods to column Year 6 and subtract integers and decimals, addition and subtraction of numbers 49, 51 to multiply and divide integers and involving decimals. 67, 69 decimals by a one-digit integer, and • Extend written methods to short to multiply two- and three-digit multiplication of numbers involving 57 integers by a two-digit integer decimals; short division of numbers involving decimals. • Express a quotient as a fraction or as a decimal rounded to one decimal place. • Relate fractions to multiplication and • Find fractions, including tenths and Year 6 1 1 division, e.g. 6 ÷ 2 = ¤2 of 6 = 6 × ¤2; hundredths, of numbers or quantities 25 5 7 9 express a quotient as a fraction or (e.g. 8 of 32, 10 of 40, 100 of 400 2 33 decimal, e.g. 67 ÷ 5 = 13.4 or 13 ¤5; cm). find fractions and percentages of • Find simple percentages of small 5 whole-number quantities, e.g. ¤8 of whole-number quantities (e.g. find 96, 65% of £260 10% of £500, then 20%, 40% and 80% by doubling). • Use a calculator to solve problems • Develop calculator skills and use a Year 6 involving multi-step calculations calculator effectively. 71

Understanding shape 2006 objectives 1999 Framework and Supplement of examples • Describe, identify and visualise • Describe and visualise properties of Year 6 parallel and perpendicular edges or solid shapes such as parallel or 103, 105 faces and use these properties to perpendicular faces or edges. classify 2-D shapes and 3-D solids • Classify quadrilaterals, using criteria such as parallel sides, equal angles, equal sides, …

30 | Framework review © Crown copyright 2006 Framework review • Make and draw shapes with • Make shapes with increasing Year 6 increasing accuracy and apply accuracy. 105 knowledge of their properties • Visualise and draw on grids of • Recognise where a shape will be Year 6 different types where a shape will be after reflection, or after two 107 after reflection, after translations or translations. 111 after rotation through 90° or 180° • Recognise where a shape will be about its centre or one of its vertices after a rotation through 90° about one of its vertices. • Use coordinates in the first quadrant • Read and plot coordinates. Year 6 to draw and locate shapes 109 • Estimate angles, and use a • Estimate angles; use a protractor to Year 6 protractor to measure and draw measure and draw acute and obtuse 111 them, on their own and in shapes; angles to the nearest degree. calculate angles in a triangle or • Check that the sum of the angles of around a point a triangle is 180°: e.g. by measuring or paper folding. • Calculate angles in a triangle or around a point.

Measuring 2006 objectives 1999 Framework and Supplement of examples • Select and use standard metric units • Use, read and write standard metric Year 6 of measure and convert between units (km, m, cm, mm, kg, g, l, ml, 91 units using decimals to two places, cl), including their abbreviations, and e.g. change 2.75 litres to 2750 ml, or relationships between them. Convert 93 vice versa 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. • Read and interpret scales on a • Record estimates and readings from Year 6 range of measuring instruments, scales to a suitable degree of 95 recognising that the measurement accuracy. made is approximate and recording results to a required degree of accuracy; compare readings on different scales, e.g. when using different instruments • Calculate the perimeter and area of • Calculate the perimeter and area of Year 6 rectilinear shapes; estimate the area simple compound shapes that can 97 of an irregular shape by counting be split into rectangles. squares

Handling data 2006 objectives 1999 Framework and Supplement of examples • Describe and predict outcomes from • Use the language associated with Year 6 data using the language of chance probability to discuss events, 113 or likelihood including those with equally likely outcomes.

31 | Framework review © Crown copyright 2006 Framework review • Solve problems by collecting, • Solve a problem by representing, Year 6 selecting, processing, presenting extracting and interpreting data in 115, 117 and interpreting data, using ICT tables, graphs, charts and diagrams, where appropriate; draw conclusions including those generated by a and identify further questions to ask computer, e.g. • Construct and interpret frequency – line graphs (e.g. for distance/time, tables, bar charts with grouped for a multiplication table, a discrete data, and line graphs; conversion graph, a graph of interpret pie charts 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, …). • Describe and interpret results and • Find the mode and range of a set of Year 6 solutions to problems using the data; begin to find the median and 117 mode, range, median and mean mean of a set of data.

32 | Framework review © Crown copyright 2006 Framework review

Year 6 progression to Year 7

Using and applying mathematics 2006 objectives KS2/KS3 Frameworks and Supplements of examples • Solve problems by breaking down • Solve word problems in a range of Year 7 complex calculations into simpler contexts: number, algebra, shape, 2–24 steps, choose and use operations space and measures, and handling and calculation strategies data; compare and evaluate appropriate to the numbers and solutions. context; try alternative approaches to overcome difficulties; present, interpret and compare solutions • Represent information or unknown • Represent problems mathematically, Year 7 numbers in a problem, e.g. in a making correct use of symbols, 26 table, formula or equation; explain words, diagrams, tables and graphs. 138–142 solutions in the context of the • Use simple formulae from problem mathematics and other subjects. 122–124 • Construct and solve simple linear 30 equations. • Present and interpret solutions in the context of the original problem. • Develop and evaluate lines of • Identify the necessary information to Year 7 enquiry; identify, collect, organise solve a problem. 26 and analyse relevant information; • Interpret diagrams and graphs, and 268 decide how best to represent draw simple conclusions. conclusions and what further 30 questions to ask • Present and interpret solutions in the context of the original problem. 138–142 • Suggest extensions to problems. • Generate sequences and describe • Generate sequences from practical Year 7 the general term; use letters and contexts and describe the general 154, 156 symbols to represent unknown term in simple cases. 112 numbers or variables; represent • Use letter symbols to represent simple relationships as graphs unknown numbers or variables. 138–142 • Suggest extensions to problems by asking 'What if...?'; begin to generalise and to understand the significance of a counter-example. • Explain and justify reasoning and • Solve geometrical problems, using Year 7 conclusions, using notation, symbols step-by-step deduction and 32, 34 and diagrams; find a counter- explaining reasoning with diagrams example to disprove a conjecture; and text. 184–188 use step-by-step deductions to solve • Explain and justify methods and 30 problems conclusions, orally and in writing.

33 | Framework review © Crown copyright 2006 Framework review Counting and understanding number 2006 objectives KS2/KS3 Frameworks and Supplements of examples • Compare and order integers and • Compare and order decimals in Year 7 decimals in different contexts different contexts; know that when 40 comparing measurements they must be in the same units. Year 6 • Order a set of positive and negative 15 integers. • Order a set of fractions by • Order fractions and position them on Year 6 converting them to decimals a number line. 23 • Recognise approximate proportions • Use percentages to compare simple Year 7 of a whole and use fractions and proportions. 74 percentages to describe and compare them, e.g. when interpreting pie charts • Use ratio notation, reduce a ratio to • Understand the relationship between Year 7 its simplest form and divide a ratio and proportion; use direct 78, 80 quantity into two parts in a given proportion in simple contexts; use ratio; solve simple problems ratio notation, reduce a ratio to its involving ratio and direct proportion, simplest form and divide a quantity e.g. identify the quantities needed to into two parts in a given ratio. make a fruit drink by mixing water and juice in a given ratio

Knowing and using number facts 2006 objectives KS2/KS3 Frameworks and Supplements of examples • Consolidate rapid recall of number • Consolidate the rapid recall of Year 7 facts, including multiplication facts to number facts, including multiplication 88, 100 10 × 10 and the associated division facts to 10 x 10, and the associated facts division facts. • Recognise the square roots of • Recognise the first few triangular Year 7 perfect squares to 12 × 12 numbers, squares of numbers to at 56, 58 least 12 × 12 and the corresponding roots. • Recognise and use multiples, • Recognise multiples up to 10 × 10. KS2: Year 6 factors, divisors, common factors, Know and apply simple tests of 19, 21 highest common factors and lowest divisibility. Find simple common common multiples in simple cases multiples. KS3: Year 7 • Factorise numbers to 100 into prime 52, 54 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. • Make and justify estimates and • Make and justify estimates and Year 7 approximations of calculations approximations of calculations. 102

34 | Framework review © Crown copyright 2006 Framework review Calculating 2006 objectives KS2/KS3 Frameworks and Supplements of examples • Understand how the commutative, • Know and use the order of Year 7 associative and distributive laws, operations, including brackets 86 and the relationships between operations, including inverse operations, can be used to calculate more efficiently; use the order of operations, including brackets • Consolidate and extend mental • Consolidate and extend mental Year 7 methods of calculation to include methods of calculation to include 92, 94, 96 decimals, fractions and percentages decimals, fractions and percentages. 98, 100 • Use standard column procedures to • Use standard column procedures to Year 7 add and subtract integers and add and subtract whole numbers 104 decimals, and to multiply two- and and decimals. 106 three-digit integers by a one- or two- • Multiply and divide three-digit by digit integer; extend division to two-digit whole numbers; extend to dividing three-digit integers by a two- multiplying and dividing decimals digit integer with one or two places by single-digit whole numbers. • Calculate percentage increases or • Calculate simple percentages. Year 7 decreases and fractions of quantities • Calculate simple fractions of 70,72 and measurements (integer quantities and measurements 66, 68 answers) (whole-number answers). • Use bracket keys and the memory of • Know and use the order of Year 7 a calculator to carry out calculations operations, including brackets. 86 with more than one step; use the • Carry out calculations with more 108 square root key 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).

Understanding shape 2006 objectives KS2/KS3 Frameworks and Supplements of examples • Use correctly the vocabulary, • Use correctly the vocabulary, Year 7 notation and labelling conventions notation and labelling conventions 178 for lines, angles and shapes for lines, angles and shapes. • Extend knowledge of properties of • Begin to identify and use angle, side Year 7 triangles and quadrilaterals and use and symmetry properties of triangles 184, 186, these to visualise and solve and quadrilaterals; solve geometrical 188 problems, explaining reasoning with problems involving these properties, diagrams using step-by-step deduction and explaining reasoning with diagrams and text. • Know the sum of angles at a point, • Know the sum of angles at a point, Year 7 on a straight line and in a triangle, on a straight line and in a triangle, 180, 182 and recognise vertically opposite and recognise vertically opposite angles angles.

35 | Framework review © Crown copyright 2006 Framework review • Use all four quadrants to find • Read and plot co-ordinates in all four Year 6 coordinates of points determined by quadrants. 109 geometric information • Use conventions and notation for 2- KS3: Year 7 D coordinates in all four quadrants; find coordinates of points 218 determined by geometric information. • Identify all the symmetries of 2-D • Recognise and visualise the Year 7 shapes; transform images using ICT transformation and symmetry of a 2- 202–212 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. • Construct a triangle given two sides • Use a ruler and protractor to Year 7 and the included angle construct a triangle given two sides 222 and the included angle.

Measuring 2006 objectives KS2/KS3 Frameworks and Supplements of examples • Convert between related metric units • Convert one metric unit to another Year 7 using decimals to three places, e.g. (e.g. grams to kilograms). 230 convert 1375 mm to 1.375 m, or vice versa • Solve problems by measuring, • Know imperial units (mile, pint, Year 6 estimating and calculating; measure gallon, lb, oz); know rough 91 and calculate using imperial units equivalents of lb and kg, oz and g, still in everyday use; know their miles and km, litres and pints or approximate metric values gallons. • Calculate the area of right-angled • Know and use the formula for the Year 7 triangles given the lengths of the two area of a rectangle; calculate the 234, 236 perpendicular sides, and the volume perimeter and area of shapes made and surface area of cubes and from rectangles. 238, 240 cuboids • Calculate the surface area of cubes and cuboids.

Handling data 2006 objectives KS2/KS3 Frameworks and Supplements of examples • Understand and use the probability • Understand and use the probability Year 7 scale from 0 to 1, find and justify scale from 0 to 1; find and justify 278, 280 probabilities based on equally likely probabilities based on equally likely outcomes in simple contexts outcomes in simple contexts.

36 | Framework review © Crown copyright 2006 Framework review • Explore hypotheses by planning • Plan how to collect and organise Year 7 surveys or experiments to collect small sets of data. 252, 254 small sets of discrete or continuous • Collect small sets of data from 262, 264 data; select, process, present and surveys and experiments. interpret the data, using ICT where 268, 270 appropriate; identify ways to extend • Construct, on paper and using ICT, the survey or experiments graphs and diagrams to represent data; use ICT to generate pie charts. • Construct, interpret and compare graphs and diagrams that represent • Interpret and discuss results. data, e.g. compare proportions in two pie charts that represent different totals • Write a short report of a statistical • Write a short report of a statistical Year 7 enquiry and illustrate with enquiry and illustrate with 272, 274 appropriate diagrams, graphs and appropriate diagrams, graphs and charts, using ICT as appropriate; charts, using ICT as appropriate; justify the choice of what is justify the choice of what is presented presented.

37 | Framework review © Crown copyright 2006