Cfss Text Template s1

Framework review: Draft for distribution

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

This document shows the links between the revised objectives and the 1999 Framework for teaching mathematics. Where objectives have been moved between year groups, they are highlighted.

The highlighted boxes in the Foundation Stage section show that there are fewer objectives in the revised framework than is the case under the section for Reception in the 1999 Framework. Additional guidance on progression across the Foundation Stage will be available in the EYFS Framework and in the Foundation Stage section of this framework.

Foundation Stage

Use and apply mathematics

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

Count, compare and order numbers, and describe relationships between them

2006 objectives 1999 Framework and Supplement of examples • Say and use the number names in order • Say and use the number names in order Reception in familiar contexts In familiar contexts such as number 2 rhymes, songs, stories, counting games and activities.

• Recite the number names in order, 2, 3 continuing the count forwards or backwards from a given number.

1 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Know that numbers identify how many • Count reliably up to 10 everyday objects Reception objects are in a set (first to 5, then 10, then beyond). 4 • Count reliably up to 10 everyday objects • Count reliably in other contexts, such as Reception clapping sounds or hopping movements. 4, 5, 6 • Recognise small numbers without counting. • Begin to recognise 'none' and 'zero' in stories, rhymes and when counting. • Estimate how many objects they can see • Estimate a number in the range that can Reception and check by counting be counted reliably, then check by 8 counting. • Make simple estimates and predictions, 19 e.g. of the number of 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 • Match then compare the number of • Use language such as more or less, Reception objects in two sets greater or smaller, to compare two 11, 12 • Use language such as more or less to numbers and say which is more or less. compare two numbers • Say a number which lies between two 12 given numbers • Use ordinal numbers in different contexts • Begin to understand and use ordinal Reception numbers in different contexts. 13 • Recognise numerals 1 to 9 • Recognise numerals 1 to 9, then 0 and Reception 10, then beyond 10. 9 • Order a given set of numbers: for Reception example, the set of numbers 1 to 6 in 12 random order.

Secure knowledge of number facts which can be recalled quickly and used and applied appropriately

2006 objectives 1999 Framework and Supplement of examples • Observe number relationships and • Separate (partition) a given number of Reception patterns in the environment and use objects into two groups. 16 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 make a • Select two groups of objects to make a Reception given total of objects given total. 16

Calculate efficiently and accurately

2006 objectives 1999 Framework and Supplement of examples • Begin to relate addition to combining two • Begin to relate addition to combining two Reception groups of objects and subtraction to groups of objects, counting all the 14 ‘taking away’ objects. 16, 17 • In practical activities and discussion • Begin to relate subtraction to 'taking begin to use the vocabulary involved in away' and counting how many are left. adding and subtracting

2 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Begin to relate addition to counting on. Reception • Find a total by counting on when one 14 group of objects is hidden. • Count repeated groups of the same size • Count in tens. Reception • Count in twos. 7 • Share objects into equal groups and count how many in each group

Position and transform shapes, recognise and use their properties to visualise and construct

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 patterns, e.g. simple repeating or 25, 26 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 ‘bigger’ • Use language such as circle or bigger to Reception to describe the shape and size of solids describe the shape and size of solids 24, 25 and flat shapes and flat shapes. • Put sets of objects in order of size. Reception • Begin to name solids such as a cube, 26, 24 cone, sphere and flat shapes such as a circle, triangle, square, rectangle. • Use everyday words to describe position • Use everyday words to describe position Reception 27 • Use everyday words to describe Reception direction and movement, e.g. follow and 27 give instructions in physical activities.

Measure accurately using appropriate units, interpret and compare scales

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 compare longer or shorter, heavier or lighter to 19 quantities compare two quantities, then more than two, by making direct comparisons of 22 lengths or masses, and by filling and emptying containers. • Use everyday language related to time; • Begin to understand and use the Reception order and sequence familiar events vocabulary of time; sequence familiar 23 events. and measure short periods of time with a non-standard unit • Begin to know the days of the week in Reception order. 23

Process, present and interpret data to pose and answer questions

2006 objectives 1999 Framework and Supplement of examples • Use developing mathematical language, • Use developing mathematical ideas and Reception ideas and methods to solve practical methods to solve practical problems 18, 20 problems involving counting and comparing in a real or role play context.

3 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Observe numbers and patterns in the • Talk about, recognise and recreate Reception indoor and outdoor environment and in patterns, e.g. simple repeating or 26 daily routines; describe these orally, in symmetrical patterns in the environment. pictures and using objects 19 • Sort familiar objects and count how • Sort and match objects, pictures or Reception many objects share a particular property, children themselves, justifying the 19 presenting results using pictures, decisions made. 4, 5 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

2006 objectives 1999 Framework and Supplement of examples •• Solve problems involving counting, • Use mental strategies to solve simple Year 1 adding, subtracting, doubling or halving problems set in ‘real life’, money or 66, 68 in the context of numbers, measures or measurement contexts, using counting, money; recognise the value of coins 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 • Describe a problem using numbers, • Choose and use appropriate number Year 1 practical materials and diagrams; use operations and mental strategies to 60 these to solve the problem and set the solve problems. 24, 28 solution back in the original context • Use the +, – and = signs to record mental calculations in a number sentence. • Answer a question by selecting and • Solve a given problem by sorting, Year 1 using suitable equipment, and sorting classifying and organising information in 90, 92 information, shapes or objects; display simple ways. Discuss and explain results using tables and pictures results. • Describe simple patterns and • Solve simple mathematical problems or Year 1 relationships involving numbers or puzzles; recognise and predict from 62, 64 shapes; decide whether examples simple patterns and relationships. satisfy given conditions 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 problems and • Explain methods and reasoning Year 1 explain choices and decisions orally or orally. 64 using pictures

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 the • Give a sensible estimate of a number of 2, 4, 6 number of objects stays the same; objects that can be checked by counting 16 estimate a number of objects that can be (e.g. up to about 30 objects). checked by counting • Compare and order numbers, using the • Understand and use the vocabulary of Year 1 related vocabulary; use the equals (=) comparing and ordering numbers, 10, 14 sign including ordinal numbers to at least 20. • 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.

5 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Read and write numerals from 0 to 20, • Read and write numerals from 0 to at Year 1 then beyond, and use knowledge of least 20. 8 place value to position these numbers on • Begin to partition two-digit numbers a number track and number line into a multiple of 10 and ones • Say the number that is one more or less • Within the range 0 to 30, say the number Year 1 than any given number and ten more or that is 1 or 10 more or less than any 12 less for multiples of ten given number. • Use the vocabulary of halves and • Read the time to the hour or half hour on Year 1 quarters in context analogue clocks. 78, 82, 88 • Fold shapes in half. • Make whole turns and half turns. • Begin to recognise and find one half and Year 2 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.

2006 objectives 1999 Framework and Supplement of examples • Derive and recall all pairs of numbers • Know by heart all pairs of numbers with Year 1 with a total of 10 and addition facts for a total of 10 (e.g. 3 + 7), addition facts for 30 totals to at least 5; work out the all totals to at least 5, and the corresponding subtraction facts corresponding subtraction 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 back 4, 6 derive the multiples of 2, 5 and 10 to the to zero; 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 at • Know by heart doubles of all number to Year 2 least 10 10 and the corresponding halves. 53

2006 objectives 1999 Framework and Supplement of examples • Relate addition to counting on; recognise • Use mental calculation strategies – Year 1 that addition can be done in any order; several objectives, including: 32, 34, 36, use practical and informal written use known number facts and place value 38, 40 methods to support the addition of a to add a pair of numbers. one-digit number or a multiple of 10 to a one-digit or two-digit number • Begin to recognise that addition can be done in any order. • Understand subtraction as ‘take away’ • Understand subtraction as ‘take away’ or Year 1 and find a ‘difference’ by counting up; ‘difference’. 28 use practical and informal written • Use mental calculation strategies – 32, 34, 36, methods to support the subtraction of a several objectives, including: one-digit number from a one-digit or two- 38, 40 digit number and a multiple of 10 from a use known number facts and place value two-digit number to subtract a pair of numbers.

6 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Use the vocabulary related to addition • Begin to use the +, – and = signs to Year 1 and subtraction and symbols to describe record mental calculations in a number 24, 28 and record addition and subtraction sentence, and to recognise the use of number sentences symbols such as  to stand for an unknown number. • Solve practical problems that involve • Understand multiplication as repeated Year 2 combining groups of 2, 5 or 10, or addition, and division as sharing. 47, 49 sharing into equal groups

2006 objectives 1999 Framework and Supplement of examples • Visualise and name common 2-D • Describe features of familiar 3-D and 2-D Year 1 shapes and 3-D solids and describe their shapes, including the cube, cuboid, 80 features; use them to make patterns, sphere, cylinder, cone…, circle, triangle, pictures and models square, rectangle, …, referring to 82 properties such as the shapes of flat 88 faces, or the number of faces or corners, or the number and types of sides. • Make and describe models, patterns and pictures using construction kits, everyday materials, Plasticine, … • Fold shapes in half, then make them into symmetrical patterns. • Use shapes to make, describe and continue repeating patterns. • Identify objects that rotate; recognise • Talk about things that turn; make whole Years 1, 2 and make whole, half and quarter turns turns and half turns. 88, 89 • Recognise quarter turns. • Visualise and describe the position of • Use everyday language to describe Year 1 objects and direction and distance when position, direction and movement. 86, 88 moving them, e.g. when placing or moving objects on a games board

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

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; present classifying and organising information in 90, 92 outcomes using practical resources, simple ways, such as: pictures, block graphs or pictograms – using objects or pictures; • Use diagrams to sort objects into groups – in a list or simple table. according to a given criterion; suggest a Discuss and explain results. different criterion for grouping the same objects • Solve a given problem by sorting, Year 2 classifying and organising information in: 91, 93 – a pictogram; – a block graph.

Year 2

2006 objectives 1999 Framework and Supplement of examples • Solve problems involving addition, • Use mental addition and subtraction, and Year 2 subtraction, multiplication or division in simple multiplication and division, to 67, 69 contexts of numbers, measures or solve simple word problems involving pounds and pence 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 number • Use the +, –, ×, ÷ and = signs to record Year 2 sentences involved in a problem, carry mental calculations in a number 25, 29, out the calculations and check that the sentence, and recognise the use of a 47, 49 solution makes sense in the context of symbol such as  to stand for an the problem unknown number. 61 • Choose and use appropriate operations 59 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 and answer • Solve a given problem by sorting, Year 2 questions by selecting and using suitable classifying and organising information in 91, 93 equipment and information, and simple ways. Discuss and explain organising and presenting the results. information in lists, tables and simple diagrams • Describe patterns and relationships • Solve mathematical problems or Year 2 involving numbers or shapes, make puzzles, recognise simple patterns and 63, 65 predictions and test these with examples 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. • Present solutions to problems in an • Explain how a problem was solved orally Year 2 organised way; explain decisions, and, where appropriate, in writing. 65 methods and results in spoken, pictorial and written form, using mathematical language and symbols

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; describe least 100 in figures and words. 9 and extend number sequences and • Describe and extend simple number 3, 5, 7 recognise odd and even numbers sequences; recognise odd and even numbers to at least 30;.

9 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Count up to 100 objects by grouping • Count reliably up to 100 objects by Year 2 them and counting in tens, fives or twos; grouping them, e.g. in tens, then in fives 3 explain what each digit in a two-digit or twos. 9, 13 number represents, including numbers • Know what each digit in a two-digit where 0 is a place holder; partition two- number represents, including 0 as a digit numbers in different ways, including place holder; partition two-digit numbers into multiples of ten and one into a multiple of ten and ones (TU). • Order two-digit numbers and position • Order whole numbers to at least 100, Year 2 them on a number line; use the greater and position them on a number line and 13, 15 than (>), less than (<) signs 100 square. • Use symbols correctly, including less Year 4 than (<), greater than (>), equals (=). 8 • Estimate a number of objects and round • Give a sensible estimate of at least 50 Year 2 two-digit numbers to the nearest 10 objects. 17, 19 • Round numbers less than 100 to the nearest 10. • Find one half, one quarter and three • Begin to recognise and find one half and Year 2 quarters of shapes and sets of objects 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.

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 at all addition and subtraction facts for each 31 least 10, all pairs with totals to 20 and all number to at least 10; 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 inverse of • Derive quickly doubles of all whole Year 3 doubling and derive and recall doubles numbers to at least 20 (e.g. 17 × 2), and 53 of all numbers to 20, and the the corresponding halves (e.g. 36 ÷ 2). corresponding halves • Derive and recall multiplication facts for • Know by heart multiplication facts for the Year 2 the 2, 5 and 10 times-tables and the 2 and 10 times-tables; begin to know 53 related division facts; ; recognise multiplication facts for the 5 times-table. multiples of 2, 5 and 10 Derive quickly the corresponding division facts. • Know by heart multiplication facts for the Year 3 5 times-table. 53 • Use knowledge of number facts and • Check results of calculations by Year 2 operations to check answers to repeating addition in a different order, or 59 calculations with an equivalent calculation.

2006 objectives 1999 Framework and Supplement of examples • Add or subtract mentally a single-digit • Use mental calculation strategies – Year 2 number or a multiple of 10 to or from any several objectives, including: 33–41 two-digit number; use practical and use known number facts and place value 25, 29 informal written methods to support to add/subtract mentally; addition and subtraction of two-digit 27 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 reverses • Understand that subtraction is the Year 2 addition and vice versa and use this to inverse of addition (subtraction reverses 25, 29 derive and record related addition and addition). 35 subtraction number sentences • State the subtraction corresponding to a given addition, and vice versa. • Represent repeated addition and arrays • Understand the operation of Year 2 as multiplication, and sharing and multiplication as repeated addition or as 47, 49 repeated subtraction (grouping) as describing an array, and begin to division; use practical and informal understand division as grouping 57 written methods to support multiplication (repeated subtraction) or sharing. and division calculations, including those • Use known number facts and place with remainders value to carry out mentally simple 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 record Year 2 record and interpret number sentences mental calculations in a number 25, 29 involving all four operations; calculate sentence, and recognise the use of a the value of an unknown in a number symbol such as  to stand for an 47, 49 sentence, e.g. 30 –  = 24,  ÷ 2 = 6 unknown number.

2006 objectives 1999 Framework and Supplement of examples • Visualise common 2-D shapes and 3-D • Use the mathematical names for Year 2 solids and identify them from pictures of common 3-D and 2-D shapes, including 81, 83 them in different positions and the pyramid, cylinder, pentagon, orientations; sort, make and describe hexagon, octagon. shapes, referring to their properties • 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, …

11 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Identify reflection symmetry in patterns • Begin to recognise line symmetry. Year 2 and 2-D shapes and draw lines of 85 symmetry in shapes • Follow and give instructions involving • Use mathematical vocabulary to Year 2 position, direction and movement describe position, direction and 87, 89 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 turns, Year 2 quarter turns, both clockwise and anti- to the left or right, clockwise or anti- 89 clockwise; know that a right angle clockwise; know that a right angle is a represents a quarter turn measure of a quarter turn, and recognise right angles in squares and rectangles.

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

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

Year 3

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

2006 objectives 1999 Framework and Supplement of examples • Read, write and order whole numbers to • Read and write whole numbers to at Year 3 at least 1000 and position them on a least 1000 in figures and words. 11, 13, 15 number line • Order whole numbers to at least 1000, and position them on a number line. • Partition three-digit numbers in different • Know what each digit represents, and Year 3 ways, including into multiples of one partition three-digit numbers into a 9 hundred, ten and one multiple of 100, a multiple of ten and ones (HTU). • Round two- or three-digit numbers to the • Round any two-digit number to the Year 3 nearest 10 or 100 and give estimates nearest 10 and any three-digit number to 19 and approximations to their sums and the nearest 100. differences • Round any positive integer less than Year 4 1000 to the nearest 10 or 100. 10, 12

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

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 20, all addition and subtraction facts for each 31 sums and differences of multiples of 10 number to 20; and number pairs that total 100 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). • Derive quickly all number pairs that total Year 4 100 (e.g. 62 + 38, 75 + 25, 40 + 60). 38 • Derive and recall multiplication facts for • Know by heart multiplication facts for the Year 3 the 2, 3, 4, 5, 6 and 10 times-tables and 2, 5 and 10 times-tables; begin to know 53 the corresponding division facts; the 3 and 4 times-tables. Derive quickly recognise two-digit and three-digit corresponding division facts. 7 multiples of 2, 5 or 10 • 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 for 2, Year 4 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 operations • Check subtraction with addition, halving Year 3 and corresponding inverses to check with doubling and division with 59 calculations multiplication. • Repeat addition or multiplication in a different order. • Check with an equivalent calculation.

2006 objectives 1999 Framework and Supplement of examples • Add or subtract mentally combinations of • Use mental calculation strategies – Year 3 one-digit and two-digit numbers several objectives, including: 37, 39, 41 use known number facts and place value 33, 35 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 refine written methods to • Use informal pencil and paper methods Year 3 support, record or explain the addition to support, record or explain HTU ± TU, 43, 45 and subtraction of two-digit and three- 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 by • Multiply mentally by 10/100 by shifting Year 3 10 or 100, and describe the effect the digits one/two places to the left. 55 • Use practical and informal written • Use known number facts and place Year 3 methods to support multiplication and value to carry out mentally simple 51, 57 division of two-digit numbers (e.g. multiplications and divisions. 13 × 3, 30 ÷ 4); round remainders up or • Begin to find remainders after simple down, depending on the context division; round up or down after division, depending on the context. • Understand that division reverses • Recognise that division is the inverse of Year 3 multiplication and vice versa and use to multiplication, and that halving is the 49 derive and record related multiplication inverse of doubling. 55 and division number sentences • Say or write a division statement corresponding to a given multiplication statement.

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

2006 objectives 1999 Framework and Supplement of examples • Relate 2-D shapes and 3-D solids to • Relate solid shapes to pictures of them. Year 3 drawings of them, and describe, classify, • Classify and describe 3-D and 2-D 81, 83 draw and make 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.

15 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Draw and complete shapes with • Identify and sketch lines of symmetry in Year 3 reflective symmetry and draw the simple shapes, and recognise shapes 85 reflection of a shape in a mirror line with no lines of symmetry. along one side • 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 vocabulary Year 3 position, direction and movement, using related to position, direction and 87 the four compass directions to describe movement, e.g. describe and find the movement about a grid 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 angles • Identify right angles in 2-D shapes and Year 3 and to identify right angles in 2-D the environment. 89 shapes; compare angles with a right • Recognise that a straight line is angle; recognise that two right angles equivalent to two right angles. can form a straight line • Compare angles with a right angle.

2006 objectives 1999 Framework and Supplement of examples • Know the relationships between • Measure and compare using standard Year 3 kilometres and metres, metres and units (km, m, cm, kg, g, l, ml) 73, 75 centimetres, kilograms and grams, litres • Know the relationships between and millilitres; choose and use kilometres and metres, metres and appropriate units to estimate, measure centimetres, kilograms and grams, litres and record measurements 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- • Read scales to the nearest division Year 3 division, scales that are numbered or (labelled or unlabelled); record estimates 77 partially numbered; use the information and measurements to the nearest whole to measure and draw to a suitable or half unit (e.g. ‘about 3.5 kg’), or in degree of accuracy mixed units (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 clock • Read the time to 5 minutes on an Year 3 and to the nearest five minutes on an analogue clock and 12-hour digital clock; 79 analogue clock; calculate time intervals use the notation 9:40. 71 and find start or end times for a given • Solve word problems involving time interval measures. • Read the time to the nearest minute from Year 4 a 12-hour digital clock. 98, 100

2006 objectives 1999 Framework and Supplement of examples • Answer a question by organising, • Solve a given problem by organising and Year 3 representing and interpreting data; use interpreting numerical data in simple 91, 93 tally charts, frequency tables, pictograms lists, tables and graphs, e.g. and bar charts to highlight results and – simple frequency tables; observations; use ICT to create a simple – pictograms; bar chart – bar charts; – Venn and Carroll diagrams (one criterion).

16 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Use Venn diagrams or Carroll diagrams • Solve a given problem by organising and Year 4 to sort data and objects using more than interpreting numerical data in Venn and 116 one criterion Carroll diagrams (two criteria).

Year 4

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 measures, problems involving numbers in ‘real life’, 82, 84, including time; choose and carry out money and measures (including time), 86, 88, 100 appropriate calculations, using calculator using one or more steps, including methods where appropriate converting pounds to pence and metres 74 • Represent a problem using number to centimetres and vice versa. 56 sentences and diagrams, use these to • Choose and use appropriate number find a strategy to solve the problem and operations and appropriate ways of present the solution in the context of the calculating (mental, mental with jottings, problem pencil and paper) to solve problems. • Round up or down after division, depending on the context. • Choose appropriate ways of calculating: Year 5 calculator. 75 • Suggest a line of enquiry and the • Solve a problem by collecting quickly, Year 4 strategy needed to pursue it; collect, organising, representing and interpreting 114, 116 organise and interpret selected data in tables, charts, graphs and information to find answers diagrams, including those generated by a computer. • Use knowledge of numbers and shapes • Solve mathematical problems or Year 4 to identify patterns, properties and puzzles, recognise and explain patterns 78 relationships, and apply them to and relationships, generalise and unfamiliar situations; investigate a predict. Suggest extensions by asking 16, 18 statement involving numbers and test it ‘What if…?’ 80 with examples • 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 problems, • Explain methods and reasoning about Year 4 explanations and reasoning orally and in numbers orally and in writing. 76 writing

2006 objectives 1999 Framework and Supplement of examples • Recognise and extend number • Recognise and extend number Year 4 sequences formed by counting in steps sequences formed by counting in steps 16 of constant size of constant size, extending beyond zero when counting back. • Use positive and negative numbers in • Recognise negative numbers in context Year 4 context; position them on a number line (e.g. on a number line, on a temperature 14 and state inequalities using the symbols scale). 8 < and >, e.g. –3 > –5, –1 < +1 • Use symbols correctly, including less than (<), greater than (>), equals (=).

18 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Use decimal notation for tenths and • Understand decimal notation and place Year 4 hundredths, relating the notation to value for tenths and hundredths, and use 28 money and measurement; position one- it in context, e.g. order amounts of and two-place decimals on a number money; convert a sum of money such as line £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 decimal 29 places. • Recognise the equivalence between • Recognise the equivalence between the Year 5 decimal and fraction forms of one half, decimal and fraction forms of tenths and 7 27 31 quarters, tenths and hundredths hundredths (e.g. 10 = 0.7, 100 = 0.27). • Recognise proportions of a whole and • Begin to relate fractions to division and Year 4 1 1 1 1 use simple fractions to describe them; find simple fractions such as 2, 3, 4, 5, 1 22, 24 use fractions to identify subsets of a set 10, … of numbers.

of objects; use diagrams to identify 2 3 3 7 6 3 • Find fractions such as 3, 4, 5, 10, … of equivalent fractions, e.g. 8 and 4, or 70 7 shapes. 100 and 10; interpret mixed numbers and position them on a number line, e.g. • Recognise the equivalence of simple 1 3 2 fractions 3 • Order a set of fractions such as 2, 2 4, 3 1 1 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 proportion: Year 4 proportion to describe the relationship for example, ‘one for every…’ and ‘one in 26 between two quantities, e.g. 2 to every 3, every…’. and between part and whole, e.g. 2 in • Solve simple problems using ideas of Year 5 every 5; estimate proportion, e.g. ‘for ratio and proportion (‘one for every…’ every 1 red car there are about 4 silver 27 and ‘one in every…’). cars’, or ‘I’m asleep for about ⅓ of the day’

2006 objectives 1999 Framework and Supplement of examples • Use knowledge of addition and • Derive quickly all pairs of multiples of 50 Year 4 subtraction facts and place value to with a total of 1000 (e.g. 850 + 150). 38 derive sums and differences of pairs of • Add three two-digit multiples of 10, 42 multiples of 10, 100 or 1000 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 subtraction 45, 47 (e.g. 470 + 380, 810 – 380). • 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 500 58 multiples of 10 and 100 and derive the and multiples of 100 to 5000, and the corresponding halves corresponding halves. • Derive and recall multiplication facts up • Know by heart all multiplication facts up Year 5 to 10 × 10, the corresponding division to 10 × 10; derive quickly corresponding 59 facts and multiples of numbers to 10 up division facts. 19 to the tenth multiple • Recognise multiples of 6, 7, 8, 9, up to the 10th multiple. • Recognise multiples of 2, 3, 4, 5 and 10, Year 4 up to the tenth multiple. 18

19 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Use knowledge of rounding, number • Check results of calculations. Year 4 operations and inverses to check 72 calculations • Identify pairs of fractions that total 1 • Identify two simple fractions with a total Year 4 3 7 of 1 (e.g. 10 and 10). 22

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

2 3 3 7 • Find fractions such as 3, 4, 5, 10, … of shapes. • Use a calculator to carry out one- and • Develop calculator skills and use a Year 5 two-step calculations involving all four calculator effectively. 71 operations; recognise negative numbers in the display, correct mistaken entries and interpret the display correctly in the context of money

2006 objectives 1999 Framework and Supplement of examples • Draw polygons and classify them by • Classify polygons using criteria such as Year 4 identifying their properties number of right angles, whether or not 102, 104 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 drawings • Visualise 3-D shapes from 2-D drawings Year 4 and make nets of common solids and identify simple nets of solid shapes. 104

20 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Recognise horizontal and vertical lines; • Recognise simple examples of horizontal Year 4 use the eight compass points to describe and vertical lines. 108 direction; describe and identify the • Use the eight compass directions N, S, position of a square on a grid of squares 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. • Know that angles are measured in • Begin to know that angles are measured Year 4 degrees and that one whole turn is 360°; in degrees and that one whole turn is 110 draw, compare and order angles less 360° or 4 right angles; a quarter turn is than 180° 90° or one right angle; half a right angle is 45°; start to order a set of angles less than 180°.

2006 objectives 1999 Framework and Supplement of examples • Choose and use standard metric units • Use, read and write standard metric Year 4 and their abbreviations when estimating, units (km, m, cm, mm, kg, g, l, ml), 90 measuring and recording length, mass including their abbreviations, and and capacity; know the meaning of kilo, imperial units (mile, pint). 92, 94 centi and milli and, where appropriate, • Know and use the relationships between use decimal notation to record familiar units of length, mass and measurements, e.g. 1.3 m or 0.6 kg 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. • Interpret intervals and divisions on • Record estimates and readings from Year 4 partially numbered scales and record scales to a suitable degree of accuracy. 94 readings accurately, where appropriate to the nearest tenth of a unit • Draw rectangles and measure and • Measure and calculate the perimeter and Year 4 calculate their perimeters, find the area area of rectangles and other simple 96 of rectilinear shapes drawn on a square shapes, using counting methods and grid by counting squares standard units (cm, cm2). • Read time to the nearest minute; use • Use am and pm and the notation 9:53. Year 4 am, pm and 12-hour clock notation; • Read simple timetables. 98, 100 choose units of time to measure time intervals; calculate time intervals from • Solve word problems involving time. 88 clocks and timetables

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

Year 5

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

2006 objectives 1999 Framework and Supplement of examples • Count from any given number in whole • Recognise and extend number Year 5 number steps and decimal number sequences formed by counting from any 17 steps, extending beyond zero when number in steps of constant size, counting backwards; relate the numbers extending beyond zero when counting to their position on a number line 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 • Read and write whole numbers in figures Year 5 whole numbers and numbers with up to and words, and know what each digit 3 two decimal places, and partition these represents. 29 numbers • Know what each digit represents in a number with up to two decimal places.

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

2006 objectives 1999 Framework and Supplement of examples • Use knowledge of place value and • Derive quickly pairs of decimals that total Year 5 addition and subtraction of two-digit 1 (e.g. 0.2 + 0.8) or 10 (e.g. 6.2 + 3.8). 39 numbers to derive sums and differences, • Use known number facts and place 45, 47 doubles and halves of decimals, e.g. value for mental addition and subtraction 6.5 ± 2.7, halve 5.6, double 0.34 (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 the 59 corresponding halves. • Recall quickly multiplication facts up to • Know by heart all multiplication facts up Year 5 10 × 10, use to multiply pairs of multiples to 10 × 10; derive quickly division facts. 59 of 10 and 100 and derive quickly • Use known facts and place value to 65 corresponding division facts multiply and divide mentally. • Identify pairs of factors of two-digit whole • Find all the pairs of factors of any Year 5 numbers and find common multiples, number up to 100. 21 e.g. for 6 and 9 • Use knowledge of number facts, place • Check results of calculations. Year 5 value and rounding to estimate and to 73 check calculations

2006 objectives 1999 Framework and Supplement of examples • Multiply mentally TU × U; use mental • Use mental calculation strategies – Year 5 methods in special cases, e.g. to several objectives, including: 41, 43 subtract 1995 from 6007, to multiply 18 partitioning; by 25 61, 63, 65 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.

23 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Use the standard written methods for • Extend written methods to: Year 5 addition and subtraction of decimals with addition of more than two integers; 49, 51 one or 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 and 100 and integers by 1000 explain the 7 decimals by 10, 100 or 1000 effect. • Use the standard written methods for • Extend written methods to HTU or U.t by Year 5 multiplication and division calculations of U; long multiplication of TU by TU; HTU 67, 69 HTU × U, U.t × U, TU × TU and by U (integer remainder). HTU ÷ U

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

5 kg, and percentages of numbers and division to find simple fractions, including 25 quantities, e.g. 10%, 5% and 15% of £80 tenths and hundredths, of numbers and 3 1 1 quantities (e.g. 4 of 12, 10 of 50, 100 of 33 £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. 3 71 fractions, e.g. to find 4 of 150 g; interpret the display correctly in the context of measurement

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, equilateral, 103, 105 regular polygons and 3-D solids; use scalene), using criteria such as equal knowledge of properties to draw 2-D sides, equal angles, lines of symmetry. shapes and identify and draw nets of 3-D • Make shapes with increasing accuracy; shapes visualise 3-D shapes from 2-D drawings; identify different nets for an open cube. • Identify different nets for a closed cube. Year 6 105 • Read and plot co-ordinates in the first • Read and plot co-ordinates in the first Year 5 quadrant and recognise parallel and quadrant. 109 perpendicular lines in grids and shapes; • Recognise perpendicular and parallel use a set-square and ruler to draw lines. perpendicular and parallel lines • Complete patterns with up to two lines of • Recognise reflective symmetry in regular Year 5 symmetry and draw the position of a polygons, e.g. know that a square has 107 shape after a reflection or translation 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.

24 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Estimate, draw and measure acute and • Understand and use angle measure in Year 5 obtuse angles using an angle measurer degrees; identify, estimate and order 111 or protractor to a suitable degree of acute and obtuse angles. accuracy; calculate angles in a straight • Use a protractor to measure and draw line acute and obtuse angles to the nearest 5°. • Calculate angles in a straight line.

2006 objectives 1999 Framework and Supplement of examples • Read, choose, use and record standard • Use, read and write standard metric Year 5 metric units to estimate and measure units (km, m, cm, mm, kg, g, l, ml), 91 length, mass and capacity; convert including their abbreviations, and larger to smaller units using decimals to relationships between them. Convert 93 one place, e.g. change 2.6 kg to 2600 g 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. • Estimate measurements of length, mass • Record estimates and readings from Year 5 and capacity to a required degree of scales to a suitable degree of accuracy. 95 accuracy, e.g. the nearest centimetre; interpret a reading that lies between two unnumbered divisions on a scale • Draw and measure lines to the nearest • Measure and draw lines to the Year 5 millimetre; measure and calculate the nearest millimetre. 97 perimeter of regular and irregular • Measure and calculate perimeters of polygons; use the formula for the area of rectangles and regular polygons. 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-hour • Read the time on a 24-hour digital clock Year 5 clock notation; use a calendar to and use 24-hour clock notation, such as 99 calculate time intervals 19:53. Use timetables. 89 • Solve word problems involving time. • Use a calendar. Year 4 100

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 or particular events. 113 likelihood • Determine the data needed to answer a • Solve a problem by representing and Year 5 set of related questions; select and interpreting data in tables, charts, graphs 115 organise relevant data using frequency and diagrams, including those generated tables; construct pictograms and bar by a computer, e.g. bar line charts, graphs, and line graphs that represent vertical axis labelled in 2s, 5s, 10s, 20s the frequencies of events and changes or 100s, first where intermediate points over time; use ICT to present and have no meaning (e.g. scores on a dice highlight features that lead to further rolled 50 times), then where they may questions have meaning (e.g. room temperature over time). • Find and interpret the mode of a set of • Find the mode of a set of data. Year 5 data 117

Year 6

2006 objectives 1999 Framework and Supplement of examples • Solve multi-step problems, and problems • Identify and use appropriate operations Year 6 involving fractions, decimals and (including combinations of operations) to 83, 85 percentages, choosing and using solve word problems involving numbers 87, 89, 101 appropriate and efficient methods at and quantities based on ‘real life’, money each stage, including calculator use or measures (including time), using one 75 • Represent a problem by identifying and or more steps; explain methods and 57 recording the calculations needed to reasoning. solve it, using symbols for unknown • Choose and use appropriate number quantities where appropriate; set operations to solve problems, and solutions in the original context and appropriate ways of calculating: mental, check their accuracy mental with jottings, written 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 represent extracting and interpreting data in tables, 115, 117 information, interpret results and review graphs, charts and diagrams, including methods; identify and answer related those generated by a computer. questions • Recognise and use sequences, patterns • Solve mathematical problems or Year 6 and relationships involving numbers and puzzles, recognise and explain patterns 79 shapes; suggest hypotheses and test and relationships, generalise and them systematically predict. Suggest extensions asking 17, 19, 21 ‘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; 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, orally Year 6 using symbols where appropriate and in writing. 77

2006 objectives 1999 Framework and Supplement of examples • Find the difference between a positive • Find the difference between a positive Year 6 and a negative integer, or two negative and a negative integer, or two negative 15 integers, in context integers, in a context such as temperature or the number line • Use decimal notation for tenths, • Know what each digit represents in a Year 6 hundredths and thousandths, partition number with up to three decimal places. 29 and order numbers with up to three • Order numbers or measurements with decimal places, and position them on the up to three decimal places. number line

26 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Round numbers, including those with up • Consolidate rounding an integer to the Year 6 to three decimal places nearest 10, 100 or 1000. 13 • Round a number with two decimal 31 places to the nearest tenth or to the nearest whole number. • Round whole numbers to the nearest 10, Year 7 100 or 1000, and decimals to the nearest 42, 44 whole number or one decimal place. • Use fractions, percentages and the • Use the vocabulary of estimation and Year 6 vocabulary of ratio and proportion to approximation. 11 describe the relationships between two • Solve simple problems involving ratio 27 quantities and solve problems, e.g. and proportion. identify the quantities needed to make a fruit drink by mixing water and juice in a given ratio • Express a larger whole number as a • Reduce a fraction to its simplest form by Year 6 fraction of a smaller one; simplify cancelling common factors in the 23 fractions by cancelling common factors; numerator and denominator.

order a set of fractions by converting 2 3 5 • Order fractions such as 3, 4 and 6 by them to fractions with a common converting them to fractions with a denominator common denominator, and position them on a number line. • Express one quantity as a percentage of • Understand percentage as the number Year 6 another, e.g. express £400 as a of parts in every hundred. Find simple 31 percentage of £1000; find equivalent percentages of whole number quantities. 33 percentages, decimals 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 (e.g. know 1 1 that 3 = 33 3%).

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 derive several objectives, including: 61, 63, 65 related multiplication and division facts partition; 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. • Use knowledge of multiplication facts to • Recognise squares of numbers to at Year 6 derive quickly squares of numbers to least 12 × 12. 21 12 × 12 and the corresponding squares • Derive quickly squares of multiples of 10 59 of multiples of 10 (e.g. 60 × 60). • 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 whole numbers • Use approximations and apply tests of • Check results of calculations. Year 6 divisibility to check results • Know and apply simple tests of 73 divisibility. 19

2006 objectives 1999 Framework and Supplement of examples • Calculate mentally with whole numbers • Use known number facts and place Year 6 and decimals, e.g. U.t ± U.t, TU × U, value to consolidate mental 45, 47 U.t × U, TU ÷ 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. • Consolidate the use of standard written • Extend written methods to column Year 6 methods to add, subtract, multiply and addition and subtraction of numbers 49, 51 divide integers and decimal numbers; involving decimals. 67, 69 calculate the answer to HTU ÷ U and • Extend written methods to short U.t ÷ U to one or two decimal places multiplication of numbers involving 57 decimals; short division of numbers involving decimals. • Express a quotient as a fraction, or as a decimal rounded to one decimal place. • Find fractions and percentages of whole- • Find fractions, including tenths and Year 6 5 number quantities, e.g. 8 of 96, 65% of hundredths, of numbers or quantities 5 7 9 25 £260 (e.g. 8 of 32, 10 of 40, 100 of 400 cm). 33 • Find simple percentages of small whole- number quantities (e.g. find 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; carry calculator effectively. 71 out calculations involving time by converting hours and minutes to minutes

2006 objectives 1999 Framework and Supplement of examples • Describe, identify and visualise parallel • Describe and visualise properties of solid Year 6 and perpendicular edges or faces and shapes such as parallel or perpendicular 103, 105 use these properties to classify 2-D faces or edges. shapes and 3-D solids • Classify quadrilaterals, using criteria such as parallel sides, equal angles, equal sides, … • Make and draw shapes with increasing • Make shapes with increasing accuracy. Year 6 accuracy and apply knowledge of their 105 properties • Visualise and draw on grids of different • Recognise where a shape will be after Year 6 types where a shape will be after reflection, or after two translations. 107 reflection, after translations or after • Recognise where a shape will be after a 111 rotation through 90° or 180° about its rotation through 90° about one of its centre or one of its vertices; transform vertices. images using ICT • Use coordinates in the first quadrant to • Read and plot coordinates. Year 6 draw and locate shapes 109

28 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Use a protractor to estimate, measure • Estimate angles; use a protractor to Year 6 and draw angles, on their own and in measure and draw acute and obtuse 111 shapes; calculate angles in a triangle or angles to the nearest degree. around a point • 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.

2006 objectives 1999 Framework and Supplement of examples • Select and use standard metric units of • Use, read and write standard metric Year 6 measure and convert between units units (km, m, cm, mm, kg, g, l, ml, cl), 91 using decimals to two places, e.g. including their abbreviations, and change 2.75 litres to 2750 ml, or vice relationships between them. Convert 93 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. • Measure and calculate using imperials • Know imperial units (mile, pint, gallon, lb, Year 6 units still in everyday use; know their oz); know rough equivalents of lb and kg, 91 approximate equivalent metric values oz and g, miles and km, litres and pints or gallons. • Read scales and record results to a • Record estimates and readings from Year 6 required degree of accuracy, recognising scales to a suitable degree of accuracy. 95 that the measurement made is approximate; compare readings on different scales and when using different instruments • Calculate the perimeter and area of • Calculate the perimeter and area of Year 6 rectilinear shapes; estimate the area of simple compound shapes that can be 97 an irregular shape by counting squares split into rectangles.

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 or probability to discuss events, including 113 likelihood those with equally likely outcomes. • Solve problems involving selecting, • Solve a problem by representing, Year 6 processing, presenting and interpreting extracting and interpreting data in tables, 115, 117 data, using ICT where appropriate; graphs, charts and diagrams, including construct and interpret frequency tables, those generated by a computer, e.g. bar charts with grouped discrete data, – line graphs (e.g. for distance/time, for and line graphs; interpret pie charts; a multiplication table, a conversion draw conclusions and identify further graph, a graph of pairs of numbers questions to ask 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 mode, data; begin to find the median and mean 117 range, median and mean of a set of data.

Year 6 progression to Year 7

2006 objectives KS2/KS3 Frameworks and Supplements of examples • Choose, use and combine any of the • Solve word problems in a range of Year 7 four number operations to solve contexts: number, algebra, shape, space 2–24 numerical problems; try alternative and measures, and handling data; approaches to overcome any difficulties; compare and evaluate solutions. present, interpret and compare solutions • Interpret and use simple formulae from • Represent problems mathematically, Year 7 mathematics and other subjects; making correct use of symbols, words, 26 represent numbers in a problem with diagrams, tables and graphs. 138–142 symbols, construct and solve simple • Use simple formulae from mathematics linear equations and set the solution and other subjects. 122–124 back in the context of the problem • Construct and solve simple linear 30 equations. • Present and interpret solutions in the context of the original problem. • Develop and evaluate lines of enquiry; • Identify the necessary information to Year 7 identify, collect, organise and analyse solve a problem. 26 relevant information; decide how best to • Interpret diagrams and graphs, and draw 268 represent conclusions and what further simple conclusions. questions to ask 30 • Present and interpret solutions in the context of the original problem. 138–142 • Suggest extensions to problems. • Generate sequences and describe the • Generate sequences from practical Year 7 general term in simple cases; use letters contexts and describe the general term 154, 156 and symbols to represent unknown in simple cases. 112 numbers or variables; represent simple • Use letter symbols to represent unknown relationships as graphs 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. • Use step-by-step deductions to solve • Solve geometrical problems, using step- Year 7 problems involving properties of shapes; by-step deduction and explaining 32, 34 explain and justify reasoning and reasoning with diagrams and text. 184–188 conclusions, and find counter-examples • Explain and justify methods and to disprove a conjecture conclusions, orally and in writing. 30

2006 objectives KS2/KS3 Frameworks and Supplements of examples • Compare and order integers and • Compare and order decimals in different Year 7 decimals in different contexts contexts; know that when comparing 40 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 converting • Order fractions and position them on a Year 6 them to decimals number line. 23

30 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Understand the relationship between • Understand the relationship between Year 7 ratio and proportion, solve problems ratio and proportion; use direct 78, 80 involving proportions; use ratio notation, proportion in simple contexts; use ratio reduce a ratio to its simplest form and notation, reduce a ratio to its simplest divide a quantity into two parts in a given form and divide a quantity into two parts ratio in a given ratio. • Recognise approximate proportions and • Use percentages to compare simple Year 7 use fractions and percentages to identify proportions. 74 and compare proportions, e.g. when interpreting pie charts

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

2006 objectives KS2/KS3 Frameworks and Supplements of examples • Use the order of operations, including • Know and use the order of operations, Year 7 brackets; understand the principles of including brackets 86 the commutative, associative and distributive laws and how they can be used to do mental and written calculations more efficiently • Consolidate and extend mental methods • Consolidate and extend mental methods Year 7 of calculation to include decimals, of calculation to include decimals, 92, 94, 96 fractions and percentages fractions and percentages. 98, 100 • Use standard written methods to add • Use standard column procedures to add Year 7 and subtract whole numbers and and subtract whole numbers and 104 decimals, and to multiply and divide decimals. 106 three-digit by two-digit whole numbers; • Multiply and divide three-digit by two- extend to multiplying and dividing digit whole numbers; extend to decimals with one or two places by multiplying and dividing decimals with single-digit whole numbers one or two places by single-digit whole numbers.

31 | Framework review © Crown copyright 2006 Framework review: Draft for distribution • Calculate percentage increases or • Calculate simple percentages. Year 7 decreases and fractions of quantities • Calculate simple fractions of quantities 70,72 and measurements (whole-number and measurements (whole-number 66, 68 answers) answers). • Use bracket keys and the memory of a • Know and use the order of operations, Year 7 calculator to carry out calculations with including brackets. 86 more than one step; use the square root • Carry out calculations with more than 108 key 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).

2006 objectives KS2/KS3 Frameworks and Supplements of examples • Extend knowledge of properties of • Begin to identify and use angle, side and Year 7 triangles and quadrilaterals and use symmetry properties of triangles and 184, 186, these to solve problems, explaining quadrilaterals; solve geometrical 188 reasoning with diagrams problems involving these properties, using step-by-step deduction and explaining reasoning with diagrams and text. • Use correctly the vocabulary, notation • Use correctly the vocabulary, notation Year 7 and labelling conventions for lines, and labelling conventions for lines, 178 angles and shapes angles and shapes. • 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-D KS3: Year 7 coordinates in all four quadrants; find coordinates of points determined by 218 geometric information. • Know the sum of angles at a point, on a • Know the sum of angles at a point, on a Year 7 straight line and in a triangle, and straight line and in a triangle, and 180, 182 recognise vertically opposite angles recognise vertically opposite angles. • Construct a triangle given two sides and • Use a ruler and protractor to construct a Year 7 the included angle triangle given two sides and the included 222 angle.

2006 objectives KS2/KS3 Frameworks and Supplements of examples • Convert between related metric units • Convert one metric unit to another (e.g. Year 7 using decimals to three places, e.g. grams to kilograms). 230 convert 1375 mm to 1.375 m, or vice versa • Read and interpret scales on a range of • Read and interpret scales on a range of Year 7 measuring instruments; compare measuring instruments. 228 readings on different scales, e.g. when using different instruments • Calculate the area of right-angled • Know and use the formula for the area of Year 7 triangles given the lengths of the two a rectangle; calculate the perimeter and 234, 236 perpendicular sides, and the volume and area of shapes made from rectangles. 238, 240 surface area of cubes and cuboids • Calculate the surface area of cubes and cuboids.

2006 objectives KS2/KS3 Frameworks and Supplements of examples • Understand and use the probability scale • Understand and use the probability scale Year 7 from 0 to 1, find and justify probabilities from 0 to 1; find and justify probabilities 278, 280 based on equally likely outcomes in based on equally likely outcomes in simple contexts simple contexts. • Analyse data from surveys and practical • Plan how to collect and organise small Year 7 experiments by selecting, processing, sets of data. 252, 254 presenting and interpreting data; plan • Collect small sets of data from surveys 262, 264 how to collect and organise small sets of and experiments. discrete and continuous data; construct, 268, 270 on paper and using ICT, graphs and • Construct, on paper and using ICT, diagrams to represent data; compare graphs and diagrams to represent data; proportions in two pie charts with use ICT to generate pie charts. different totals; identify ways of • Interpret and discuss results. extending the survey or experiment • Write a short report of a statistical • Write a short report of a statistical Year 7 enquiry and illustrate with appropriate enquiry and illustrate with appropriate 272, 274 diagrams, graphs and charts, using ICT diagrams, graphs and charts, using ICT as appropriate; justify the choice of what as appropriate; justify the choice of what is presented is presented.