2 Bridging the Gap The introduction of the new National Curriculum in September 2015 means that a huge gap has opened up between the skills needed to master P8 and those needed to complete in Mathematics. Seven Birmingham Special Schools have worked together, funded by the National Centre for Excellence in the Teaching of Mathematics (NCEMT), to look at ways of helping teachers to bridge this gap. It is expected to be useful to both SEN and Mainstream schools. The top box in each section refers to the New National Curriculum objectives. Underneath are listed objectives from the old National Curriculum - Number (N), Space, Shape & Measures (SS&M) and Data (D)- and the level they are taken from Statements highlighted in red correlate directly to objectives in the new National Curriculum for Mathematics All the Bridging the Gap (BTG) documents, links to resources, moderation materials etc are available here. Documents are available to track back to provide information on essential steps using the old National Curriculum. They include possible teaching activities / outcomes and resources Currently these track back from the new NC for Number, Place Value & Rounding Addition & Subtraction Multiplication & Division Fractions In addition Mathematics is tracked back through the P levels from P1 to P8 providing teaching activities / outcomes and resources all the way from P1(i) to of the new NC. It is hoped this will be useful to both SEN and Mainstream schools
3 Number Place Value & Rounding Statutory count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens given a number, identify one more and one less identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least read and write numbers from 1 to 20 in numerals and words. Pupils accurately count, read, write and order whole numbers to at least 100 and understand the place value of each digit N.S They recognise odd and even numbers to about 50 Pupils count, read, write and order accurately whole numbers to at least 50 2C N They recognise odd and even numbers to 20 and other simple number sequences Pupils are confident in using numbers up to 20 and are beginning to understand place value 1A N Pupils count, read and order numbers from B N They write numerals up to 10 with increasing accuracy 1C N They count from one to ten objects They make attempts to record numbers up to 10 Pupils read most numbers up to 10 in familiar contexts Pupils recognise 0 as 'none' and 'zero' in stories and rhymes and when counting and ordering They record numbers from 0-10 and associate these with the number of objects they have counted Pupils count and order numbers (including ordinal numbers) up to 10 in a range of settings N.S Number Place Value & Rounding Non Statutory (N.S) Pupils practise counting (1, 2, 3 ), ordering (for example, first, second, third ), and to indicate a quantity (for example, 3 apples, 2 centimetres), including solving simple concrete problems, until they are fluent. Pupils begin to recognise place value in numbers beyond 20 by reading, writing, counting and comparing numbers up to 100, supported by objects and pictorial representations. They practise counting as reciting numbers and counting as enumerating objects, and counting in twos, fives and tens from different multiples to develop their recognition of patterns in the number system (for example, odd and even numbers), including varied and frequent practice through increasingly complex questions. They recognise and create repeating patterns with objects and with shapes.
4 3 Addition & Subtraction Statutory read, write and interpret mathematical statements involving addition (+), subtraction ( ) and equals (=) signs represent and use number bonds and related subtraction facts within 20 add and subtract one-digit and two-digit numbers to 20, including zero solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = 9. Pupils use mental recall of addition and subtraction facts to 20 in solving problems involving larger numbers They use mental recall of addition facts up to 10 to add and subtract whole numbers, including multiples of 10 They recognise that subtraction is the inverse of addition and use this to solve addition and subtraction problems 2C N They begin to know by heart all pairs of whole numbers with totals up to 10 and can use these facts to add or subtract a pair of numbers mentally Pupils are confident in using numbers up to 20 and are beginning to understand place value 1A N 1B N 1C N They add and subtract numbers when solving problems involving up to 10 objects in a range of contexts They understand the operations of addition and subtraction and use the related vocabulary Using numbers up to 10, they solve problems involving addition or subtraction, including comparing two sets to find a numerical difference They demonstrate an understanding of subtraction as the taking away of objects from a group In practical situations they use the vocabulary involved in adding and subtracting and demonstrate an understanding of addition as the combining of two or more groups of objects and subtraction as the taking away of objects from a group They count from one to ten objects They make attempts to record numbers up to 10 Pupils read most numbers up to 10 in familiar contexts Addition & Subtraction Non Statutory Pupils memorise and reason with number bonds to 10 and 20 in several forms (for example, = 16; 16 7 = 9; 7 = 16 9). They should realise the effect of adding or subtracting zero. This establishes addition and subtraction as related operations. Pupils combine and increase numbers, counting forwards and backwards. They discuss and solve problems in familiar practical contexts, including using quantities. Problems should include the terms: put together, add, altogether, total, take away, distance between, difference between, more than and less than, so that pupils develop the concept of addition and subtraction and are enabled to use these operations flexibly.
5 Multiplication & Division Statutory solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher. Pupils understand the operation of multiplication as repeated addition and as a way of representing the number of items in a rectangular array, and of division as repeated subtraction or sharing They understand halving as the inverse of doubling and use this to derive and learn multiplication and division facts from the 2 times table They can identify doubles and halves using numbers up to 20 and are beginning to understand the concept of 'a quarter' N.S Multiplication & Division Non Statutory Through grouping and sharing small quantities, pupils begin to understand: multiplication and division; doubling numbers and quantities; and finding simple fractions of objects, numbers and quantities. They make connections between arrays, number patterns, and counting in twos, fives and tens.
6 Fractions Statutory recognise, find and name a half as one of two equal parts of an object, shape or quantity recognise, find and name a quarter as one of four equal parts of an object, shape or quantity. They understand halving as the inverse of doubling and use this to derive and learn multiplication and division facts from the 2 times table They can identify doubles and halves using numbers up to 20 and are beginning to understand the concept of 'a quarter' Fractions Non Statutory Pupils are taught half and quarter as fractions of discrete and continuous quantities by solving problems using shapes, objects and quantities. For example, they could recognise and find half a length, quantity, set of objects or shape. Pupils connect halves and quarters to the equal sharing and grouping of sets of objects and to measures, as well as recognising and combining halves and quarters as parts of a whole.
7 Measure Statutory compare, describe and solve practical problems for: lengths and heights [for example, long/short, longer/shorter, tall/short, double/half] mass/weight [for example, heavy/light, heavier than, lighter than] capacity and volume [for example, full/empty, more than, less than, half, half full, quarter] time [for example, quicker, slower, earlier, later] measure and begin to record the following: lengths and heights mass/weight capacity and volume time (hours, minutes, seconds) recognise and know the value of different denominations of coins and notes sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening] recognise and use language relating to dates, including days of the week, weeks, months and years tell the time to the hour and half past the hour and draw the hands on a clock face to show these times. They tell the time using hours, half-hour and quarter-hour units and use the vocabulary related to time Pupils begin to use standard units of length (cm, m), mass or weight (g, kg) and capacity (l) to measure and compare quantities and objects They compare events and timescales using an appropriate standard unit of time (hour, minute, second). They understand and use p notation for money They are beginning to make simple measurements of length, mass/weight and capacity accurately, becoming familiar with using standard units of measurement They recognise 1p, 2p, 5p, 10p, 20p and 50p coins and can choose coins to make amounts up to 50p 2C N They are beginning to link everyday language with mathematical language They suggest suitable units and measuring equipment to estimate and measure a length, mass / weight or capacity 1A N 1B N 1C N They order objects They compare two lengths, masses/weights by direct comparison They continue and create simple spatial patterns They recognise directional symbols such as arrows They recognise terms describing position auch as 'on top', 'in front of', 'behind', 'in the middle' and 'in between' They measure and order more than two objects, using direct comparison They order everyday events logically and begin to use the vocabulary of time Measure Non Statutory The pairs of terms: mass and weight, volume and capacity, are used interchangeably at this stage. Pupils move from using and comparing different types of quantities and measures using non-standard units, including discrete (for example, counting) and continuous (for example, liquid) measurement, to using manageable common standard units. In order to become familiar with standard measures, pupils begin to use measuring tools such as a ruler, weighing scales and containers. Pupils use the language of time, including telling the time throughout the day, first using o clock and then half past.
8 2A SS & M Geometry Statutory recognise and name common 2-D and 3-D shapes, including: 2-D shapes [for example, rectangles (including squares), circles and triangles] 3-D shapes [for example, cuboids (including cubes), pyramids and spheres]. describe position, direction and movement, including whole, half, quarter and three-quarter turns. Pupils can identify common shapes by their properties and describe them in terms of their properties, including recognising right angles in 2-D and 3-D shapes They can sort one collection of 2-D or 3-D shapes in more than one way They can identify lines of symmetry in simple shapes and recognise shapes with no lines of symmetry They are beginning to understand angle as a measure of turn They show an understanding of right angles through movement, including using clockwise and ant-clockwise 2B SS & M Pupils use correct terms for common shapes and recognise properties such as faces, edges, sides and corners They can distinguish between straight and turning movements and can describe positions using terms such as 'at the corner of', 'further away from' They can recognise and draw a line of symmetry or construct patterns with a line of symmetry 2C SS & M Pupils use the correct terms for common shapes and can describe their properties using everyday language They are beginning to link everyday language with mathematical language 1A SS & M Pupils sort and describe 3D & 2D shapes in terms of their properties and positions They recognise directional symbols such as arrows 1B SS & M Pupils work with, recognise and name common 3D shapes They describe the basic properties of these shapes and make simple comparisons between them using terms such as 'larger', 'smaller', 'curved' and 'straight' 1C SS & M They match and sort these shapes in activities They recognise and name some familiar 2D shapes such as circle, triangle and square Pupils construct with 3D shapes and make some arrangements and patterns of 2D shapes Geometry Non Statutory Pupils handle common 2-D and 3-D shapes, naming these and related everyday objects fluently. They recognise these shapes in different orientations and sizes, and know that rectangles, triangles, cuboids and pyramids are not always similar to each other.
9 Geometry Position & Direction Statutory describe position, direction and movement, including whole, half, quarter and three-quarter turns. 2A SS & M They are beginning to understand angle as a measure of turn They show an understanding of right angles through movement, including using clockwise and ant-clockwise 2B SS & M 2C SS & M They are beginning to link everyday language with mathematical language 1A SS & M They recognise directional symbols such as arrows 1B SS & M 1C SS & M They use everyday vocabulary for properties and positions They recognise terms describing position auch as 'on top', 'in front of', 'behind', 'in the middle' and 'in between' Geometry Position & Direction Non Statutory Pupils use the language of position, direction and motion, including: left and right, top, middle and bottom, on top of, in front of, above, between, around, near, close and far, up and down, forwards and backwards, inside and outside. Pupils make whole, half, quarter and three-quarter turns in both directions and connect turning clockwise with movement on a clock face.
10 Year 2 Statistics interpret and construct simple pictograms, tally charts, block diagrams and simple tables ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity ask and answer questions about totalling and comparing categorical data. They sort objects and classify them using more than one criterion Pupils present data they have collected in simple lists, tables or block graphs and communicate their findings to others Pupils organise and classify data using simple lists and tables 2C They collect data by counting and they record the data in a tally or block graph 2 D Pupils sort objects and classify them using more than one criterion When they have gathered information, pupils record results in simple lists, tables and block graphs, in order to communicate their findings 1 D Pupils sort objects and classify them, demonstrating the criterion they have used Year 2 Statistics Non Statutory Pupils record, interpret, collate, organise and compare information (for example, using many-to-one correspondence in pictograms with simple ratios 2, 5, 10).
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