Geometry - position and direction Pupils should be taught to: order and arrange combinations of mathematical objects in patterns and sequences use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and. Pupils use the concept and language of angles to describe turn by applying rotations, including in practical contexts (for example, pupils themselves moving in turns, giving instructions to other pupils to do so, and programming robots using instructions given in right angles). Statistics Pupils should be taught to: interpret and construct simple pictograms, tally charts, block diagrams and 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. Lower key stage 2 - years 3 and 4 The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the 4 operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers. At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value.
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Measurement Pupils should be taught to: choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm mass (kg/g temperature (C capacity (litres/ml) to the sonnet nearest appropriate unit, using rulers, scales, thermometers and measuring vessels compare and order lengths, mass, volume/capacity. They use the appropriate language and record using standard abbreviations. Comparing measures includes simple multiples such as half as high; twice as wide. Pupils become fluent in telling the time on analogue clocks and recording. They become fluent in counting and recognising coins. They read and say amounts of money confidently and use the symbols and p accurately, recording pounds and pence separately. Geometry - properties of shapes Pupils should be taught to: identify and describe the properties of 2-D shapes, including the number of sides, and line symmetry in a vertical line identify and describe the properties of 3-D shapes, including the number of edges, vertices and. Pupils identify, compare and sort shapes on the basis of their properties and use vocabulary precisely, such as sides, edges, vertices and faces. Pupils read and write names for shapes that are appropriate for their word reading and spelling. Pupils draw lines and shapes using a straight edge.
They begin to use other multiplication tables and recall multiplication facts, including using related division facts to perform written and mental calculations. Pupils work with a range of materials and contexts in which multiplication and division relate to grouping and sharing discrete and continuous quantities, to arrays and to repeated addition. They begin to relate these to fractions and measures (for example, 20 is a half of 40). They use commutativity and inverse relations to develop multiplicative reasoning (for example, and 20 5 4). Number - fractions Pupils should be taught to: recognise, find, name and write fractions, and of a length, shape, set of objects or quantity write simple fractions, for example of 6 3 and recognise the equivalence of and Notes and guidance (non-statutory) Pupils use fractions. They connect unit fractions to equal sharing and grouping, to numbers when they can be calculated, and to measures, finding fractions of lengths, quantities, sets of objects or shapes. They meet as the first example of a non-unit fraction. Pupils should count in fractions up to 10, starting from any number and using the and equivalence on the number line (for example, 1, 1 (or 1 1, 2). This reinforces the concept of fractions as numbers and that they can add up to more than.
They check their calculations, including by adding to check subtraction and adding numbers in a different order to check addition (for example, ). This establishes commutativity and associativity of addition. Recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers. Number - multiplication and division Pupils should be taught to: recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers calculate mathematical statements for multiplication and division within the multiplication tables and write them. Pupils are introduced to the multiplication tables. They practise to become fluent in the 2, 5 and 10 multiplication tables and connect them to each other. They connect the 10 multiplication table to place value, and the 5 multiplication table to the divisions on the clock face.
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They recognise these shapes in different orientations aang and sizes, and know that rectangles, triangles, cuboids and pyramids are not always similar to each other. Geometry - position and direction Pupils should be taught to: describe position, direction and movement, including whole, half, quarter and three-quarter turns Notes and guidance (non-statutory) Pupils use the language of position, direction and motion, including: left and right, top, middle and bottom, on top. Pupils make whole, half, quarter and three-quarter turns in both directions and connect turning clockwise with movement on a clock face. Year 2 programme of study number - number and place value pupils should be taught to: count in steps of 2, 3, and 5 from 0, and in 10s from any number, forward work and backward recognise the place value of each digit in a two-digit. They count in multiples of 3 to support their later understanding of a third. As they become more confident with numbers up to 100, pupils are introduced to larger numbers to develop further their recognition of patterns within the number system and represent them in different ways, including spatial representations.
Pupils should partition numbers in different ways (for example, and ) to support subtraction. They become fluent and apply their knowledge of numbers to reason with, discuss and solve problems that emphasise the value of each digit in two-digit numbers. They begin to understand 0 as a place holder. Number - addition and subtraction Pupils should be taught to: solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures applying their increasing knowledge of mental and written methods recall and use addition and subtraction facts. Pupils practise addition and subtraction to 20 to become increasingly fluent in deriving facts such as using 3 7 10; and to calculate ; and.
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. Number - multiplication and division, pupils should be taught to: 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. Notes and guidance (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 2s, 5s and 10s. Number - fractions Pupils should be taught to: recognise, find and name a half as 1 of 2 equal parts of an object, shape or quantity recognise, find and name a quarter as 1 of 4 equal parts of an object, shape or quantity notes. 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. Measurement Pupils should be taught to: 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. 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 oclock and then half past. Geometry - properties of shapes Pupils should be taught to: 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 Notes and guidance (non-statutory) Pupils handle.
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Notes and guidance (non-statutory 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 english 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 2s, 5s and 10s from different multiples to develop their recognition of patterns retrolisthesis in the number system (for example, odd and even numbers including varied and frequent practice through increasingly complex. They recognise and create repeating patterns with objects and with shapes. Number - addition and subtraction, pupils should be taught to: 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 0 solve. Notes and guidance (non-statutory pupils memorise and reason with number bonds to 10 and 20 in several forms (for example, 9 7 16; 16 7 9; 7 16 9). They should realise the effect of adding or subtracting. This establishes addition and subtraction as related operations.
The principal focus of mathematics teaching in key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve working with numerals, words and the 4 operations, including with practical resources for example, concrete objects and measuring tools. At this stage, pupils should develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching should also involve using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money. By the end of year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value. An emphasis mental on practice at this early stage will aid fluency. Pupils should read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at key stage. Year 1 programme of study, number - number and place value. Pupils should be taught to: 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 2s, 5s and 10s given a number, identify.
as others, and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions. School curriculum, the programmes of study for mathematics are set out year-by-year for key stages 1 and. Schools are, however, only required to teach the relevant programme of study by the end of the key stage. Within each key stage, schools therefore have the flexibility to introduce content earlier or later than set out in the programme of study. In addition, schools can introduce key stage content during an earlier key stage, if appropriate. All schools are also required to set out their school curriculum for mathematics on a year-by-year basis and make this information available online. Attainment targets, by the end of each key stage, pupils are expected to know, apply and understand the matters, skills and processes specified in the relevant programme of study. Schools are not required by law to teach the example content in square brackets or the content indicated as being non-statutory. Key stage 1 - years 1 and.
However, decisions about when to progress should always be based on the security of vegetarianism pupils understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving. Calculators should not be used as a substitute for good written and mental arithmetic. They should therefore only be introduced near the end of key stage 2 to support pupils conceptual understanding and exploration of more complex number problems, if written and mental arithmetic are secure. In both primary and secondary schools, teachers should use their judgement about when ict tools should be used. Spoken language, the national curriculum for mathematics reflects the importance of spoken language in pupils development across the whole curriculum cognitively, socially and linguistically.
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Purpose of study, mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of historys most intriguing problems. It is essential to everyday dessay life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject. Aims, the national curriculum for mathematics aims to ensure that all pupils: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge. Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects. The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace.