Main points and highlights of the draft mathematics programme of study Year One in brief
Pupils should develop confidence and mental fluency with whole numbers, counting and place value, "This should involve working with numerals, words and the four operations, including with practical resources (concrete objects, measuring tools, etc.). 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 their use and understanding of place value. An emphasis on practice at this early stage will aid fluency.
"Ensure pupils read and write mathematical vocabulary, consistent with their increasing phonic knowledge at Key Stage 1."
Number: pupils practice counting in ones, twos, fives and tens from different multiples to recognise patterns; starting to recognise place values beyond 20; recognise odd and even numbers.
Addition and subtraction/multiplication and division: pupils practice reading and writing mathematical statements so they become fluent; learn number bonds to 20.
Fractions: recognise and name 1/2, 1/4 and 3/4 of shapes or quantities.
Geometry and measures: pupils use and name common 2D and 3D shapes; describe position; directions and movements using turns. Pupils use rulers; scales and containers to get used to standard measures; and to compare and record measurements. Learn to tell the time to the hour and half hour; sequence time events; recognise and use the language of dates; and recognise and use pounds and pence.
Year 2 in brief
Number: pupils taught to read and write numbers to at least 100 in words and numerals; recognise place value in 2 digit numbers; compare and order numbers up to 100; count in steps of 2,3,5 and 10, count in tens from any number; solve word problems with place value and number facts with increasing precision.
Addition and subtraction: pupils add and subtract numbers of up to 2 digits without carrying or borrowing; add and subtract 2 digit numbers mentally; recognise that addition can be done in any order but subtraction cannot; use them as inverse operations to check calculations.
Multiplication and Division: pupils recall multiplication and division facts for the 2, 5 and 10x tables.
Fractions: pupils recognise, name and write factions of 1/3, 1/4, 1/2, 2/3, and 3/4 of a whole. They count in halves and quarters to ten.
Geometry and measures: Pupils identify properties of shapes, including the number of sides, right angles and line symmetry. They read, write and accurately name 2-D and 3-D shapes and practise using a ruler to draw polygons accurately. They tell the time to 5 minutes, estimate and measure length, height, mass, temperature volume and capacity.
Data: Construct and interpret pictograms, tables and simple graphs.
Lower KS 2
"At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching should also ensure pupils draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. It should ensure they can use measuring instruments with accuracy and make connections between measure and number. By the end of Year 4, pupils should have memorised their times tables up to and including 12 times tables and show precision and fluency in their work."
Year 3 in brief
Number: pupils continue to practise counting in units, tens and hundreds, so that they become fluent in the order and place value of numbers to 1000.
Addition and subtraction: of numbers with up to three digits, on paper. Mental adding and subtraction including pairs of one and two-digit numbers, 3-digit numbers and ones, tens or hundreds. Pupils solve word problems. recall and use multiplication and division facts for the 2, 3, 4, 5, 8 and 10 multiplication tables. They write and calculate mathematical statements for multiplication and division within the multiplication tables; and for 2-digit numbers x 1-digit numbers, using mental and written methods
Multiplication and Division: pupils recall and use multiplication and division facts for the 2, 3, 4, 5, 8 and 10 multiplication tables; write and calculate mathematical statements for multiplication and division within the multiplication tables; and for 2-digit numbers x 1-digit numbers, using mental and written methods.
Fractions: pupils identify, name and write unit fractions up to 1/12, compare and order unit fractions and fractions with the same denominators, add and subtract fractions with the same denominator within one whole, and count up and down in tenths.
Geometry and measures
make 2-D and 3-D shapes; recognise in different orientations; and describe with increasing accuracy;
recognise angles as a property of shape and associate angle as an amount of turning identify right angles, recognise that two right-angles make a half-turn and four a complete turn; identify whether angles are greater or less than a right angle;
identify horizontal, vertical, perpendicular, parallel and curved lines;
use a compass to draw circles and arcs with a given radius.
Pupils will also be able to tell and write the time from an analogue clock, one with Roman numerals, and digital clocks, and do this to the nearest minute, know the number of seconds in a minute, and measure compare and add and subtract lengths, mass, volume and time.
Data: pupils use both horizontal and vertical representations as well as scales for pictograms, for example, where each picture represents 10 bags.
Year 4 in brief
Number: pupils read, write, order and compare numbers to at least 10,000; recognise place value in a 4-digit number; read and write negative numbers; read Roman numerals to 100 and understand that Hindu-Arabic numerals introduced the concept of zero and place value.
Addition and subtraction: pupils add and subtract numbers using formal written methods with up to 4 digits; accurately add and subtract numbers mentally including two 2-digit numbers; estimate, within a range, the answer to a calculation and use inverse operations to check answers.
Multiplication and Division: pupils learn times tables up to 12x12; multiply and divide 2 and 3 digit numbers by a one-digit number, interpret remainders as integers; mentally multiply and divide up to three digit numbers; recognise and use factor pairs to 144.
Fractions: pupils find equivalent fractions of one with a denominator not more than 12; reduce them to their simplest form; add and subtract two fractions with common denominators and one whole.
Decimals: "Ensure pupils are taught decimal notation and vocabulary, including in the context of measurements. Ensure pupils are taught to make comparisons and order decimal amounts and quantities that are expressed to the same number of decimal places.
"Ensure pupils’ understanding of decimal place value is extended to tenths and then hundredths. This will prepare them for Year 5 when they are taught how to relate the decimal notation to division of 2-digit numbers by 10 and later 100, and to the groups of fractions for 1/10 and later 1/100."
Geometry and measures: work on shapes continues, including identifying acute and obtuse angles. "Ensure pupils draw a pair of labelled axes in one quadrant and regularly read, write and use pairs of coordinates, e.g. (2, 5).
"Ensure pupils regularly practise recognising line symmetry in a variety of diagrams. Exclude rotational symmetry." Pupils are introduced to area, initially by counting squares (e.g. cm2 squares) and later using perimeter measurements to calculate areas.
Data: pupils to continue reading, interpreting and solving problems using information in bar graphs.
Upper Key Stage 2
Pupils extend their understanding of the number value and place system to include larger integers, developing connections between multiplication and division with fractions, decimals, percentage and ratio. Pupils should develop their ability to solve a wider range of problems including increasingly complex properties of numbers and arithmetic. "By the end of Year 6, pupils should be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages."
Year 5 in brief
Number: pupils read, write, order and compare numbers to a million, counting up and down in steps of 100,1000, or 10,000, estimate answers and read Roman numbers to 1000.
Addition and subtraction: numbers should now have up to five digits , and practise mental maths with increasingly large numbers.
Multiplication and Division: "Ensure pupils extend their use of written methods for multiplication to practise long multiplication. Also, ensure pupils continue to practise and apply all the multiplication tables and related division facts as often as possible to ensure they are committed to memory and can be used confidently to make larger calculations.
"Ensure pupils record answers for non-integer division in different ways, including: with remainders, fractions, decimals or with rounding, for example: 98 ÷ 4 = 24 r 2 = 24½ = 24.5 = 25."
Fractions: pupils now compare and order fractions with different denominators; recognise mixed numbers and improper fractions and convert from one to the other, write mathematical statements that exceed one as a mixed number; multiply proper fractions and mixed numbers by whole numbers.
Decimals: pupils read and write decimal numbers as fractions (e.g. 0.71 = 71/100) and recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents. They also work with decimals of up to three decimal places.
Percentages: Pupils recognise the per cent symbol and what it means, and write simple fractions and decimals as percentages.
Geometry and measures: pupils continue to practise regularly drawing lines with a ruler and measuring with a protractor and become confident with using conventional markings for parallel lines and right angles. The term diagonal and its properties is introduced.
Position, direction, motion: pupils recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2-D grid and co-ordinates in the first quadrant.
Data: pupils to complete tables and bar graphs from information and solve problems using bar graphs, tables and simple pie charts.
Year 6 in brief
Number: pupils are now working with numbers of up to 10 million, can round any number to a required degree of accuracy, and recognise binary numerals to 15, converting these to decimals.
Addition and subtraction, multiplication and division: problem-solving now includes adding and subtracting negative numbers, multiplying numbers with at least 4-digits by 2-digits of whole number using long multiplication; divide numbers up to 4-digits by a 2-digit whole number using long division, and interpret remainders as whole number remainders, fractions, decimals or by rounding, using brackets.
Fractions: pupils will now be adding and subtracting mixed numbers and fractions with different denominators, dividing proper fractions by whole numbers, calculate decimal fraction equivalents. Calculators can be used for a division calculation to convert a simple fraction to a decimal fraction.
Decimals: pupils learn to identify the value of each digit to three decimal places and multiply and divide numbers up to three decimal place by 10, 100 and 1000, and multiply and divide numbers with up to two decimal places by 1-digit and 2-digit whole numbers.
Ratio and proportion: pupils start using the correct notation and symbol in the context of comparing quantities, sizes and scale drawings.
Algebra: "Ensure pupils write some known arithmetical rules algebraically, such as a + b = b + a, and known relations such as p = 4s for the perimeter of a square. They should also interpret word problems as statements about number and record as a mathematical statement.
Pupils should also write missing number problems algebraically; for example, 2x – 4 = 8 therefore 2x = 12 therefore x = 6 or finding missing lengths in perimeters and missing angles at a point. Pupils should also find possible solutions for equations with two unknown variables, for example x + y = 5 includes solutions x = 1 and y = 4, x = 2 and y = 3."
Geometry: The curriculum includes finding unknown angles, and illustrating and naming parts of circles, including radius, diameter and circumference. Pupils recognise, describe and build simple 3D shapes including making nets.
Position, direction and motion
Pupils should be taught to:
describe positions on the full coordinate grid (all four quadrants)
construct, translate and reflect simple shapes on the coordinate plane.
Measures: pupils use, add and subtract positive and negative integers for measures such as temperature and money. They use the formula to calculate area of a triangle and a parallelogram. This includes identifying the base and its corresponding height, but excludes finding the base or height of a triangle given its area. Pupils can be introduced to other compound units for speed such as miles per hour and apply their knowledge in science as appropriate.