### Mathematics Key Stage 2

During Key Stage 2 pupils use the number system more confidently. They move from counting reliably to calculating fluently with all four number operations deciding which operation to use and the best method to use, depending on the numbers involved.. They always try to tackle a problem with mental methods before using any other approach. Pupils explore features of shape and space and develop their measuring skills in a range of contexts. They discuss and present their methods and reasoning using a wider range of mathematical language, diagrams and charts.

At St Mark’s we use a range of resources including ICT to teach maths and take our learning objectives straight from the National Curriculum.

Here are the programmes of study for each area of maths for Years 5 and 6. Children spend one or two weeks focusing on each of the areas every term. Their level of understanding is then assessed and picked up from there when the topic is revisited.

 Number- numbers and the number system Year 5 Year 6 Pupils should be taught to:  read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit  count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000  interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero  round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000  solve number problems and practical problems that involve all of the above  read Roman numerals to 1000 (M) and recognise years written in Roman numerals. Pupils should be taught to:  read, write, order and compare numbers up to 10 000 000 and determine the value of each digit  round any whole number to a required degree of accuracy  use negative numbers in context, and calculate intervals across zero  solve number and practical problems that involve all of the above. Number- addition and subtraction Number-addition, subtraction, multiplication and division Pupils should be taught to:  add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)  add and subtract numbers mentally with increasingly large numbers  use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy  solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why. Pupils should be taught to:  multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication  divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context  divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context  perform mental calculations, including with mixed operations and large numbers  identify common factors, common multiples and prime numbers  use their knowledge of the order of operations to carry out calculations involving the four operations  solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why   solve problems involving addition, subtraction, multiplication and division  use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy. Number- multiplication and division Pupils should be taught to:  identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers  know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers  establish whether a number up to 100 is prime and recall prime numbers up to 19  multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers  multiply and divide numbers mentally drawing upon known facts  divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context  multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)  solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes  solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign  solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates. Number- fractions (including decimals and percentages) Pupils should be taught to:  compare and order fractions whose denominators are all multiples of the same number  identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths  recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2/5+4/5=6/5= 1 1/5]  add and subtract fractions with the same denominator and denominators that are multiples of the same number  multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams  read and write decimal numbers as fractions [for example, 0.71 = 100 71 ]  recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents  round decimals with two decimal places to the nearest whole number and to one decimal place  read, write, order and compare numbers with up to three decimal places  solve problems involving number up to three decimal places  recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal  solve problems which require knowing percentage and decimal equivalents of ½, ¼, 1/5, 2/5 , 4/5  and those fractions with a denominator of a multiple of 10 or 25. Pupils should be taught to:  use common factors to simplify fractions; use common multiples to express fractions in the same denomination  compare and order fractions, including fractions > 1  add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions  multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4x1/2=1/8]  divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6 ]  associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8 ]  identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places multiply one-digit numbers with up to two decimal places by whole numbers  use written division methods in cases where the answer has up to two decimal places  solve problems which require answers to be rounded to specified degrees of accuracy  recall and use equivalences between simple fractions, decimals and percentages, including in different contexts. Ratio and proportion Pupils should be taught to:  solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts  solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison  solve problems involving similar shapes where the scale factor is known or can be found  solve problems involving unequal sharing and grouping using knowledge of fractions and multiples. Algebra Pupils should be taught to:  use simple formulae  generate and describe linear number sequences  express missing number problems algebraically  find pairs of numbers that satisfy an equation with two unknowns  enumerate possibilities of combinations of two variables.

 Measurement Pupils should be taught to:  convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)  understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints  measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres  calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes  estimate volume [for example, using 1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water]  solve problems involving converting between units of time  use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling. Pupils should be taught to:  solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate§ use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places  convert between miles and kilometres  recognise that shapes with the same areas can have different perimeters and vice versa  recognise when it is possible to use formulae for area and volume of shapes  calculate the area of parallelograms and triangles  calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic metres (m3), and extending to other units [for example, mm3 and km3]. Geometry-properties of shapes Pupils should be taught to: identify 3-D shapes, including cubes and other cuboids, from 2-D representations  know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles  draw given angles, and measure them in degrees (o)  identify:  angles at a point and one whole turn (total 360o)  angles at a point on a straight line and 2 1 a turn (total 180o)  other multiples of 90o  use the properties of rectangles to deduce related facts and find missing lengths and angles  distinguish between regular and irregular polygons based on reasoning about equal sides and angles. Pupils should be taught to:  draw 2-D shapes using given dimensions and angles  recognise, describe and build simple 3-D shapes, including making nets  compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons  illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius  recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles. Geometry- position and direction Pupils should be taught to:  identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed. Pupils should be taught to:  describe positions on the full coordinate grid (all four quadrants)  draw and translate simple shapes on the coordinate plane, and reflect them in the axes. Statistics Pupils should be taught to:  solve comparison, sum and difference problems using information presented in a line graph  complete, read and interpret information in tables, including timetables. Pupils should be taught to:  interpret and construct pie charts and line graphs and use these to solve problems  calculate and interpret the mean as an average.