Key Learning in Mathematics – Year 5
Number – number and place value  Number – addition and subtraction  Number – multiplication and division  
· Count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000
· Count forwards and backwards in decimal steps · Read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit · Read, write, order and compare numbers with up to 3 decimal places · Identify the value of each digit to three decimal places · Identify represent and estimate numbers using the number line · Find 0.01, 0.1, 1, 10, 100, 100 and other powers of 10 more or less than a given number · Round any number up to 1 000 000 to the nearest 10, 100, 1000, · Round decimals with two decimal places to the nearest whole number and to one decimal place · Multiply/divide whole numbers and decimals by 10, 100 and 1000 · Interpret negative numbers in context, count on and back with positive and negative whole numbers, including through zero · Describe and extend number sequences including those with multiplication/division steps and where the step size is a decimal · Read Roman numerals to 1000 (M); recognise years written as such · Solve number and practical problems that involve all of the above 
· Choose an appropriate strategy to solve a calculation based upon the numbers involved (recall a known fact, calculate mentally, use a jotting, written method)
· Select a mental strategy appropriate for the numbers involved in the calculation · Recall and use addition and subtraction facts for 1 and 10 (with decimal numbers to one decimal place) · Derive and use addition and subtraction facts for 1 (with decimal numbers to two decimal places) · Add and subtract numbers mentally with increasingly large numbers and decimals to two decimal places · Add and subtract whole numbers with more than 4 digits and decimals with two decimal places, including using formal written methods (columnar addition and subtraction) · Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy · Solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why · Solve addition and subtraction problems involving missing numbers 
· Choose an appropriate strategy to solve a calculation based upon the numbers involved (recall a known fact, calculate mentally, use a jotting, written method)
· 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 (nonprime) numbers · Establish whether a number up to 100 is prime and recall prime numbers up to 19 · Recognise and use square (^{2}) and cube (^{3}) numbers, and notation · Use partitioning to double or halve any number, including decimals to two decimal places · Multiply and divide numbers mentally drawing upon known facts · Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes · Multiply numbers up to 4 digits by a one or twodigit number using a formal written method, including long multiplication for twodigit numbers · Divide numbers up to 4 digits by a onedigit number using the formal written method of short division and interpret remainders appropriately for the context · Use estimation/inverse to check answers to calculations; determine, in the context of a problem, an appropriate degree of accuracy · 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 

Geometry – properties of shapes  
· Distinguish between regular and irregular polygons based on reasoning about equal sides and angles
· Use the properties of rectangles to deduce related facts and find missing lengths and angles · Identify 3D shapes from 2D representations · Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles · Draw given angles, and measure them in degrees (°) · Identify: – angles at a point and one whole turn (total 360°) – angles at a point on a straight line and half a turn (total 180°) 

Number – fractions, decimals and percentages  
· Recognise mixed numbers and improper fractions and convert from one form to the other
· Read and write decimal numbers as fractions (e.g. 0.71 = · Count on and back in mixed number steps such as 1 · Compare and order fractions whose denominators are all multiples of the same number (including on a number line) · Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths · Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents · Add and subtract fractions with denominators that are the same and that are multiples of the same number (using diagrams) · Write statements > 1 as a mixed number (e.g. + = =1 ) · Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams · 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 involving fractions and decimals to three places · Solve problems which require knowing percentage and decimal equivalents of , , , , and fractions with a denominator of a multiple of 10 or 25 

Measurement  
· Use, read and write standard units of length and mass
· Estimate (and calculate) volume ((e.g., using 1 cm^{3} blocks to build cuboids (including cubes)) and capacity (e.g. using water) · Understand the difference between liquid volume and solid volume · Continue to order temperatures including those below 0°C · Convert between different units of metric measure · Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints · Measure/calculate the perimeter of composite rectilinear shapes · Calculate and compare the area of rectangle, use standard units square centimetres (cm^{2}) and square metres (m^{2}) and estimate the area of irregular shapes · Continue to read, write and convert time between analogue and digital 12 and 24hour clocks · Solve problems involving converting between units of time · Use all four operations to solve problems involving measure using decimal notation, including scaling 

Geometry – position and direction  
· Describe positions on the first quadrant of a coordinate grid
· Plot specified points and complete shapes · 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 

Statistics  
· Complete and interpret information in a variety of sorting diagrams (including those used to sort properties of numbers and shapes)
· Complete, read and interpret information in tables and timetables · Solve comparison, sum and difference problems using information presented in all types of graph including a line graph · Calculate and interpret the mode, median and range 