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,
10 000 and 100 000

·   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 multi-step 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 (non-prime) 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 two-digit number using a formal written method, including long multiplication for two-digit numbers

·   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

·   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 3-D shapes 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 (°)

·   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°)
– other multiples of 90°

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

·   Use, read and write standard units of length and mass

·   Estimate (and calculate) volume ((e.g., using 1 cm3 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 (cm2) and square metres (m2) and estimate the area of irregular shapes

·   Continue to read, write and convert time between analogue and digital 12 and 24-hour 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

·   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