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Maths in Year 5

Maths in Year 5 2021 / 22

End of Year Expectations for Maths in Year 5

Please note that in line with the progress children make this list is subject to change and the objectives
are not necessarily taught in the order listed below.

The National Curriculum for mathematics aims to ensure that all pupils:

  • Become FLUENT in Maths, meaning they are able to calculate quickly and effectively using both mental and written methods,
  • Are able to REASON and EXPLAIN mathematically, meaning they can think logically about Maths, link different pieces of learning, and demonstrate their understanding of a concept through explanation,
  • Are able to SOLVE PROBLEMS, demonstrating that they can use their mathematical understanding to evaluate, understand and solve a variety of mathematical problems. For more information on our problem solving strategies, please refer to the Hutton Rudby Primary School Problem Solving Policy, which can be found at

Maths in Year 5
Number and Place Value
Read, write, order and compare numbers to at least 1000000 and determine the value of each digigit.

Count forwards and 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 problems and practical problems that involve all of the above.

Read Roman numerals to 1000 (M) and recognise years written in Roman numerals.
Addition & Subtraction
Add and subtract whole numbers with more than four digits, including using formal written methods (columnar addition and subtraction).

Add and subtract numbers mentally with increasingly large numbers (e.g. 12462 – 2300 = 10162).

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.
Multiplication & Division
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 four digits by a 1 or 2-digit number using a formal written method, including long multiplication for 2-digit numbers.

Multiply and divide numbers mentally drawing upon known facts.

Divide numbers up to four digits by a 1-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.

Use 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.
Fractions, Decimals & Percentages
Compare and order fractions whose denominators are 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.

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 numbers up to three decimal places.

Read and write decimal numbers as fractions [e.g 0.71 = 71/100].

Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’.

Write percentages as a fraction with denominator 100, and as a decimal.

Solve problems which require knowing percentage and decimal equivalents of 1/ 2 , 1/ 4 , 1 /5 , 2/ 5 , 4/ 5 and those fractions with a denominator of a multiple of 10 or 25.
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 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 ).

Estimate the area of irregular shapes.

Estimate volume (for example, using 1cm3 blocks to build cubes and cuboids) 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.
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)

angles at a point and one whole turn (total 360o)
angles at a point on a straight line and 1/2 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.
Solve comparison, sum and difference problems using information presented in a line graph.

Complete, read and interpret information in tables, including timetables.
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