Posted by Peter on 5th May 2011

What maths should children know by the end of Year 6?

This is the final article in our series on what maths children should know, although I will be returning to this theme again and again in the future.
Much of the work carried out in year 5 eg addition and subtraction will need to be reinforced and is not covered in these targets for year 6. Please note that this is only a summary of the key areas of maths to be covered in the year. Some of the work here will be too difficult for many year 6 children: it is very much a set of targets published by the Primary Framework rather than a realistic review of what children can actually achieve. It does give you a good idea of what teachers are hoping to achieve with their children by the end of year 6.
I believe that if a child can successfully meet these challenges then they have a very bright future in maths ahead of them.

Counting and understanding number:

By the end of year 6 children should
• be able to add or subtract using negative numbers in contexts such as temperature.
(eg The temperature is -7 degrees. It rises by 3 degrees. What is the new temperature?)

• understand decimals up to thousandths and partition numbers.
(eg 4.567 = 4 units + 5 tenths + 6 hundredths + 7 thousandths.)

• round decimals.
(eg round 4.56 to the nearest tenth.)

• order decimals up to 3 decimal places and place them on a number line.
(eg order these numbers: 0.7, 0.77, 0.707.)

• understand and use improper fractions.
(eg recognise that 8 pieces of a 5-piece chocolate cake is 8/5 or 1 and 3/5.)

• simplify fractions by cancelling.
(eg 6/10 = 3/5.)

• write one quantity as a percentage of another.
(eg write £30 as a percentage of £300.)

• find equivalence between percentages, decimals and fractions.
(eg 1/10 = 10% = 0.1.)

• solve simple problems involving ratio and proportion.
(eg Sarah has 15 sweets. She gives Tasha 1 sweet for every 4 she keeps herself. How many sweets does Tasha get?)

Knowing and using number facts:

By the end of year 6 children should
• use knowledge of tables to multiply decimals.
(eg multiply 0.6 by 8.)

• use knowledge of tables to divide decimals.
(eg divide 4.8 by 8.)

• use knowledge of tables to work out square numbers up to 12 x 12.
(eg the square of 11?)

• use knowledge of tables to work out the squares of multiples of 10.
(eg the square of 30?)

• understand that prime numbers only have two factors and identify prime numbers up to 100.
(eg what is the next prime number after 17?)

• find the prime factors of 2-digit numbers.)
(eg find the prime factors of 12.)

• use various methods to check answers to calculations, including rules of divisibility.)
(eg if the sum of the digits of a number is divisible by 3 then so is the number.)


By the end of year 6 children should
• mentally add decimals.
(eg 4.5 + 3.2)

• mentally subtract decimals.
(eg 5.4 – 3.8)

• mentally multiply decimals.
(eg 3.6 x 5)

• mentally divide decimals.
(eg 4.5 divided by 9.)

• use efficient (standard) methods to add numbers, including decimals.
(eg £6.78 + £9.85)

• use efficient (standard) methods to subtract numbers, including decimals.
(eg £9.78 – £5.85)

• use efficient (standard) methods to multiply numbers, including decimals.
(eg 345 x 67)

• use efficient (standard) methods to divide numbers, including decimals.
(eg 456 /8)

• relate fractions to multiplication and division.
(eg 8 divided by 2 = ½ of 8 = 8 x ½)

• know the term quotient and state as a fraction or a decimal.
(eg 54 divided by 5 = 10.8 or 10 and 4/5.)

• find fractions of whole numbers.
(eg find 4/5 of 60.)

• find percentages of whole numbers
(eg find 60% of 48.)

• make sensible use of a calculator to solve multi-step problems.

Understanding shape:

By the end of year 6 children should
• classify 2-D and 3-D shapes according to their properties, including recognising parallel and perpendicular sides/edges.
(eg know the diagonals of a square intersect at right angles.)

• become increasingly accurate when drawing or making shapes.

• be able to reflect, translate and rotate shapes through 90 degrees or 180 degrees.
(eg sketch the reflection of a 2-D shape on a grid.)

• use co-ordinates in the first quadrant to draw and complete shapes.
(eg sketch the position of a triangle after it has been translated 2 units down.)

• learn to use a protractor to measure and draw angles.
(eg draw an angle of 45 degrees.)

• calculate the angles in a triangle.
(eg if two angles of a triangle are 60 and 70 degrees, calculate the third angle.)


By the end of year 6 children should
• choose and use to a suitable degree of accuracy metric units of measurement.
(eg measure 450 ml of water in a jug.)

• convert between units using decimals to two places.
(eg change 3750 ml to 3.75 litres.)

• recognise that measurement is approximate and decide on the necessary degree of accuracy when measuring.
(eg measure the length of a tray to the nearest 1 cm.)

• calculate the perimeter and area of rectangles.
(eg know the formula for finding the area of a rectangle.)

• estimate the area of irregular shapes by counting squares.
(eg count any square more than half covered as a whole square and any less than half as zero.)

Handling data:

By the end of year 6 children should
• use the language of chance or likelihood to describe and predict outcomes.
(eg answer the question; what is the probability of throwing a 5 with a 1 to 6 dice?)

• collect, sort, process and present data to solve a problem and interpret the results.
(eg find the most common period of time that goals are scored in the Premier League.)

• construct frequency tables, bar charts, line graphs and pie charts to show results of investigations.
(eg show frequency table for times of goals scored.)

• identify the difference between discrete and continuous data.
(eg draw a line graph in which intermediate values have meaning.)

• use the terms mode, range, median and mean.
( eg know that mode means the most common.)

Using and applying mathematics:

By the end of year 6, when investigating, children should
• choose appropriate operations to solve multi-step problems.

• decide whether to calculate mentally, on paper, or by calculator.

• use tables to show the steps taken.

• record results and check accuracy.

• suggest plans and lines of enquiry.

• review methods used.

• begin to use simple formulae in words and then symbols.

• explain orally, in words or diagrams their reasoning and conclusions.

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