
Maths in Year 6
End of Year Expectations for Maths in
Year 6
Autumn 1st half term objectives highlighted
Objectives previously taught are highlighted
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 the fundmentals of mathematics, so that
pupils have conceptual understanding and can recall and
apply their knowledge rapidly and accurately to
problems.
reason mathematically by following a line of enquiry,
conjecturing relationships and generalisations, and
developing an argument or proof using mathematical
language.
can solve problems by applying their mathematics to a
variety of routine and nonroutine problems with
increasing sophistication, including breaking down
problems into a series of simpler steps and persevering
in seeking solution.

Learning Objectives 
Additional Information 
Number and Place Value 
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 0.
Solve number and practical problems that involve all of the above.

For whole numbers, the more digits a number has, the larger it must be: any 4digit whole number is larger than any 3digit whole number. But this is not true of
decimal numbers: having more digits does not make a decimal number necessarily bigger. For example, 0•5 is larger than 0•35.
Ordering decimal numbers uses the same process as for whole numbers i.e. we look at the digits in matching places in the numbers, starting from the place with the
highest value ie from the left. The number with the higher different digit is the higher number. For example, 256 is greater than 247 because 256 has 5 tens but 247
has only 4 tens. Similarly 1•0843 is smaller than 1•524 because 1•0843 has 0 tenths but 1•524 has 5 tenths.

Addition and Subtratcion 
Solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why.
Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

Deciding which calculation method to use is supported by being able to take apart and combine numbers in many ways. For example, calculating 8.78 + 5.26 might
involve calculating 8.75 + 5.25 and then adjusting the answer.
The associative rule helps when adding three or more numbers: 367 + 275 + 525 is probably best thought of as 367 + (275 + 525) rather than (367 + 275) + 525
Calculation policy page:
P14
St
Dunstan's Catholic Primary School Calculation Policy 
Multiplication and Division 
Multiply multidigit numbers up
to four digits by a 2digit whole number using the
formal written method of long multiplication.
Divide numbers up to four digits by a 2digit 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 four digits by a 2digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
Use their knowledge of the order of operations to carry out calculations involving the four operations.
Solve problems involving addition, subtraction, Multiply 1digit numbers with up to two decimal places by whole numbers
(taken from Fractions including Decimals and Percentages).

Standard written algorithms use the conceptual structures of the mathematics to produce efficient methods of calculation.
Standard written multiplication method involves a number of partial products. For example, 36 × 24 is made up of four partial products 30 × 20, 30 × 4, 6 × 20, 6 × 4.
There are connections between factors, multiples and prime numbers and between fractions, division and ratios.
Calculation policy page:
P1718
St
Dunstan's Catholic Primary School Calculation Policy 
Fractions and Decimals 
Use factors to simplify fractions; use common multiples to express fractions in the same denominator.
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, 14 × 12 = 18 ]
Divide proper fractions by whole numbers [for example, 13 ÷ 2 = 16 ]
Multiply 1digit numbers with up to two decimal places by whole numbers
Use equivalences between simple fractions, decimals and percentages, including in different contexts

Fractions express a relationship between a whole and equal parts of a whole. Pupils should recognise this and speak in full sentences when answering a question
involving fractions. For example, in response to the question ‘What fraction of the journey has Tom travelled?’ the pupil might respond, ‘Tom has travelled two thirds of
the whole journey.’
Equivalent fractions are connected to the idea of ratio: keeping the numerator and denominator of a fraction in the same proportion creates an equivalent fraction.
Putting fractions in place on the number lines helps understand fractions as numbers in their own right.

Ratio 
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.

It is important to distinguish between situations with an additive change or a multiplicative change (which involves ratio). For example, if four children have six
sandwiches to share and two more children join them, although two more children have been added, the number of sandwiches then needed for everyone to still get the same amount is calculated multiplicatively.

Algebra 
Generate and describe linear number sequences
Express missing number problems algebraically
Find pairs of numbers that satisfy an equation with two unknowns.

A linear sequence of numbers is where the difference between the values of neighbouring terms is constant. The relationship can be generated in two ways: the sequencegenerating rule can be recursive, i.e. one number in the sequence is generated from the preceding number (e.g. by adding 3 to the preceding number), or ordinal, i.e. the position of the number in the sequence generates the number (e.g. by multiplying the position by 3, and then subtracting 2).
Sometimes sequence generating rules that seem different can generate the same sequence: the ordinal rule ‘one more than each of the even numbers, starting with 2’ generates the same sequence as the recursive rule ‘start at 1 and add on 2, then another 2, then another 2, and so on’.
Sequences can arise from naturally occurring patterns in mathematics and it is exciting for pupils to discover and generalise these. For example adding successive odd numbers will generate a sequence of square numbers.
Letters or symbols are used to represent unknown numbers in a symbol sentence (i.e. an equation) or instruction. Usually, but not necessarily, in any one symbol sentence (equation) or instruction, different letters or different symbols represent different unknown numbers.
A value is said to solve a symbol sentence (or an
equation) if substituting the value into the sentence
(equation) satisfies it. 
Measurement 
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.
Recognise that shapes with the same areas can have different perimeters and vice versa.
Calculate the area of parallelograms and triangles.

To read a scale, first work out how much each mark or division on the scale represents.
The unit of measure must be identified before measuring. Selecting a unit will depend on the size and nature of the item to be measured and the degree of accuracy required.

Geometry 
Draw 2D shapes using given dimensions and angles.
Recognise, describe and build simple 3D 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.
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.

Variance and invariance are important ideas in mathematics, particularly in geometry. A set of quadrilaterals for example may vary in many ways in terms of area, length of sides and the size of individual angles. However there are a set of invariant properties which remain common to all quadrilaterals, namely they have four sides and their internal angles sum to 360o. Some of these properties emerge from naturally occurring constraints, for example the sum of the internal angles will always sum to 360o, they can do nothing else! The questions ‘What’s the same?’ and ‘What’s different?’ can draw pupils’ attention to variance and invariance.
Shapes can be alike in essentially two different ways: congruent and similar. Congruent shapes are alike in all ways: they could occupy exactly the same space. Similar
shapes share identical geometrical properties but can differ in size. All equilateral triangles are similar, but only identically sized ones are congruent. Not all isosceles triangles are similar.
Angle properties are a mix of necessary conditions and conventions. It is a necessary condition that angles on a straight line combine to a complete half turn. That we measure the half turn as 180^{o} is conventional.

Statistics 
Interpret and construct pie charts and line graphs and use these to solve problems.
Calculate and interpret the mean as an average. 
Pie charts visually display relative proportions, for example, that the proportion of pupils at School A liking reading is greater than the proportion at School B. 
