The Year 6 Learner
Working mathematically
By the end of year 6, children will structure their own investigations and solve a wide variety of increasingly complex
problems. They will independently develop their own lines of enquiry and be expected to prove their solutions in a variety
of ways including algebra, negative proof (use a counter example to prove the rule) and be able to communicate their
results using accurate mathematical language. Children will demonstrate secure knowledge and confidence to talk in depth
about mathematical concepts and explain their solutions, decisions and reasoning.
Number
•
Counting and understanding numbers
Children extend and apply their knowledge of place value for numbers up to and beyond one million (including decimals
and negative numbers) in a variety of situations. Special numbers are extended to include common factors, common
multiples and a deeper understanding of prime numbers. Children will be able to round numbers and identify what degree
of accuracy is appropriate.
•
Calculating
Children will be fluent in a wide range of mental and formal written calculation strategies for all operations, extending to
long division (four digit numbers by two digit numbers) by the end of the year. They will apply estimation in a range of
ways. Through investigations, they explore the effect of the order of operations including the use of brackets.
•
Fractions including decimals and percentages
Children recall and using equivalences between simple fractions, decimals and percentages. Additionally, they are able to
express fractions in their simplest form and calculate the decimal equivalent, for example
= 3 ÷ 8 = 0.375.
Applying this understanding of equivalent fractions, children will order, add and subtract fractions (including mixed
numbers and those with different denominators) by the end of the year e.g.
+
+  = 1. Using hands-on resources and
images, they will multiply and divide proper fractions and mixed numbers by whole numbers e.g.
. Children will solve problems involving the calculation of percentages linked to real life situations.
x
=
and
÷ 2 =
Ratio and proportion
Pupils explore ratio and proportion through real life experiences such as changing the quantities in recipes (scaling), scale
drawings and maps.
Algebra
Throughout their primary experience children will have encountered algebra in a number of different situations which is
drawn together and formalised in year 6. By the end of the year, they will confidently use symbols and letters to
represent variables and unknowns in mathematical situations that they already understand, for example, simple formula
and equivalent expressions a+b = b+a. Children will describe number sequences and missing number calculations.
Measurement
Through investigation and problem solving, children convert between a range of measurement units (including both
imperial and metric). Calculation of perimeter and area is extended to include parallelograms and triangles. Additionally,
they will explore the relationship between area and perimeter. They will know how to calculate, estimate and compare
volume of cubes and cuboids identifying when it is appropriate to use formula.
Geometry
Children will draw 2-D and build 3-D shapes with accuracy using given dimensions and angles. They will create nets of
common 3-D shapes. They will consolidate their knowledge of angles within shapes and extend it to find missing angles
in triangles, quadrilaterals and regular polygons. Children name parts of circles, including radius, diameter and
circumference, and explore the relationships between these elements. Children will use four quadrant co-ordinate grids to
describe positions, draw and translate simple shapes. Using their knowledge of the properties of shape, they will be able
to predict missing co-ordinates and express these algebraically.
Statistics
Children will increase their knowledge of different data representations to include interpreting and constructing pie charts
(using their knowledge of angles, fractions and percentages) and line graphs (e.g. miles to km conversion). They will
know when it is appropriate to use the mean as an average and how to calculate it.
Year 6 Programme of Study
Maths – Number
Understanding the number system
Yr6 Focus
I can identify the value of each digit in numbers to 10 000 000 and
numbers with up to 3 decimal places and multiplies and divides by 10,
100 and 1000
Calculating
Arithmetical laws and relationships
 u s e s t h eir kn o w l ed g e o f t h e o r d e r o f o p e r a t io n s t o c a r r y o u t c a l c u la t io n s
involving the four operations e.g.
2 + 1 x 3 = 5 and (2 + 1) x 3 = 9
Mental fluency
 u s e s es t im a t io n t o c h ec k a n s w er s t o c a l c u la t io n s a n d d e t e r m in e s in t h e
I can compare and order fractions, including fractions >1
context of a problem, an appropriate degree of accuracy
 id e n t if ies c o m m o n f a c t o r s , c o m m o n m u l t ip le s a n d p r im e n u m b er s
I can recognise, describe and use number patterns and relationships to
 p e r f o r m s m e n t a l c a l c u la t io n s , in c l u d in g w it h m ix ed o p e r a t io n s a n d la r g e
make generalisations about sequences within the whole number system
numbers
 c o n t in u es t o u s e a l l kn o w n f a c t s t o c a l c u l a t e m a t h e m a t ic a l s t a t e m e n ts
I can use negative numbers in context, and calculates intervals across
zero
with increasing complexity
Written fluency
I can use common multiples to express fractions in the same denomination
 s o l v e s a d d it io n a n d s u b t r a c t io n p r o b l e m s w it h in t h e f l u e n c y f o c u s a n d
gives reasons why operations and methods are appropriate
I can recall and use equivalences between simple fractions, decimals and
percentages
 m u l t ip l ie s m u l t i-digit numbers up to four digits by a two digit number
using the formal written method of long multiplication and divides numbers
up to four digits by a two digit number using the formal written methods
I can solve number problems and practical problems within different
contexts
of long and short division and interprets remainders as whole numbers,
fractions, or by rounding, as appropriate for the context
Fractions, decimals and percentages
 u s e s c o m m o n f a c t o r s t o s im p lif y f r a c t io n s
 a d d s a n d s u b t r a c t s f r a c t io n s w it h d if f er en t d en o m in a t o r s a n d m ix ed
numbers, using the concept of equivalent fractions
 m u l t ip l ie s s im p le p a ir s o f p r o p er fractions, writing the answer in its
simplest form [e.g. ¼ x ½ = 1/8]
 d iv id es p r o p e r f r a c t io n s b y w h o le n u m b er s e.g. 1/3 ÷2=1/6
 a s s o c ia t es a f r a c t io n w it h d iv is io n a n d c a l c u la t e s d e c im a l f r a c t io n
equivalents for a simple fraction e.g.
Measurement
3 ÷ 5 = 0.6 = 3/5
 m u l t ip l ie s o n e-digit numbers with up to two decimal places by whole
Metric / imperial measures
numbers
 uses, reads, writes and converts between standard units, converting
 u s e s w r it t en d iv is io n m e t h o d s in c a s e s w h e r e t h e a n s w er h a s t w o
measurements of length, mass, volume and time from a smaller unit of
measure to a larger unit, and vice versa, using decimal notation of up to
three decimal places
 converts between miles and kilometres
- connects conversion from kilometres to miles in measurement to its
graphical representation
Perimeter, Area, Volume
 recognises that shapes with the same areas can have different perimeters
and vice versa
 calculates the area of parallelograms and triangles
decimal places
Ratio and proportion
Solves problems involving:
- relative sizes of two quantities where missing values can be found by
using integer multiplication and division
- calculation of percentages and the use of percentages for comparison
(percentages of 360° to calculate angles on a pie chart)
- similar shapes where the scale factor is known or can be found
- unequal quantities (e.g. for every egg you need three spoonful of flour)
Algebra
 u s e s s im p le f o r m u l a e t o g en er a t e, e x p r e s s a n d d es c r ib e :
 recognises when it is possible to use the formulae for the area of
- linear number sequences
shapes
- mathematical formula
 calculates, estimates and compares volume of cubes and cuboids using
standard units, including centimetre cubed (cm³) and cubic metres (m³), and
extending to other units e.g. mm³ and km³
 recognises when it is possible to use the formulae for the volume of
shapes
- missing number, lengths, coordinates and angles problems
- equivalent expressions (a + b = b + a)
 f in d s p a ir s o f n u m b e r s t h a t s a t is f y a n e q u a t io n w it h t w o u n kn o w n s
 f in d s a l l p o s s ib ilit ies o f c o m b in a t io n s o f t w o v a r ia b l es
Solving numerical problems (using a range of mental and written methods
across routine and non-routine problems)
Solve problems
 solves problems involving the calculation and conversion of units of
measure, using decimal notation up to three decimal places where
appropriate
 s o l v e s in c r e a s in g ly c o m p le x n u m er ic a l p r o b le m s ( in c l u d in g m u l t is t e p )
within the fluency focus and through a range of contexts using estimation
to check answers and an appropriate degree of accuracy
 s o l v e s p r o b l em s w h ic h r e q u ir e a n s w e r s t o b e r o u n d ed t o s p e c if ied
degrees of accuracy
Statistics
Processing, representing and interpreting data
 interprets and constructs pie charts and line graphs and uses these to
solve problems (6S1)
- connects work on angles, fractions and percentages to the interpretation
of pie charts
 recognises the difference between discrete and continuous data
 recognises when information is presented in a misleading way, e.g.
compares two pie charts where the sample sizes are different
 when drawing conclusions, identifies further questions to ask
- begins to decide which representation of data is most appropriate and
why
 calculates and interprets the mean as an average
- knows when it is appropriate to find the mean median and mode of a
data set
Geometry
Properties of shape
 compares and classifies geometric shapes based on their properties and
sizes (6G2a)
 describes simple 3D shapes (6G2b)
 draws 2D shapes using given dimensions and angles (6G3a)
 recognises and builds simple 3D shapes including making nets (6G3b)
- visualises a 3D shape from its net and matches vertices that will be
joined
- visualises where patterns drawn on a 3D shape will occur on its net
 finds unknown angles in any triangles, quadrilaterals and regular
polygons (6G4a)
 recognises angles where they meet at a point, are on a straight line, or
are vertically opposite, and finds missing angles (6G4b)
- explains how unknown angles and lengths can be derived from known
measurements
- relationships might be expressed algebraically e.g. d = 2 x r; a = 180 –
(b + c)
 illustrates and name parts of circles, including radius, diameter and
circumference and know that the diameter is twice the radius (6G5)
Position and direction
 draws and translates simple shapes on the coordinate plane, and reflects
them in the axis (6P2)
- predicts missing coordinates using the properties of shapes. These might
be expressed algebraically for example, translating vertex (a, b) to (a-2,
b+3); (a, b) and (a+d, b+d) being opposite vertices of a square of side d
 describes positions on the full coordinate grid (all four quadrants) (6P3)