Year 6
PROPERTIES OF NUMBERS AND NUMBER
SEQUENCES
number, count, how many…?
odd, even
every other
how many times?
multiple of
digit
next, consecutive
sequence
continue
predict
pattern, pair, rule
relationship
sort, classify, property
formula
divisible (by), divisibility, factor, factorise
square number
one squared, two squared… (12, 22…)
prime, prime factor
PLACE VALUE, ORDERING AND ROUNDING
units, ones
tens, hundreds, thousands
ten thousand, hundred thousand, million
digit, one-, two-, three- or four-digit number
numeral
‘teens’ number
place, place value
stands for, represents
exchange
the same number as, as many as
equal to
Of two objects/amounts:
>, greater than, more than, larger than, bigger than
<, less than, fewer than, smaller than
≥, greater than or equal to
≤, less than or equal to
Of three or more objects/amounts:
greatest, most, largest, biggest
least, fewest, smallest
one… ten… one hundred… one thousand more/less
compare, order, size
ascending/descending order
first… tenth… twentieth
last, last but one
before, after
next
between, half-way between
guess how many, estimate
nearly, roughly, close to, about the same as
approximate, approximately
+ is approximately equal to
O,
just over, just under
exact, exactly
too many, too few, enough, not enough
round (up or down), nearest
round to the nearest ten/hundred/thousand
integer, positive, negative
above/below zero, minus
MAKING DECISIONS AND REASONING
pattern, puzzle
calculate, calculation
mental calculation
method, strategy
jotting
answer
right, correct, wrong
what could we try next?
how did you work it out?
number sentence
sign, operation, symbol, equation
USING A CALCULATOR
calculator, display, key
enter, clear, sign change
constant, recurring, memory, operation key
ADDITION AND SUBTRACTION
add, addition, more, plus, increase
sum, total, altogether
score
double, near double
how many more to make…?
subtract, subtraction, take (away), minus, decrease
leave, how many are left/left over?
difference between
half, halve
how many more/fewer is… than…?
how much more/less is…?
equals, sign, is the same as
tens boundary, hundreds boundary, units boundary,
tenths boundary
inverse
MULTIPLICATION AND DIVISION
lots of, groups of
times, multiply, multiplication, multiplied by
multiple of, product
once, twice, three times… ten times…
times as (big, long, wide… and so on)
repeated addition
array, row, column
double, halve
share, share equally
one each, two each, three each…
group in pairs, threes… tens
equal groups of
divide, division, divided by, divided into
remainder
factor, quotient, divisible by
inverse
General
same, identical, different
missing number/s
number facts, number pairs, number bonds
greatest value, least value
number line, number track
number square, hundred square
number cards, number grid
abacus
counters, cubes, blocks, rods
die, dice, spinner
dominoes
pegs, peg board, pin board
geo-strips
same way, different way
best way, another way
in order, in a different order
not
all, every, each
Year 6 Programme of Study
Number - number and place value
Pupils should be taught to:
• 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 zero
• s olve number and practical problems that involve all of the above.
Number - addition, subtraction, multiplication and division
Pupils should be taught to:
• multiply multi-digit numbers up to 4 digits by a two-digit whole number
using the formal written method of long multiplication
• divide numbers up to 4 digits by a two-digit 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 4 digits by a two-digit number using the formal
written method of short division where appropriate, interpreting
remainders according to the context
• perform mental calculations, including with mixed operations and large
numbers
• identify common factors, common multiples and prime numbers
• use their knowledge of the order of operations to carry out calculations
involving the four operations
• solve addition and subtraction multi-step problems in contexts, deciding
which operations and methods to use and why
• solve problems involving addition, subtraction, multiplication and
division
• use estimation to check answers to calculations and determine, in the
context of a problem, an appropriate degree of accuracy.
Number - fractions (including decimals and percentages)
Pupils should be taught to:
• use common factors to simplify fractions; use common multiples to
express fractions in the same denomination
• 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, 1/4 x 1/2 = 1/8]
• divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6 ]
• associate a fraction with division and calculate decimal fraction
equivalents [for example, 0.375] for a simple fraction [for example, 3/8]
• identify the value of each digit in numbers given to three decimal places
and multiply and divide numbers by 10, 100 and 1000 giving answers up
to three decimal places
• multiply one-digit numbers with up to two decimal places by whole
numbers
• use written division methods in cases where the answer has up to two
decimal places
• solve problems which require answers to be rounded to specified
degrees of accuracy
• recall and use equivalences between simple fractions, decimals and
percentages, including in different contexts.
Ratio and proportion
Pupils should be taught to:
• 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.
Algebra
Pupils should be taught to:
• use simple formulae
• generate and describe linear number sequences
• express missing number problems algebraically
• find pairs of numbers that satisfy an equation with two unknowns
• e numerate possibilities of combinations of two variables.
Measurement
Pupils should be taught to:
• 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
• convert between miles and kilometres
• recognise that shapes with the same areas can have different perimeters
and vice versa
• recognise when it is possible to use formulae for area and volume of
shapes
• c alculate the area of parallelograms and triangles
• calculate, estimate and compare volume of cubes and cuboids using
standard units, including cubic centimetres (cm3) and cubic metres (m3),
and extending to other units [for example, mm3 and km3].
Geometry – properties of shapes
Pupils should be taught to:
• draw 2-D shapes using given dimensions and angles
• recognise, describe and build simple 3-D 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.
Geometry - position and direction
Pupils should be taught to:
• 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.
Statistics
Pupils should be taught to:
• interpret and construct pie charts and line graphs and use these to solve
problems
• calculate and interpret the mean as an average.
In order to encourage children to work mentally, calculations should always be presented horizontally so children can make decisions about how to tackle them.
Encourage children to choose to use the most efficient method for the numbers and the context. Teach operations together to emphasise the importance of inverse.
Addition
Subtraction
to be taught alongside each other
Children should be taught to add increasingly larger numbers.
Multiplication
Children should be taught to subtract increasingly larger
numbers.
Short multiplication (by a single digit), Grid Method, Expanded and
Compact Methods (3 and 4 digit x 1 and 2 digit numbers).
Children will continue to use written methods to solve short
division (by a single digit).
4346 x 8
Number lines
401.2
26.85
+ 0.71
1
x 4000 300 40 6
3 32000 2400 320 48
‘Find the difference by counting on’
Where the numbers are involved in the calculation are close
together or near to multiples of 10, 100 etc counting on using a
number line should be used. E.g. 3002 – 1997 = 1005
428.76
6584
+ 5848
1 1 1
42
6432
786
3
+ 4681
12 1
12432
+1000
+3
+2
1997 2000
0
3000 3002
Partitioning and Decomposition
5000
1300
160
5 13
Check using inverse.
1
6000 400 60 7
6467
3783
686.56m
- 2000 600 80 4
- 2684
+ 1216 8 4
- 637.06m
3000 700 80 3
= 3783
6467
11944
7 1
049.50m
6467
2684
- 2684
34768
Compact
Method
4346
x 2 3 48
= 646 7
Negative Column Subtraction
(optional)
4
3 2
-2
5 7
200 -20 -5 = 175
4563.5km - 3872.4km
4563.5km
- 3872.4km
1400
160
4000 500 60 3 0 . 5
- 3000 800 70 2 0 . 4
0 600 90 1 0 . 1
600
90
1
+ 0.1
691.1
3 141
4563.5km
- 3872.4km
0691.1
+ 13872.4
1
Continue to use informal jottings on an empty number line to
show chunking. E.g. 972 ÷ 36 = 27 36 x 27 = 972
34768
Children will approximate first.
372
x
24
2
1488
1
7440
1
8928
Long
Multiplication
+
+
+
+
+
972 ÷ 36
6000
1400
1200
280
40
1 8
8928
Using similar methods, they will be able to multiply decimals with up
to two decimal places by a single digit number and then two digit
numbers, approximating first. They should know that the decimal
points line up under each other.
496 ÷ 11
12
2.7
+0.06
Check using inverse.
14.76
45 r1
5
11 496
Answer: 45 1/11
4.92 x 3 is approximately 5 x 3 = 15
x 4 0.9 0.02
3 12 2.7 0.06
27
36 972
- 720 20x
252
- 252 7x
0
Answer: 27
Any remainders should be shown as fractions, i.e. if the children
were dividing 32 by 10, the answer should be shown as 3 2/10
which could then be written as 3 1/5 in it’s lowest terms.
4563.5
3872.4km
+
?
= 4563.5km
36 x 20 = 720 36 x 5 = 180 36 x 2 = 72
Long division using chunking
372 x 24 is approximately 400 x 25 = 10000
x 300 70 2
20 6000 1400 40
4 1200 280 8
1200 ÷ 4 = 300
60 ÷ 4 = 15
8÷4=2
1268 ÷ 4 = 317
Solve divisions with up to 4 digit numbers ÷ 2 digit numbers.
34768
+
=
3000
Expanded
Method
48
320
2400
32000
1268 ÷ 4 =
4 x = 1268
800 = 4 x 200
400 = 4 x 100
40 = 4 x 10
20 = 4 x 5
8=4x2
1268 = 4 x 317
32000
+ 2400
+ 320
+ 48
Grid Method
4346
x
8
Division
to be taught alongside each other
432 ÷ 15
Both Expanded and Compact methods to be used only when
children are confident with the Grid method.
28
15 432
300
132
120
12
15 x 20
15 x 8
12/15 = 4/5
Answer: 28 4/5
know that decimal points should line up under each other,
particularly when adding or subtracting mixed amounts,
e.g. 401.2 + 26.85 + 0.71
By the end of year 6, children will have a range of calculation methods, mental and written.
They should not be made to go onto the next stage if they are not ready or if they are not confident.
Children should be encouraged to approximate their answers before calculating.
Children should be encouraged to consider if a mental calculation would be appropriate before using written methods.
BODMAS - Brackets Over Division,
Multiplication, Addition, Subtraction