Download Number and Calculations Framework

1
Carr Lodge Academy
Number and Calculations Framework
Foundation Stage
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
NUMBER
NUMBER
NUMBER
NUMBER
NUMBER
NUMBER
NUMBER
● Say which number is
1 more or 1 less
●
● Count reliably from
1-20
●
Use the vocabulary
of equal to, more
than, less than
(fewer)most, least
with objects,
pictures and a
number line.
Count to and across
reliably from 0-100
forwards and
backwards from 0 or
1.
● Count from any
given number in
steps of 1,2,5 and 10
● Use appropriate
vocabulary for
comparing numbers
from 0-100 and
beyond and use: < >
= signs
●
Use appropriate
vocabulary for
comparing numbers
up to 1000
●
●
●
Count in multiples of
2,3,4,5,8,10, 50 and
100 from any given
number.
●
Count in steps of
2,3, 5 or 10 forwards
and backwards.
Use appropriate
vocabulary for
comparing numbers
from up to 10,000
Count in multiples of
2,3,4,5,6,7,8,9,10,25
, 50, 100 and 1000
from any given
number.
● Count forwards and
backwards through
0 including negative
numbers.
● Use appropriate
vocabulary for
comparing numbers
up to 1,000,000
●
Use appropriate
vocabulary for
comparing numbers
up to 10,000,000
● Count forwards or
backwards in steps
of 100, 1000 or
10,000 from any
given number up to
1,000,000
● Count forwards and
backwards through
0 including negative
numbers.
●
Regularly practise
counting in:
Multiples of
2,3,4,5,6,7,8,9,10,25
, 50, 100 and 1000
from any given
number. Forwards
or backwards in
steps of 100, 1000
or 10,000 from any
given number up to
1,000,000
2
● Count, read and
write numbers up to
10.
●
Count, read and
write numerals to
100; read and write
numbers from 1-20
in numerals and
words.
●
Count, read and
write numbers to
100 in numerals and
words.
●
Count, read and
write numbers to
1000 in numerals
and words.
●
Read and write
numbers to 10,000
●
Give 1 more or 1
less than
●
Give 10 more or 10
less.
● Give 10 or 100 more
or less.
●
Give 1000 more or
less than any given
number.
● Order and compare
numbers from
0-1000
●
Order and compare
numbers from
0-10,000
● Recognise the place
value of each digit in
a 3 digit number
(hundreds, tens,
ones)
●
● Recognise odd and
even numbers
● Recognise odd and
even numbers
st​ nd​ rd​
● Use 1​
, 2​, 3​etc
● Arrange read and
write numbers in
increasing and
decreasing order
● Recognise the place
value of each digit in
a 2 digit number
(tens, ones)
● Begin to recognise
the place value of
each digit in a 2 digit
number (tens, ones)
Recognise the place
value of each digit in
a 4 digit number
(thousands,
hundreds, tens,
ones)
● Round any number
to the nearest 10,
100 or 1000.
● Read, write and
order negative
numbers through 0
● Read Roman
Numerals to 100.
● Read and write
numbers to
1,000,000
● Read and write
numbers to
10,000,000
● Order and compare
numbers from
0-1,000,000
● Order and compare
numbers from
0-10,000,000
● Recognise the place
value of each digit in
numbers to at least
1,000,000
● Recognise the place
value of each digit in
numbers to at least
10,000,000
● Round any number
up to 1,000,000 to
the nearest 10, 100,
1000, 10,000 and
100,000.
● Read, write and
order negative
numbers through 0
● Round any number
● Read Roman
Numerals to 1000
including years.
● Read Roman
Numerals to 1000
including years.
● Read, write and
order negative
numbers through 0
3
ADDITION AND
SUBTRACTION
● Add and subtract
two 1-digit numbers.
ADDITION AND
SUBTRACTION
ADDITION AND
SUBTRACTION
ADDITION AND
SUBTRACTION
ADDITION AND
SUBTRACTION
ADDITION AND
SUBTRACTION
● Read and practise
writing number
sentences involving
+-=
● Add and subtract
1-digit and 2-digit
numbers to 20
including 0.
● Add and subtract
two 2-digit
quantities and
measures (possible
use of columns)
● Add and subtract
two numbers with
up to 3-digits
(column addition)
● Add and subtract
numbers using
formal written
methods up to
4-digits
● Add and subtract
numbers using
formal written
methods above
4-digits.
● Recall number
bonds and
subtraction facts
within 20.
● Rapid recall of
addition and
subtraction facts to
20 and use facts up
to 100.
● Mentally add and
subtract numbers
including:
-2 digit numbers and
ones
-2 digit number and
tens
-two 2-digit
numbers
- three 1 digit
numbers.
● Mentally add and
subtract numbers
including:
-3 digit numbers and
ones
-3 digit number and
tens
-3 digit numbers and
hundreds
● Mentally add and
subtract numbers
with increasingly
large numbers.
● Mentally add and
subtract numbers
with increasingly
large numbers.
● Solve word
problems that
involve addition and
subtraction.
● Solve problems
involving missing
numbers.
● Solve word
problems that
involve addition and
subtraction up to
2-digits
● Solve word
problems with more
complex addition
and subtraction
including missing
number problems.
● Show subtraction in
take away and find
the difference
problems.
● Use the inverse
operation to check
answers.
● Solve one and two
step word problems
with more complex
addition and
subtraction with
increasingly large
positive numbers.
● Use the inverse
operation to check
answers.
● Solve multi-step
word problems with
more complex
addition and
subtraction with
increasingly large
positive numbers.
● Estimate accuracy of
answers using
rounding.
ADDITION AND
SUBTRACTION
● Add and subtract
numbers using
formal written
methods up to
5-digits
● Add and subtract
negative integers.
● Carry out combined
operations including
the use of brackets.
● Solve word
problems that
involve all four
operations.
● Estimate accuracy of
answers.
● Decide whether an
answer should be
4
MULTIPLICATION AND
DIVISION
MULTIPLICATION AND
DIVISION
● Solve problems
including:
-Doubling
-Halving
-Sharing
● Recognise and write
x and ÷ in simple
number sentences
and word problems
such as ÷ 2 (using
objects and adult
support)
● Show addition can
be done in any order
(commutative)
● Recognise and use
inverse to check
answers and solve
missing number
problems.
MULTIPLICATION AND
DIVISION
● Estimate accuracy of
answers.
● Estimate accuracy of
answers.
MULTIPLICATION AND
DIVISION
MULTIPLICATION AND
DIVISION
MULTIPLICATION AND
DIVISION
MULTIPLICATION AND
DIVISION
● Recall multiplication
and division facts for
2,5 and 10.
● Write and calculate
number sentences
and word problems
(using x ÷ and =)
within the
multiplication tables
for 2,5 and 10.
(Using objects,
arrays and repeated
addition.)
● Recognise that X can
be done in any order
but ÷ cannot.
● Recall and use
multiplication and
division facts for
2,3,4,5,8 and 10
multiplication
tables.
● Write and calculate
number sentences
and word problems
for 2-digit X/ ÷
1-digit numbers
(mentally or number
line)
● Recall multiplication
and division facts up
to 12x12; mentally
perform
multiplication and
division calculations.
● Multiply or divide 2
and 3 digit numbers
by a 1 digit number
using formal
methods. (two-step
word problems)
● Multiply and divide
by 10 and 100.
● Recall multiplication
and division facts up
to 12x12; mentally
perform
multiplication and
division calculations
accurately.
● Multiply numbers up
to 4-digits by a 1 or
2-digit number using
an efficient written
method (long
multiplication)
(Word problems)
● Divide numbers up
to 4-digits by a
1-digit number using
chunking and
interpret
remainders as
integers, decimals,
fractions or with
rounding. (Word
problems)
● Solve problems
which use all four
operations.
● Multiply and divide
by 10, 100 and 1000.
● Recall multiplication
and division facts up
to 12x12; mentally
perform
multiplication and
division calculations
accurately. Include
mixed operations
and larger numbers
● Multiply numbers up
to 4-digits by a
2-digit number using
long multiplication
(Word problems)
● Divide numbers up
to 4-digits by a
2-digit number using
long division
(chunking/bus stop)
and interpret
remainders as
integers, decimals,
fractions or with
rounding. (Word
problems)
rounded, written as
a fraction or a
decimal.
5
● Recognise and use
factor pairs within
144
FRACTIONS, DECIMALS
AND PERCENTAGES
FRACTIONS, DECIMALS
AND PERCENTAGES
FRACTIONS, DECIMALS
AND PERCENTAGES
FRACTIONS, DECIMALS
AND PERCENTAGES
FRACTIONS, DECIMALS
AND PERCENTAGES
● Recognise, name,
write and find ½ ¼
and ¾ as parts of an
object, shape or
quantity.
● Recognise, name,
write and find ½ ⅓¼
and ¾ as parts of an
object, shape or
quantity.
● Identify, name, write
fractions up to ​
⅟
12
​
(unit fractions e.g. ½
● Compare and order
numbers with up to
2 decimal places
(linked to money)
● Round decimals with
1 decimal place to
the nearest whole
number.
● Begin to use
equivalence e.g. ½ =
● Recognise fractions
equivalent to 1
2/4
⅓¼ ⅕⅙⅟
7​
​
⅛⅟
9​
​
⅟
10​
​
⅟
11
​
⅟
​
1
2​
)
● Compare and order
unit fractions
● Compare and order
fractions with the
same denominator
● Identify and name
equivalent fractions
of a given fraction
● Identify factors of
numbers by
identifying multiples
(can find common
multiples/factors)
● Establish whether a
number up to 100 is
prime
● Recall prime
numbers up to 19
● Recognise and use
square numbers (²),
cube numbers (³)
and square roots
(√)
FRACTIONS, DECIMALS
AND PERCENTAGES
● Compare and
order fractions
with different
denominators (find
common
denominator)
● Read, write,
compare and order
numbers with up
to 3 decimal
places.
● Round decimals
with 2 decimal
places to 1 decimal
place or the
nearest whole
number.
● Recognise mixed
numbers and
improper fractions
and convert from
● Identify factors of
numbers by
identifying multiples
(can find common
multiples/factors)
● Establish whether a
number up to 100 is
prime
● Recall prime
numbers up to 19
● Recognise and use
square numbers (²),
cube numbers (³)
and square roots
(√)
FRACTIONS, DECIMALS
AND PERCENTAGES
● Use percentages for
comparison
● Compare and order
fractions including
those greater than 1.
● Recall and use
equivalences between
fractions, decimals
and percentages
6
● Count in halves and
quarters to 10.
● Recognise pairs of
fractions that add up
to 1.
including tenths and
hundredths.
● Recognise and write
decimal equivalents
to ½, ¼, ¾ and any
number of tenths
and hundredths.
one form to
another.
● Read and write
decimal numbers
as fractions
● Write simple
fraction, decimal
and percentage
equivalents
● Use common factors
to simplify fractions.
● Use multiples to
express fractions in
the same
denomination.
● Count up and down
in tenths
● Recognise tenths
arise when you
divide by 10 (use a
0-1 number line to
demonstrate with
tenths, decimals and
percentages)
● Count up and down
in tenths and
hundredths.
● Recognise
hundredths arise
when dividing by
100 and dividing
tenths by 10.
● Find the effect of
dividing a 2-digit
number by 10 and
100 identifying the
value of the digits in
the answer as ones,
tenths and
hundredths
● Reduce fractions to
their simplest form
● Perform addition
and subtraction
calculations of
fractions with the
same denominator
up to one whole
● Recognise and use
thousandths and
relate them to
tenths, hundredths
and relate them to
decimal
equivalents.
● Recognise the ​
% symbol and link to
parts per 100
● Associate a fraction
with division to
calculate decimal
fraction equivalents (⅜
is 3÷8 =0.375) using a
calculator
● Identify the value of
each digit to 3 decimal
places
● Add and subtract
fractions with the
same denominator
or related
denominators (⅟​
2
and ¼)
● Write number
sentences where
the total exceeds
one.
● Multiply proper
fractions and
mixed numbers by
whole numbers (1
½ x 3)
● Add and subtract
mixed number and
fractions with
different
denominators using
equivalency
● Multiply simple unit
fractions by fractions
and pairs of proper
fractions writing the
answer in its simplest
form
● Divide proper
fractions by whole
numbers.
● Solve problems that
involve addition and
subtraction
calculations of
fractions with the
same denominator
up to one whole
7
● Add and subtract
decimals with up
to 3 decimal places
● Multiply and divide
numbers with 3
decimal places by 10,
100 and 1000
● Multiply and divide
numbers with up to 2
decimal places by
1-digit and 2-digit
whole numbers
● Calculate percentages
whole numbers
RATIO AND PROPORTION
● Use ratios to show the
relative sizes of two
quantities
● Solve problems
involving unequal
sharing and grouping
e.g. recipes.
8
ALGEBRA
● Express linear
missing number
problems
algebraically
● Find pairs of
numbers that
satisfy number
sentences
involving two
unknowns e.g.
+ 12 = 48 –
Or
X + 12 = 48 – Y
● Use simple formulae
expressed in words
● Generate and
describe linear
number sequences