Transcript Addition IMAGES RESOURcES Add, more, and, make, altogether

ADDITION
PRE-STAGE 1
VOCABULARY
SUMMARY
Add, more, and, make,
altogether, equals, most,
count on, number track
Children should begin to be able to count up from zero to ten
and be able to read and sequence numerals to ten. Children
need to understand the concept of combining two sets of
objects into one group is a total.
•
IMAGES
•
Counting using fingers –
starting with the thumb
as one
Recognising pattern of
numbers on a dice or on
fingers instantly
Example of a number
track – like a train track
and easy to jump/move
along. Tracks precede
number lines
Conservation of numberKnowing the amount stays
the same even when the
arrangement changes
•
•
•
•
•
•
•
•
•
•
Use Numicon to support number
recognition and combining
numbers to make a total
RESOURCES
Children should have access to wide range of resources such as
counting equipment, everyday objects, number tracks, Numicon.
•
•
KEY SKILLS
Count numbers up to 10 and
beyond
Count from a given number
up to 10 eg: start at
7…8,9,10
Read numerals to 10
Begin to write numerals to
10
Show numbers using fingers
correctly – counting from
thumb
Combine two groups and
calculate the total to 10
Begin to use a number track
correctly
Quick recognition of
numbers in a group / on a
dice / fingers (subitising)
Estimate the quantity of
objects up to 10
Count in steps of 1’s
Use key vocabulary such as;
more, a lot, altogether.
Recognise that a group of
objects is more than one.
Recognise groups with 1,2 or
3 objects.
Represent amounts with
symbols and marks.
ADDITION
STAGE 1
VOCABULARY
SUMMARY
Add, more, plus, and, make,
altogether, total, equal to,
equals, double, most, count
on, number line, tens, ones
Children should begin to be able to count up from zero to
twenty and be able to read and write numerals to twenty.
Children need to understand the concept of combining two
sets of objects into one group is a total.
KEY SKILLS
IMAGES
•
•
Example of a number
track – like a train track
and easy to jump/move
along
Counting using fingers –
starting with the thumb
as one
Recognising pattern of
numbers on a dice or on
fingers instantly
Example of a number
line where children need
to use fingers to move
up and down correctly
and can jump in steps
•
•
•
•
•
•
•
•
•
Use Numicon to support number
recognition and combining
numbers to make a total
RESOURCES
Children should have access to wide range of resources such as
counting equipment, everyday objects, number tracks, number lines,
numicon, 100 square.
•
Count numbers up to 20 and
beyond
Count from a given number
up to 10 eg: start at
7…8,9,10
Read numerals to 20
Write numerals to 20
Form numerals correctly
Show numbers using fingers
correctly – counting from
thumb
Combine two groups and
calculate the total to 20
Begin to use a number track
correctly
Begin to use a number line
correctly
Quick recognition of
numbers in a group / on a
dice / fingers (subitising)
Estimate the quantity of
objects up to 20
Begin to count in steps of
1’s, 2’s, and 10’s
ADDITION
STAGE 2
SUMMARY – ADDING SINGLE AND
TWO DIGIT.
VOCABULARY
Children should begin to be able to count up from zero to one
hundred and be able to read and write numerals to one hundred.
Children should be able to add single digit numbers together and
single digit to 2-digit numbers by counting on mentally or using a
number line – usually knowing to start with the bigger number. They
should be able to read and understand number sentences and solve
missing number problems.
Add, adding, addition,
more, plus, and, make,
altogether, total, equal to,
equals, double, most, count
on, number line, digit, place
value, tens, units, ones
+1 + 1
IMAGES
KEY SKILLS
•
Holding the initial
number and counting on
Adding using a number
line starting from 0
Write addition number sentences using
correct operational signs using (+) and (=)
signs
3+4=7
13 + 4 = 17
23 + 4 = 27
33 + 4 = 37
Use known number facts
to identify number
patterns and solve
calculations.
•
•
•
•
•
•
Interpret addition number sentences and 8+3 =
solve missing number problems using
5+3+1 =
concrete objects and number lines.
RESOURCES
•
15+4 =
+ 4 = 10
+
=6
Children should still have access to wide range of resources such as
counting equipment, everyday objects, number tracks, number lines,
numicon.
•
•
•
•
•
•
Count numbers to 100 (and
cross the 100 boundary)
Count up from a given
number up to 100 eg: start
at 27….28,29,30,31…
Read numerals to 100 (and
beyond)
Write numerals to 100 (and
beyond)
Number pairs (bonds) that
total 10 and 20.
Number facts within 20
including doubles and number
pairs.
Calculate using a numberline
Calculate by counting on
mentally
Count in steps of 1’s, 2’s, 5’s
and 10’s confidently.
Say the number one, two or
ten more or less than any
number to 100.
Understand value of digits
(tens and ones)
Add single digit numbers
mentally
Add teen digit and single
digit numbers using a number
line
Add three single digit
numbers
ADDITION
STAGE 3
SUMMARY – ADDING WITH 2 DIGITS
VOCABULARY
Children begin to solve calculation by use of blank number
lines and then to expanded horizontal methods (by tens and
ones). Children are always expected to use one digit in one
box. Answers should always be underlined twice. Children
must be confident in mentally adding tens and ones before
moving to these methods.
Add, adding, addition,
more, plus, and, make,
altogether, total, equal to,
equals, double, most, count
on, number line, digit, place
value, tens, ones, partition,
sum, addition, column, tens
boundary
IMAGES
+10
+10
+4
KEY SKILLS
+3
•
•
27
47
37
16
+10
34
44
+3
57
54
•
Add 2 digit numbers and
units: 16+7
Add 2 digit numbers and
tens: 37+20
+10
23
20
3 0
+
4
2 0
+
3
5 0
+
7
= 5
•
•
7
Add pairs of 2 digit numbers, moving to partitioned column
method when secure in adding in tens and units: 34+23
Only provide examples that do NOT cross the tens boundary.
•
•
•
•
•
5 0
+
4 0
+ 3
9
0 +
8
1
•
1
= 1
0
1
Once children can add a multiple of ten to a two digit number
mentally eg: 80+11, they are ready for adding pairs of 2 digit
numbers that DO cross the tens boundary eg: 58+43
•
Add a 2 digit number and
ones (eg: 27+6)
Add a 2 digit number and
tens (eg: 23+40)
Add pairs of 2 digit numbers
eg: (35+47)
Show that adding can be done
in any order (commutative
law)
Recall instantly number bonds
to 20 and bonds in tens to
100 (eg: 30+70)
Count in steps of 2,3,5
Count in tens from any
number eg: 42,52,62,72
Understand the place value
of 2 digit numbers (tens and
ones)
Compare and order numbers
using < and >
Write in words numbers to
100
Solve problems with addition,
using concrete objects,
pictorial representations,
numbers, quantities and
measures and applying
written and mental methods.
Recognise the inverse
relationships between
addition and subtraction and
use this to work and check
out missing number
problems
ADDITION
STAGE 4
VOCABULARY
SUMMARY – ADDING WITH 3 DIGITS
Add, adding, addition, more,
plus, and, make, altogether,
total, equal to, equals, double,
most, count on, number line,
digit, place value, tens, units,
ones, partition, sum, addition,
column, tens boundary,
hundreds boundary, increase,
vertical, ‘carry’, expanded,
compacted, inverse
Children begin to solve addition calculations using vertical
column addition. This is done in an ‘expanded’ way to begin
with. Children commence with the ones, then tens, then
hundreds. This prepares children for the compacted method
which they then move to when they are confident to add in
columns. Children are always expected to use one digit in one
box and always mark HTO as a reference point.
IMAGES
H
T
0
1 0 0
+ 4
0
+ 6
2
0 0
+ 5
0
+
3
3
0 0
+
0
+
9
3
9 9
9
146+253=
Add the ones first
(6+3), then the true
value of the tens
(40+50), then the
hundreds (200). Then
add the totals
horizontally.
KEY SKILLS
•
•
•
•
Move to the compact addition method with ‘carrying’.
H
T O
2
3
6
7
3
0
9
1
3
236+73
Add the ones first
(6+3), then the true
value of the tens
(30+70) carrying over
any tens or hundreds
above the answer
accordingly.
Children are expected to mark any ‘carried’ values above the line.
Children still begin with the ones, then tens, then hundreds. Pupils are
reminded that three tens and seven tens equals ten tens (not just
3+7=10)
Please note, some children prefer to use the expanded method, whilst
others may choose the compact methods. Both are always taught to
ensure children are fully aware of the value of each column.
•
•
•
•
•
•
•
Read and write numbers to
1000 in numerals and words.
Add 2 digit numbers including
those greater than 100.
Add three digit number and
ones mentally eg: 175+8.
Add a three digit number and
tens mentally eg: 249+40.
Add a three digit number and
hundreds mentally eg: 381 +
500.
Recognize the value of 3 digit
numbers (H,T,0).
Begin to be confident to use
expanded column addition for
up to 3 digit numbers.
When confident, begin to
move to compacted column
addition methods with
‘carrying’.
Estimate answers to
calculations, using inverse to
check answers.
Solve problems including
missing number problems.
Continue to practice a wide
range of mental addition
strategies ie. Number bonds,
adding to the nearest
multiple, adjusting,
partitioning and recombining.
ADDITION
STAGE 5
VOCABULARY
SUMMARY – ADDING WITH 4 DIGITS
Children continue to solve addition calculations using vertical
column addition. As children progress to larger numbers they
are still encouraged to use an ‘expanded’ method to begin with.
Children are always expected to use one digit in one box and
always mark Th H T U as a reference point.
IMAGES
Th
H
T
O
3
5
1
2
5
4
5
3512+545
Add the ones first
(2+5), then tens
(10+40), then the
hundreds (500 +500),
then the thousands. •
Then add these values
vertically.
•
7
5
0
1
0
0
0
3
0
0
0
4
0
5
7
•
Move to the compact addition method with ‘carrying’.
Th
H
T
O
3
5
1
2
5
4
5
0
5
7
4
1
3512+545
Add the ones first
(2+5), then tens
(10+40), then the
hundreds (500 +500),
carrying the values
then the thousands.
•
•
•
•
•
Children are expected to mark any ‘carried’ values under the line. Correct
place value is reinforced by reminding them the actual value of 500 add
500 is 1000 not 5 and 5. These methods should be used and applied to
money and measurement addition problems.
Please note, some children prefer to use the expanded method, whilst
others may choose the compact methods. Both are always taught to
ensure children are fully aware of the value of each column.
•
•
Add, adding, addition, more,
plus, and, make, altogether,
total, equal to, equals, double,
most, count on, number line,
digit, place value, tens, units,
ones, partition, sum, addition,
column, tens boundary,
hundreds boundary, increase,
vertical, ‘carry’, expanded,
compacted, inverse, more than,
thousands, digits
KEY SKILLS
Select most appropriate
method: mental, jottings or
written – and explain why
Recognise the place value of
each digit in a four digit
number
Round any number to the
nearest 10, 100, 1000
Estimate and use the inverse
operations to check answers
Solve 2 step problems in
context, deciding which
operations amd methods to
use and why
Find 1000 more or less than a
given number
Continue to practice a wide
range of mental strategies
Add numbers with up to 4
digits using formal written
method of calculation
Solve 2 step problems in
contexts deciding which
operations and methods to
use and why
Estimate and use the inverse
operations to check answers
to a calculation
ADDITION
STAGE 6
VOCABULARY
SUMMARY - ADDING WITH MORE THAN 4 DIGITS
Children begin to solve problems with more than four digits
and use of decimal place is introduced where relevant. The
decimal place should be aligned in the same way as other place
value columns and must be the in the same column in the
answer. Children are always expected to use one digit in one
box.
IMAGES
£
3
.
5
9
7
.
5
5
3
1
.
1
4
1
1
2
+£
£
3
+
3
1
5
4
8
1
1
2
6
2
7
4
3
6
,
1
9
.
0
1
3
.
6
5
0
.
7
0
2
3
.
3
6
1
1
1
+
£23.59 + £7.55
Continue with column
addition methods,
lining up where each
place value column
goes, including the
decimal point. If
questions relate to
money, the £ notation
must be used in both
the question and
answer.
Add, adding, addition, more, plus,
and, make, altogether, total, equal
to, equals, double, most, count on,
number line, digit, place value,
tens, units, ones, partition, sum,
addition, column, tens boundary,
hundreds boundary, increase,
vertical, ‘carry’, expanded,
compacted, inverse, more than,
thousands, digits, decimal places,
decimal point, tenths,
hundredths, thousandths
KEY SKILLS
•
35,481 + 1,262
Continue with column
•
addition methods.
Children are
•
encouraged to use a
comma in their
•
answer to make it
clearer how to say
the answer i.e.
36,743.
•
19.01 + 3.65+ 0.7
Always ensure that empty
decimal places are filled with
zero to show the place value
in each column.
•
•
Add mentally with
increasingly large numbers,
using and practicing a range
of mental strategies i.e. add
to the nearest multiple of
10, 100, 1000 and adjust;
inverse; partitioning etc.
Use rounding to check for
accuracy
Solve multi step problems in
contexts deciding which
operations to use and why
Read, write, order and
compare numbers to at least
1 million and determine each
value of the digit
Round any number up to 1
million to the nearest 10,
100, 1000, 10,000 and
100,000.
Add numbers with more than
four digits using formal
methods
Confidently use decimal
place notation to solve
calculations involving tenths,
hundredths and thousandths
ADDITION
STAGE 7
SUMMARY - ADDING WITH MORE THAN 4 DIGITS
Children are able to solve complex multi step addition
problems with more than four digits and use of decimal place
is used where relevant. The decimal place should be aligned in
the same way as other place value columns and must be the in
the same column in the answer. Children are always expected
to use one digit in one box and
IMAGES
3
6
1
9
.
.
0
8
0
9
.
7
7
0
1
.
3
0
0
9
3
.
5
1
1
2
1
2
5
3
1
2
1
2
1
,
3
,
5
,
0,
0
,
1
1
2
0
5
9
6
6
8
3
0
1
5
5
1
5
7
9
1
1
Add, adding, addition, more, plus,
and, make, altogether, total, equal
to, equals, double, most, count on,
number line, digit, place value,
tens, units, ones, partition, sum,
addition, column, tens boundary,
hundreds boundary, increase,
vertical, ‘carry’, expanded,
compacted, inverse, more than,
thousands, digits, decimal places,
decimal point, tenths,
hundredths, thousandths
Adding several
numbers with
different numbers of
decimal places means
that tenths,
hundredths and
thousandths need to be
properly aligned.
Zeros could be added
into any empty decimal
places to show there is
no value to add.
8
VOCABULARY
KEY SKILLS
•
•
•
•
•
Perform mental calculations,
including with mixed
operations and large numbers
using and practicing a range
of mental strategies.
Solve multistep problems in
context, deciding which
operations and methods to
use and why.
Use estimation to check
answers to determine in the
context of a problem the
level of accuracy.
Read, write, order and
compare numbers up to 10
million and determine the
value of each digit.
Round any whole number to a
required degree of accuracy.