Transcript power point presentation - Mawsley Community Primary School

Mawsley Primary School
Calculation Policy
Addition and Subtraction
Models for addition
Combining two sets of objects (aggregation)
Issue:
125
7
Tend to count one set,
count the other and
then count all.
Adding on to a set (augmentation)
Issue:
Requires fluency
with counting
from any number.
12
11
10
7
6
5
9
8
Counting on with a bead bar/number line
+7
Issues:
Also:
0
5
+5
10
+2
12
is a useful
bridge
from
Bead bar and
number
line (showing
cardinal
to ordinal.
10s)
encourages
use of number bonds
2
Number
line
helps
stop counting
and
place
value
forto
added
efficiency.all
Commutative Laws
The "Commutative Laws" say you can swap
numbers over and still get the same
answer ...
... when you add:
a+b = b+a
Models and images
Associative Laws
• The "Associative Laws" say that it doesn't
matter how you group the numbers (i.e.
which you calculate first) ...
... when you add:
(a + b) + c = a + (b + c)
Vocabulary
Foundation stage
•
•
•
•
•
•
Recognise numbers 0 to 20, including Numicon.
Count beyond 10 everyday objects.
Find one more than a number
Count in ones and tens
Begin to relate addition to combining 2 groups
Count along a number line to add numbers
together
• Begin to use + and = to record mental
calculations in a number sentence
• Be able to calculate doubles
Level 1
• Know by heart all pairs of numbers with a
total of 10 and 20
• Know that addition can be done in any
order
• Using a number line adding by counting up
to the next ten then counting in ones.
• Draw own number lines to add
• Begin to partition numbers in order to add
Level 2
• Add 2 single digits that bridge 10
• Use base 10 apparatus to add two 2-digit
numbers together up to =100, exchanging
ten units for a ten.
• add a number up to =50 on a number line,
in jumps of 1, 5 or 10
• Adding two 2-digit numbers first without
and then with bridging 10’s boundary
• Start to use partititioning
Level 3
• Expanded method of addition
• Column method, first without and then with
carrying
• Column addition to add money without
carrying
Level 4
• Continue with the strategies to add
numbers up to 2 decimal places,
including numbers which do not have
the same number of decimal places
Overview
Number line
Partitioning
Expanded method
Standard written method
Models for subtraction
Removing items from a set (reduction or take-away)
N.B.
When
this is done on a bead
Issue:
there are
links with both
on ‘counting
12 - 5
1 = 7 bar,Relies
2
3
4
counting
back and difference on
all’, again.
a number line
Comparing two sets (comparison or difference)
Issue:
Useful when two numbers
are ‘close together’, where
‘take-away’ image can be
cumbersome
Seeing one set as partitioned
Seeing 12 as
made up of 5
and 7
Issue:
Helps to see the related calculations;
5+7=12, 7+5=12, 12-7 = 5 and 12-5=7 as
13
all in the same diagram
Models for subtraction
Counting back on a number line
Also:
Issue: of place value
Knowledge
-5
0
7
10 -2
-3
12
helps
andNumber
number line
bonds
canto
stop more
‘counting
all’.
support
efficient
calculating
Finding the difference on a number line
Issue:
7
0
5
5
10
2
12
Useful when two numbers
are ‘close together’, use of
number bonds and place
value can help.
14
Subtraction key vocabulary
Foundation stage
• Begin to count backwards in familiar
contexts
• Continue the count back in ones from any
given number
• Find one less than a number
• Count back in tens
Level 1
• Draw on a number line to count back in
ones
• Draw own number line to take away
• Find the difference between 2 numbers
less than 20
• Subtract single digit numbers bridging
through 10
• Begin to find the difference by counting up
from the smallest.
Level 2
• Know by heart subtraction facts for 10 and
20
• Subtract a single digit from a 2 digit
number
• Begin to use partitioning
Level 3
• Decide whether to count on or back
• Compensation method
• Take too much and add back
84 – 56
-60
+4
24
28
(84 – 60) +4 = 28
84
• Partitioning when there is an exchange:
57 – 28
50 & 7
- 20 & 8
•
40 & 17
- 20 & 8
20 & 9
50 & 7
- 20 & 8
20 & 9
• Expanded method
500
+
- 100 +
400 +
40 +
20 +
10 +
30
3
7
6
10 +
Level 4
• Formal column method
• Continue with the strategies to subtract
numbers up to 2 decimal places,
including numbers which do not have
the same number of decimal places.
Overview
Number line
Partitioning
Expanded method
Standard written method