Transcript Adding and subtracting

Addition and
Subtraction
Calculating efficiently
and accurately
[KS1]
Objectives

To explore the knowledge, skills and
understanding required for children to add,
subtract, multiply and divide efficiently and
accurately

To explore the progression in recording and
(some of) the teaching approaches used
Rapid recall
Models, images &
concrete materials
Understanding
Use of ICT
The Four
Rules
Problem solving
and role play
Mental
calculations
Stories / rhymes
Efficient written
methods
Progression for addition and subtraction
•
Counting
•
One more / less
•
Addition as combining two groups, then counting on
•
Subtraction as take away or difference (eg how many more is
… than …?)
•
Ten more/less
•
Recall of addition/subtraction facts to 10, 20 and beyond
•
Understand that subtraction and addition are inverses
Counting and estimation
There are 5 principles of counting:
1.
The stable order principle - understanding that the number
names must be used in that particular order when counting
2.
The one-to-one principle - understanding and ensuring that
the next item in a count corresponds to the next number
3.
The cardinal principle - knowing that the final number
represents the size of the set
4.
The abstraction principle - knowing that counting can be
applied to any collection, real or imagined
5.
The order irrelevance principle - knowing that the order in
which the items are counted is not relevant to the total
value
94
65
48
30
71
28
36
56
97
32
12
24
51
82
19
77
63
44
53
28
60
96
75
17
43
2+3=
I buy 2 cakes and my friend buys 3 cakes.
How many cakes did we buy altogether?
Addition
pictures
(Children could draw a picture to help them work out the answer)
8+5=
8 people are on the bus. 5 more get on at the next stop. How
many people are on the bus now?
symbols
(Children could use dots or tally marks to represent objects – quicker than drawing a picture)
Counting on – jumps of 1
(modelled using bead strings)
18 + 5 = 23
+1
18
+1
19
+1
20
+1
21
+1
22
23
24
35 + 47 = 82
(+ 30)
(+ 3)
47
77
No number line
35 + 47
= 47 + 30 + 5
= 77 + (3 + 2)
= 82
(+ 2)
80
82
Addition by partitioning
374 + 248
300 + 200 = 500
70 + 40 = 110
4 + 8 = 12
622
Column addition
374
+ 248
622
1 1
Extend to:
1247 + 367
£2.36 + £6.48
3.5 + 4.8
7.48 + 2.6
12.5 km + 6.08 km
Three in a row
Choose two
numbers from the
row of numbers
above the grid.
Find the difference
between these
numbers.
If the answer is on
the grid, cover that
number with a
counter.
14 20 21 34 39 45 50
31
24
30
11
14
6
29
7
20
5
18
13
16
25
36
1
5–2=
I have five cakes. I eat two of them.
How many do I have left?
A teddy bear costs £5 and a doll costs £2.
How much more does the bear cost?
Subtraction
(Take away)
(Find the difference)
Drawing a
picture helps
children to
visualise the
problem
13 – 5 =
Mum baked 13 biscuits. I ate 5. How many were left?
(Take away)
Lisa has 13 felt tip pens and Tom has 5. How many more does Lisa have?
(Find the difference)
Using dots
or tally
marks is
quicker
than
drawing a
detailed
picture
Taking away – jumps of 1
(modelled using bead strings)
13 – 5 = 8
-1
8
-1
9
-1
10
-1
11
-1
12
13
Counting on – jumps of 1
(modelled using bead strings)
11 – 8 = 3
+1 +1
0
1
2
3
4
5
6
7
8
9 10
+1
11
Number lines - taking away
74 – 26 = 48
− 20
−4
−2
48
50
54
74
Number lines - counting on
74 – 26 = 48
+ 40
+4
0
26
+4
30
70
74
Subtraction by partitioning
754 - 186
754 – 100 = 654
654 – 80 = 574
574 – 6 = 568
Subtraction by decomposition