Transcript add & substract document

Addition and
Subtraction
Calculating efficiently
and accurately
Objectives


To explore the knowledge, skills and
understanding required for children to
add / subtract efficiently and accurately
To explore the progression in recording
and (some of) the teaching approaches
used
Self-esteem
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 in knowledge
and understanding for + / •
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
Addition
2+3=
I buy 2 cakes and my friend buys 3 cakes.
How many cakes did we buy altogether?
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
35 + 47
77
= 47 + 30 + 5
= 77 + (3 + 2)
= 82
(+ 2)
80
82
Column addition
374
374
+ 248
+ 248
12
622
110
1 1
500
622
Extend to:
1247 + 367
7.48 + 2.6
£2.36 + £6.48
12.5 km + 6.08 km
3.5 + 4.8
5–2=
I have five cakes. I eat two of them.
How many do I have left?
Subtraction
(Take away)
Drawing a
picture helps
children to
visualise the
problem
A teddy bear costs £5 and a doll costs £2.
How much more does the bear cost?
(Find the difference)
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 +1
0
1
2
3
4
5
6
7
8
9 10 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
Three in a row
Choose two
14
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.
20 21 34 39 45 50
31 14 20 16
24 6
5 25
30 29 18 36
11 7 13 1
Subtraction by decomposition
No breaking down needed:
Using red alerts:
563 − 248
563 − 241
500 + 60 + 3
− 200 + 40 + 1
300 + 20 + 2
Leading to:
−
563
241
322
500 and 60 and 3
− 200 and 40 and 8
Re-written as:
500 and 50 and 13
− 200 and 40 and 8
300 and 10 and 5
Leading to:
5
−
5 61 3
248
315