Transcript St Pius X Numeracy Evening

Explaining how we
teach mathematics,
and what you can do
to help your child
become a confident
mathematician.
Addition and subtraction
What are we going to talk about
this afternoon?
•Number:
Place value, partitioning, ordering,
comparing, sequencing, rounding, estimating
•Calculations: Addition and subtraction
•Vocabulary, and ability to explain methods
•Using and applying
• We use a consistent, progressive approach
•KS1 –
•KS2 -
Focus on mental calculation strategies
Informal written method leading to a
standard written method
Place value and partitioning
A vital skill.
It is understanding
that what each digit is worth
is dependent on its position in a number.
Visually supported with use of arrow cards, digit
cards and base blocks.
Using
base
blocks
572 is partitioned into
500
and
70
and
500
702
2
Place value grid
http://www.primaryresources.co.uk/online/numberboard2.swf
or PV Chart v8.exe
Then
e.g.
adding and subtracting 1, 10 and 100.
spreadsheet
1 or 10 more
or less bingo
Hundred square
Ordering
Being able to put numbers in order
and place them on a number line.
Ordering numbers:
10 8 6 12
Number
line
112
165 178
125
194
143
Which number is bigger? Which number is smaller?
Using the symbols:
is smaller than
<
is greater than
>
Identifying the sequence and adding to it.
This includes completing dot to dot pictures and making
patterns with coloured beads then goes on to completing
number sequences such as:
a) 2 4
6 ___ 10
33
12
___ 23
___
b) 43
38
18 ___
c) 4.3
3.8 3.3 ___ 2.3 1.8 ___
___
Children also need to be able to explain what the
sequence/pattern is e.g. a) adding 2, b) subtracting 5 c)
subtracting 0.5
We use a counting stick to practise
counting in sequences.
Need to know the multiples of 10 and 100
Multiples of 10 are:
0
10 20 30 40 50 60 70 80 90 100 110
etc.
65
Post box
sorting
Which multiple of 10 is 65 between?
Which multiple of 10 is 65 nearest?
60
61
62
63
64
65
66
67
68
69
65 rounds to 70
70
Estimating
How many
sweets?
How many
shells?
Rounding to estimate what the
answer will be near.
64 + 57 rounds to 60 + 60 = 120
so the answer must be near 120
Adding
4 + 7
Start with the biggest number first
7 + 4
Key stage 1:
Count on
Use a number line
1
7
2
8
3
9
4
10
11
Any written work is done horizontally
7 + 4 = 11
Number bonds
We can’t emphasise enough the need for children to confidently know their
number facts before they progress to more formal written methods.
•addition and subtraction bonds for totals up to 10
Triangular
cards
•addition and subtraction bonds for totals up to 20
•doubles of all numbers up to 10 and then 20
Hit the
button
•addition and subtraction bonds with multiples of 10 for totals up to 100
•addition and subtraction bonds with multiples of 5 for totals up to 100
These facts will enable them to carry out the more formal methods of
addition and subtraction with confidence.
Adding two digit numbers using
informal methods
•23 + 32 = (20 + 30) + (3 + 2)
50
+ 5
= 55
Easy sums:
Then
20 + 30 = 50
20 + 32 = (20 + 30) + 2
50 + 2 = 52
and finally
Adding with
arrow cards
25 + 37 = (20 + 30) + (5 + 7)
50 + 12 = 62
The aim is that, eventually children will be able to add
two 2 digit numbers mentally.
We introduce more formal written methods in stages.
First this:
23 + 32 =
+
35 + 39 =
+
Then this:
35
+ 39
14
60
74
Expanded
addition
20 3
30 2
50 + 5
= 55
30 5
30 9
60 + 14
= 74
Then this:
35
39
74
1
352
+ 189
541
11
Key stage 1:
Subtracting
7 – 4 = 3
Any written work is done horizontally
Count back
Use a number line
4
3
3
4
2
5
1
6
7
The difference between 7 and 4 is 3
4
3
5
2
6
1
7
Subtraction
After lots of visual, practical and mental subtraction work
with single digit numbers including use of a number line
and use of relevant language such as difference between,
minus, how many less is?... how many less than?...,
subtract, take, take away etc. children learn to subtract
larger numbers.
We begin to teach more formal methods using partitioning.
67 – 23 =
-
60
20
40
7
3
4
= 44
63 - 27
60
- 20
3
7
Because we can’t take 7
from 3 we re-partition,
moving 10 across.
-
50 13
20 7
30 6
= 36
Decomposition
Finally we move to the more compact method, when we feel children are ready for this.
For some children the final compact method will be difficult and they will continue to
use informal methods into year 6.
This compact method is known as 'decomposition‘.
They will progress to using bigger numbers and decimals.
63 – 27
363 – 127
424 – 178
56 13
35 6 1 3
-1 2 7
236
34 112 14
-2 7
3 6
-1 7 8
2 4 6
Thank you for reading this.
We hope you find it useful.
Wizard
number
What is the
Number?