Friday 20th September
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To develop an understanding of how
calculation strategies are developed from
Key Stage 1 to Key Stage 2
To experience examples of Key Stage 2
maths investigations
To gain an understanding of age-related
expectations in maths at Key Stage 2
To give examples of home-learning activities
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How did you feel about maths?
What were your experiences of maths like?
How do you feel about maths now?
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Maths is fun!
Children are encouraged to “have a go”!
They are not afraid to be wrong – mistakes
are part of the learning
Maths is made purposeful and interesting
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Children used to learn “standard methods” –
we were shown what to do before
understanding was consolidated
If you couldn’t remember, or hadn’t
understood the methods…you went wrong
Today, we teach methods that help children to
understand the underlying maths and the basic
concepts involved
Children need to develop “number sense” –
more insight into mathematics
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…are not just about getting the right answer – but
about knowing and understanding how you got
there
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…are not new – many pre-date the techniques you
learned
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…eventually join up with the ones you did in school
– but the children understand them thoroughly
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…reduce the chance of mistakes being made
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…build a firm foundation for understanding more
complicated mathematics later on
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Using and applying mathematics
Counting and understanding number
Knowing and using number facts
Calculating
Understanding shape
Measuring
Handling data
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Our number system consists of ten digits
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
The place of each digit determines its value.
For example, the “6” digit can represent for 6, sixty,
six hundred. It depends where we place it…
6….65….653
Game
We expect children at the start of Yr3 to be able to:
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count, read, write and order whole numbers to at least 100; know
what each digit represents (including 0 as a place holder)
partition 2 digit and some 3 digit numbers in different ways and use
this to help solve problems
know by heart all addition and subtraction facts for each number to
at least 10, all pairs with totals to 20, all pairs of multiples of 10 with
totals up to 100
add or subtract mentally a one digit number or a multiple of 10 to or
from any two digit number
begin to bridge through tens numbers using known number facts
when adding and subtracting
understand multiplication as repeated addition or as an array, solve
simple x and ÷ problems by pictorial or abstract methods
derive and recall facts for the 2, 5 and 10 multiplication tables
use and interpret the symbols +/-/x/÷ and = in number sentences
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We expect children at the start of Yr5 to be able to:
read, write and order whole numbers to 10 and 100s of thousands, know what
each digit represents and can partition 4 and 5 digit numbers into multiples of
1000, 100, 10 and 1 in different ways
use diagrams to identify equivalent fractions; interpret mixed numbers and position
them on a number line
round fractions or decimals to the nearest and/or next whole number
use mental recall of addition and subtraction facts up to 20 in solving problems
involving larger numbers
use informal methods to add two numbers together that have one decimal place
use efficient written methods are used to add and subtract three digit and four
digit whole numbers and £.p.
know by heart 2,3,4,5,and 10X tables, use them to solve multiplication and division
problems and begin to know 6,7,8 and 9X
find pairs of factors of any number to 30
recognise two digit multiples of 2,5, 10 and three digit multiples of 2, 5, 10, 50 and
100
find remainders after division and round up or down after depending upon the
context
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They help to develop an ability to order numbers, and give
children a sense of where numbers sit in our number system
They allow children to draw a picture – or model – in their
heads when calculating
Can be used in a range of aspects of mathematics – numbers
and the number system, fractions, decimals, percentages,
addition, subtraction, multiplication, division, measures,
handling data
Number tracks
1
2
3
4
5
6
7
10
11
12
8
9
10
Numbered lines
5
6
7
8
9
13
14
15
16
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5
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Partly numbered line
10
The empty number line
15
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This means breaking up numbers into smaller
numbers
All numbers can be partitioned in many
different ways
If children understand about partitioning
numbers in different ways, they will calculate
more efficiently – and with understanding.
Jump 10’s first –
Typical at end of Yr 1/start of Yr 2
+10
+10
26 + 23
+1
26
36
46
+1
47
+1
48
49
-10
-10
44 - 25
19
20
21
22
23
24
34
44
Jump and adjust
26 + 9
“Compensating”
+10
26
44 - 9
34 +1 35
35
-10
44
36
-1
We constantly draw upon mental strategies that
we know and have internalized when we carry
out calculations
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doubling
adding multiples of ten
Partitioning
compensating
applying known facts
Children need to learn and understand these
strategies – and know how and when to apply
them.
47 + 76 = 40 + 70 = 110
7 + 6 = 13
110 + 13 = 123
40 + 7
70 + 6
------110 + 13 = 123
47
76
---110 (70+40) then…
13 ( 7+ 6)
---123
Adding 1s first
47
76
----13
110
123
h t u
4 7
71 6
-------1 2 3
7 + 6 = 13 which is: 1 ten and
3 units
We exchange 1 group of
ten for ten units
Expanded by partitioning:
563 – 241
then…
500 + 60 + 3
200 + 40 + 1
------------300 + 20 + 2 = 322
563241
-----322
The previous method does not always work…
74 – 27
70 + 4
20 + 7
------40 + 7 = 47
6
1
3 41 268
-----073
2
1
3
1
Arrays are important because they provide a
good visual image of the multiplication that links
closely to the concept of repeated addition.
2+2+2+2
4x2=8
2x4=8
They are the visual image which leads directly into grid multiplication
a key strategy in KS2
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They show the link between
multiplication and division – these are
not concepts taught in isolation
2x4=8
4x2=8
8÷2=4
8÷4=2
2
0
+
2
2
+
4
2
+
6
2
+
8
2
10
This image can be expressed as 2 multiplied by 5,
two, five times, 5 groups of 2, 5 lots of 2 and 5 hops of
2 on a number line.
There are 5 cakes in one box. How many cakes in 4 boxes?
Encourage estimation first…
38 x 7 (approx 40 x 7 = 280)
x
7
30 210
8
56
210 + 56 = 266
Column but showing working…
38 x 7
then…
30 + 8
7
--------56 (7 x 8)
210 (7 x 30)
h
t
3
u
8
7
------5 6
2 1 0
2 6 6
38 x 7
grid for 2dp x
2dp
38 x
7
266
5
then…
x
20
7
50 1000 350= 1350
6 120 42 = 162
1512
Children find this tricky!
Division can be GROUPING or SHARING
Sharing:
We have 20 marbles in the marble run to share between
4 children. How many marbles do they get each?
=5 marbles
Grouping:
We have 25 marbles and they come in packets of 5. How
many packets were there?
Putting 20 into groups of 5. Answer is how many in each
group
=4
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I have 12 lollipops and I share them among 4
people. How many lollipops will they have
each?
I have 12 lollipops and I want to put 4 lollipops
in each bag. How many bags will I need?
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Chunking
345 ÷ 3
300 (100 x 3)
45 (15 x 3)
45
00
= 115
See progression in calculation document
http://www.mathsisfun.com/numbers/longdivision-animation.html
425 ÷ 25
200 225200
25
2500
(8 x 25)
(8 x 25)
(1 x 25)
= 17
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Resources, models and images help children to
visualise and understand mathematical
concepts
They build up – and remember - the mental
picture in their minds
They should be available throughout the primary
years. Children will rely on them less and less
TABLES!
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What do I know about these numbers?
Can I do this in my head?
Do I know the approximate size of the answer?
If I can’t do it all in my head, what do I need to
write down to help me?
“Above all – have fun! Children often say that
maths is their favourite subject and they get
quicker and better at it when they
understand what they are doing. There’s no
need for you to “teach” your child: you help
by helping them to explain their thinking and
their understanding”
From “Count on me – 200 ways to help with mathematics”
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“It’s the school’s job to provide the structured
learning….Your role is to nurture and support
your child’s mathematical knowledge away
from school, to bring it into their real lives and,
most important of all, to turn it into an exciting
adventure”
From “Maths for Mums and Dads” – Rob Eastaway and Mike
Askew