Transcript CPD2 SLT making the Best of AfL

Mathematics at St. Hilary School
~ Calculation Strategies
Tuesday 27th of January 2009
© Crown copyright 2007
Format of mathematics session:
1) Brief introduction to mathematics at
St. Hilary School
2) Mathematics in the Foundation Stage
(EYFS)
3) Calculation strategies, and how they
are taught (addition, subtraction,
multiplication, division)
© Crown copyright 2007
Recent history of mathematics ...
• Numeracy strategy first introduced in 1999 –
comprehensive learning objectives and strict
lesson structure (including a compulsory mental
starter and plenary).
• This has continuously evolved over the past 8
years, where many teachers have taken the
initiative and made it their own.
• Renewed framework for English and mathematics
introduced in 2008 – main changes are longer
© Crown copyright 2007
The Renewed Framework ...
 Encourages flexibility in the organisation of the curriculum and the
structure of literacy and mathematics lessons
 Structures learning over sequences of lessons as well as within
lessons – promotes learning being built over time
 Raises expectations for all children, especially those at greatest risk
of underachievement
 Uses assessment more effectively to inform and direct teaching
and learning
 Adds breadth and strengthens pedagogy to include a clearer
focus on inclusion, the use of ICT, using and applying
mathematical skills and knowledge, the teaching of early reading,
speaking, listening and learning, and developing core areas of
learning in literacy and mathematics
© Crown copyright 2007
Our classrooms provide rich
mathematical environments ...
 mathematics is learnt by children exploring and making sense of
concepts
 all children can explore and develop their thinking and understanding
 children should work on ‘rich learning’ tasks in different ways and to
different depths, discussing their work with each other as well as with the
teacher
 ‘rich learning’ tasks will enable children to think mathematically, to
reason and to communicate
 children will need time to develop mathematical understanding and
skills, especially number and how it works
 Equipment is provided to scaffold their learning, like stabilisers
on a bike. It is then adapted, and finally taken away as
confidence and skill levels improve.
© Crown copyright 2007
The Teaching of Blocked Units
Using and applying mathematics
Counting and understanding number
Knowing and using number facts
Calculating
Understanding shape
These strands
are put
together into
units of
teaching ...
Measuring
Handling data
© Crown copyright 2007
Block A
Counting,
partitioning
and calculating
Block B
Securing number
facts, understanding
shape
Block C
Handling
data and measures
Using and applying mathematics
Counting and understanding number
Calculating
Using and applying mathematics
Knowing and using number facts
Understanding shape
Using and applying mathematics
Measuring
Handling data
Block D
Calculating,
measuring and
understanding
shape
Block E
Securing number
facts, relationships
and calculating
Using and applying mathematics
Calculating
Measuring
Understanding shape
Using and applying mathematics
Counting and understanding number
Knowing and using number facts
The ‘using and
applying of
mathematics’ is
now integral in
every unit, either
as a main focus,
or as a starter /
plenary – the
children are
continually
practising what
they are learning.
Calculating
© Crown copyright 2007
Problem-Solving, Reasoning and
Numeracy in the Foundation Stage
Requirements:
“Children must be supported in developing their understanding of
Problem Solving, Reasoning and Numeracy in a broad range of
contexts in which they can explore, enjoy, learn, practise and talk
about their developing understanding. They must be provided with
opportunities to practise and extend their skills in these areas and to
gain confidence and competence in their use.”
EYFS statutory guidance 2007
© Crown copyright 2007
ADDITION
Early stages
• Practical activities and discussions.







Recognising numbers.
Count objects up to 10.
Find one more than a number.
Count in ones and tens.
Relate addition to combining two groups of objects.
Count along a number line to add numbers.
Begin to use + and = signs in a number sentence.
© Crown copyright 2007
Mid-stages
• Mental Strategies & Informal Methods
 Looking for pairs that make 10 then 20, 30 etc.
16 + 12 + 4=
 Using a number square, count on the units then the tens –
Get your Number Squares out
 Adding ‘nearly’ numbers – To add 9 add 10 then subtract 1
32 + 9 =
32 +10 =42 -1 =41
 Using a number line, bridging through a multiple of 10 e.g 27 + 8
+3
+5
_______________________________________________
27
30
35
© Crown copyright 2007
Mid-stages
• Formal Methods – Start to emerge:
 Add using partitioning: 47 + 34 =
Add units
Add tens
Total

40 + 7 +30 + 4=
4 + 7 = 13
40 + 30 = 70
70 + 13 = 83
Expanded Method: 47 + 34 =
TU
T U
47
40 + 7
34
30 + 4
70 + 3 = 83
10
00887-2007DWO-EN-19
© Crown copyright 2007
Later stages
• Standard Methods
HTU
HTU . t h
147
+ 534
683
1
347 . 36
126 . 17
473 . 53
1 1
© Crown copyright 2007
SUBTRACTION
Early stages
• Practical activities and discussion.







Count backwards in number rhymes or stories.
Count back from a given number.
Begin to relate subtraction to take away.
Find one less than a number.
Counting back in tens
Count backwards along a number line to take away.
Begin to use the – and = signs to record mental additions.
© Crown copyright 2007
Mid-stages
• Mental Strategies & Informal Methods
 Using a number square, partition the number, then count back the
units then the tens.
 Subtracting ‘nearly’ numbers – To take 9 take 10 then add 1
32 - 9 =
32 -10 =22 +1 =23
 Using a number line, bridging through a multiple of 10 e.g 63 – 26
37
47
57
60
63
-10
-10
-3
-3
 Recognise when to count on- when 2 numbers are close together
106 – 98=
2
6
=8
_________________________
98
100
106
© Crown copyright 2007
Mid-stages
• Methods which lead to Standard Methods
 Can also use counting on:
374
22
100
74
= 196
- 178
___________________________________
178
200
300
374
 Expanded Method – Exchanging 10
43 – 27=
T 10 U
T
U
40 + 3
30 + 13
20 + 7
20 + 7
10 + 6 = 16
This leads to understanding how the standard written method works.
00887-2007DWO-EN-19
© Crown copyright 2007
Later stages
• Standard Methods
Can you remember those good old fashioned maths lessons?!!
343
65. 08
- 297
- 37. 35
© Crown copyright 2007
MULTIPLICATION
Early stages
• Practical Activities
 Counting in twos, fives and tens.
 Using activities to recognise doubles and halves.
 Using equipment to give lots of practice of
making groups of.
© Crown copyright 2007
Mid-stages
• Mental Strategies & Informal Methods
 Using arrays.
●●●●
2 x4 means 2 lots of/ groups of 4
●●●●
2 x 4 =8
OR 4 x2
is 4 lots of/ groups of 2 ●●
●● 4 x 2 =8
Therefore demonstrating
●●
that multiplication can be
●●
done in any order.
 Partitioning
e.g. 4 x 13 =
4 x 3 = 12
4 x 10 = 40 Total 12 + 40 =52
 Counting on using our tables. They really need to know tables!!
© Crown copyright 2007
Later stages
• Methods which lead to Standard Methods
 Use easy sums to help with harder:
30 x 40 = take off zeros
3 x 4 = 12
put zeros back on = 1200
7 x 0.8 = we know 7 x 8 =56 therefore 10 x smaller = 5.6
 The grid method: 33 x 248
1) First partition & put numbers in grid
200
40
8
2) Multiply each number together,
30
=
remembering to use easier sums to
4
=
help, take off zeros & add them
_____
back on.
3) Total each row & then add
together.
© Crown copyright 2007
Later stages
Standard Methods – Can you remember them?!
 Short Multiplication
7 x 48
48
x 7
 Long multiplication
67 x 36
67
x 36
(6 x 67)
0 ( 30 x 67)
Total
00887-2007DWO-EN-19
© Crown copyright 2007
DIVISION
Early stages
• Practical Activities.
 Counting back in tens, twos and fives.
 Know halves ... half of 6 is 3
© Crown copyright 2007
Mid-stages
• Mental Strategies & Informal Methods
 Counting on and back using tables
 Understanding division as sharing e.g if 20 sweets are shared
between 4 people:
 Understanding division as grouping e.g. How many groups of 5 are
there in 20? (Using apparatus and then our tables)
 Using arrays ●●●●●
10 divided into 2 groups = 5 in each group
●●●●●
●●
OR 10 divided into 5 groups = 2
●●
●●
●●
© Crown copyright 2007
●●
Mid-stages
• Mental Strategies & Informal Methods (Contd)
 Repeated subtraction 12 ÷ 3 means how many 3’s in 12, therefore
keep subtracting 3’s : 12 - 3 = 9, 9 – 3 = 6 etc.
__-3____-3____-3____-3___ How many 3’s? = 4
0
3
6
9
12
 Start to understand remainders and if you need to round up or down
e.g If I have 14 eggs, how many egg boxes will I need?
14 ÷ 6 = 2 remainder 2 2 full egg boxes and 2 in the other.
00887-2007DWO-EN-19
© Crown copyright 2007
Later stages
• Standard Methods
• Short Multiplication
237 ÷ 6
• Long Multiplication
427 ÷ 24
Remember these?
© Crown copyright 2007
Children should develop habits as:
pattern sniffers ……… experimenters …. tinkerers
……. inventors ………visualisers ………conjecturers
and be able to:
investigate… deduce… communicate… reason…
analyse…
scrutinize… discuss…. explore...
decipher… solve problems…
formulate…
© Crown copyright 2007
Thank you so
much for
attending – your
interest means a
lot to us and your
children!
Please complete an
evaluation form.
© Crown copyright 2007