Transcript - Ashford Park Primary School

Aims:
• to inspire pupils’ confidence in
mathematics;
• to develop their ability to use and
apply mathematics across the
curriculum;
• to share ways in which you can help
your child at home and the fun you
can have with maths;
• to explain some of the methods used
at school.
Big Maths (mental strategies)
• Daily 20 minute mental arithmetic, this is split into 4
sections:
• Counting e.g. counting in 7s, 0.2s, 1/5s
• Learn its: facts that they need to know and this should be
supported at home e.g. times tables and number bonds
• It’s nothing new: applying their learning so 5+6=11,
0.5+0.6=1.1, 500+600=1100
• Calculations: linked to addition, subtraction, multiplication
and division
• The children take an assessment on a Friday (Big Maths Beat
That), designed to increase their fluency, accuracy and speed.
The main focus of this workshop is to
explain the progression in calculations
for all four operations.
Addition
Subtraction
Multiplication
Division
In the New National Curriculum, which will be
implemented in schools from September 2014, it is
expected that children should be using formal
written methods for all operations by the end of
Year 4.
Mental Calculations
The ability to calculate mentally forms the basis
of all methods of calculation. This involves:
• instant recall of number facts (+ - x ÷);
• having a secure understanding of place value
and the number system;
• having a range of strategies to apply to a
calculation;
• understand the language and rules of maths.
Written Calculations
•Throughout their primary years, children
should progress from informal jottings to
efficient written methods for each of the four
operations.
•Standard written methods should only be
introduced when a child has a secure knowledge
and understanding of the process involved and
can clearly explain the strategies they have
used.
•Children become secure with these methods
when they have regular practice and persevere!
Addition
Stage 1 The Empty Number Line
Stage 2 Partitioning
48 + 36 = 84
+30
48
+2
78
+2
48
40
50
8
30
+4
80
84
40 + 30 + 8 + 6
40 + 30 = 70
+34
84
8 + 6 = 14
70 + 14 = 84
6
Addition
Stage 3: The Expanded Method
48 + 36
48
+ 36
U
HT U
40 + 8
4 8 6
30 + 6
5 2 1
T
80 + 4
H 9 0 0
10
T
1 0 0
U
7
1 0 0 7
Addition
Stage 4: Standard Written Method
t u
48
+36
8 4
1
htu
156
+ 75
231
11
u.1/10
3.6
+ 1.6
5.2
1
Subtraction
Stage 1: Number Line Method
Subtraction
Stage 2: Partitioning
43 - 27 = 16
43 –
4
20
43 – 20 = 2 3
23 –
7= 16
3
20
7
7
Subtraction
Stage 3: The Expanded Column Method and
Dienes
43 - 27 = 16
to subtract 7 units
we need to exchange
a ten for ten units
T
U
- 2
7
10 +
30 40
+
3
- 20
+
7
10
+
6
Subtraction
Stage 4: Standard Written Method
3
4 3
1
3
4 3 5
12
1
- 2 7
- 1 5 7
1 6
2 7 8
Multiplication – Factors and Repeated
Addition
Understand that …
24
x 20 = 24 x 2 x 10
24
x 50 = 24 x 5 x 10
Use factors to multiply
Understand multiplication as repeated
addition
2+2+2+2=8
4x2=8
2 multiplied by 4
4 lots of 2
Multiplication – Arrays and the Number
Line
Understand
multiplication
as an array
Understand how to
represent arrays on a
number line
Multiplication – Place Value apparatus
Use place value
apparatus to represent
the multiplication of U
x TU alongside the grid
method
4 x 23
10
10
3
4
10
4
10
40
40
20
4
( 2 x 10 )
80
80 + 12 = 92
3
12
3
12
Multiplication – Grid Method
Multiplying 14 x 33
30
3
10
300
30
= 330 +
4
120
12
= 132
462
Children should be able to explain
their strategy orally and by using
informal jottings.
Multiplication – Expanded & Standard
Written Method
Multiplying 56 x 27
56
× 27
42
(7 × 6)
350 (50 × 7)
120
(20 × 6)
1000 (20 × 50)
1512
1
56
× 27
1120 (56 × 20)
392 (56 × 7)
1512
1
Division– Using the Number Line
Represent ‘groups’ for
division on a number line
using apparatus alongside
the line
0
3
18 divided into groups of 3
18  3 = 6
6
9
12
15
18  3 = 6
0
18
18
Division – Repeated Subtraction
18
18 ÷3 = 6
-3
18
15
-3
12
-
15
-
-3
3 (1x3)
9
-
6
3 (1x3)
6
-3
-
3 (1x3)
3
3
0
3 (1x3)
12
-3
9
3 (1x3)
-3
3 (1x3)
0
Understand division as repeated
subtraction using a vertical line
and apparatus to make the links
Division – The Chunking Method
Children need to see that as the numbers
get larger, large chunk subtraction is the
more efficient method. Multiples of the
divisor (large chunks) are taken away.
Multiplication facts are needed to see the
size of the ‘chunk’.
What facts do I know
about the 7 timestable?
518 ÷ 7 = 74
100 ÷ 7 = 14 r 2
- 70
( 10 x 7 )
2
518
2 x 7 = 14
(4x7)
( 20 x 7 )
0
20 x 7 = 140
50 x 7 = 350
100 x 7 = 700
28
- 28
5 x 7 = 35
10 x 7 = 70
168
- 140
30
- 28
1x7=7
- 350 ( 50 x 7 )
100
Fact Box
(4x7)
Division – The Standard Written Method
560 ÷ 24
2 3 r8
24
5 6 0
- 48 0
8 0
-
7 2
8
Mathletics –
www.mathletics.co.uk
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and Password
Ways to support your child:
• Displaying a positive attitude towards
Maths
• Supporting with times tables and learn its
• Mathletics
• Relate operations to everyday examples
• Using a range of vocabulary
• Ensure children are completing their home
learning
More ways you can help with
mathematics at home.
Cooking
• Measuring;
• Reading scales with different
intervals;
• Capacity and weight;
• Time;
• Fractions/ratio/proportion
More ways you can help with
mathematics at home.
Money
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Discuss how much items cost and the value of
things;
Work out what coins they need to pay for
something and talk about how much change
they will have left over;
Look at the current offers – are they good
value?
Work out the cost of items in a sale e.g. 25%
off;
Imaginary shopping lists (Argos List!)
Role play.
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More ways you can help with mathematics at home.
Card games and counting games (e.g. Snakes & Ladders, Ludo,
any dice game
Recognising numbers and sequences when out and about (e.g.
house number – odds and evens, bus numbers, car number
plates etc.)
Recognising shapes (e.g. buildings, windows, food packaging
etc.)
Helping in the kitchen (e.g. weighing ingredients, time
duration, volume of liquids etc.)
Helping in the supermarket (e.g. paying and change, weighing
fruit and vegetables, calculating better value etc.)
Posters in bedroom (e.g. 1-100 square, multiplication square,
times table lists)
CD’s / games for learning times tables
Take and compare measurements when DIY shopping (e.g.
measuring spaces for curtains, furniture, wall paper etc.)
Tell the time / use timetables (e.g. bus/train, TV guides, Sky
plus/Tivo Programming to record for time durations etc.)
Any Questions?
Thank you for coming.