Transcript 5 - SES Insight

Welcome to SJS and an
Evening of Maths!
Calculation Strategies
Calculating
• The purpose of the National Numeracy Strategy
was to improve standards in Mathematics.
• Emphasis upon developing pupils’ mental
calculation strategies and their understanding.
Calculating
• Younger children are encouraged to use mental strategies to
calculate but when the numbers become ‘too big’ they begin
the process of using pencil and paper to support these
mental calculations.
• These ‘jottings’ develop into expanded methods of calculating
which support the mental methods and make the processes
clear.
• In the later primary years, children are taught conventional
written methods, many of which you will recognise. However
the route to reach these methods you may not recognise.
Written Methods of
Calculation
Aim – by the end of Key Stage 2, majority of
children are able to use an efficient written
method for each operation with confidence and
understanding.
Expanded methods lead children into compact methods
so that they understand structure and efficiency.
An expanded form is needed before the steps in the
traditional standard written method are meaningful and
can be used with understanding.
AIM – To develop the children’s understanding of the
process rather than the process itself.
Attitudes Towards Maths
Jo Boaler – Professor of Maths at Stanford University
Everyone can learn Maths to a high level
Believe in yourself – Growth Mindset - Persistence
Struggle and learning from mistakes are really important Challenge
Speed is not important
It is important to think visually and creatively. Maths is not
just about calculations. It is about patterns and space,
thinking deeply and seeing things differently and making
connections.
You can achieve whatever you want to!
Importance of knowing
basic number facts.
1284 + 863
1284+
863
21 4 7
1
1
8034 - 1863
7 9
80341863
61 7 1
1
1
23 484 ÷ 6
3914
5
2
6 )2 3 4 8 4
Partitioning
98 = 90 + 8
523 = 500 + 20 + 3
1 578 = 1 000 + 500 + 70 + 8
Addition
Number Line
Partitioning
47 + 72 =
=
=
Stamford Endowed Schools
40 + 70 + 7 + 2
110 + 9
119
Adding by Partitioning Vertically
156
+
232
300
80
8
388
1 0 0 + 200
50+30
6+2
Partitioning
Vertically
+
Formal
Written
Method
2378
2 3 7 8
1149
+ 1 1 4 9
3000
3 5 2 7
400
110
17
3527
1 1
Adding the most significant digits first
Adding the least significant digits first
400 + 200 = 600
60 + 70 = 130
8 + 6 = 14
744
468
+ 276
600
130
14
744
468
+ 276
14
130
600
744
I have £7587 in my savings account. I get
five numbers in the National Lotto game
and win £5675. How much money do I
have now?
+
7587
5675
12
150
1100
12000
13262
(
7+
( 80
( 500
(7000
5)
+ 70)
+ 600)
+ 5000)
1284 + 863
1284+
863
21 4 7
1
1
Adding Decimals
Formal
Written
Method
Partitioning
Vertically
65.4
+
39.3
.7
14.0
90.0
104.7
65.4
+
39.3
10 4. 7
1
Subtraction
Number Line
847 - 63
+7
63
+30 +700 +40
+7
70 100 800 840 847
=784
Subtraction by counting up.
502 - 198 = 304
+2
198
+300
200
500
502
- 198
+2
502
2
(to 200)
300
(to 500)
2
(to 502)
304
Counting Up
Counting Up
Expanded Column Subtraction
Subtracting Decimals
Subtraction by counting up.
24.3 - 7.9 = 16.4
+0.1
7.9
+2.0
8.0
+10.0 +4.3
10.0
20.0 24.3
24.3
- 7.9
0.1
2.0
10.0
4.3
16 .4
(to 8.0)
(to 10.0)
(to 20.0)
(to 24.3)
Decimals
Division
Grouping
Using appropriate chunks
The easy way to divide!
Stamford Endowed Schools
72 ÷ 4 = 18
4
18
72
we know 10 x 4
40
we know 8 x 4
32
32
0
We highlight the times table we are using.
We circle the number of groups.
Stamford Endowed Schools
84 ÷ 6 = 14
6
14
84
we know 10 x 6
60
we know 4 x 6
24
24
0
We highlight the times table we are using.
We circle the number of groups.
112 ÷ 8 = 14
we know 10 x 8
14
112
80
we know 4 x 8
32
32
8
0
23 484 ÷ 6
3914
5
2
6 )2 3 4 8 4
The fun way to multiply!
Stamford Endowed Schools
Mental Multiplication
using Partitioning
27 x 4 = ?
36 x 3 = ?
X
4
X
3
20
80
30
90
7
28
6
18
= 108
= 108
Partition each number first
25 x 35=
20 + 5
X
30
5
30 + 5
20
5
25 x 35=
X
20
5
30
600
150
5
100
25
7 5 0
+ 1 2 5
8 75
Multiplying using the Grid
Method
X
70
3
50
3500 150
8
560
24
3650
+ 584
4234
37 x 86
30
80
6
7 x
2400 560
180
42
2580 +
602
3182
1
2580 602
a.
b.
c.
d.
e.
f.
If a baker bakes 52 loaves of bread every day, how many
will he have baked in 7 days?
Charlie has packed his soldiers into 4 boxes ready to move
house. In each box he has managed to pack 65 soldiers.
How many soldiers does Charlie have altogether in the
boxes?
For the Oscars, 76 special goody bags have been
prepared. Each bag has 6 special presents inside. How
many presents has the organiser had to buy for these
bags?
Nine children each bring in 47p towards their class’ Comic
Relief fund. How much money did they bring in altogether?
At a theme park, 92 people each paid an £8 entrance fee.
How much did the park make from these people?
Now have a go at writing your own word problems based on
these calculations………..
71x9= 53x9= 68x4=
Does your word problem match the calculation?