Transcript Maths presentation - Orleans Primary School

Maths
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How do we teach it?
Why do we teach it like that?
What do the written methods look like?
What can you do at home to help?
How do our children learn in
Maths lessons at Orleans?
 Encouraged to use mental calculation methods
 Practise recall of number facts to become quicker
and more accurate
 They are more aware of the strategies they use
to calculate
 Focus on correct use of vocabulary and talk for
learning
 Real-life, contextual learning
 Practical and engaging lessons – fascinators! CB's
‘It just doesn’t look like it did in my day.’
‘I hear and I forget. I see and I remember.
I do and I understand.’
(A Chinese proverb)
Until fairly recently, maths was taught using
Victorian era methods.
Were you one of the lucky ones?
Logical and strong with numbers?
Victorian Times
 Vast numbers of clerks to
perform calculations every day.
 Today, calculators and
spreadsheets can do this car
quicker, so the need for
everybody to be able to do big
calculations by hand has largely
disappeared
That’s not to say we don’t need strong
number skills!
We are inundated by numbers all the time…
Do we all need to be able to work out 27 x 43
precisely with a pen and paper?
Probably not…but we do need to know that:
27 x 43 is roughly 30 x 40 and…
that this is roughly 1,200
It's partly the need to have a good feel for
numbers that is behind the modern methods.
National Numeracy Strategy
1999
• The revolution in the teaching of maths
at primary school kicked in with this
strategy.
• The emphasis moved away from blindly
following rules (remember borrowing one
from the next column and paying back?)
towards techniques a child understood
The Aim
 for children to do mathematics in
their heads, and if the numbers are too
large, to use pencil and paper to avoid
losing track.
 To do this children need to learn quick and
efficient methods, including mental methods and
appropriate written methods.
Learning written methods is not
the ultimate aim.
Mathematics is foremost an activity of
the mind; written calculations are an aid
to that mental activity.
We want children to ask themselves:
1. Can I do this in my head?
2. Can I do this in my head with the help of
drawings or jottings?
3. Do I need to use an expanded or compact
written method?
4. Do I need a calculator?
A sledgehammer to crack a nut!
0
9
1
1
9
1
1
0
16
- 9
7
1000
7
993
08
7 56
0
5
97
x 100
00
000
9700
9700
Addition
Addition – progression
• Y3 Programme:
• To add mentally combinations of 1-digit and 2-digit
numbers
• Develop written methods to record, support or
explain addition of 2-digit and 3-digit numbers
• Y4 Programme:
• To add mentally pairs of 2-digit numbers
• To refine and use efficient written methods to add
2-digit and 3-digit numbers and £.p
How would you solve these?
● 25 + 42
● 25 + 27
● 25 + 49
● 145 +127
Partitioning
48 + 33
40 8 30 3
70 + 11 = 81
Number line
26 + 12 = 38
+ 10
36
26
+1
+1
37 38
+ 100
242
+6
+ 30
342
372
242 + 136 = 378
378
Use the number line to work
these out…
• 67 + 48 =
• 346 + 237 =
• 3241 + 1471 =
+ 30
+ 100
242
242 + 136 = 378
342
+6
372
378
Column Method
Compact
Expanded
358
+ 33
11
80
300
391
Leading to
358
+ 33
391
1
Subtraction
Subtraction - progression
Y3 Programme:
 To subtract mentally combinations of 1-digit and 2digit numbers
 Develop written methods to record, support or explain
subtraction of 2-digit and 3-digit numbers
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
Y4 Programme:
To subtract mentally pairs of 2-digit numbers
To refine and use efficient written methods to
subtract 2-digit and 3-digit numbers and £.p
How would you solve these?
• 67 - 45
● 67 – 59
● 178 - 99
● 3241 - 2167
Number line
• Subtraction as taking away
13
-2
30 – 17 = 13
- 10
-5
15
20
30
• Subtraction as finding the difference
Difference
5
12
Number line
• Subtraction as finding the difference
34 – 18 =
+ 10
+2
18 20
+4
30
34
• Jump to next multiple of 10
• Count the jumps
10 + 4 + 2 = 16
Column Method
547
134
413
1
82
- 57
25
7
Use the number line to work
these out…
• 48 – 31 =
• 256 - 167 =
+2
18 20
+ 10
+4
30
34
Multiplication
Multiplication - progression
Y3 Programme:
• Multiply one digit and two digit numbers by 10 or 100 and describe
the effect;
• Derive and recall multiplication facts for the 2, 3, 4, 5, 6, and 10
times tables;
• Use informal and practical methods to multiply two digit numbers
e.g. 13 x 3.
Y4 Programme:
• Multiply numbers to 1000 by 10 and then 100 and describe the
effect;
• Derive and recall multiplication facts up to 10 x 10;
• Use written methods to multiply a two digit number by a one digit
number e.g. 15 x 9.
How would you solve these?
● 24  50
● 24  4
● 24  15
● 136  9
Number line
Multiplication as repeated addition
+2
0
+2
2
+2
4
4x2
+2
6
4x2=2+2+2+2
So, 2 x 4 = 8
8
Arrays
3x6
Or
Add the dots
What multiplication
are these arrays
showing?
Partitioning
24 x 5
20 x 5 = 100
4 x 5 = 20
100 + 20 = 120
Grid Method
24 x 5
20
x 5 100
4
20
100 + 20 = 120
BBC News Video Link
Expanded Multiplication
38
x 7
210
56
266
(30 x 7)
(8 x 7)
Use the grid method to work
these out:
24 x 7
142 x 3
24 x 5
20
x 5 100
4
20
100 + 20 = 120
Division
Division - progression
Y3 Programme:
Use practical and informal written methods to
divide two-digit numbers (e.g. 50 ÷ 4);
Y4 Programme:
Develop and use written methods to record,
support and explain division of two-digit numbers
by a one-digit number, including division with
remainders (e.g. 98 ÷ 6)
How would you solve these?
● 123  3
● 165  10
● 325  25
● 623  24
Division
Arrays
First group of
3
12 ÷ 3 = 4
Repeated subtraction
12 ÷ 3 = 4
-3
0
-3
3
12 - 3 – 3 – 3 – 3
-3
-3
6
9
12
Counting in steps
12 ÷ 3 = 4
+3
0
Add the jumps
+3
3
+3
+3
6
9
Fingers
“3
”
“6
“9
“12
”
12
Chunking
75 ÷ 5
5x5
0
Need to
know
tables!
10 x 5
25
75
- 50 (10 x 5)
25
- 25 (5 x 5)
0
BBC News Video Link
75
75 ÷ 5 = 15