Transcript Maths calculation presentation

Berkeley Primary
School
Calculation Evening,
May 2013
Please sit anywhere for the
moment
Objectives for the
evening:
•To share how we teach calculation at
Berkeley.
•To give an understanding of progression in
calculation.
•To let adults experience what their children
experience.
•To have FUN!
•Don’t be shy – get stuck in
Our children...
are all different (believe it or not). They are
not widgets at exactly the same point on
the ‘production line’.
That’s why we teach them as individuals
and tailor maths to suit them. They are all
on individual journeys and at varying
stages in their progression.
Rapid recall
Models, images &
concrete materials
Understanding
Use of ICT
The Four
Rules
Problem solving
and role play
Mental
calculations
Stories / rhymes
Efficient written
methods
ADDITION AND
SUBTRACTION
PROGRESSION FOR ADDITION AND
SUBTRACTION
• Counting
• One more / less
• Addition as combining two groups, then counting on
• Subtraction as take away or difference (eg how many
more is … than …?)
• Ten more/less
• Recall of addition/subtraction facts to 10, 20 and
beyond
• Understand that subtraction and addition are inverses
2+3=
I buy 2 cakes and my friend buys 3 cakes.
How many cakes did we buy altogether?
Addition
pictures
(Children could draw a picture to help them work out the answer)
8+5=
8 people are on the bus. 5 more get on at the next stop. How
many people are on the bus now?
symbols
(Children could use dots or tally marks to represent objects – quicker than drawing a picture)
Counting on – jumps of 1
(modelled using bead strings)
18 + 5 = 23
+1
18
+1
19
+1
20
+1
21
+1
22
23
24
35 + 47 = 82
(+ 30)
(+ 3)
47
77
No number line
35 + 47
= 47 + 30 + 5
= 77 + (3 + 2)
= 82
(+ 2)
80
82
Addition by partitioning
74 + 48
70 + 40 = 110
4 + 8 = 12
122
Addition by partitioning
374 + 248
300 + 200 = 500
70 + 40 = 110
4 + 8 = 12
622
300 + 70 + 4
200 + 40 + 8
500 + 110 + 12
COLUMN ADDITION
374
+ 248
622
1 1
Extended to:
1247 + 367
£2.36 + £6.48
3.5 + 4.8
7.48 + 2.6
12.5 km + 6.08 km
MORE
TRADITIONAL
METHODS
ARE STILL
USED!
SUBTRACTION
Earlier work involves taking away objects
from groups, counting back on a number
line or using number beads.
Counting on fingers etc
5–2=
I have five cakes. I eat two of them.
How many do I have left?
A teddy bear costs £5 and a doll costs £2.
How much more does the bear cost?
Subtraction
(Take away)
(Find the difference)
Drawing a
picture helps
children to
visualise the
problem
13 – 5 =
Mum baked 13 biscuits. I ate 5. How many were left?
(Take away)
Lisa has 13 felt tip pens and Tom has 5. How many more does Lisa have?
(Find the difference)
Using dots
or tally
marks is
quicker
than
drawing a
detailed
picture
Taking away – jumps of 1
(modelled using bead strings)
13 – 5 = 8
-1
8
-1
9
-1
10
-1
11
-1
12
13
Counting on – jumps of 1
(modelled using bead strings)
11 – 8 = 3
+1 +1
0
1
2
3
4
5
6
7
8
9 10
+1
11
Number lines - taking away
74 – 26 = 48
− 20
−4
−2
48
50
54
74
Number lines - counting on
74 – 26 = 48
+ 40
+4
0
26
+4
30
70
74
As they move up into KS2, the
children will begin to use partitioning
to subtract too- breaking down the
numbers into Hundreds, Ten’s, Units
etc
89 =
- 57
80 + 9
50 + 7
30 + 2 = 32
We then move onto the RED ALERT
questions (or decomposition) where
borrowing is introduced:
352
- 136
= 300
= 100
200
50 40
30
10
12
6
6
= 216
Does this look more familiar?!
7 1
6867
- 2684
4183
MORE
TRADITIONAL
METHODS ARE
STILL USED!
Our children are always encouraged to
have a go and to not be afraid of making
mistakes. That’s how we learn.
OK…
If you’re still awake, time to head for a
maths group and try an activity or two.
MULTIPLICATION
AND DIVISION
Progression for multiplication and division
• Counting
• Doubling and halving
context
• Multiplication as repeated addition and describing an
array
• Division as grouping and sharing
• Understand that multiplication and division are
inverses
• Recall of multiplication and division facts
• Multiply two / three-digit numbers by 10 / 100
Dice race game
COUNTING IN CONTEXT
How many 10p coins are here?
How much money is that?
How many toes are there on 2 feet?
How many gloves in 3 pairs?
If Sarah counts in 2s and Nigel counts in 5s, when
will they reach the same number?
How many lengths of 10m can you cut from 80m of
rope?
DOUBLING AND HALVING IN CONTEXT
There are 8 raisins. Take half of them.
How many have you taken?
One snake is 20cm long.
Another snake is double that length.
How long is the longer snake?
I double a number and then double the
answer.
I now have the number 32.
What number did I start with?
2 x 3 or 3 x 2
Multiplication
3 plates, 2 cakes on each plate
pictures
(Children could draw a picture to help them work out the answer)
2 x 3 or 3 x 2
3 plates, 2 cakes on each plate
symbols
(Children could use dots or tally marks to represent objects – quicker than drawing a picture)
Number tracks and number lines
(modelled using bead strings)
2 x 3 or 3 x 2
[two, three times] or [three groups of two]
0
2
4
6
Arrays
5 x 3 or 3 x 5
14 x 2 = 28
x
2
10
20
4
8
Array creator
Arrays then can lead into what we
call grid multiplication- partitioning
numbers for multiplication
43 x 6
X
6
40
240
3
18
40 x 6 = 240
3 x 6 = 18
43
x 6
258
1
TU x TU
(Short multiplication - multiplication by more than a single digit)
64 x 34
X
60
4
30
1800
120
4
240
16
1800
240
120
+ 16
2176
HTU x TU
(Short multiplication - multiplication by more than a single
digit)
372 x 24
X
300
70
2
20
6000
1400
40
4
1200
280
8
6000
1400
40
1200
280
8
8928
HTU x TU
(Standard Method for long multiplication)
372 x 24
Multiplying 4 x
2 then 4 x 70
then 4 x 300
etc
372
x 24
372
8
280
1200
1488
+ 7440
8928
40
1400
6000
8928
24
1
( 372 x 20)
( 372 x 4)
DIVISION
6÷2
Division
6 cakes shared between 2
pictures
6 cakes put into groups of 2
(Children could draw a picture to help them work out the answer)
6÷2
6 cakes shared between 2
6 cakes put into groups of 2
symbols
(Children could use dots or tally marks to represent objects – quicker than drawing a picture)
Number tracks and number lines - grouping
(modelled using bead strings)
8÷2=4
6÷2=3
0
2
4
6
Number lines / Arrays
15 ÷ 5 = 3
0
5
10
15
Sharing equally
8 sweets are shared between 2 people.
How many do they each receive?
GROUPING OR REPEATED
SUBTRACTIONASKING IN A DIFFERENT WAY!
There are 8 sweets. How many
people can have two sweets each?
As children progress in division, they will
continue to use:
repeated subtraction using a number line. They
may use an empty number line or a hand drawn
jumping line.
e.g. 24 ÷ 4 = 6 - children will start at 0 and
jump forwards in 4’s to find how many 4’s go
into 24 or they may do a multiplication
(repeated addition from earlier)
Children will also move onto remainders
e.g. 13 ÷ 4 = 3 r 1
24 ÷ 4 = 6
0
4
8
12
16
20
24
As children continue with their progress, they
will learn methods such as chunking!
This is chunking!
http://www.bbc.co.uk/news/11260872
97 ÷ 9 = 10 r 7
EFFICIENT METHODS . . . .
754 ÷ 6
Approximation:
Answer lies between 100 (600 ÷ 6) and
150 (900 ÷ 6)
Answer = 125 r 4
754
- 600
154
- 120
34
- 30
4
(6 x 100)
(6 x 20)
(6 x
Extend to U.t ÷ U and HTU ÷ TU
5)
Efficient methods . . . .
Short division
291 ÷ 3 = 97
Estimation: 270 ÷ 3 = 90
97
3
2 2
291
43.4 ÷ 7 = 6.2
6.2
Estimation: 42 ÷ 7 = 6
7
4
43.4
1
OK…
Time to try some multiplication and division
activities.
Useful websites
and resources
• Transum http://www.transum.org/Software/ - provides a
mathematics challenge for every day of the year!
• Nrich http://nrich.maths.org/public/ - thousands of FREE
mathematics enrichment materials for ages 5 to 19 years. The resources
are designed to develop problem-solving and mathematical thinking
skills.
• Woodlands http://resources.woodlands-junior.kent.sch.uk/maths/
- interactive maths games and activities for both KS1 and 2
• BBC Bitesize http://www.bbc.co.uk/bitesize/ - useful summary of
KS1/KS2 content with interactive activities [also has KS3/KS4 materials]
• I Love Maths Games – games, puzzles and investigations
http://www.ilovemathsgames.com/
• Professor Kageyama’s maths training for DS consoles
Maths for mums and dads – Rob Eastaway
Rob Eastaway has been Director of Maths Inspiration since it began in 2004.
He is an author whose books on everyday maths include the bestselling Why Do
Buses Come In Threes? and The Hidden Maths of Sport. He appears regularly
on BBC Radio 4 and 5 Live to talk about the maths of everyday life and has
given maths talks across the world to audiences of all ages
http://www.bbc.co.uk/news/11260872
Three in a row
Choose two
numbers from the
row of numbers
above the grid.
Find the difference
between these
numbers.
If the answer is on
the grid, cover that
number with a
counter.
14 20 21 34 39 45 50
31
24
30
11
14
6
29
7
20
5
18
13
16
25
36
1
Y3
A Square of Numbers
http://nrich.maths.org/public/viewer.php?obj_id=2005