Working together with mathematics

1
Working together with mathematics

• Workshop for parents
• Holywell Primary and Nursery School
• Tuesday 13th May 2008
• Wednesday 14th May 2008

2
Which of these words would you use to describe
mathematics?

• Maths is

exciting
useful
easy
scary
hard
boring
uncomfortable
frightening
challenging
fun
important
3
Maths is like cabbage

• you love it or hate it,
• depending on how it
• was served up to you
• at school!

4
Maths learning and teaching has changed (for the
better!)

• It is more active and collaborative than it used
  to be
• Having a go and talking maths are encouraged
• Mental methods (being able to work things out in
  your head) are more important than
• written methods

5
What maths have you done already today?

• Sound familiar?

Can I risk another 5 minutes in bed when Ive got
so much to do before taking the children to
school/going off to work?
6
Time

• Managing time

Have I got time to put a load of washing in the
machine before going out?
7
Time

• Reasoning

What time do I need to leave if Ive got to drop
Charlie off at mums before going to the meeting
at school?
8
Estimating
Reading the gauge- understanding fractions
Have I got enough petrol in the car to get me to
school and back?
And, have I got enough money to pay for the
petrol?!!!
9
Estimating
Have I got time and space to overtake the car in
front thats going so slowly?
10
Estimating

• These are all examples of estimating
• the passage of time
• capacity
• speed
• duration of time
• Was any of it written down?!
• MENTAL MATHS IS IMPORTANT!

11
Some other examples

• Shopping

Do I need a trolley, or will a basket do, given
that I only need a carton of milk and a loaf of
bread?
(Estimation of weight) We always get this one
wrong!
12
Estimating

• Shopping

Will this sale price sweat shirt do for Joe for
next year as well, given the rate hes growing?
(estimation of time growth rate)
13
Estimating

• Shopping

Have I got enough cash to pay for all this, or
will I need to use my bank card?
(estimation of cost and available money! )
14
Order of numbers

• Will I be able to remember my chip and pin
  number?

15
Estimating

• DIY

Can we afford to re-carpet the living room this
month, given that the carpet is 20 a square
metre?
(estimation of area money)
16
We want our children to develop a feel for
number so that

• They know the size of the numbers and where they
  fit into the number system.
• They know number facts, such as number bonds to
  10, 20 100, are able to recall multiplication
  and division facts.
• They understand place value and partitioning
• They know the relationship between the
  operations.
• 
  

17
Place Value and Partitioning

• What is place value?
• Understanding the value of the digits eg
• 2394 2000
• 300
• 90
• 4
• What is partitioning?
• Splitting the number up into the value of
  the digits
• As above.

18
Working towards formal Calculations

• Mental Calculations are very important
• Children need to have a secure understanding of
  number.
• Need to be able to understand what they are doing
  to be able to enjoy maths!

19
Relaxed and happy!

• Research shows that when learners are relaxed
  their brains are able to function well. If they
  are frightened it closes down.
• They need to be confident.
• They need to build up skills slowly.
• They need to have basic skills at their finger
  tips.
• They need to learn some facts off by heart.

20
Facts need to be learnt off by heart

• Tables Vital for multiplication, division,
  fractions, percentages
• Doubles - up to 10, then 20 then 50
• Halves even numbers up to 10 then 20 then odd
  numbers
• Need to practise counting up and down in
  different amounts.

21
Number Bonds

• Need to know bonds for all digits up to 10.
• For example for number 8
• 17
• 26
• 35
• 44
• 53 etc

• Then they ll know
• For number 18
• 117
• 126
• 135
• 144
• 153 etc

22
Making 10, 100, 1000

• 010 0100
  0 1000
• 19 1090
  100 900
• 28 Once making 208
  200 800
• 37 10 is mastered 30 70
  300 700
  
• 46 this can be used 4060
  400 600
• 55 for making 5050
  500 500
• 64 100 then 1000 6040
  600 400
• 73 7030
  700 300
• 82 8020
  800 200
• 91 9010
  900 100
• 100 1000
  1000 0

23
Number Lines
2p

• Number Lines are very useful.
• They can be used successfully for
• - giving change
• - adding
• - subtracting
• - working out time

8p 10p
70p
30p 1
10mins
15 mins
5 hrs
245pm 300
800 810pm
24
Progression Of Addition

• Recognising numbers
• Counting 1 on 1
• Addition of numbers using objects or fingers
• Adding two numbers by keeping one in head and
  adding on another
• Using a number line eg 7425 99
• 
  

20
5
74
94 99

25
Informal Written Methods

• 7425
• 90 9
• Or write down as
• 702090
• 45 9
• 909 99

26
Efficient Written Method

• 3 5 7
• 4 6 2
• 8 1 9
• 1
• Need this method when you can not do mental
  calculation, ie when numbers are too big.

27
Progression of Subtraction

• Using Objects
• Using Fingers
• Counting backwards
• Using a number line
• 9 4 - 8 5 9

-5
-80
94 14
9

28
Progression of Subtraction

• 94-85 Numbers are close together so add on.
• 
  
  
• To add on, start at the lower number and find the
  difference between the two numbers.

5
4
85 90
94

29
Progression of subtraction

• Informal Jottings
• 8 4 - 6 5 Need to know the
  value of 6 in 65
• and
  the value of the 5.
• 84 60 24
• 24 5 19

30
Efficient Written Method

• 5 9 7
• - 4 8 6 Straight Forward
• 1 1 1
• 5 6 13 4 12
• - 2 7 8 Decomposition
• 3 6 4

31
Progression of subtraction

• 56 90 17
• - 1 8 9 These two are examples
• 4 1 8 of decomposition
• 1 2123 145 16
• - 1 8 9 7
• 4 5 9

32
Formal or Informal ?

• Spend 5.62
• How much change from 10?
• Either 10 - 5.62 Take 5 then 62p
• Or a sum
• 01 90 . 90 10
• - 5 . 6 2
• 4 . 3 8

33
Formal or informal?

• Or counting up on a number line.
• 8p 30p
  4
• 4.38

5.62 5.70 6
10
34
Progression of Multiplication

• Count in 2s
• Count along a number track whispering one number
  then shouting the next
• Count in 2s, 10s, 5s,
• Learn doubles
• Describe repeated addition as lots of
• eg 6 lots of 2 222222

35
Progression of Multiplication

• Use x sign
• Use an array of dots . .
• 6x2 . .
• . .
• . .
• . .
• . .

36
Progression of Multiplication

• Know tables off by heart
• 40 x 3 120
• Use 4 x 3 12 12 x10 120
• 45 x 3
• Partition 45 into 40 and 5
• 40 x 3 120
• 5 x 3 15
• 120 15 135

37
Progression of Multiplication

• Short multiplication
• 4 5
• x 3
• 1 3 5
• 1

38
Progression of Multiplication

• Grid Method 25 x 16
• This is a very successful method.

X 20 5
10 200 50 250
6 120 30 150
400
39
Progression of Multiplication

• Long Multiplication 24 x 16
• 2 4
• x 1 6
• 2 4 0 This
  method
• 1 4 4 is
  more
• 3 8 4
  confusing but
• 
  uses less space.
• There is no requirement that the children use
  this method.

40
Progression of Division

• Practical sharing of sweets, marbles, conkers,
  etc
• Halving even amounts
• Grouping how many groups of 3 in 15
• 15 3 Understand the sign means sharing or
  grouping
• .. .. ..

41
Progression of Division

• Link between subtraction and division
• 15 3 15 - 3 12
• 12 3 9
• 9 3 6
• 6 3 3
• 3 3 0
• Use a number line 15 3
• 5 jumps
• 15 3 5

0 3 6 9
12 15
42
Progression of Division

• 17 3 5 r 2

3
3
3
3
3
2
0 3 6 9
12 15 17
43
Progression of Division

• Short Division sometimes called the bus stop!
• 1 3 4
• 2 2 6 8
• 5 0
• 3 1 15 0
• 1 5 3 r 1
• 3 4 16 10

44
Progression of Division

• Long Division 2 3 4 17
• 1 4
• 1 7 1 2 13 8
• - 1 7
• 6 8
• - 6 8
• 0

45
Long Division

• 1 4
• 1 7 1 2 13 8
• - 1 7 0 ( 10 x
  17 170)
• 6 8
• - 6 8 ( 4x
  17 68)
• 0

46
The snake and ladder game

• A great game for counting on.

47
Play games that involve counting

• Cards, board games,
• dominoes.

48
Involve your child in shopping

• Children these days have less opportunities than
  we did to use money
• Adults use money differently from twenty years
  ago
• Help your child to recognise coins
• and understand equivalent values
• e.g. 5p1p1p1p1p1p
• 5p2p2p1p

49
Measures from shopping

50
Play money games with them

• Count amount of money in pockets, purses, jars!

51
Maths at Home

• Do we create an atmosphere at home where
  exploration and having a go is seen as more
  important than getting the answer right?
• Do we provide a rich and interesting home
  environment with plenty of opportunities for
  problem solving with numbers, measures and
  shapes?
• Do we use opportunities to talk about maths?

52
Remember!

• Be positive even if you dont feel it
• Ask your child to explain to you how they are
  doing their maths (it may be different to the way
  you were taught)
• Talk to them about and involve them in everyday
  maths
• Ask the teachers if you have any questions about
  the maths your child is doing
• Have fun!