How to measure angles'''

1
Progression in addition and subtraction
2
Readiness for written calculations (/-)

• In order to prepare the children for written
  calculations, we do lots of work on mental
  strategies and number facts. This includes

• Knowledge of their number bonds to 10 and 20
  (and-)
• A sound understand of place value and
  partitioning numbers into H, T and U
• Being able to add at least three single-digit
  numbers mentally
• Being able to add and subtract any pair of
  two-digit numbers mentally
• Children also need to be able to explain their
  mental strategies orally and record them using
  informal jottings

3
Methods of Addition

• Children need to know their number bonds to 10
  and 20.

• Next step is to use number lines e.g 24 12

24 12 36

• Then progress onto recording with partitioning
• 76 47 76 40 7
• 116 7
• 123

4
Methods of Addition (continued)

• Then children move on to vertical addition,
  through partitioning using expanded working,
  before moving on to the standard short method.
• 47 76 (40 70) (7 6)

or 40 7 70 6
110 13

• An example using larger numbers e.g. 166 129

166 129 15 (96) 80
(60 20) 200 (100 100) 295
5
Methods of Subtraction

• Again, children need to know their number bonds
  to 10 and 20!

• Next step is to use number lines to COUNT UP
  eg 48 - 29

6
Methods of Subtraction..(continued)

• The next step is to begin recording vertically,
  using partitioning e.g. 81 57
• 81 80 1 70 11
• - 57 50 7 50 7
• 20 4 24

• This then leads to the standard written method
  and will involve larger numbers .
• 81
  754
• - 57 - 236
• 24 518

7
1
4
7
Readiness for written calculations (x/)

• As with and , in order to prepare the children
  for formal written calculations using x and , we
  do lots of work on mental strategies. This
  includes

• A SOUND knowledge of their times tables and the
  corresponding division facts.
• A thorough understanding of place value
• Multiplying 2 and 3 digit numbers by 10 and 100
• Doubling and halving 2 digit numbers mentally
• An ability to use multiplication facts they know
  to derive mentally other multiplication facts
  that they do not know e.g. 3 x 4 12, so 30 x 4
  120
• Understanding that multiplication and division
  are inverses
• Again, children need to be able to explain their
  mental strategies orally and record them using
  informal jottings
• Children also need to be able to explain their
  mental strategies orally and record them using
  informal jottings

8
Multiplication and Division

• At whatever stage in their learning, and
  whatever method is being used, it must still be
  underpinned by a secure and appropriate knowledge
  of number facts, along with those mental skills
  that are needed to carry out the process and
  judge if it was successful.

9
Why teach them different methods and not just one?

• The aim is that by the end of Key Stage 2, the
  great majority of children should be able to use
  an efficient written method for each operation
  with confidence and understanding.
• At St Lawrence, we want our children to know that
  they have such a reliable, written method to
  which they can turn when the need arises.

10
Multiplication

• 15 x 9???
• How many different ways can we work this out?
  When faced with a calculation, no matter how
  large or how difficult the numbers may appear to
  be, pupils should ask themselves
• Can I do this in my head? then
• Do I know the approximate size of the answer?
  and more importantly,
• What do I already know that will help me solve
  this?

11
15 x 9???

• We can look at approximation.
• 15 x 9 is nearly 15 x 10 which is 150.
• In turn, we can use this information to solve the
  answer
• 15 x 9 is the same as 15 x 10 (150)and then
  subtract 1 lot of 15.(150-15135)

12
15 x 9???
We can use partitioning.
15
5
10
X 9
90
45


135
13
The Grid Method
Links need to be made to the expanded short
multiplication
14
Short Multiplication
15
Two-digit by two-digit multiplication
Links need to be made to the expanded short
multiplication
16
Division

• The main point to realise is that
  childrens mental methods are practised and
  secured alongside their learning and use of an
  efficient written method of division. Children
  also need to be able to
• Understand divison as repeated subtraction.
• Understand that divison is the inverse operation
  of multiplication.
• Estimate how many times one number divides into
  another.

17
Subtracting groups of 5

• 72 5
• 72
• 50 10 x 5
• 22
• - 20 4 x 5
• 2 Answer 14
  remainder 2

18
Chunking

• The previous method is called chunking. It is
  based on subtracting chunks of the divisor. It
  is useful in reminding children about the link
  between division and repeated subtraction.

19
196 6
20
A greater understanding of multiples will allow
this
21
Multiplication and Division

• The Last Word
• With both these operations, children who have
  a secure knowledge of multiplication facts and
  place value will be able to move on quickly to
  more efficient paper and pencil recordings.