Addition and Subtraction

1
Addition and Subtraction
Calculating efficiently and accurately
2
Objectives

• To explore the prerequisite skills required to
  help children develop written methods for
  addition and subtraction.
• To agree the progression from mental to written
  methods and the strategies to develop childrens
  understanding.
• To consider models, images and activities for
  early work on addition and subtraction.

Self-esteem
3
Rapid recall
Models, images concrete materials
Use of ICT
The Four Rules
Mental calculations
Understanding
Stories / rhymes
Problem solving and role play
Paper / pencil procedures
4
2
4
3
1
This is an addition wall.
NB could also be
subtraction / difference wall The value of
each brick can be found by adding the pair of
numbers on the row below. What is the number
that needs to be put into the brick at the top?
5
Number

• Size appreciation straws, Dienes blocks
• Words saying, spelling
• Symbols writing in digits
• Spatial position where numbers live
• Partitioning may illustrate place value
  (breaking down)

6
Progression in knowledge and understanding for
/ -

• Counting
• One more / less
• Addition as counting on
• Subtraction as take away, difference and how many
  more to make
• Ten more / less (constant function on calc.)
• Recall of addition / subtraction facts to 10, 20
  and beyond
• Understand that addition subtraction are
  inverses

7
Counting and estimation

• There are 5 principles of counting
• The stable order principle - understanding that
  the number names must be used in that particular
  order when counting
• The one-to-one principle - understanding and
  ensuring that the next item in a count
  corresponds to the next number
• The cardinal principle - knowing that the final
  number represents the size of the set
• The abstraction principle - knowing that counting
  can be applied to any collection, real or
  imagined
• The order irrelevance principle - knowing that
  the order in which the items are counted is not
  relevant to the total value

8
When faced with a calculation problem, we
encourage children to ask . . .

• Can I do this in my head?

• Can I jot something down to help me?
  (eg diagram, picture, blank number
  line)

• Do I need to use a written method?

• Should I use a calculator?

9
Readiness for written calculations ( / -)

• Know /- facts within 20
• Understand place value and partition numbers into
  H, T and U
• Use and apply the commutative and associative
  laws of addition
• Add at least three single-digit numbers mentally
• Add and subtract any pair of two-digit numbers
  mentally
• Explain mental strategies orally and record them
  using informal jottings
• Teaching Written Calculations (QCA/99/486)

10
Total squares
Use 8 different dominoes. The sides of each
square must have the same number of dots as the
middle number.
11
Addition 47 76 76 40 7
116 7 123 Extend to HTU
HTU with estimation
( 40)
( 4)
( 3)
76
116
120
123
NB Show other mental calculation strategies
(eg partition / recombine)
12
Addition (cont.)
Move to a vertical layout, using expanded
working 47 47 76
76 13
123 110 123
1
13
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
14

Subtraction Mental methods 84 - 56 a) as
take away
- 60
- 50
- 4
- 2
4
84
28
30
34
24
28
84
15
Subtraction (cont.)
b) as difference
20
4
4
0
56
60
80
84
16
Subtraction by decomposition

• No breaking down needed
• 563 - 241
• 500 60 3
• - 200 40 1
• 300 20 2
• Leading to
• 563
• - 241
• 322

• Using red alerts
• 563 - 248
• 500 and 60 and 3
• - 200 and 40 and 8
• Re-written as
• 500 and 50 and 13
• - 200 and 40 and 8
• 300 and 10 and 5
• Leading to 5 6 3
• - 2 4 8
• 3 1 5

5
1
17
Checking calculations ( / -)

• Year 2
• Check 6 13 4 with 6 4 13
• Check 31 7 with 31-1 and then 30 6
• Year 3
• Check 52 25 27 with 27 25 52
• Check 40 36 with double 40 - 4
• Year 4
• Check 297 406 by rounding to 300 400
• I know 78 26 will be even and 68 49 will be
  odd
• Year 5
• Use calculator to check 3685 - 987 2698 with
  2698 987 3685
• Use rounding to approximate eg 523 228 is more
  than 500 200
• Year 6
• Use calculator to check 6.5 9.8 3.3 with
  3.3 9.8 6.5
• Use rounding to approximate eg 2593 6278 is
  more than 2500 620

18
Most likely to / -
Which ever methods children are taught, it is
still important that they choose and use
appropriate ways of calculating (mental,
mental with jottings, pencil and paper).

• 38 21
• 82 79
• 25 26
• 97 25
• 324 58
• 284 9
• 47 76

• 64 - 27
• 80 70 40
• 283 - 71
• 500 800
• 4005 - 1999
• 1.5 1.6
• 6.1 2.4