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Session 2Session 2Addition and SubtractionAddition and Subtraction
Why is it all so different today?Why is it all so different today?• A desire to do something different to counter the nations phobia around mathematics
• Development of understanding of effective methods to teaching mathematics since mid 1990s
• Exploration of effective approaches from some of the most successful education systems in the world
• Extensive research and trialling
There is no “right” way to work! There is no “right” way to work! Children exposed to a range of methods – if you get Children exposed to a range of methods – if you get an answer, then the method works.an answer, then the method works.Methods selected will depend upon the situation Methods selected will depend upon the situation and the numbers involved, including when to use and the numbers involved, including when to use calculators. Efficiency is as important as accuracy.calculators. Efficiency is as important as accuracy.Children make decisions about methods and draw Children make decisions about methods and draw on a range of strategies and approaches when on a range of strategies and approaches when applying Maths is context.applying Maths is context.Children in same class could be using different Children in same class could be using different methods to others depending on their ability, methods to others depending on their ability, confidence and stage of mathematical confidence and stage of mathematical development.development.
Total of 11Total of 11
101 Down101 Down
Domino totalsDomino totals
The Numberline!!The Numberline!!
16 + 816 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
16 17 18 19 20 21 22 23 24
The Numberline!!The Numberline!!
16 + 816 + 2+ 2 + 2 + 2
16 17 18 19 20 21 22 23 24
The Numberline!!The Numberline!!
16 + 816 + 4 + 4
16 17 18 19 20 21 22 23 24
Expanded AdditionExpanded Addition
43+25
Try this method with these!!
54+67
123+241
43
+ 25
8
68
60
Towards the Standard MethodTowards the Standard Method
63+3963+39
6 36 3
++ 3 93 9
1 21 2
9 09 0
11 0 20 2
6 36 3++ 3 93 9
22 11
6 36 3++ 3 93 9 11 0 20 2 11
The Standard Method - The Standard Method - DecompositionDecomposition
Linked initially with use of images and practical Linked initially with use of images and practical apparatus to secure understanding of how place apparatus to secure understanding of how place value is being used in the calculationvalue is being used in the calculation
Lots of stages where children can make errorsLots of stages where children can make errors
Not always the most efficient method to useNot always the most efficient method to use
If children can obtain an answer using another If children can obtain an answer using another method, that is OK.method, that is OK.
33 - 17
Can I do this mentally?
Shall I use a written method?
Which written method is most appropriate to use for these numbers?
33 - 17
3 3
- 1 7
33 - 17
3 3
- 1 7
I’m going to partition the numbers.
33 - 17
3 3
- 1 7= 30 and 3
- 10 and 7
33 - 17
3 3
- 1 7
30 and 3
- 10 and 7=
33 - 17
3 3
- 1 7 I start with the units, so I need to take away 7 small
cubes.
But I only have 3 of them.
I’ll break up one of the 10s into 10
units.
30 and 3
- 10 and 7=
33 - 17
3 3
- 1 7
I’ve now got 2 lots of 10, so that’s 20, as well as 13
units, so let’s write it down
to show what I am doing.
30 and 3
- 10 and 7
20 and 13
- 10 and 7= =
33 - 17
3 3
- 1 7
Now I can take
away 7!
30 and 3
- 10 and 7
20 and 13
- 10 and 7= =
33 - 17
3 3
- 1 7
30 and 3
- 10 and 7
20 and 13
- 10 and 7
6
= =
33 - 17
3 3
- 1 7
Now I can take
away 10!
30 and 3
- 10 and 7
20 and 13
- 10 and 7
6
= =
33 - 17
3 3
- 1 7
30 and 3
- 10 and 7
20 and 13
- 10 and 7
10 and 6
= =
33 - 17
3 3
- 1 7
30 and 3
- 10 and 7
20 and 13
- 10 and 7
10 and 6
= 1 6
= =
There will be examples like this…
75 – 32
where no exchange is needed, but partitioning is still useful as children are more successful at working with tens and units separately.
7 5 7 0 + 5
3 2 3 0 + 24 0 + 3 = 4 3
- =
Next stages will involve increasing the number of digits in the numbers (HTU, the ThHTU), working with apparatus, then without, to ensure children are secure with place value before moving on to the final stage. Often this would be taught side by side with the more expanded method so that children can se how they relate.
2 7 1 2 0 0 + 7 0 + 1 2 0 0 + 6 0 + 1 1
1 5 8 = 1 0 0 + 5 0 + 8 = 1 0 0 + 5 0 + 8
1 0 0 + 1 0 + 3 = 1 1 3
2 7 1 2 7 1 2 7 1 2 7 1 2 7 1
1 5 8 1 5 8 1 5 8 1 5 8 1 5 8
3 1 3 1 1 3
-
- -- - -
16666 111
Why the additional steps?
1 6 3 0 4 1 6 3 0 4
3 2 0 7 3 2 0 7
1 3 0 0 7
--
2 1
3 0 0 0 5 3 0 0 0 5
4 8 5 7 4 8 5 7
3 4 8 5 2
- -
