maths the modern way!! addition and subtraction st teresa’s primary school with essex county...
TRANSCRIPT
Maths the Modern Way!!Maths the Modern Way!!
Addition and SubtractionAddition and Subtraction
St Teresa’s Primary SchoolSt Teresa’s Primary School
withwith
Essex County CouncilEssex County Council
The Primary National The Primary National StrategyStrategy
Basis of teaching since 1999 – based on Basis of teaching since 1999 – based on extensive research and proven successextensive research and proven success
Daily entitlement to maths lessonDaily entitlement to maths lesson Key featuresKey features
Progression carefully set outProgression carefully set out Interactivity – use of models, images, games, Interactivity – use of models, images, games,
practical activitiespractical activities Focus on mental skills as well as writtenFocus on mental skills as well as written Vocabulary, problem solving, communication, Vocabulary, problem solving, communication,
explanation and reasoningexplanation and reasoning
There is no “right way” to There is no “right way” to work!!work!!
Children exposed to a range of methods.Children exposed to a range of methods. Methods selected will depend upon the Methods selected will depend upon the
situation and the numbers involved, situation and the numbers involved, including when to use calculators.including when to use calculators.
Children make decisions about methods and Children make decisions about methods and draw on a range of strategies and draw on a range of strategies and approaches when applying Maths in context.approaches when applying Maths in context.
Children in same class could be using Children in same class could be using different methods to others depending on different methods to others depending on their ability, confidence and stage of their ability, confidence and stage of mathematical development.mathematical development.
AdditionAddition
Foundation Stage (Reception)Foundation Stage (Reception) Counting and recognising numbersCounting and recognising numbers Counting on using number lines or Counting on using number lines or
apparatusapparatus Recall of facts and number bondsRecall of facts and number bonds Numbers to 10, then beyond.Numbers to 10, then beyond.
Key Stage 1Key Stage 1
Year 1Year 1 Introduce + and = signs to record Introduce + and = signs to record
calculations done mentallycalculations done mentally Securing bridge over 10s boundarySecuring bridge over 10s boundary Mental recall of factsMental recall of facts Numbers extend to 30, 40…Numbers extend to 30, 40… Recognise patterns in 100 square (+10, Recognise patterns in 100 square (+10,
+1)+1) Splitting numbers and recombiningSplitting numbers and recombining
The Importance of Place The Importance of Place ValueValue
Place Value Runaround!Place Value Runaround!
Key Stage 1Key Stage 1
Year 2Year 2 Extension of Year 1Extension of Year 1 Introduction of partitioningIntroduction of partitioning Adding significant digits firstAdding significant digits first
How to PartitionHow to Partition
35 + 7235 + 72
3030 55 7070 22
30 + 70 = 10030 + 70 = 100
5 + 2 = 75 + 2 = 7
100 + 7 = 107100 + 7 = 107
Try these by partitioning!!Try these by partitioning!!
45+6745+67 154+78154+78 327+198+23327+198+23
This can work with any size of number – is itThis can work with any size of number – is it
efficient to use this method for this?efficient to use this method for this? 40187+63742+3124340187+63742+31243 10005+12010+300010005+12010+3000
Key Stage 2Key Stage 2The Numberline!!The Numberline!!
67 + 3267 + 10 + 10 + 10 + 2
67 77 87 9997
Expanded AdditionExpanded Addition(Introduced Year 3)(Introduced Year 3)
43+25
43
+ 25
60
8
68
Try this method with these!!
254+167
423+541
Standard MethodStandard 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
You may like to try these problems You may like to try these problems
using some of the methods that we using some of the methods that we
have used so far.have used so far.
623+12623+12
352+231+101352+231+101
16+746+23316+746+233
The Roundabouts of HarlowThe Roundabouts of Harlow
FINISH
START
1 421
11 8 5 9
12532
7 6 1 10
SubtractionSubtraction
Foundation Stage (Reception)Foundation Stage (Reception) Counting and recognising numbersCounting and recognising numbers Counting back using numberlines or Counting back using numberlines or
apparatusapparatus Recall of facts and number bondsRecall of facts and number bonds Numbers to 10, then beyond.Numbers to 10, then beyond.
Key Stage 1Key Stage 1
Year 1Year 1 Introduce - and = signs to record Introduce - and = signs to record
calculations done mentallycalculations done mentally Mental recall of factsMental recall of facts Subtracting 10 from “teens” numberSubtracting 10 from “teens” number Recognise patterns in 100 square (-10, -Recognise patterns in 100 square (-10, -
1)1) Splitting numbers and recombiningSplitting numbers and recombining
Key Stage 1Key Stage 1
Year 2Year 2 Extension of Year 1Extension of Year 1 Crossing 10s boundary with Crossing 10s boundary with
numbers to 20,30…. (crossing 100s numbers to 20,30…. (crossing 100s boundary in Y3)boundary in Y3)
May use splitting of May use splitting of numbers/partitioning to assist in numbers/partitioning to assist in calculation (e.g. 27–15 = 27–5–2–8)calculation (e.g. 27–15 = 27–5–2–8)
Key Stage 2Key Stage 2The Numberline!!The Numberline!!
67 - 3267 - 10 - 10 - 10 - 2
35 37 47 6757
-2 -10 -10 -10
ANSWER!!!
OR….OR….67 - 32
32 42 52 6762
+10
+10
+10
+5
10 + 10 + 10 + 5 = 35
32 40 50 6760
+8 +10
+10
+7
10 + 10 + 8 + 7 = 35
Complementary AdditionComplementary Addition
6 7
- 3 2
8 to 4 0
2 0 to 6 0
7 to 6 7
3 5
32 40 50 6760
+8 +10
+10
+7
10 + 10 + 8 + 7 = 35
The Standard Method - The Standard Method - DecompositionDecomposition
Introduced from Year 3Introduced from Year 3 Linked initially with use of images and Linked initially with use of images and
practical apparatus to secure understanding of practical apparatus to secure understanding of how place value is being used in the how place value is being used in the calculationcalculation
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 + 3
- 10 + 7
33 - 17
3 3
- 1 7
30 + 3
- 10 + 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 + 3
- 10 + 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 + 3
- 10 + 7
20 + 13
- 10 + 7= =
33 - 17
3 3
- 1 7
Now I can take
away 7!
30 + 3
- 10 + 7
20 + 13
- 10 + 7= =
33 - 17
3 3
- 1 7
30 + 3
- 10 + 7
20 + 13
- 10 + 7
6
= =
33 - 17
3 3
- 1 7
Now I can take
away 10!
30 + 3
- 10 + 7
20 + 13
- 10 + 7
6
= =
33 - 17
3 3
- 1 7
30 + 3
- 10 + 7
20 + 13
- 10 + 7
10 + 6
= =
33 - 17
3 3
- 1 7
30 + 3
- 10 + 7
20 + 13
- 10 + 7
10 + 6 = 1 6
= =
Have a Go!Have a Go!
There is some base 10 apparatus in the There is some base 10 apparatus in the
tables if you would like to run through tables if you would like to run through using using
this to be clear about the process this to be clear about the process involved.involved.
42 – 2742 – 27 51 – 2951 – 29 90 - 3690 - 36
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 + 22 0 + 3 = 2 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 see 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?
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
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
- -
Maths the Modern Way!!Maths the Modern Way!!
Addition and SubtractionAddition and Subtraction
St Teresa’s Primary SchoolSt Teresa’s Primary School
withwith
Essex County CouncilEssex County Council