Maths the Modern Way!! Multiplication and Division St Teresa’s Primary School Paul Hargreaves...
-
Upload
douglas-ray -
Category
Documents
-
view
214 -
download
0
Transcript of Maths the Modern Way!! Multiplication and Division St Teresa’s Primary School Paul Hargreaves...
Maths the Modern Way!!Maths the Modern Way!!Multiplication and DivisionMultiplication and DivisionSt Teresa’s Primary SchoolSt Teresa’s Primary School
Paul HargreavesPaul HargreavesPrimary Strategy Consultant – Primary Strategy Consultant –
MathematicsMathematicsEssex County CouncilEssex County Council
Total Recall!Total Recall!
Select pairs of numbers from the target board on Select pairs of numbers from the target board on your table. Add these using one of the methods your table. Add these using one of the methods from last session. Will you use a number line? Will from last session. Will you use a number line? Will you partition and add mentally? Do you need to you partition and add mentally? Do you need to make jottings? make jottings? BE BRAVE – try to avoid using the standard BE BRAVE – try to avoid using the standard method!method!Now try with three numbers! Or try pairs of Now try with three numbers! Or try pairs of numbers and carry out a subtraction!numbers and carry out a subtraction!
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 is context.approaches when applying Maths is 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.
The Importance of The Importance of VocabularyVocabulary
Key to success in mathematicsKey to success in mathematics Can be confusion between school Can be confusion between school
and homeand home Children need opportunities in class Children need opportunities in class
and in homework to use and in homework to use mathematical vocabulary – games, mathematical vocabulary – games, collaborative work, open ended collaborative work, open ended investigationsinvestigations
Mathematical Vocabulary Mathematical Vocabulary BookletBooklet
Guide to which words and phrases Guide to which words and phrases are introduced to each year groupare introduced to each year group
Schools many make decisions Schools many make decisions regarding vocabularyregarding vocabulary
It is not a checklistIt is not a checklist Check with children and teachers if Check with children and teachers if
there are unfamiliar wordsthere are unfamiliar words
MultiplicationMultiplication
Calculate the answer to this…Calculate the answer to this…
5 65 6
xx 3 3
Did you do this?Did you do this?
5 65 6
xx 3 3
11 6 86 811
Or did you use a mental method?Or did you use a mental method?Why did you choose the method Why did you choose the method
you used?you used?
Repeated Addition (Year Repeated Addition (Year 2/3)2/3)
5 added to 5 added to 55 added to 5 added to 5
5 + 5 + 55 + 5 + 5
3 lots of 53 lots of 5
5 x 35 x 3
3 x 53 x 5
Lots of practical experiences and use of Lots of practical experiences and use of number lines. Children will begin to use x and number lines. Children will begin to use x and
= signs.= signs.
Multiplication as an ArrayMultiplication as an Array
4 x 2 = 8
2 lots of 4 = 8
2 x 4 = 8
4 lots of 2 = 8
Arrays are quite common – ice cube trays, egg boxes, chocolate boxes, medicine wrapping, tiles etc.
Multiplication by 10Multiplication by 10
7 x 10 = 707 x 10 = 70
BUT WE DIDN’T JUST ADD A 0!BUT WE DIDN’T JUST ADD A 0!
Multiplication by 10Multiplication by 10
7 x 10 = 707 x 10 = 70
BUT WE DIDN’T JUST ADD A 0!BUT WE DIDN’T JUST ADD A 0!
77
7.07.0
Both of these numbers are worth the Both of these numbers are worth the same!same!
7 add a 0 is 7 + 0 = 77 add a 0 is 7 + 0 = 7
We haven’t multiplied here!We haven’t multiplied here!
PartitioningPartitioning
15 x 515 x 5 This is 10 x 5 and 5 x 5 added
together. 10 x 5 = 505 x 5 = 25
50 + 25 = 75
PartitioningPartitioning
36 x 436 x 4
36 x 4 is 30 x 4 and 6 x 4 added together. I know that 30 is three
lots of 10, so 30 x 4 is 10 x 4 added to 10 x 4 added to 10 x 4.
10 x 4 = 4010 x 4 = 4010 x 4 = 406 x 4 = 24
40 + 40 + 40 + 24 = 144
PartitioningPartitioning
36 x 436 x 4
36 x 4 is 30 x 4 added to 6 x 4I know that 30 x 4 is 10 times
bigger than 3 x 43 x 4 = 12, so 30 x 4 = 120
6 x 4 = 24120 + 24 = 144
Grid MethodGrid Method
346 x 4346 x 4
xx
44
300300 4040 66
242416016012001200
12001200160160
+ 24+ 24
13841384
Grid MethodGrid Method
72 x 3872 x 38xx
88
3030
7070 22
560560
21002100 6060
1616
21002100
560560
6060
+ 16+ 16
27362736
Standard MethodStandard Method
23 x 823 x 8
1 8 41 8 4
3 x 83 x 82 42 4
20 x 820 x 81 6 01 6 0
x 8x 82 32 3
Standard MethodStandard Method
23 x 823 x 8
1 8 41 8 4
3 x 83 x 82 42 4
20 x 820 x 81 6 01 6 0
x 8x 82 32 3
x 8x 82 32 3
4422
Standard MethodStandard Method
23 x 823 x 8
1 8 41 8 4
3 x 83 x 82 42 4
20 x 820 x 81 6 01 6 0
x 8x 82 32 3
x 8x 82 32 3
1 8 41 8 422
Why Not Just Teach the Why Not Just Teach the Standard Method?Standard Method?
1 0 0 0 7
x 3 x 4 25 6
Why Not Just Teach the Why Not Just Teach the Standard Method?Standard Method?
1 0 0 0 7
x 3 x 4 25 6
0 0 0 2 1
Why Not Just Teach the Why Not Just Teach the Standard Method?Standard Method?
1 0 0 0 7
x 3 x 4 25 6
0 0 0 2 1 1 2
2 0
3 2
DivisionDivision
Share 8 sweets between two children.Share 8 sweets between two children.
4 sweets in each pile
Repeated Subtraction Repeated Subtraction (Grouping)(Grouping)
8 8 2 can be thought of as 2 can be thought of as
8 – 2 = 68 – 2 = 6
6 – 2 = 46 – 2 = 4
4 – 2 = 24 – 2 = 2
2 – 2 = 02 – 2 = 0
I’ve taken 2 away 4 times, so the answer
is 4!!
0 2 4 6 8
-2-2-2 -2
13 13 3 3
13 – 3 = 1013 – 3 = 10
10 – 3 = 710 – 3 = 7
7 – 3 = 47 – 3 = 4
4 – 3 = 14 – 3 = 1I cannot make
anymore groups of 3 out of 1, so there is one
left over.
13 13 3 = 4 r 1 3 = 4 r 1
13 – 3 = 1013 – 3 = 10
10 – 3 = 710 – 3 = 7
7 – 3 = 47 – 3 = 4
4 – 3 = 14 – 3 = 1I cannot make
any more groups of 3 out of 1, so there is one
left over.
72 72 55
72 – 5 = 6772 – 5 = 67 37 – 5 = 3237 – 5 = 32
67 – 5 = 6267 – 5 = 62 32 – 5 = 2732 – 5 = 27
62 – 5 = 5762 – 5 = 57 27 – 5 = 2227 – 5 = 22
57 – 5 = 5257 – 5 = 52 22 – 5 = 1722 – 5 = 17
52 – 5 = 4752 – 5 = 47 17 – 5 = 1217 – 5 = 12
47 – 5 = 4247 – 5 = 42 12 – 5 = 712 – 5 = 7
42 – 5 = 37 42 – 5 = 37 7 – 5 = 2 7 – 5 = 2
72 72 55
72 – 5 = 6772 – 5 = 67 37 – 5 = 3237 – 5 = 32
67 – 5 = 6267 – 5 = 62 32 – 5 = 2732 – 5 = 27
62 – 5 = 5762 – 5 = 57 27 – 5 = 2227 – 5 = 22
57 – 5 = 5257 – 5 = 52 22 – 5 = 1722 – 5 = 17
52 – 5 = 4752 – 5 = 47 17 – 5 = 1217 – 5 = 12
47 – 5 = 4247 – 5 = 42 12 – 5 = 712 – 5 = 7
42 – 5 = 37 42 – 5 = 37 7 – 5 = 2 7 – 5 = 2
Too long winded!!
!!
7272-- 50 (10 x 5)50 (10 x 5)
2222-- 5 5 (1 x 5)(1 x 5)
1717-- 5 5 (1 x 5)(1 x 5)
1212-- 5 5 (1 x 5)(1 x 5)
77 5 (1 x 5)5 (1 x 5)
22
72 72 5 = 14 r 5 = 14 r 22
7272-- 50 (10 x 5)50 (10 x 5)
2222-- 5 5 (1 x 5)(1 x 5)
1717-- 5 5 (1 x 5)(1 x 5)
1212-- 5 5 (1 x 5)(1 x 5)
77 5 (1 x 5)5 (1 x 5)
22
72 72 5 = 14 r 5 = 14 r 22
5 )5 )14 r 214 r 2
7272
-- 50 (10 x 50 (10 x 5)5)
2222
-- 2020 ( 4 x 5)( 4 x 5)
22
72 72 5 = 14 r 5 = 14 r 22
5 5 ) )14 r 214 r 2
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 3
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 30
1
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 30 2
1 1
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 30 2 2 r 1 1 1
It does work, but many It does work, but many children make the following children make the following
errors…errors…
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 3
Hmmm! I can’t make any groups of 6 out of 1,
so…
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 3
Hmmm! I can’t make any groups of 6 out of 3,
so…
0
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 3
Hmmm! I can’t make any groups of 6 out of 3,
so…
0 0
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 3
Hmmm! I can’t make any groups of 6 out of 3,
so…
0 0 0
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 3
Great! The answer is 0!
0 0 0
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 3
OK – 6s into 1 don’t go, so…..
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 31
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 31
Now, 6s into 13. I know that two 6s
are 12 and I’ll have 1 left over.
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 31
121
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 31
121
Oh, look! 6s into 13 again! I know that!
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 31
121
12 r 1
The method that we are used The method that we are used to looks like this…to looks like this…
6 ) 1 3 36 ) 1 3 31
121
12 r 1
The answer is 1212 r 1!
The method that we are used The method that we are used to looks like this…to looks like this…
18 )1 1 0 18 )1 1 0
The method that we are used The method that we are used to looks like this…to looks like this…
18 )1 1 0 18 )1 1 0 0
1
The method that we are used The method that we are used to looks like this…to looks like this…
18 )1 1 0 18 )1 1 0 0 0
1 11
The method that we are used The method that we are used to looks like this…to looks like this…
18 )1 1 0 18 )1 1 0 0 0
1 11
Back to square one! Lots more learning and understanding is needed here. To successfully tackle this problem, you need to know how to use repeated subtraction!
Multiplication TablesMultiplication Tables
Year 1 – begin to learn 2x, 5x and Year 1 – begin to learn 2x, 5x and 10x10x
Year 2 – know 2x, 5x and 10x. Year 2 – know 2x, 5x and 10x. Year 3 – know 2x, 3x, 4x, 5x, 6x and Year 3 – know 2x, 3x, 4x, 5x, 6x and
10x. 10x. Year 4 – know all facts to 10 x 10Year 4 – know all facts to 10 x 10
Multiplication TablesMultiplication Tables
Three for free!Three for free!
If you know 3 x 5 = 15, you also knowIf you know 3 x 5 = 15, you also know
5 x 3 = 155 x 3 = 15
15 15 5 = 3 5 = 3
15 15 3 = 5 3 = 5
Maths the Modern Way!!Maths the Modern Way!!Multiplication and DivisionMultiplication and DivisionSt Teresa’s Primary SchoolSt Teresa’s Primary School
Paul HargreavesPaul HargreavesPrimary Strategy Consultant – Primary Strategy Consultant –
Mathematics Mathematics Essex County CouncilEssex County Council