primary advantage mathematics programme a model of best practice ks1 parents workshop –...
TRANSCRIPT
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PRIMARY ADVANTAGE
MATHEMATICS PROGRAMME
A MODEL OF BEST PRACTICEKS1 Parents Workshop –
Mathematics
Elizabeth Winterton, Jane Woolley and Catherine Thomas
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The Fundamentals – Year 1
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The Fundamentals – Year 2
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Experience and the National Curriculum
What does this mean for how we
teach?
Procedural Fluency
Conceptual Understanding
Primary Advantage
Maths Programme
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Key Concepts - CPA
The concrete-pictorial-abstract approach, based on research by psychologist Jerome Bruner, suggests that there are three steps (or representations) necessary for pupils to develop understanding of a concept.
Reinforcement is achieved by going back and forth between these representations.
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Concrete Pictorial Abstract
3 + 4 = 7
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Addition – Mental Methods
5 + 31 32 + 8 60 + 60
32 + 19 15 + 16 27 + 36 + 13Did you:•Count on from the largest number?•Re-order the numbers?•Partition the numbers into tens and ones?•Bridge through 10 and multiples of 10?•Add 9, 11, etc. by adding a multiple of 10 and compensating?•Use near doubles?•Use knowledge of number facts?These are all strategies that children need to be aware of when carrying out addition calculations.
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Models for Addition
Combining two sets of objects (aggregation)
Tom had two sweets and John had three sweets: how many did they have altogether?
Adding onto a set (augmentation)
Tom had two sweets and bought two more. How
many sweets does he have now?
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Counting on with a bead bar/number line
12 5 0
+ 7
10 +2+5
Counting on with straws
+ =
Models for Addition
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25 + 47
Models for addition
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25 + 47
Models for Addition
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25 + 47
Models for Addition
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Use the deines to complete these sums: 1.17 + 14
1.22 + 19
2.16 + 16
1.172 + 50
Your turn:
Remember to use the terms regroup and rename.
T O
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Expanded MethodModels for Addition
20 + 510 + 4 +30 + 9
20 + 710 + 5 +40 + 210
regrouped and renamed
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Subtraction – Mental Methods
95 - 86 32 - 8 60 - 30
30 - 14 25 - 9 27 - 18Did you:•Count up from the smallest number?•Round the numbers?•Partition the numbers into tens and ones?•Adjust the place value?•Subtract 9, 11, etc. by subtracting a multiple of 10 and compensating?•Use near halves?•Use knowledge of number facts?These are all strategies that children need to be aware of when carrying out subtraction calculations.
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12
Removing items from a set (reduction or take-away)
- 1- 2- 3- 4- 5 = 7
Comparing two sets (comparison or difference)
Seeing one set as partitioned
Seeing 12 as made up of 5
and 7
Models for Subtraction
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Counting back on a number line
Finding the difference on a number line
12 0
- 5
7
12 0 5
7
5 2 10
10-2-3
- 5 =
Models for Subtraction
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72 - 47
Models for Subtraction
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72 - 47
Models for Subtraction
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72 - 47
This is now “Sixty-twelve”
7 126
Models for Subtraction
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72 - 47
Models for Subtraction
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72 - 47
Models for Subtraction
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72 - 47 = 25
Models for Subtraction
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Use the deines to complete these sums: 1.17 - 14
1.22 - 9
2.32 - 16
1.172 - 61
Your turn:
T O
32 – 16
1 6
Remember to use the terms regroup and rename.
= 16
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Expanded MethodModels for Subtraction
20 + 510 + 4 -10 + 1 20 + 3
10 + 5 -+
30
10
10
8
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Bead Bar
Number Line
Fingers“6” “9” “12”“3”
0 3 6 9 12
Lots of the ‘same thing’
Models for Multiplication
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3 44 3
Models for Multiplication
Four groups of 3 Three groups of 4
x x
Multiplication is commutative
How can it be represented?
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12 ÷ 3
41 2
The power of the place value counters for larger numbers
Models for Division
11
11
11
11
11
11
11
11
11
11
11
11
3
11
1111
11
11
11
11
11
1111
1111
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The Facts
• Number bonds within 10
• Number bonds to 10
• Number bonds to 20
• Doubles and halves to 20
• Two times tables
• Five times tables
• Ten times tables
1. Look, cover, write and check
1. I say, you say
1. Five minutes whenever you get the chance
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