Transcript Year 1 and 2 Maths Parents Workshop

PRIMARY
ADVANTAGE
MATHEMATICS
PROGRAMME
A MODEL OF BEST PRACTICE
KS1 Parents Workshop –
Mathematics
Elizabeth Winterton,
Jane Woolley and
Catherine Thomas
The Fundamentals – Year 1
The Fundamentals – Year 2
Experience and the National Curriculum
Conceptual
Understanding
Procedural
Fluency
Primary
Advantage
Maths
Programme
What does
this mean
for how we
teach?
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.
Concrete
Pictorial
Abstract
Addition – Mental Methods
5 + 31
32 + 8
60 + 60
32 + 19
15 + 16
27 + 36 + 13
Did 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.
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?
Models for Addition
Counting on with a bead bar/number line
+7
0
5
+5
10 +2 12
Counting on with straws
+
=
Models for addition
25 + 47
Models for Addition
25 + 47
Models for Addition
25 + 47
Your turn:
Use the deines to
complete these sums:
T
O
1. 17 + 14
1. 22 + 19
2. 16 + 16
1. 172 + 50
Remember to use the terms
regroup and rename.
Models for Addition
Expanded Method
20 + 5
10 + 4 +
30 + 9
regrouped and renamed
20 + 7
10 + 5 +
40 + 2
10
Subtraction – Mental Methods
95 - 86
32 - 8
60 - 30
30 - 14
25 - 9
27 - 18
Did 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.
Models for Subtraction
Removing items from a set (reduction or take-away)
12 - 5
1 = 7
2
3
4
Comparing two sets (comparison or difference)
Seeing one set as partitioned
Seeing 12 as
made up of 5
and 7
Models for Subtraction
Counting back on a number line
-5
0
7
-3
10-2 12
Finding the difference on a number line
7
0
5
- 5 =
5
10 2
12
Models for Subtraction
72 - 47
Models for Subtraction
72 - 47
Models for Subtraction
72 - 47
This is now “Sixtytwelve”
6
1
7 2
Models for Subtraction
72 - 47
Models for Subtraction
72 - 47
Models for Subtraction
72 - 47 = 25
Your turn:
Use the deines to
complete these sums:
32 – 16 = 16
T
O
1
6
1. 17 - 14
1. 22 - 9
2. 32 - 16
1. 172 - 61
Remember to use the terms
regroup and rename.
Models for Subtraction
Expanded Method
20 + 5
10 + 4 10 + 1
10
30
20 + 3
10 + 5 10 + 8
Models for Multiplication
Lots of the ‘same thing’
Bead Bar
Number Line
0
Fingers
6
3
“3”
9
“6”
“9”
12
“12”
Models for Multiplication
How can it be represented?
Multiplication is commutative
4x3
Four groups of 3
3x4
Three groups of 4
Models for Division
The power of the place value counters for larger
numbers
12 ÷ 3
1
1
1
1
1
1
1
1
1
1
1
1
4
3 12
1
1
1
1
1
1
1
1
1
1
1
1
The Facts
• Number bonds within 10
• Number bonds to 10
1. Look, cover,
write and check
• Number bonds to 20
1. I say, you say
• Doubles and halves to 20
• Two times tables
• Five times tables
• Ten times tables
1. Five minutes
whenever you
get the chance
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