progression in calculations lower key stage 2. beginning column addition t u 6 7 2 4 1 8 0 9 1 +
TRANSCRIPT
![Page 1: Progression in Calculations Lower Key Stage 2. Beginning Column Addition T U 6 7 2 4 1 8 0 9 1 +](https://reader035.vdocuments.net/reader035/viewer/2022062516/56649e2a5503460f94b17c68/html5/thumbnails/1.jpg)
Progression in Calculations
Lower Key Stage 2
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Beginning Column Addition
T U6 72 4
1 1
8 0
9 1
+
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Efficient Column Addition
H T U
+
4
1
2
1
1
1 6 42 5 7
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Moving on to Number lines
61 - 52
52 61
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Beginning Column Subtraction
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Beginning Column Subtraction (Exchange)
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Continuing Column Subtraction
H T U
e.g. 321 - 157
300 20 1
100 50 7-
101
4
200 1
60100 = 164
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1
H T U
-
1 6 4
3 2 11 5 7
2 1 1
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Multiplication
Children need to understand the concept of multiplication, that it is:
•Repeated addition
•Can be represented as an array
They also need to understand and work with certain principles:
•Inverse of division
•Is commutative i.e. 3 x 5 = 5 x 3
•Is associative i.e. 2 x (3 x 5) = (2 x 3) x 5
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Use of Arrays
Children need to understand how arrays link to multiplication through repeated addition and be able to create their own arrays.
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Continuation of Arrays
Creating arrays on squared paper (this also links to understanding area).
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Grid Method
16 x 7
10 x 7 = 6x 7 =
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Grid Method
7
10 6
70 42 7042
112+
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Grid Method
600100 90 15805
+
x 20 3
30 600 90
5 100 15
Children have to develop their understanding of related facts.
e.g. 23 x 35
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Division
Children need to understand the concept of division, that it is:
•Repeated subtraction
They also need to understand and work with certain principles:
•Inverse of multiplication
•Is not commutative i.e. 15 ÷3 ≠ 3 ÷ 15
•Is not associative i.e. 30 ÷ (5 ÷ 2) ≠ (30 ÷ 5) ÷ 2
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Division as Sharing
Children naturally start their learning of division as division by sharing, e.g. 6 ÷2.
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Division as Grouping
To become more efficient, children need to develop the understanding of division as grouping, e.g. 6 ÷2.
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Division as Grouping
To continue their learning, children need to understand that division calculations sometimes have remainders, e.g. 13 ÷ 4.
They also need to develop their understanding of whether the remainder needs to be rounded up or down depending on the context.
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-4-4
-4-4
-4-4
-4-4
48 ÷ 4 = 12
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-4-4
-4-4
-4-4
-4-4
-4-4
-4-4
10 groups
2 groups
48 ÷ 4 = 12
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Division by Chunking
Recall of multiplication tables helps make this method more efficient, e.g. 72 ÷ 3.
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Key Messages
• For written calculations it is essential that there is a progression which culminates in one method.
• The individual steps within the progression are important in scaffolding children’s understanding and should not be rushed through.
• Practical equipment, models and images are crucial in supporting children’s understanding.