numeracy. teaching numeracy at ks2 calculations done horizontally first emphasis on mental...
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Numeracy
Numeracy
Teaching Numeracy at Teaching Numeracy at KS2KS2
Calculations done horizontally first
Emphasis on mental calculation
Emphasis on place value
Core Principles
Two key pointsTwo key points
The children need to know their multiplication (and division) tables OFF BY HEART. These should be taught in a fun way the children are likely to enjoy. For example:
Place value means the value of digits depending on the column they are in
Place ValuePlace Value
Money is the best vehicle for teaching PLACE VALUE.The children use money in real life and need to be encouraged to know the decimal value of it’s coins.
How many of these are there in £20?
How many 5p make this?
If I split a pound up, how many of these will I
have?
How would you work out ….How would you work out ….
23 + 24 =
45 + 46 =
68 – 34 =
101 – 59 =
AdditionAdditionAt Key Stage 1 calculations are
usually written horizontally
Number lines are often used to support informal methods and help build up imagery
132 + 29 =
Addition continued…Addition continued…
Children are introduced to ‘partitioning’
Early stage:
38 + 27 =
30 + 20 = 50
8 + 7 = 15
38 + 27 = 65
Then:
38 38+ 87 + 87 110 15 15 110 125 125
Lastly:
Subtraction at KS2Subtraction at KS2Children are taught to subtract by finding thedifference between the two numbers.This method involves counting on from the smallerto the larger number and is called ’complementaryaddition’
85 – 57 _85 57 3 (60)
25 (85) 28
Subtraction with larger numbersSubtraction with larger numbers
326 – 178
326- 178 22 (200) 126 (326) 148
Subtraction at KS2Subtraction at KS2Finding the difference continues to be an important informal method
When children are ready, they are introduced to ‘decomposition’, which involves partitioning
Leading (eventually) to:
MultiplicatiMultiplicationonEarly work on multiplication involves images of groups and arrays:
26 x 7 =
20 x 7 = 140 6 x 7 = 42
26 x 7 = 182
Next children use partitioning
for calculations:
Multiplication – children move on to Multiplication – children move on to the ‘grid method’the ‘grid method’7 x 237 x 23 = = 161 161
x 20 3
7 140 21
Multiplication - Multiplication - continuedcontinued
The following method of recording istaught to children when they are ready
534 468 x 6 x 52
DivisioDivisionnEarly work on division involves
‘sharing’and ‘grouping’
6 pens shared between 2 children.They get 3 each.
2 groups of 3 pens. 6 pens in total.
It helps if the children are taught thisusing practical apparatus (counters
arebest as they can be placed in ‘arrays’
– see previous)
Division – the ‘chunking Division – the ‘chunking method’method’
305 ÷ 7 =(estimate: 40 x 7= 280 so the answer is a
bit more than 40.)
305- 280 (40 x 7) 25 - 21 ( 3 x 7) 4
305 ÷ 7 = 43 r 4
Next children are encouraged to understand division as building up multiples (chunking)
Division continuedDivision continuedChildren who are ready, are taughtother methods of recording267 ÷ 8 =
… and, only after much work on the value of fractions:
In conclusion …In conclusion …Children are always encouraged to
think which is the most appropriate and efficient method for the numbers involved
An understanding of place value is vital
Mental methods should be the first resort
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