heatherside junior school progression in subtraction parents’ information evening
TRANSCRIPT
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HEATHERSIDE JUNIOR SCHOOL
PROGRESSION IN SUBTRACTION
Parents’ Information
Evening
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Progression towards a short column method for
subtraction• Establish mental methods, based on a knowledge of
number bonds and an understanding of place value.
• With more difficult calculations, approximate first, using mental methods.
• Show children how to set out written calculations using jottings and expanded layouts.
• Gradually refine their written recording into a more compact and efficient formal method.
• Extend to larger numbers and to decimals.
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What does your child need to know?
Mental Skills
• recognise the size and position of numbers
• count back in steps of different sizes
• know number facts for all numbers to 20
• subtract multiples of 10 from any number
• partition and recombine numbers
• bridge through multiples of 10
Key Vocabulary
• subtract
• take away
• minus
• count back / up
• less than
• fewer
• difference
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Step 1Using everyday objects children
will:
• begin to count backwards in familiar contexts such as number rhymes or stories;
• count back in ones from any given number;
• begin to relate subtraction to ‘ taking away ’;
• find one less than a number;
• count back in larger steps, (tens, then twos and fives).
I cansubtrac
t 5 – 1
= 4
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Using pictures and marks
There were five monkeys. Three ran away.
How many monkeys were left?
5 – 3 =2
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Step 2
Progression in the use of number lines
Firstly, children will count backwards in steps along a number track to ‘take
away’.
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Children will then use a numbered number
line, counting back in steps of one, then ten, two and five.
10 – 5 = 5
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Children will then begin to use a number line with regular interval
markings and some or no numbers marked.
24 – 5 =
15 20
19
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Children will then use an empty number line
to count back by partitioning a number
35 – 7 =
28 30 35
- 5- 2
5 + 2
28
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Step 3
Next children begin to find the difference by counting up from the smallest number
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Step 4Next they use a number line to ‘take-away’ and
find the difference by counting back and up using
the nearest multiple of 10 and adjusting.
36 – 19 =
- 20
16 17 36 + 1
17
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Step 5
Children then partition numbers to be subtracted mentally.
(linked to counting back on a number line)
83 – 53 = 83 – 50 – 3 =
83 – 50 = 33
33 – 3 = 30
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Partitioning then leads to the start of the expanded column method
5 2
-
8 7
3 5
50 2
-
80 7
30 5
87 - 35 =
The numbers do not need to be adjusted.
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Step 6
Expanded short column method
The numbers are then adjusted when necessary.
40 + 3- 20 + 7 10 + 6
30 10+
43 - 27 = 16
to subtract 7 units we need to exchange
a ten for ten units
This method enables children to see what happens to numbers in the short column
method.
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This is then extended to
subtracting three digit numbers and decimals
563 – 141 with no adjustment
563 – 227 with adjustment from the tens to the units
561 – 272 with adjustment from the hundreds to the tens and then
the units
503 – 278 dealing with zeros when adjusting, first in the
units then the tens and hundreds
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Step 7Short column method
The previous stages reinforce what happens to numbers when they are subtracted using more
formal written methods.
This is then extended to usinglarger numbers and decimals.
3 4 3- 1 2 7 2 1 6
3 1