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HEATHERSIDE JUNIOR SCHOOL
PROGRESSION IN SUBTRACTION
Parents’ Information
Evening
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.
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
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
Using pictures and marks
There were five monkeys. Three ran away.
How many monkeys were left?
5 – 3 =2
Step 2
Progression in the use of number lines
Firstly, children will count backwards in steps along a number track to ‘take
away’.
Children will then use a numbered number
line, counting back in steps of one, then ten, two and five.
10 – 5 = 5
Children will then begin to use a number line with regular interval
markings and some or no numbers marked.
24 – 5 =
15 20
19
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
Step 3
Next children begin to find the difference by counting up from the smallest number
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
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
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.
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.
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
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
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