Transcript Multiplication / Division by 4 & 8 with decimal answers Second Level

Scottish Survey of Literacy &
Numeracy
Support Material
Produced by Education Scotland
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Multiplication / Division by 4 & 8
with decimal answers
Second Level
• The move from answers such as 3 r 2 to 3.5 is a key
milestone in progression.
• Changing the remainder to a fraction and finally a
decimal fraction is a clear progression pathway.
• This process is challenging and different approaches
should be investigated that promote pupil
understanding.
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When number processes are carried out, checking the
answer using reverse processes should be automatic.
If 27 is divided by 4, giving an answer of 6 r 3 or a more
sophisticated answer of 6.75, checking that
(6 x 4) + 3 or (6.75 x 4) takes us back to 27, should
become automatic classroom practice.
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The understanding that zeros can be added to a number
such as 3 and the 3 is promoted up the powers of ten to
give 30,300,3000,etc is developed in other sections of
work, and should be re-visited.
The progression milestone that when the zeros are
added after the decimal point, the value of the number
stays the same, is far more challenging.
Using price tags, such as £3 and £3.00 , introduces
familiar contexts and aids understanding.
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As so many everyday contexts are based on the decimal
system, practical approaches should always be
encouraged.
£3 shared equally among 4 would be ideal to investigate
the answer of 0.75
This could be extended to 8 litres of water shared
equally among 7 containers. Remember to tie in the
practical with 8 divided by 7 on the calculator.
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• Dividing by 2,4 and 8 through repeated halving is an
excellent approach to arriving at answers with decimals.
• Dividing by 10 and then doubling the answer to divide
by 5 is also a key step on the progression pathway.
• This may suggest that division by 3,6,7 and 9 could be
investigated as a group, when division leads to a
decimal answer.
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• The most sophisticated step on the progression
pathway is knowing how many zeros are needed to
arrive at a suitable answer.
• If asked to divide 3 by 2 or 4 or 5 etc, should 3 become
3.0, 3.00, 3.000?
• Remember how effective a calculator could prove here.
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