Why do this problem :
draws attention to the way digits are arranged in a
written calculation. The traditional representation for basic
computation can be taken for granted. This problem allows the
display choices made to become conspicuous and appreciated.
Possible approach :
Ask the group to do the first calculation on a calculator to get
'an answer' and then ask questions about what that decimal display
Draw attention to the fact that people have been successfully
calculating results of value for centuries, long before electronic
calculation, and ask what calculations might have been important
Ask how these calculations might have been achieved and in
particular why some of our standard non-calculator algorithms work
(include long multiplication, and long division, plus finding prime
factors if that is within the students' experience).
Draw the students into a similar discussion about the Galley method
for arranging and holding digits during a calculation.
Ideally this should be group work with lots of talk : noticing
possible positioning of digits, reasoning to support or challenge
the validity of those conjectures, and gradually building up a
complete understanding of the whole method. This can then be
practised with new numbers, rehearsing the reasoning in the
Key questions :
- What does 'division' mean ?
- How would you work out 65284 divided by 594 ?
- How do we know that's an 'OK method' ?
- Any thoughts on how the Galley way of setting out the
calculation works ?
Possible extension :
Unusual Long Division - Square Roots Before Calculators
Possible support :
Multiplying with Lines