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'More and More Buckets' printed from http://nrich.maths.org/
Why do this
is a good one to try when pupils are used to doing
some investigations with just a little prompting from the teacher.
It is not obvious how to go about working on solutions and so this
leaves scope for children to tackle it in many different ways. No
particular skills of the four rules of number are required so it is
appropriate for a very wide attainment range. It can be a catalyst
to encourage pupils to work in a systematic way.
It is not essential for children to have tackled Buckets of
but it may be helpful to have done so.
You could create some images of buckets on an interactive
whiteboard, or on card to fix to an ordinary board. This may help
as you can drag buckets around the board so that the rules become
clear. You could introduce the example and ask everyone to write
down on a strip of paper one way of filling the buckets with water.
Ask them to compare what they have written with others sitting near
them and encourage them to find other solutions. You could invite
learners to pin up their strips on the board so that you can order
them in some way. This will help the whole group decide whether any
have been missed out. Of course there are many different ways to
order the possibilities so encourage and discuss different
Leave pupils to work on some examples of their own and then to
share anything they notice with a partner or in a small group. This
investigation would lend itself to being worked on over an extended
period of time. You could devote an area of the classroom wall to
it and ask learners to contribute findings, comments and questions
to this wall space over the next few days. It may be that they will
be able to predict the number of possibilities as they identify and
Tell me about the answers you've got.
How do you know you have got all the possibilities?
What do you now think is a good way of doing this kind of
Can you predict the number of different possibilities you
might get before you work them out?
How did you make your prediction?
Some children can be challenged to produce a table or spreadsheet
to show what you get with all the possible choices of groups of
buckets that can be made.
Having pictures of buckets of different sizes cut out of card and
laminated will help some children with this problem. They can be
encouraged to write (using a 'wipeable' marker) on each bucket the
amount of water it contains or they could use digit cards to place
on the buckets.