Why do this
problem?
This problem gives plenty of opportunity for both discussion
and exploring patterns, properties and relationships involving
numbers. It also helps learners to make general statements about
properties of numbers such as squares, factors, multiples, odd and
even, and to identify examples for which a statement is true or
false.
Possible approach
You could also use
this interactivity as a
starter to this problem where you drag numbers you "like" (i.e. are
part of a set) to one side and numbers you "don't like" (i.e. are
not in your set) to the other. The children then have to ask
questions with yes/no answers to determine the name of your set.
You could invite some learners to take the lead on this themselves,
with the rest of the group asking questions.
You could then introduce the problem itself and learners could
work in pairs from
this
sheet so that they are able to talk through their ideas with a
partner. (The sheet has two copies of the box of numbers on it.)
You could also challenge pairs to find two other possible members
for their sets from the numbers under $150$.
At the end learners could be asked for the titles of the sets
they have found and then others could suggest members for these
sets. You could make statements such as "$9$ is a member of this
set" and ask learners to identify whether the statement is true or
false. When sets of multiples of $2$, $4$ and $8$ have been found
and discussed, learners could be asked to explain why no other sets
of multiples of even numbers are possible from the numbers in the
box.
Key questions
What can you tell me about this number?
Is this odd or even? What else do you know about it?
Which multiplication tables will you find this number
in?
Can you see any other multiples of that number?
Can you suggest other numbers that could go together in this
set?
Possible extension
Learners could make their own list of numbers to make into as many
sets as possible. You could suggest using triangular and cube
numbers as well as various multiples.
Possible support
Some children might find it useful to list all the properties of
each number in the box.