Balance of Halves
Why do this problem?
Whether this problem is
done with a balance or with pencil and paper, there is more to it
than just doing addition. Although addition and subtraction are
involved, you are likely to find the children using all sorts of
language associated with these two operations and one of the main
points here is to establish a balance or equivalence as well as
"equals". Some pupils are not so readily used to coming across
situations like $3 + 5 = 6 + 2$, for example. You could use this
activity to introduce some algebraic ideas, by encouraging the
class to articulate what they are trying to find in a general
sense. For example "$7$ balances two other numbers", or "$7$ =
'something' add 'something'"or "$7$ = ? $+$ ?". This will help them
to get the idea that they are finding different numbers which fit
this criterion - not just one answer.
Key questions
How might you
start?
How might you record your
thinking?
How do you know you've
got all the possibilities?
Possible extension
As the question suggests, some learners might like to look at a
balance involving other fractions.
Possible support
Children might like to try Getting the
Balance instead.