This problem invites students to explore the power of reasoning
based on algebraic forms.
It is important for students to feel confident with the context and
therefore spending time on the problem "Consecutive sums" may be an
important starting point. By working on this problem the
difficulties with solving for powers of 2 often occurs
Why are powers of 2 impossible? We are aware of two
approaches to explaining this:
- one is using an argument based on the diagram offered in the
hints and the relationship of the rectangle with odd and even
- the other involves examination of an algebaric expression that
represents the sum - this links with the arguments offered in the
solution to the problem "Make 24".
But of course there might be some neater explanations.
The problem Sequences
has an interactivity you might wish to use.