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## 'Direct Logic' printed from http://nrich.maths.org/

### Why do this problem?

This set of interactive problems will allow students to develop
their understanding of clear mathematical proof. The
interactivities provide a helpful scaffold to students just
starting out with their understanding of proof. Students might be
used to trying to do several algebraic steps in their heads at
once. In these proof sorters, the logic is broken down into
individual steps. This atomistic approach will help to train the
minds of all students, even those who might already understand well
the mathematical ideas involved in the interactitvities.

### Possible approach

This problem would work well in small groups or individually.
The proof sorters could be used when studying series or as a
refresher at a later point in the syllabus.

Each interactivity could also usefully be projected onto the
board at the start of a lesson. As students enter the room they
could try to work out which cards would come first in the
proof.

### Key questions

Is there an obvious first line of the proof in each
case?

Which line follows immediately from the previous
line?

### Possible extension

Can students create the proofs on paper directly without the
assistance of the indicator to the left of the interactivity? Can
they then recreate these proofs?

Perhaps students could create their own proof sorters?

### Possible support

Encourage a trial and error to work out the order of some of
the trickier cards (the indicator on the left of each proof sorter
will go higher as a proof card is moved into the correct position).
Once the cards are in place, can students understand the flow of
logic?