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Direct Logic

Age 16 to 18
Challenge Level

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?