Direct logic
Can you work through these direct proofs, using our interactive proof sorters?
Problem
To prove a theorem directly we start with something known to be true and then proceed, making small logical steps which are clearly correct, until we arrive at the desired result. So, because the starting point was true and each small step clearly correct, we know the result to be true.
Breaking down a mathematical argument into small steps requires patience and clear thinking.
In the following interactivities we have written out three proofs, broken them into small steps and then shuffled up the steps. Can you rearrange them into the correct logical order?
Proof of the formula for the roots of a quadratic equation
Proof of the formula for the sum of an arithmetic progression
Teachers' Resources
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
Key questions
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