Explaining, convincing and proving

Which of the cards provides the counter example?

Which statement correctly describes the real roots of the equation?

If the statement is not true, what can we say will be true?

Can you use Proof by Induction to establish what will happen when you add more and more odd numbers?

Can you prove that a quadrilateral drawn inside a tetrahedron is a parallelogram?

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?

Explore a number pattern which has the same symmetries in different bases.