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?

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

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

Investigate the number of points with integer coordinates on circles with centres at the origin for which the square of the radius is a power of 5.