Explaining, convincing and proving

Here you have an opportunity to explore the proofs of the laws of logarithms.

Which of the statements is true?

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?

Do you have enough information to work out the area of the shaded quadrilateral?