Explaining, convincing and proving

How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

Find the relationship between the locations of points of inflection, maxima and minima of functions.

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?