Posing Questions and Making Conjectures - Advanced
Difference Dynamics
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
Least of All
A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.
Trig Rules OK
Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...
Painting by Numbers
How many different colours of paint would be needed to paint these pictures by numbers?
Impossible Triangles?
Which of these triangular jigsaws are impossible to finish?
Polite Numbers
A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?
The Clue Is in the Question
Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?
Few and Far Between?
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?