Exploring and noticing

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Is it the fastest swimmer, the fastest runner or the fastest cyclist who wins the Olympic Triathlon?

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

How can we make sense of national and global statistics involving very large numbers?

Match the cumulative frequency curves with their corresponding box plots.

Can you match these calculations in Standard Index Form with their answers?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Two ladders are propped up against facing walls. At what height do the ladders cross?

Can you explain the surprising results Jo found when she calculated the difference between square numbers?