Being curious

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Can you deduce which Olympic athletics events are represented by the graphs?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

Can you find six numbers to go in the daisy from which you can make all the numbers from 1 to a number bigger than 25?

What are the possible areas of triangles drawn in a square?