Take any triangle, and construct squares on each of its sides. What do you notice about the areas of the new triangles formed?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What sizes of rectangle contain exactly 100 squares? Can you find them all?
A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?
Trinni rearranges numbers on a clock face so each adjacent pair add up to a triangle number... What number did she put where 6 would usually be?
The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
Two vases are cylindrical in shape. Can you work out the original depth of the water in the larger vase?
There are lots of ideas to explore in these sequences of ordered fractions.
