Exploring and noticing

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Use 4 four times in a calculation. What answers can you get?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

Can you place the blocks so that you see the reflection in the picture?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

Try out these calculations. Are you surprised by the results?