At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.
At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening?
According to Plutarch, the Greeks found all the rectangles with
integer sides, whose areas are equal to their perimeters. Can you
find them? What rectangular boxes, with integer sides, have their
surface areas equal to their volumes?
What fraction of the whole piece of paper is the largest
What fraction of the whole piece of paper is the second triangle
which is labelled number 2?
Try adding the area of the next triangle in the series each time
and noting the answer.
As you keep adding areas on, what fraction are your answers
getting closer to?
Try working out equivalent fractions so that they all have the same
denominator, then you can compare sizes easily - you may like to
use a calculator to help with the larger numbers!