There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?
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?
The problem helps to extend
learners' familiarity with fractions, but has the potential to
prompt discussion about limits and infinity. Learners have the
chance to develop convincing arguments and to share with others
different ways of seeing the images.
What fraction of the square
Can you convince someone else that your calculations are
How can you visualise the pattern to help you to find the
Can you continue the
patterns outwards? Can you use this to find a way of working out
successive approximations to the limit?
Learners could investigate
the perimeters of successive shapes in the sequences.
The patterns could be used
as a brief introduction to the idea of self-similarity in fractal
Challenge learners to make
the patterns out of squares of paper in contrasting colours. By
folding paper to create each section, learners will be able to spot
relationships between the area of consecutive pieces of the
pattern. Learners could work in pairs to create two copies of the
pattern from two squares of contrasting colour by swapping
The article Zooming
in on the squares discusses the idea of starting the process
off and looking at successive estimates for the area.