It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Here are four tiles. They can be arranged in a 2 by 2 square so
that this large square has a green edge. If the tiles are moved
around, we can make a 2 by 2 square with a blue edge... Now try. . . .
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Place a red counter in the top left corner of a 4x4 array, which is
covered by 14 other smaller counters, leaving a gap in the bottom
right hand corner (HOME). What is the smallest number of moves. . . .
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being
visible at any one time. Is it possible to reorganise these cubes
so that by dipping the large cube into a pot of paint three times
you. . . .
Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .
Derek offered some interesting insights into this problem and explained it nicely too. Chen and Andrei took a slightly different approach.
Go to last month's problems to see more solutions.
Written for teachers, this article discusses mathematical
representations and takes, in the second part of the article,
examples of reception children's own representations.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.