Can you describe this route to infinity? Where will the arrows take you next?
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Collect as many diamonds as you can by drawing three straight lines.
In this problem, we have created a pattern from smaller and smaller
squares. If we carried on the pattern forever, what proportion of
the image would be coloured blue?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Can you picture how to order the cards to reproduce Charlie's card trick for yourself?
Can you find the squares hidden on these coordinate grids?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
What's special about the area of quadrilaterals drawn in a square?