How many lines are there in your diagrams? How many lines are there in the original diagram? Can you find a way of working out […]
Five red-eye frogs and five orange frogs line up in a row with a space between them.
They have to change places but they can only hop, one frog over another frog or slide to an empty space next to them.
Red-eye frogs can […]
What do you notice about the pattern? Draw the pattern and make a list of what you see in it.
Describe the shapes of the tangram pieces.
What is the same and what is different about the shapes of […]
For a start: how many small tetrahedra, like the blue model shown, were used to make the 6.5 metre high red balloon model shown below.
The smallest tetrahedron (Stage 0), the blue model, is made from 6 balloons, each […]
When you turn this star around it looks exactly the same in 5 different positions so we say it has ROTATIONAL SYMMETRY of order 5.
Is it possible to draw a 6-pointed star in the same way […]
Look at this square divided into four pieces : two identical triangles and two identical trapezia.
The edge of length 3 from each triangle matches with the edge of length 3 from a trapezium so that the four pieces from the square now occupy a rectangular space.
The square had side length 8 […]
Find some sticks, they could be twigs, or matchsticks or cocktail sticks, or rolled paper sticks, or pasta like spaghetti broken into short lengths, but they must all be the same length.
Arrange 16 sticks into this pattern.
As an easy starter, can you remove 4 sticks and leave […]
Look for squares of different sizes and also tilted squares
Start with a 3 by 3 grid of nine dots. Can you find six squares?
Then go on to the 4 by 4 grid of sixteen dots.
What can you say […]
1.1 The square grids below the continuous line depict negative numbers and those above the line positive numbers. Study the square grids shown above with black squares forming a pattern. How is the pattern growing? Create square grids 9, 10 and 11; complete them with black squares to further develop the […]
These straight lines form a family and the curves that you see, called envelopes, are tangent to each line in the family.
Draw two base lines and mark the same number of points at equal distances along each line. Join the outermost point on one base […]