Arrange the shapes in a line so that you change either colour or
shape in the next piece along. Can you find several ways to start
with a blue triangle and end with a red circle?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Investigate the positions of points which have particular x and y
coordinates. What do you notice?
Write down what you can see at the coordinates of the treasure
island map. The words can be used in a special way to find the
buried treasure. Can you work out where it is?
Find the missing coordinates which will form these eight
quadrilaterals. These coordinates themselves will then form a shape
with rotational and line symmetry.
Freddie Frog visits as many of the leaves as he can on the way to
see Sammy Snail but only visits each lily leaf once. Which is the
best way for him to go?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
What are the coordinates of the coloured dots that mark out the
tangram? Try changing the position of the origin. What happens to
the coordinates now?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
What are the coordinates of this shape after it has been
transformed in the ways described? Compare these with the original
coordinates. What do you notice about the numbers?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Draw some spirals with the LOGO programming language.
Is it possible to use all 28 dominoes arranging them in squares of
four? What patterns can you see in the solution(s)?
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides
exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest
power of two that divides exactly into 100!?
ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
By inscribing a circle in a square and then a square in a circle
find an approximation to pi. By using a hexagon, can you improve on
Try out this geometry problem involving trigonometry and number theory
Re-arrange the pieces of the puzzle to form a rectangle and then to
form an equilateral triangle. Calculate the angles and lengths.
What are the possible remainders when the 100-th power of an
integer is divided by 125?
If a number N is expressed in binary by using only 'ones,' what can
you say about its square (in binary)?