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The Lily Pond

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?

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Treasure Island

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?

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What Are You Plotting?

Investigate the positions of points which have particular x and y coordinates. What do you notice?

Dotty Relationship

Age 7 to 11 Challenge Level:
On the grid below, join the two blue dots, A and B, together with a straight line.

Now join the green dots, C and D, with a straight line.

grid with four dots marked
At what angle do the two lines cross?

Investigate the number of squares "along" and "down" from A to B compared with the number of squares "along" and "up" from C to D. What do you notice?

Using what you have found out, can you draw lines that are perpendicular (at $90^{\circ}$) to the lines drawn below?

line connecting points by 3 along and 3 up
line connecting points by 4 along 1 down
line connecting points by 1 along 3 down
Is there only one solution each time?

Do the two lines have to be the same length? Why or why not?