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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?

A Cartesian Puzzle

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

Transformation Tease

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?

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?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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