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The Lily Pond

Age 7 to 11
Challenge Level

The Lily Pond

Once there was a rectangular lily pond. In it there were $12$ lily leaves and $6$ lily flowers.

Freddy the forggy on his lilly pad.

Freddie the Frog lived on one lily leaf which we will call "leaf $1$, row $4$". Sammy Snail lived on another leaf which we will call "leaf $2$, row $3$". Freddie used to jump from leaf to leaf but he did not like jumping over the lily flowers so he never jumped diagonally.

One day Freddie went to see Sammy Snail. He visited as many of the leaves as he could on the way but only visited each leaf once. Which was the best way for him to go?

If Sammy lived on a different leaf Freddie would be able to go on every leaf on his way to see Sammy. Which leaves would make this possible?

Why do this problem?

This problem can be a useful introduction to the idea of coordinates. It lends itself to working together in a systematic way.

Key questions

Where could Freddie go from here?
Can you find another way for Freddie to go?
How will you keep track of Freddie's jumps?
Can you find another place for Sammy to go so that Freddie jumps on all the leaves?

Possible extension

Children who are familiar with the coordinate system might like to try the Treasure Island problem.

Possible support

Some learners will find it helpful to have a copy of the picture and to draw routes onto it.