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The Lily Pond

Age 7 to 11
Challenge Level Yellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

Alistair explains how Freddie the Frog jumps:

  • First of all, Freddie Frog hops to
  • Row 3, Leaf 1 then to
  • Row 2, Leaf 1 then to
  • Row 1, Leaf 1 then to
  • Row 1, Leaf 2 then to
  • Row 1, Leaf 3 then to
  • Row 2, Leaf 3 then to
  • Row 3, Leaf 3 then to
  • Row 4, Leaf 3 then to
  • Row 4, Leaf 2 then to
  • Row 3, Leaf 3 to meet Sammy Snail.

Including the first leaf, Freddie has hopped on 11 leaves. He missed out Row 2, Leaf 2.

There is also another way to get to Sammy Snail that includes Row 2, Leaf 2, but it misses out a few more leaves.

Alistair goes on to say:

Freddie could jump on all the leaves if Sammy lived on

  • Row 1, Leaf 3, or if she lived on
  • Row 2, Leaf 2 or
  • Row 3, Leaf 3, or
  • Row 1, Leaf 1.

Alistair tells us that his mum thinks there is another place too. What do you think?


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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?

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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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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