# World of Tan 25 - Pentominoes

##### Stage: 2 Challenge Level:

This activity follows on from World of Tan 24 - Clocks .

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School is over for the week. In the yard the workmen are getting ready to go home. Little Fung and Little Ming are getting in the way as usual .. but they have already attracted the attention of Chi Wing - the foreman. They are making shapes using five small squares on a grid.

LM: The teacher says there are twelve different shapes!

CW: That may be so, but I don't believe it.

LF: If joined together properly there are twelve - she said so.

CW: Have you found them?

(...pause)

CW: NO. You have not! I don't think you have anywhere near twelve solutions. You pair never work systematically at anything.

LM: We do have seven though Chi Wing.

CW: Listen just what were you asked to do? Little Fung you explain...

LF: Each 'animal' is made up of five squares.

LM: Always five squares!

CW: Little Ming shush, Little Fung carry on please..

LF: The squares have to be joined in a special way...

CW: Before, you said ONLY edge to edge, that is right isn't it?

LM: Yes, not corner to corner or ....

CW: Little Ming quiet - you never listen to the whole story..

LF: The edges must be completely touching each other.

CW: Show me please..explain..

( With squares of paper CW is shown....)

LM: But not like this ..

CW: So if we move them around systematically we should be able to find the twelve different ones.

LF: Yes...but we can only find seven..

LM: Perhaps we should have sketched out those we have already found.

LF: I think we should start again ..

CW: Yes let us start at the beginning ...with all the squares in a line..

LM: Let us begin by moving one square at a time..

CW: So which square shall we start with?

LF: Does it matter?

LM: Yes, if we are to be systematic like Chi Wing always is, and find all twelve..

CW: So instead of bickering - which square shall we start with?

In the meantime, complete the silhouettes of Chi Wing studying the problem, then working systematically. There are more activities in the notes , and the story continues in World of Tan 26 - Old Chestnut .