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Season 2 • Episode 13 • Polyominoes


Academic year: 2022

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Season 2Episode 13Polyominoes



Season 2

Episode 13 Time frame 1 period

Objectives :

Introdue the onept of polyominoes.

Enumerate all polyminos and nd out their orders.

Materials :

Dominoeswith mathematial symbols.



1 – Enumerate the polyminoes 25 mins

The teaher explainstheonept ofpolyominoeswith abeamer.Then, workingingroups

of 4 or5, students have to enumerate all the triominoes, tetrominoesand pentominoes.

2 – Speed contest : find out the orders 25 mins

Stillworking ingroups, studentshavetond the order ofallthe triominoes,tetrominoes

and pentominoes. The rst team to omplete the task(or the most advaned at the end

of the hour)gets anA*, the seondanA and the thirda B. Aone minute malusis given

eah time someone in the group speaksFrenh.

3 – Buffer : the hexominoes Remaining time



Season 2

Episode 13 Document Lesson

In rereationalmathematis, apolyomino is apolyform with the squareas itsbase form.

It is a onneted shape formed as the union of one or more idential squares in distint

loations on the plane, suh that every square an be onneted to every other square

through a sequene of shared edges (i.e., shapes onneted only through shared orners

of squares are not permitted).

Definition 1 Small polyominoes

A monomino is made of just one square, domino is made of two, a triomino of three and so on for tetrominoes, pentominoes, hexominoes, etc.

In this sequene, we will work on free polyominoes, that are onsidered dierent from

eah other aslong as none isa translation, rotation,orreetion of another.

Proposition 1 Numbers of small polyominoes

There are one free monomino, one free domino, two free triominoes, five free tetro- minoes and twelve pentominoes.

The 5free tetrominoes.


Season 2Episode 13Polyominoes


Definition 2 Order of a polyomino

The order of a polyomino is the number of copies of itself you need to build a rec- tangle.

Proposition 2 Some orders

The monomino, the domino, the triominoes and most of the tetrominoes and pentomi-

noes have order 1 or 2, except the T tetromino which has order 4 and the Y pentomino

which has order 10.


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