Polyonimo: Poly from the Greek Word Polus for Many

POLYOMINOES

There are some words used in this work that you may have not seen before.

Polyonimo: Poly from the Greek word polus for many.

Monomino: Mono from the Greek work monos for one.

Domino: Duo from the Latin work duo for two.

Triomino: Tri from the Greek work tries and the Latin work for tres for three.

Tetromino: tetra from the Greek word tettares for four.

Pentomino: Penta from the Greek word pente for five.

Kexomino: Hex from the Greek word hex for six.

Try to remember these words they are used a lot in Mathematics.

This is a Monomino. It is made from one square. There is only one monomino.

This is a Domino. It is made using two square. There is only one domino. You cannot have this as another domino. It is the same as the one above, it has only been turned round

Polyonimoes can only join the squares along their edges. So this one is not allowed, as they are joined by their corners!

These are Triominoes. They are made from three squares. There are only two different triominoes.

Copy the above into your books, or on the paper you have been given. Draw all the different Tetrominoes (these have four squares). Write down how many different Tetrominoes there are. Draw all the different Pentominoes (these have five squares). Write down how many different Pentominoes there are.

Label your pentominoes with letters and numbers. You may like to give them names instead. Some names that have been invented so far are; “The cross” “The big tee” “The little tee”.
Write down the perimeter of each pentomino. For example, the cross has a perimeter of ____cm.
Which pentomino has the smallest perimeter.
Which pentomino has the biggest perimeter.
Write down the pentominoes with a vertical axis of symmetry.
Write down the pentominoes with a horizontal axis of symmetry.
Draw the pentominoes that have no lines of symmetry.
Draw the pentominoes that have more than two lines of symmetry.
Make all the pentominoes using card.
Fit all your pentominoes in a 5 x 12 rectangle.
Fit all your pentominoes in a 6 x 10 rectangle.

This is one solution of the 5 x 12 rectangle. There are 2339 different ones!!

A

B

C

D

E

F

/ S

1Which three pentominoes are exactly the same shape?

2Which pentomino has four symmetry (mirror) lines?

3What is the name of the shape of pentomino L?

4How mant internal right angles are there in pentomino S?

5Copy pentomino G. Draw a line of symmetry on your shape.

6Which pentomino has only two symmetry lines?

7What is the perimeter of pentomino J?

8Copy pentomino F. Draw a line of symmetry on your shape.

9How many internal right angles are there in a pentomino P?

10Pentomino R has rotational symmetry. Write down the order of rotational symmetry.

11If you could pick up pentomino C and turn it over, which one would it fit onto?

12If you could turn pentomino A through180, which one would it fit onto?

13What is the total area of all 17 pentominoes?

14Which pentomino has rotational symmetry order 4?

15If you rotate pentomino J clockwise through 90, which one would it fit onto?

1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
21 / 22 / 23 / 24 / 25 / 26 / 27 / 28 / 29 / 30
31 / 32 / 33 / 34 / 35 / 36 / 37 / 38 / 39 / 40
41 / 42 / 43 / 44 / 45 / 46 / 47 / 48 / 49 / 50
51 / 52 / 53 / 54 / 55 / 56 / 57 / 58 / 59 / 60
61 / 62 / 63 / 64 / 65 / 66 / 67 / 68 / 69 / 70
71 / 72 / 73 / 74 / 75 / 76 / 77 / 78 / 79 / 80
81 / 82 / 83 / 84 / 85 / 86 / 87 / 88 / 89 / 90
91 / 92 / 93 / 94 / 95 / 96 / 97 / 98 / 99 / 100

Do these in the same way.

2. / 2 / 3. / 3 / 4. / 11

Sum=

/ Sum= / Sum=
5. / 37 / 6. / 13 / 7. / 58
Sum= / Sum=
8. / 43 / 9. / 68 / 10. / 38
Sum= / Sum= / Sum=

11 What happens to the sum as the pentomino is moved one square to the right?

12What happens to the sum as the pentomino is moved one square downwards?

13Can you predict the sum for S78 and S79?

Copy the diagrams.

Fill in squares or triangles to give the shape the order of symmetry shown.

1 / 2 / 3
Order 1
4 / Order 4
5 / Order 2
6
Order 1
7 / Order 2
8 / Order 2
9
/ Order 4 / 10 / Order 2 / Order 2
11
Order 3 / Order 2

Copy the diagrams.

Fill in squares or triangles to give the shape the order of symmetry shown.

/ 3 / 4
1 / 2
Order 3 / Order 3 / Order 2 / Order 4
5 / 6 / 7
Order 2 / Order 4
8 / 9 / 10 / Order 4
Order 4 / Order 2 / Order 2

Draw two of your own shapes that have a rotational symmetry order 2.

Draw two of your own shapes that have a rotational symmetry order 3 (use isometric paper).

Draw two of your own shapes that have a rotational symmetry order 4.

Draw two of your own shapes that have a rotational symmetry order 6 (use isometric paper).