6 x 10 P E N TO M I N O E S More of that later! Poly-ominoes Many-squares Rules Full edge to edge...

6 x 10

P E N T O M I N O E S

More of that later!Poly-ominoes Many-squares Rules

Full edge to edge contact only.

Mon-omino

1

Domino

1

Triominoes

2

?

?

Tetrominoes

5

Find all of the?

Think systematically!

Don’t forget to avoid duplicates. Remember, rotations and

reflections are not allowed!

P O L Y O M I N O E S

12

The pentominoes have lots of interesting properties. Find and draw all of the pentominoes.? Don’t forget to think systematically!

P E N T O M I N O E S

Alphabet Pentominoes!

P E N T O M I N O E S

Some of the pentominoes (like the one shown)can be folded to make open-top boxes. Can you find them all and shade their

bases?

P E N T O M I N O E S

Find the pentominoes with line/mirror symmetries

P E N T O M I N O E S

Find the pentominoes with turn/rotational symmetry.

P E N T O M I N O E S

¼ turn

½ turn

¾ turn

Full turn

Order 2

Find the pentominoes with turn/rotational symmetry.

P E N T O M I N O E S

¼ turn ½ turn ¾ turn Full turn

Order 2

Find the pentominoes with turn/rotational symmetry.

Order 2

P E N T O M I N O E S

¼ turn ½ turn ¾ turn Full turn

Order 4

Find the pentominoes with turn/rotational symmetry.

Order 2 Order 2

P E N T O M I N O E S

12 12

10

12 12

12

12

12 12 12

12

Do they all have the same perimeter?

12

How many different size rectangles can be made using 60 squares?

6

10

3

20

5

12

4

15

2

30

160

6 x 10

P E N T O M I N O E S

1 of 2339!

P E N T O M I N O E S

1 of 2339 2 of 2339 3 of 2339

1 of 1010 2 of 1010

1 of 368 2 of 368

Build the 12 pentominoes using the 2 cm cubes provided. Use you’re A3

worksheet to try and find a solution of your own!

P E N T O M I N O E S

1 of 2339 2 of 2339 3 of 2339

1 of 1010 2 of 1010

1 of 368 2 of 368

H E X O M I N O E S

There are 35 distinct hexominoes. You will need patience and

systematic thinking to find all of them.

H E X O M I N O E S

Some of the hexominoes can be folded to make closed boxes. They are nets of cubes. Can you

find them?

H E X O M I N O E S

Hexominoes with line symmetry?

H E X O M I N O E S

Hexominoes with rotational symmetry?

H E X O M I N O E S

They all have the same area but do they

all have the same perimeter?

14 14 14 14 12

14 14 14 14 14 14

12

14 14 14 14 14 14 12

10 14 14 14 14 14

14 12 12 12 12 14

14 14 14 14

H E X O M I N O E S

Possible rectangles with an area of:

1 x 210

2 x 105

3 x 70

5 x 42

6 x 35

7 x 30

10 x 21

14 x 15

210 units2

15

14

It is not possible to cover any of these

rectangles with the 35

hexominoes.

P O L Y O M I N O E S

Monominoes

Dominoes

Triominoes

Tetrominoes

Pentominoes

Hexominoes

HeptominoesOctominoes 369

108

35

12

5

2

2

1

A formula for calculating the number of n-ominoes has not been found.

1. Make drawings of all 12 pentominoes. (avoid duplicates)2. Eight of the pentominoes can be folded to make an “open-top”

box. Draw and shade the base (bottom) of the ones that can.3. Draw the pentominoes that have line/reflective symmetry and

draw the lines on them.4. Draw the pentominoes that have turn/rotational symmetry and

write down the order of this symmetry in each case.5. All pentominoes have the same area but do they all have the

same perimeter? Investigate and provide examples.6. What is the total area of all 12 pentominoes?7. Make a list of all possible rectangles (l x w) that could be made

from this area.

1. Make drawings of all 35 hexominoes (avoid duplicates)2. Eleven of the hexominoes can be folded to make closed boxes.

Draw the ones that can.3. Draw the hexominoes that have line/reflective symmetry and

draw the lines on them.4. Draw the hexominoes that have turn/rotational symmetry and

write down the order of this symmetry in each case.5. All hexominoes have the same area but do they all have the

same perimeter? Investigate and provide examples.6. What is the total area of all 35 hexominoes?7. Make a list of all possible rectangles (l x w) that could be made

from this area.

Pentominoes

Hexominoes

Worksheet

1

Worksheet 2

P E N T O M I N O E S

6 x 10

2339 solutions

3 x 20

2 solutionsWorksheet 3: A3 front(enlarge)

P E N T O M I N O E S

5 x 12

1010 solutions

4 x 15

368 solutionsWorksheet 3: A3 reverse(enlarge)

Worksheet 4