pentominoes what is a pentomino? well – you know what a domino is 2 squares joined exactly edge to...

PentominoesWhat is a pentomino?

Well – you know what a domino is

2 squares joined exactly

edge to edge

Triominoes

Both have line symmetry, only 1 has rotational symmetry

4 Squares - Tetrominoes

3 have line symmetry

3 have rotational symmetry

Pentominoes‘pent’ means.....

5as in pentagon and

pentagram

It’s Greek, by the way

Pentominoes

Now pentominoes are how many squares joined

exactly edge to edge?

5

Pentominoes

How many different pentominoes are there?

Pentominoes

How many different pentominoes are there?

Different – meaning not the same one another way round

Back to dominoes

is the same as 

  ‘do’ is Greek for 2

Pentominoes be systematic to get

them all

12

Pentominoes – the taskChoose a pentomino.

Now using only the numbers 1-5 any way you want to,

add up pairs of adjacent numbers and total

Pentominoes – the taskNow using only the numbers 1-5

any way you want to, add up pairs of adjacent numbers and

total

25

What’s the biggest total you can make?

+= 6

+= 7

+= 5

+= 7

Pentominoes

What’s the biggest total we can make?

What’s the smallest total?

Pentominoes

Now choose one of your shapes...and I want you to fill each square

with one of the numbers 1-5

Pentominoes

What’s the biggest total you can make?

What’s the smallest total?

Hint – choose your shape wisely

Maximum totals

Why?

Which shape do you think will give the biggest total?

Minimum totals

Why?

Which shape do you think will give the smallest total?

PentominoesNext task

How about multiplying pairs of adjacent numbers and making a total?

1 x 5 =

5 x 2 =

2 x 3 =

3 x 4 =

Total

5

14

6

12

37

Where is the mistake?

Maximum totals for multiplying

Why?

Which shape do you think will give the biggest total?

Minimum totals for multiplying

Why?

Which shape do you think will give the smallest total?

How many pentominoes have line symmetry?

6

How many pentominoes have rotational symmetry?

Rotational symmetry 2

Rotational symmetry 2

Rotational symmetry 4

3

Hexominoes

Hexominoes

Hexominoes

Symmetry

10 have mirror symmetry (Red, Green, Purple)

7 have rotational symmetry (Blue and Purple)

Hexominoes

• How many of them can be folded to make cubes?

• First group to identify them all wins...

Cube Nets

11 – might use one of these later....

7 Squares - Heptominoes – 108!

8 Squares - Octanominoe – 369!

Poly - nominoes

Number of squares Number of combinations?

How long will it take to count to these numbers?

1 1

2 1

3 2

4 5

5 12

6 35

7 108

8 369

9 1285

10 4665

How long would it take to count to a million?

What do you want to do tomorrow?

Do an activity involving going outside for some of the time?

Make 3D Shapes

Carry on investigating what we started today

Investigating Patterns – Magic Squares, Magic triangles

Something not on this list...