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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
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...