pentominoes what is a pentomino? well – you know what a domino is 2 squares joined exactly edge to...
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PentominoesWhat is a pentomino?
Well – you know what a domino is
2 squares joined exactly
edge to edge
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Triominoes
Both have line symmetry, only 1 has rotational symmetry
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4 Squares - Tetrominoes
3 have line symmetry
3 have rotational symmetry
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Pentominoes‘pent’ means.....
5as in pentagon and
pentagram
It’s Greek, by the way
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Pentominoes
Now pentominoes are how many squares joined
exactly edge to edge?
5
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Pentominoes
How many different pentominoes are there?
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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
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Pentominoes be systematic to get
them all
12
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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
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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
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Pentominoes
What’s the biggest total we can make?
What’s the smallest total?
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Pentominoes
Now choose one of your shapes...and I want you to fill each square
with one of the numbers 1-5
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Pentominoes
What’s the biggest total you can make?
What’s the smallest total?
Hint – choose your shape wisely
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Maximum totals
Why?
Which shape do you think will give the biggest total?
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Minimum totals
Why?
Which shape do you think will give the smallest total?
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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?
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Maximum totals for multiplying
Why?
Which shape do you think will give the biggest total?
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Minimum totals for multiplying
Why?
Which shape do you think will give the smallest total?
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How many pentominoes have line symmetry?
6
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How many pentominoes have rotational symmetry?
Rotational symmetry 2
Rotational symmetry 2
Rotational symmetry 4
3
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Hexominoes
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Hexominoes
Symmetry
10 have mirror symmetry (Red, Green, Purple)
7 have rotational symmetry (Blue and Purple)
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Hexominoes
• How many of them can be folded to make cubes?
• First group to identify them all wins...
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Cube Nets
11 – might use one of these later....
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7 Squares - Heptominoes – 108!
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8 Squares - Octanominoe – 369!
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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
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How long would it take to count to a million?
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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...