Transcript Pentominoes - Bedfordmathsacademy

Pentominoes
What 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.....
5
as 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 task
Choose a pentomino.
Now using only the numbers 1-5
any way you want to,
add up pairs of adjacent numbers and total
Pentominoes – the task
Now using only the numbers 1-5
any way you want to,
add up pairs of adjacent numbers and total
+
=
6
+
=
7
+
=
5
+
=
7
25
What’s the biggest
total you can make?
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
Which shape do you think will give the biggest total?
Why?
Minimum totals
Which shape do you think will give the smallest total?
Why?
Pentominoes
Next task
How about multiplying pairs of adjacent numbers
and making a total?
1x5=
5
5x2=
14
2x3=
6
3x4=
12
Total
37
Where is the mistake?
Maximum totals for multiplying
Which shape do you think will give the biggest total?
Why?
Minimum totals for multiplying
Which shape do you think will give the smallest total?
Why?
How many pentominoes have line symmetry?
6
How many pentominoes have rotational symmetry?
Rotational symmetry 2
3
Rotational symmetry 2
Rotational
symmetry 4
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?
1
1
2
1
3
2
4
5
5
12
6
35
7
108
8
369
9
1285
10
4665
How long will it take
to count to these
numbers?
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...