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Pentominoes

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

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Pentominoes

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  1. Pentominoes What is a pentomino? Well – you know what a domino is 2 squares joined exactly edge to edge

  2. Triominoes Both have line symmetry, only 1 has rotational symmetry

  3. 4 Squares - Tetrominoes 3 have line symmetry 3 have rotational symmetry

  4. Pentominoes ‘pent’ means..... 5 as in pentagon and pentagram It’s Greek, by the way

  5. Pentominoes Now pentominoes are how many squares joined exactly edge to edge? 5

  6. Pentominoes How many different pentominoes are there?

  7. 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

  8. Pentominoes be systematic to get them all 12

  9. 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

  10. Pentominoes – the task + = 6 + Now using only the numbers 1-5 any way you want to, add up pairs of adjacent numbers and total = 7 What’s the biggest total you can make? + = 5 + = 7 25

  11. Pentominoes What’s the biggest total we can make? What’s the smallest total?

  12. Pentominoes Now choose one of your shapes... and I want you to fill each square with one of the numbers 1-5

  13. Pentominoes What’s the biggest total you can make? What’s the smallest total? Hint – choose your shape wisely

  14. Maximum totals Which shape do you think will give the biggest total? Why?

  15. Minimum totals Which shape do you think will give the smallest total? Why?

  16. PentominoesNext task 1 x 5 = 5 x 2 = 2 x 3 = 3 x 4 = Total 5 14 6 12 37 How about multiplying pairs of adjacent numbers and making a total? Where is the mistake?

  17. Maximum totals for multiplying Which shape do you think will give the biggest total? Why?

  18. Minimum totals for multiplying Which shape do you think will give the smallest total? Why?

  19. How many pentominoes have line symmetry? 6

  20. How many pentominoes have rotational symmetry? Rotational symmetry 2 3 Rotational symmetry 2 Rotational symmetry 4

  21. Hexominoes

  22. Hexominoes

  23. Hexominoes Symmetry 10 have mirror symmetry (Red, Green, Purple) 7 have rotational symmetry (Blue and Purple)

  24. Hexominoes • How many of them can be folded to make cubes? • First group to identify them all wins...

  25. Cube Nets 11 – might use one of these later....

  26. 7 Squares - Heptominoes – 108!

  27. 8 Squares - Octanominoe – 369!

  28. Poly - nominoes

  29. How long would it take to count to a million?

  30. 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...

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