Exploring mathematical problems
beyond the tip of the iceberg
Exploring mathematical
problems
beyond the tip of the
iceberg
Pick problems...
Pick problems...
maths300.esa.edu.au
maths300.esa.edu.au
Attributes of a
Maths 300 lesson

maths300.esa.edu.au
Challenges in my classroom...
Arithmagons
Strategy Board
Arithmagons
Learning outcomes and related concepts
•basic addition
•difference between
•algebraic representation
•problem ...
Pen
thickness

Pen colour
t1 = a + b
t2 = b + c
t3 = a + c
t1 = a + b
t2 = b + c
t3 = a + c

The number on the edge is
the sum of the two numbers
on the vertices.
t1 = a + b
t2 = b + c
t3 = a + c
t1 - t2 = (a + b) - (b - c)
this becomes
t1 - t2 = a - c
t1 = a + b
t2 = b + c
t3 = a + c
t1 - t2 = (a + b) - (b - c)
this becomes
t1 - t2 = a - c
Put your finger near the top circle to
highlight the difference between 13 and 8,
which is 5.
Put your finger near the top
circle to highlight the
difference between 13 and 8,
which is 5.

So, the opposite circle num...
Put your finger near the top
circle to highlight the
difference between 13 and 8,
which is 5.

So, the opposite circle num...
Put your finger near the top
circle to highlight the
difference between 13 and 8,
which is 5.

So, the opposite circle num...
Put your finger near the top
circle to highlight the
difference between 13 and 8,
which is 5.

So, the opposite circle num...
Pick any number

Another approach...
Pick any number
Complete the other
other two vertices
Pick any number
Complete the other
other two vertices

Total needs to be 9, but
10 + 5 = 15...over by 6.
Pick any number
Complete the other
other two vertices

Total needs to be 9, but
10 + 5 = 15...over by 6.

6 needs to be sh...
Add 3

Total needs to be 9, but
10 + 5 = 15...over by 6.

6 needs to be shared
between two vertices
Add 3

Take 3

Total needs to be 9, but
10 + 5 = 15...over by 6.

6 needs to be shared
between two vertices
Add 3

Take 3

Total needs to be 9, but
10 + 5 = 15...over by 6.

6 needs to be shared
between two vertices
Add 3

Take 3

Total needs to be 9, but
10 + 5 = 15...over by 6.

6 needs to be shared
between two vertices
Extensions...
Extensions...
Challenge older kids to program a SS
Challenge older kids to program a SS
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
Connect with Maths webinar "Beyond the tip of the iceberg mathematics"
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Connect with Maths webinar "Beyond the tip of the iceberg mathematics"

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'Tip of the Iceberg' Maths Problems
A constant challenge for teachers is to cater for the diversity of students in my classes. Matt Skoss is always looking to incorporate rich Maths tasks that are easy for students to make a start on the problem, but once students are engaged in the problem, they are exposed to the deeper, richer Mathematics lurking beneath the surface, hence the use of the 'iceberg' metaphor.
to support the professional growth of teachers.
Connect with Maths ~ supporting teachers of mathematics ONLINE
http://connectwith.indigenous.aamt.edu.au

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Connect with Maths webinar "Beyond the tip of the iceberg mathematics"

  1. 1. Exploring mathematical problems beyond the tip of the iceberg
  2. 2. Exploring mathematical problems beyond the tip of the iceberg
  3. 3. Pick problems...
  4. 4. Pick problems...
  5. 5. maths300.esa.edu.au
  6. 6. maths300.esa.edu.au
  7. 7. Attributes of a Maths 300 lesson maths300.esa.edu.au
  8. 8. Challenges in my classroom...
  9. 9. Arithmagons
  10. 10. Strategy Board
  11. 11. Arithmagons Learning outcomes and related concepts •basic addition •difference between •algebraic representation •problem posing and solving •
  12. 12. Pen thickness Pen colour
  13. 13. t1 = a + b t2 = b + c t3 = a + c
  14. 14. t1 = a + b t2 = b + c t3 = a + c The number on the edge is the sum of the two numbers on the vertices.
  15. 15. t1 = a + b t2 = b + c t3 = a + c t1 - t2 = (a + b) - (b - c) this becomes t1 - t2 = a - c
  16. 16. t1 = a + b t2 = b + c t3 = a + c t1 - t2 = (a + b) - (b - c) this becomes t1 - t2 = a - c
  17. 17. Put your finger near the top circle to highlight the difference between 13 and 8, which is 5.
  18. 18. Put your finger near the top circle to highlight the difference between 13 and 8, which is 5. So, the opposite circle numbers must have a difference of 5 AND sum to 9.
  19. 19. Put your finger near the top circle to highlight the difference between 13 and 8, which is 5. So, the opposite circle numbers must have a difference of 5 AND sum to 9. Zero is not being used. The only pairs of numbers which sum to 9 are: (8, 1), (7, 2), (6, 3), (5, 4)
  20. 20. Put your finger near the top circle to highlight the difference between 13 and 8, which is 5. So, the opposite circle numbers must have a difference of 5 AND sum to 9. Zero is not being used. The only pairs of numbers which sum to 9 are: (8, 1), (7, 2), (6, 3), (5, 4)
  21. 21. Put your finger near the top circle to highlight the difference between 13 and 8, which is 5. So, the opposite circle numbers must have a difference of 5 AND sum to 9. Zero is not being used. The only pairs of numbers which sum to 9 are: (8, 1), (7, 2), (6, 3), (5, 4)
  22. 22. Pick any number Another approach...
  23. 23. Pick any number Complete the other other two vertices
  24. 24. Pick any number Complete the other other two vertices Total needs to be 9, but 10 + 5 = 15...over by 6.
  25. 25. Pick any number Complete the other other two vertices Total needs to be 9, but 10 + 5 = 15...over by 6. 6 needs to be shared between two vertices
  26. 26. Add 3 Total needs to be 9, but 10 + 5 = 15...over by 6. 6 needs to be shared between two vertices
  27. 27. Add 3 Take 3 Total needs to be 9, but 10 + 5 = 15...over by 6. 6 needs to be shared between two vertices
  28. 28. Add 3 Take 3 Total needs to be 9, but 10 + 5 = 15...over by 6. 6 needs to be shared between two vertices
  29. 29. Add 3 Take 3 Total needs to be 9, but 10 + 5 = 15...over by 6. 6 needs to be shared between two vertices
  30. 30. Extensions...
  31. 31. Extensions...
  32. 32. Challenge older kids to program a SS
  33. 33. Challenge older kids to program a SS
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