Transforming Maths lessons: From ordinary to extraordinary

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Transforming Maths lessonsFrom ordinary to
extraordinary
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The only person I can can change is myself!
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12 day challenge

• Trial 2-3 ideas

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Creating urgency...

• At a personal level
• With colleagues
• With kids

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Implementation Dip
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No such thing as a lousy lesson or activity!

• What would I do differently next time?

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What are you thinking about now...

• that you werent thinking about
• 6 months ago?

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How do we leverage the Cloud for Mathematics
learning?
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Shared document for reflections

• http//tinyurl.com/shared-doc
• instead of
• https//docs.google.com/Doc?iddhcpgz6t_83fqjng7jd

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John Mason Mathematics hasnt been done in a
Mathematics lesson unless it has involved
generalising.
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Jumping Kangaroos

• 2 families of roos need to pass each other on a
  mountain slope.
• Constraints
• Can only jump into a vacant square
• Can jump over a roo into a vacant square
• Cant jump backwards
• Minimum number of moves

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in Adelaide
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Which is the odd one out, and why?
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Is there a Maths task lurking in there?
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Mathematicians ask...

• How many ways are there of arranging... ?
• How can I convince you Ive found them all?

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Pentomino tiles

• How many ways of arranging five tiles?

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• Allowed? Yes or no?

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Pentomino tiles

• How many ways of arranging five tiles?

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• How can all the Pentomino tiles be arranged?
• What rectangles are possible?
• What are not possible?

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• Not possible?
• Argue a mathematical case
• why some rectangles are not possible?

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Building new tasks...
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Perimeters - Which has biggest? Smallest? What
about two shapes together?
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Symmetry - Where could you add a 6th square to
give the shape symmetry?
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Symmetry - Where could you add a 6th square to
give the shape symmetry?
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Symmetry - Where could you add a 6th square to
give the shape symmetry?
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Symmetry - Where could you add a 6th square to
give the shape symmetry?
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Symmetry - Where could you add a 6th square to
give the shape symmetry?
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Symmetry - Where could you add a 6th square to
give the shape symmetry?
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Symmetry - Where could you add a 6th square to
give the shape symmetry?
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Symmetry - Where could you add a 6th square to
give the shape symmetry?
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Soma cube

• How many ways of arranging 3 or 4 cubes?
• What constraints are possible?

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Soma cube

• How many ways of arranging 3 or 4 cubes?
• What constraints are possible?

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Viewing my classroom as anarchaeological dig...
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Challenge students sense of mathematical
attributes
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Say what you see!
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What would a typical 7 year old say?
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25 cm
32
x
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or
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x
25 cm
32
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25 cm
Hypotenuse
32
x
Adjacent
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Cos Rule cos 32 Adjacent
Hypotenuse
25 cm
Hypotenuse
32
x
Adjacent
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25 cm
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Questions to provoke mathematical thinking,
triggering changes in practice

• Good sources
• Thinkers
• Primary Questions Prompts
• Questions Prompts for Mathematical Thinking
• Building on the work from Zygfryd Dyrszlag, a
  Polish Mathematics Educator
• Published by ATM(UK)
• Available online from www.aamt.edu.au, search on
  Mason Watson

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Questions...
Extended Investigation
Open
Closed
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Questions...
Extended Investigation
Open
Closed
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Questions...
Extended Investigation
Closed
Open
What pairs of numbers add to 7?
How many pairs of numbers add to a given sum?
What is 3 4?
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Questions...
Extended Investigation
Closed
Open
What pairs of numbers add to 7?
How many pairs of numbers add to a given sum?
What is 3 4?
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Additional Conditions

• Imposing a constraint, then repeating the same
  question with additional constraints added one by
  one.
• Each additional constrain prompts learners to
  think more precisely about the properties of the
  example they are creating.

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Give me an example of...

• a set of numbers whose mean is 5
• and whose mode is 4
• and whose median is 3
• and whose range is 6
• and whose standard deviation is 1 (for the brave!)

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Give me an example of...

• a quadrilateral with at least two right angles
• and whose sides are not all the same length
• and which has reflective symmetry about at least
  one diagonal

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Always, sometimes never true

• All numbers in the 5 times tables end in a five
• To multiply by ten put a 0 on the end
• Division always makes smaller
• Squaring a number makes it larger