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Fraction Talks
“You get a lolly”
“You get a lolly”
Adam Hillman @witenry
“Make it real world”
“Make it real world”
love2learn2day.blogspot.com.au
Conrad Wolfram
tapintoteenminds.com
I want to convince you maths is worth doing for its own sake.
Pure maths is maths we do not because it is useful, but because it is beautiful.
We do it to try to understand the nature of shape, number, structure, and pattern.
Applied maths = useful
Pure maths = beautiful
How applied maths works
1. Pose the right “real world” question 2. Translate into maths,
i.e. Build a mathematical model 3. Do maths/compute to get an answer 4. Translate the answer back to the real world,
verify/interpret/refine the model
Conrad Wolfram
Applied Mathematics is about building models that help
explain the world.
https://www.npr.org/2013/05/11/182951560/to-count-elephants-in-the-forest-look-down
If applied mathematics is for power
starpolygons.compure maths is for beauty…
If applied mathematics is for power
starpolygons.compure maths is for beauty… and power
Pure Mathematics happens in the mathematical world,
where we make all the rules.
Why not take control?
Why not let students own their mathematical experiences?
What is 3-2?
What is 3-2?
33 = 27 32 = 9 31 = 3
What is 3-2?
33 = 27 32 = 9 31 = 3 30 = ?
÷ 3÷ 3
What is 3-2?
33 = 27 32 = 9 31 = 3 30 = ?
÷ 3÷ 3÷ 3
What is 3-2?
33 = 27 32 = 9 31 = 3 30 = 1
÷ 3÷ 3÷ 3
What is 3-2?
33 = 27 32 = 9 31 = 3 30 = 1 3-1 = ? 3-2 = ?
÷ 3÷ 3÷ 3
What is 3-2?
33 = 27 32 = 9 31 = 3 30 = 1 3-1 = 1/3 3-2 = 1/9
÷ 3÷ 3÷ 3÷ 3÷ 3
What is 3-2?
(33) x (3-2)= 3(3-2)
What is 3-2?
(33) x (3-2)= 3(3-2) 27 x (3-2) = 3
What is 3-2?
(33) x (3-2)= 3(3-2) 27 x (3-2) = 3 (3-2) = 3/27
What is 3-2?
(33) x (3-2)= 3(3-2) 27 x (3-2) = 3 (3-2) = 3/27 3-2 = 1/9
Maths ownership only happens when we have faith that it should make
sense.
Then we can be honest about what doesn’t yet make sense
And relentless about our own understanding
What fraction is blue?
1/81/8
1/8
1/8
1/81/8
1/8
1/8
Triangle Area = 1/2 Rectangle Area = 1/2 (base x height)
Image from Wikipedia
Image from Wikipedia
Image from Wikipedia
Image from Wikipedia
Image from Wikipedia
Image from Wikipedia
Image from Wikipedia
Image from Wikipedia
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Behold!
The adventure starts with what we understand, and progresses
toward what we don’t
And be models for what developing ownership looks like
So let’s seize control of the adventure
