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Plenary 1
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• I need a volunteer. (I won’t tell you for what.)
• How many years have you taught?
• Who has taught about twice as many years?
Getting acquainted
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• I need a volunteer.
• Can you please stand up?
• I need someone who is about 10% taller. Who are you?
Getting acquainted
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• I need a volunteer.
• How many kilometres did you drive or fly to get here?
• Who came from about half as far?
Getting acquainted
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• We say “kilometres per hour” to talk about speed or “per capita” to describe economic or social data.
• We could talk about “good deeds per day” to describe how thoughtful someone is.
Let’s think about rates
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• Make up your own situation that uses “per”, but try to make it unique.
• Now create a related problem someone else might solve based on your idea.
Let’s think about rates
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• Look at the 4 x 6 and 5 x 7 “pi pie” pictures that were distributed.
• Are the pictures exactly alike, except for size?
• What about the 4 x 6 and 5 x 7 stick people pictures?
Photo problem
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Choice 1:
Choose a problem
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• Choice 1: Which parking lot is more full?
Lot 1: 24 of 40 spots are filled
Lot 2: 56 of 80 spots are filled
• Choice 2:
Group A: 2 people 5 people.
Group B: 92 people 100 people.
Which group’s size changed more?
Choose a problem
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• Create both an example and a non-example of proportional reasoning.
• Try to use different contexts than you just saw.
What is proportional reasoning?
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SEE NEXT SLIDE
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• Proportional reasoning involves the deliberate use of multiplicative relationships to compare quantities and to predict the value of one quantity based on the values of another.
Proportional reasoning
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• When you decide that is a bit less
than since 18 is just less than half
of 37, you are using proportional reasoning.
Example of proportional reasoning
18
371
2
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• When you decide that an increase from 1 to 5 is more significant than an increase from 96 to 106 because the percent increase is much more substantial, you are using proportional reasoning.
Example of proportional reasoning
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• Suppose y = 3x + 2.• When you realize that if you multiply x
by 100, you almost, but not quite, multiply y by 100, you are using proportional reasoning.
Example of proportional reasoning
x 20 30 40 … 200 300 400
y 62 92 122 602 902 1202
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A Fermi problem, e.g.
Estimate the number of square centimetres of pizza that all of the students in Toronto eat in one week.
Example of proportional reasoning (maybe)
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• Proportion:
• Proportional: Two variables are proportional if the values of one are a constant multiple of the corresponding values of the other.
Some other definitions
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• Ratio:
Some other definitions
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• Rate: A comparison of two values with different units*
• Percent: A ratio with a second term of 100
Some other definitions
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Why is it important?
Proportional reasoning
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Why are they useful?
Big ideas
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The list of big ideas we will be using is listed in your program.
Big ideas relevant to proportional reasoning
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• Match the provided questions in your grade band (PJ, JI, IS) to the big ideas.
Matching activity
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Complete:
• At this point, I think the value of focusing on the same big ideas in proportional reasoning K-12 might be that…..
Reflection