Plenary 1

• 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

• I need a volunteer.

• Can you please stand up?

• I need someone who is about 10% taller. Who are you?

Getting acquainted

• I need a volunteer.

• How many kilometres did you drive or fly to get here?

• Who came from about half as far?

Getting acquainted

• 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

• 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

• 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

Choice 1:

Choose a problem

• 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

• Create both an example and a non-example of proportional reasoning.

• Try to use different contexts than you just saw.

What is proportional reasoning?

SEE NEXT SLIDE

• 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

• 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

• 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

• 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

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)

• 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

• Ratio:

Some other definitions

• Rate: A comparison of two values with different units*

• Percent: A ratio with a second term of 100

Some other definitions

Why is it important?

Proportional reasoning

Why are they useful?

Big ideas

The list of big ideas we will be using is listed in your program.

Big ideas relevant to proportional reasoning

• Match the provided questions in your grade band (PJ, JI, IS) to the big ideas.

Matching activity

Complete:

• At this point, I think the value of focusing on the same big ideas in proportional reasoning K-12 might be that…..

Reflection