Mathematizing the World: Seeing Reasonable Math in the World

All Around Us

Tyee Middle SchoolBellevue, Washington

April, 2015

Mark Roddy, Ph.D. Seattle University

Master in Teaching Program

Mathematizing is the quantification and analysis of things happening all around

us, like music, sunlight, trees and coffee, and it enables the construction of

mathematical understanding that lasts.

10 cm in 10 minutes => 1 cm/min

Wow!… really??

2 highs and 2 lows/day => 6 hours betweenEach high and low ….

15 ft high and -1 ft low => 16 ft change

16 ft is ~5m = 500 cmand 6 hours is 6 x 60 = 360 minutes

So 500 cm/360 min …

= ~1.4 cm/minute!

and ….And now, …

Eight cups coolingBut hold on! Is this really math? science?

According to our newest standards, students will … CCSSm NGSS

Represent and interpret data;

Analyze patterns and relationships;

Understand ratio concepts and use ratio reasoning to solve problems;

Represent and analyze quantitative relationships between dependent and independent variables;

Understand the connections between proportional relationships, lines, and linear equations;

Use functions to model relationships between quantities.

Construct and present arguments using evidence to support the claim that .…

Plan an investigation to provide evidence that ….

Conduct an investigation and evaluate the experimental design to provide evidence that ….

Develop a model that predicts and describes ….

Ask questions about data to determine the factors that ….

Gather and make sense of data in order to describe….

Eight cups cooling

Eight cups cooling

What if I used a glass instead of a mug?

Which cup cools fastest?

Why does the metal tra

vel cup work so well?

Would a grande cool at the same rate as a venti?

Why is the cup warmer so useless?

Why are the curves … curved? Why not straight?

What if we did this with cold drinks warming up?

Salt makes ice melt. Does sugar

make coffee stay hot longer?

And now, …

70 years• - - - - - - - - - - -- - - - - - - - - - - - - - - - - -•

Does a tree continue

putting on weight (mass)

at the same rate, or

does that slow down

as it gets older?

Stand Back!I’m going to try MATH!

ArborDay.org [ http://www.arborday.org/trees/treeGuide/ ]

Douglas Fir Medium Growth => 13-24 “/year

1.5 ft/year70 years x 1.5 ft/year =105 feet √

More Math!

671 in3 5,278 in3 12,260 in3 18,653 in3 90,914 in3

Sunlight, CO2, H2O -> Glucose, O2

Each year terrestrial and marine plants makeenough glucose to fill a freight train 30 million miles long.

But how much does all that weigh?

But how much does all that weigh?

1 cm3 of water weighs a gram.

1 inch = 2.54 cm, so 1 in3 = 2.543 cm3 = 16.39 cm3

So … 138,627 in3 = 2,271,690 cm3

Wood floats … estimate .5 grams/cm3

~ 1,136 kg = 2,500 lbs! And now it’s firewood.

100 ft ÷ 1.5ft/round = about 67 rounds About 250 split pieces of firewood

~10 lbs apiece

At .5 gr/cm3, that’s .5 x 2,271,690 cm3 = 1,135,845 gr

mathematizing.wikispaces.com