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