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Mathematizing the World: Seeing Reasonable Math in the World All Around Us Tyee Middle School Bellevue, Washington April, 2015 Mark Roddy, Ph.D. Seattle University Master in Teaching Program
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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.
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10 cm in 10 minutes => 1 cm/min Wow! … really?? 2 highs and 2 lows/day => 6 hours between Each high and low …. 15 ft high and -1 ft low => 16 ft change 16 ft is ~5m = 500 cm and 6 hours is 6 x 60 = 360 minutes So 500 cm/360 min … = ~1.4 cm/minute! and …. And now, …
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Eight cups cooling But hold on! Is this really math? science?
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Represent and interpret data; Analyze patterns and relationships; Understand ratio concepts and use ratio reasoning to solve problems; 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; 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….
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Eight cups cooling
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What if I used a glass instead of a mug? Which cup cools fastest? Why does the metal travel 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? 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, …
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70 years - - - - - - - - - - -- - - - - - - - - - - - - - - - - -
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Does a tree continue putting on weight (mass) at the same rate, or does that slow down as it gets older?
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ArborDay.org [ http://www.arborday.org/trees/treeGuide/ ]http://www.arborday.org/trees/treeGuide/ Douglas Fir Medium Growth => 13-24 “/year 1.5 ft/year 70 years x 1.5 ft/year =105 feet √ 671 in 3 5,278 in 3 12,260 in 3 18,653 in 3 90,914 in 3
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Sunlight, CO 2, H 2 O -> Glucose, O 2 Each year terrestrial and marine plants make enough glucose to fill a freight train 30 million miles long.
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1 cm 3 of water weighs a gram. 1 inch = 2.54 cm, so 1 in 3 = 2.54 3 cm 3 = 16.39 cm 3 So … 138,627 in 3 = 2,271,690 cm 3 Wood floats … estimate.5 grams/cm 3 ~ 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/cm 3, that’s.5 x 2,271,690 cm 3 = 1,135,845 gr
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mathematizing.wikispaces.com
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