Archive for the ‘Uncategorized’ Category

Exchange Rates

Posted: January 18, 2011 in Uncategorized
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Talking about proportions in my Pre-Pre-Algebra class (called Integrated Math).   We got on the topic of exchange rates.  A student asked how you can make money through exchange rates.   I’m a big fan of these Google graphs.  Lots of questions to ask.   We assumed we invested $1000 in Euros and exchanged them again to see if we made profits.  Lots of questions you can explore here…. also a very scalable problem for higher classes.

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Metrodome Collapses

Posted: December 17, 2010 in Uncategorized
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River Falls got around 20 inches of snow over the weekend and it caused some havoc in our area.  The most popular story being the Metrodome’s roof collapsing.   Here is the video:

The student’s came up with a quick list of questions:

… The best question being  “Why did Brett do it?”.   Just Kidding.  The real question we wanted to pursue was “How much weight did the snow put on the roof?”.  I printed off a few resources for the students to use as they came up with their estimations:

The Storm
Metrodome Statistics
Snow to Liquid
Weight of Water
 

Our Solution

Our estimate was  about 3,852,429.412 pounds.

Varying the snow density

Let d = the number of inches of snow it takes to make one inch of water

w = \frac{17 in}{d} \cdot \frac{1ft}{12in} \cdot \frac{435600ft^2 }{1} \cdot \frac{62.42796 lbs}{1 ft^3}

w = \frac{38524294.12}{d}

More questions to consider

– How was the snow distributed on the dome?

– What type of shape is the roof?

– What was the exact snow to water ratio?

– How does temperature relate to snow density?

Conclusion

I like this video because it’s relevant, fun to watch, and stirs up a lot of questions.  I think we just scratched the surface on some of the math you could do with this video.    We covered: conversions, volume, area, estimation, ratios, density, rational functions.  I think this would also work great in a geometry class or lower.

Since state testing is going on this week, my Algebra 2 first block class was ahead of the other class.  I decided to take on one of Dan Meyer’s WCYDWT problems and see what the students came up with.  To set the stage, we first looked at a Jacoby Ford video where he takes it 94 yards for a touchdown.  We talked about a common football player benchmark, the 40 yard dash. 

Video:

We paused it at about 1:37 and the students came up with questions that they had towards the video. 

They came up with a list very fast.  We decided  to analyze the speed at Rich Eisen was running.  The question we started with was

“How fast is Rich moving?”

Sub-Questions:

“How can we measure speed if it is changing?”

“How long should the distance intervals be?”

“How can we minimize error in our calculations?”

Students decided we would need stopwatches.  Luckily I had a box of them =)  Students got into groups and we decided to give each of them different 10 yard intervals to analyze.   We replayed the video and about 20 stopwatches went to work.

Our data:

Students got 4 times for each interval and decided taking an average of these was a good idea.  Next they needed to figure out how to change it to miles per hour which we decided before would be our units.  They went through the unit conversions and put their answers on the board. 

We also put up a distance vs. time graph from our data:

 

Questions:

“What do you think the graph will look like”  (asked before we graphed it obv)

“How would the graph continue if it were 100 yards? 200 yards? ”

“How long does it take for a typical athlete to reach top speed?”

“What would it look like if Rich truly ran like our graph?”

“How is the slope changing?”

“How would this graph compare to Jacoby Ford’s graph?”

“Sources of error?”, “How can we improve?”

“If given a 5 yard head start, where would Rich and Jacoby’s graph cross?”

“What type of function best reprents the start and end of his run?”

Conclusion:

As we watched the ending part of the video, students became very interested to see the reults.  We noticed that when we stopped the video after the 10 yard mark the speed was higher than our interval speed so we got to have a discussion on average vs. instant speed.  How could we get our average speed closer to the instant speed?  Little did they know, the students started thinking about a Calculus topic.  The students and our discussion came up with more questions than we could handle, which was a good thing.  Props to Dan Meyer for the idea.