8 of 8 Items .... Type: Comparisons

Problems, Questions, and Puzzles to spark discussion and argument in the maths classroom.

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A slightly different question about tangential circles and the spaces in between.




Compare this question to the following, from the 2004 SAT Practice Test:





  • Which question seems harder? What are the difficult aspects of each?

  • Do we have to specify the angle APB?

  • How are these two questions different in terms of the knowledge they require for solving?

  • Is this question made harder by the "how many times" part? Does that phrasing make the question unnatural?


.: [GEOM], [Emma Bell], [Comparisons].

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Scenario 1: Which winning number group is more likely to occur?


1-2-3-4-5-6 OR 4-8-15-16-23-42


Scenario 2: Which winning number group is more likely to occur if the numbers are drawn in any order and THEN put into ascending order by the presenter?

1-2-3-4-5-6 OR 4-8-15-16-23-42


In which of the above two scenarios is getting the winning numbers more likely?


.: [STATS], [Jeff Suzuki], [Comparisons].

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We've all seen this problem, but many of our students haven't. It's the related rate problem from calculus: the balloon being filled with air.

There are two questions being demonstrated here.
(1) "If the volume increases at a constant rate, what is happening to the radius?" and
(2) "If the radius increases at a constant rate, what is happening to the volume?"

The first question is to figure out which situation is modeled in red and which in blue.
Then we can ask:


  • Does the radius increase at a constant speed in both models? How can you tell?

  • Does the volume increase at a constant speed in both models? How can you tell?

  • Where or how, in the RealWorldtm, could we see the constant increase in volume?

  • Where or how, in the RealWorldtm, could we see the constant increase in radius?


.: [CALC], [Kate Nowak], [Comparisons].

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Which is true?


Left side is larger than Right side
Right Side is larger than Left Side.
The two sides are equal.
Not enough information?



How can we deal with this WITHOUT a calculator?


.: [SAT], [Curmudgeon], [Comparisons].

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Which one is the better question?

Which one is easier to solve?


.: [GEOM], [internet], [Comparisons].

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Which lock is more secure?

1.



2.



3. (three numbers needed)



.: [PROBABILTY], [T.R.Milne], [Comparisons].

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Which one is most secure?

Three numbers ...




This one with three extra wheels you can swap in ...



Or this one, with three letters?



.: [PROBABILTY], [T.R.Milne], [Comparisons].

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Is this the largest parabolic segment that can fit in a square?



... You sure this one isn't just a little bit larger?



.: [PRE-CALC], [Matt Enlow], [Comparisons].
that's it.