12 of 126 Items .... Type: Notice, Wonder

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

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In a set of data, can the outlier also be the mode or does a number stop being an outlier if it occurs often enough to be a mode?


.: [STATS], [T.R.Milne], [Notice, Wonder].

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Read this post on lost learning time.



Here's his basic point:

... roughly 10 of 60 minutes are not spent learning.
In one day, roughly 50 minutes.
In a 5 day week, 250 minutes.
In a typical school year, 8,700 minutes not utilized for learning.

Now, let's be realistic and cut that number in half because we all know there are assemblies and other events that cut into learning time throughout the school year. That leaves us with 4,350 minutes of time not spent learning.


  1. Do you agree with his analysis?

  2. How about his calculations?

  3. What should be done?



.: [ALL], [T.R.Milne], [Notice, Wonder].

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Consider a normal, everyday clock.

How many times per day do the hands make a straight angle? What are some of these times?

How many times per day do the hands make a right angle? What are some of these times?


.: [GEOM], [internet], [Notice, Wonder].

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What do you think? Where's the mistake and why do you think they presented it this way?




.: [MS Math], [Michael Pershan], [Notice, Wonder].

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Go to this page at Desmos, and hit play. Explain what you see and why it is behaving that way.













There is obvious symmetry in the figure at each value of a but should we be defining something new to describe the sequence of images? A dynamic symmetry, of sorts?


.: [PRE-CALC], [Curmudgeon], [Notice, Wonder].

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What do you see?
What do you wonder?


.: [PREALG], [David Wees], [Notice, Wonder].

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What do you notice?
What do you wonder?


.: [LOGIC], [Steve Wyborney], [Notice, Wonder].

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A closed rectangular box whose dimensions are 8 feet by 5 feet by 3 feet has some water in it. When the box is resting on its smallest face, the water is 5 feet deep. How deep will the water be if the box is resting on its largest face?


.: [MS Math], [internet], [Notice, Wonder].

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"The Wisconsin Republican's remarks, which received a standing ovation, started with the Badger State governor touting his middle class credentials. Before the speech, he had stopped by Kohl's Department Store and used Kohl's coupons to buy his sweater from the 70 percent off rack for one dollar.

Walker said he considered Kohl's successful low-price strategy a model for reforming the tax code so that more people pay taxes, but the tax rate is much lower."

What the easiest way to find out the original cost of that sweater?

From another site: "If you’ve ever shopped at Kohl’s, you know that it’s the store that generally always has a sale. Take a clearance item, apply a 15 percent off coupon with some Kohl’s Cash, and on the surface, Walker’s claim isn’t totally outrageous."


.: [PREALG], [internet], [Notice, Wonder].

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That's an 18" diameter pizza plate.
It's the same area as that slice.

What's the girl's name?

Oh, you think you have a better question? Well, do you?


.: [MS Math], [T.R.Milne], [Notice, Wonder].

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What question do you want to ask?


.: [PREALG], [T.R.Milne], [Notice, Wonder].

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Here are my three brackets:




Which of these is most useful in determining how many people are playing?
How jealous are you right now?


.: [PREALG], [T.R.Milne], [Notice, Wonder].