12 of 466 Items .... Course: GEOM

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

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Does the topology matter? If I were to completely separate the two halves, would it make a difference?


.: [GEOM], [internet], [Topology].

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Can you come up with other, better, divisions?









.: [GEOM], [Don Steward], [Understandings].

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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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What car will have the shorter path?

How could you tell for certain?




.: [GEOM], [Justin Aion], [Which Would You Choose?].

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This is a straightforward question. I'd like to make all of you students into teachers for a minute ... Let's create a test question!


  • Do we have to specify angle AOB?

  • Is there a better way to say something without actually saying it?

  • What other instructions and given information could we provide that would lead to the same answer?

  • What is the best question here?



.: [GEOM], [Emma Bell], [What Questions].

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On a square lattice, a circle can pass through 2, 3, or 4 points, as in the diagram below. The original question asks for a circle that passes through 5 points, but can you define a circle that passes through other numbers of points? and explain how the circle was created?




.: [GEOM], [Matt Enlow], [Puzzle].

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If we are told that we have a quadrilateral inscribed in a circle with diameter 10, do we KNOW if the angle at B and the angle at D are \( 90^o \)? Because that sure would make it easier to find x.



.: [GEOM], [internet], [Wait. Really?].

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If the time is 10:10, what is the exact angle between the minute hand and hour hand?

How about 7:30?

How about 7:35?


.: [GEOM], [internet], [Puzzle].

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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 is the red area?

The two vertices of the square are the centers of two tangent and congruent circles. If the length of a side is \( 8\sqrt{2} \), what is the area of the red part peeping out?

Here is another question: Does it matter if the circles are congruent, as long as they're tangent and the centers are at the vertices of the square?


.: [GEOM], [David Marain], [Geometry Snacks].

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What's the angle between the red lines?


.: [GEOM], [internet], [New Understanding].

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W

The Salinon was first introduced in the Book of Lemmas, a work attributed to Archimedes


.: [GEOM], [Cliff Pickover], [Geometry Snacks].