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

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That's pretty much it: How many Geometry Theorems are needed to solve this extended problem?




.: [GEOM], [SolveMyMaths], [Strategy].

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Mr Smith has two children. One of them is a boy. What is the probability the other child is also a boy?


.: [PROBABILTY], [SolveMyMaths], [Puzzle].

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What positive and negative shapes (and their dimensions) go into making this yellow figure?

3

On a side note: isn't it cool that I can say the phrase "negative shape" and no one bats an eye?


.: [GEOM], [SolveMyMaths], [Explainer].

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In terms of "this inscribed in that", what do we have here?
Describe the squares and their sizes compared to the circle.

1. If you were to calculate distances (radii, side lengths) or areas, what given information would you like to start with and what would you like to solve for?


  • What "givens -- answer" path would be easiest?

  • What "givens -- answer" path would be difficult?

  • Which would you choose to give to your fellow students as a collaborative question?


N.B. The original question is slightly different. You can see it below.
Original image, click to enlarge.



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

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What's a good problem you can make based on this video?



https://pbs.twimg.com/tweet_video/B0Qu4GjIgAACdCD.mp4


.: [ALL], [SolveMyMaths], [Modeling].

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What might all these kids be proving?



.: [ALL], [SolveMyMaths], [Proof Without Words].

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What do you notice about the "orthic triangle"?




Is its area related to the area of ABC?

Is it similar?

What other triangles could be made with other features of triangle ABC (medians, angle bisectors)?


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

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Assume the vertex of the angle is at the center of the circle.
Should we add pieces together to make this or subtract pieces?
What are the relevant dimensions?


.: [GEOM], [SolveMyMaths], [Raw Pure Math].

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Two opposite vertices of a square lie on a circle. Sure as sunrises, someone is going to ask about area.

What information do we need?

What would be the easiest scenario?

Is there more than one easy scenario?


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

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What question do you want your neighbor to answer here?




.: [GEOM], [SolveMyMaths], [Create a Problem].

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Here are twelve dots equally spaced around a circle. There are two triangles created by connecting three of the dots.

1. Which three dots will give the triangle with the LARGEST area?
2. Which three dots will give the triangle with the SMALLEST area?




Challenge:
What are those two areas?


.: [GEOM], [SolveMyMaths], [Raw Pure Math].

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This one is going to need a whole-class, team effort.




.: [GEOM], [SolveMyMaths], [Raw Pure Math].