9 of 9 Items .... Source: Patrick Honner

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

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To increase the volume of a cylinder, is it better to increase the radius or the height? Great conversation starter today.




.: [ALG1], [Patrick Honner], [New Understanding].

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Take a polynomial, divide by \((x-a)^2\), and the remainder is the tangent line at \(x=a\).

Magic!

Wait ... Are we sure this works?








.: [PRE-CALC], [Patrick Honner], [New Understanding].

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Can you find the area of a triangle whose side lengths are 46, 85 and 38?


.: [GEOM], [Patrick Honner], [Puzzle].

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Find a perfect square, all of whose digits are in the set {2, 3, 7, 8}.


.: [MS Math], [Patrick Honner], [Explainer].

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Let \( f(x) = 2x^3 + bx^2 + cx + d\). Find integers b, c and d such that \(f(\frac{1}{4}) = 0\).


.: [PRE-CALC], [Patrick Honner], [Impossible Problem].

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Try to find six consecutive integers that sum to 342


.: [MS Math], [Patrick Honner], [Impossible Problem].

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Find the cubic polynomial with integer coefficients that has three complex roots.


.: [PRE-CALC], [Patrick Honner], [Impossible Problem].

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I invite students to create an unfair coin — one that is biased toward coming up heads or tails — that has the following property: When the coin is flipped twice, the results of the two flips are more likely to be different than the same. In other words, you’re more likely to get heads and tails than to get heads and heads or tails and tails.


.: [PROBABILTY], [Patrick Honner], [Impossible Problem].

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Construct a convex octagon with four right angles.

Does this one work?


.: [GEOM], [Patrick Honner], [Impossible Problem].
that's it.