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## You Must Be Joking!

May 2020 For the Love of Mathematics Jokes

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## Triangles from Three Points

Using technology to solve triangle construction problems, students apply their knowledge of points of concurrency, coordinate geometry, and transformational geometry.

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## Technology-Enhanced Discovery

Exploration, innovation, proof: For students, teachers, and others who are curious, keeping your mind open and ready to investigate unusual or unexpected properties will always lead to learning something new. Technology can further this process, allowing various behaviors to be analyzed that were previously memorized or poorly understood. This article shares the adventure of one such discovery of exploration, innovation, and proof that was uncovered when a teacher tried to find a smoother way to model conic sections using dynamic technology. When an unexpected pattern regarding the locus of an ellipse's or hyperbola's foci emerged, he pitched the problem to a ninth grader as a challenge, resulting in a marvelous adventure for both teacher and student. Beginning with the evolution of the ideas that led to the discovery of the focal locus and ending with the significant student-written proof and conclusion, we hope to inspire further classroom use of technology to enhance student learning and discovery.

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## Using KenKen to Build Reasoning Skills

Through KenKen puzzles, students can explore parity, counting, subsets, and various problem-solving strategies.

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If students suspect that a problem is solvable, they will persevere in their efforts to analyze and solve it.

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## Improving Student Reasoning in Geometry

Parallel geometry tasks with four levels of complexity involve students in writing and understanding proof.

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## Counterexamples as Starting Points for Reasoning and Sense Making

Asked to “fix” a false conjecture, students combine their reasoning and observations about absolute value inequalities, signed numbers, and distance to write true mathematical statements.

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## Geometric Reasoning about a Circle Problem

An open-ended problem about a circle illustrates how problem-based instruction can enable students to develop reasoning and sense-making skills.

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## Thinking Like a Mathematician

The moves that mathematicians use to generate new questions can also be used by teachers and students to tie content together and spur exploration.

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## Fifteen: Combining Magic Squares and Tic-Tac-Toe

The game Fifteen can motivate students to develop problem-solving skills and mathematical thinking.