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## Puddle Play!

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## You Must Be Joking!

May 2020 For the Love of Mathematics Jokes

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## GPS: Working Backward with Data

This month's Growing Problem Solvers focuses on Data Analysis across all grades beginning with visual representations of categorical data and moving to measures of central tendency using a “working backwards” approach.

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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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## Math for Real: Shaking Things Up with the Richter Scale

### “when will I ever use this?”

This problem ties into the real-life measurement found in the Richter scale.

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## Arithmogons

Easy-to-design puzzles that encourage mathematical reasoning and promote numerical fluency, arithmogon puzzles are simple: Add the numbers in two circles to get the number in the square. Every month, this final page of the journal highlights a quick game, puzzle, activity, or instructional strategy and suggestions for teachers of different grade bands to use the idea in the classroom.

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## Everybody, SCATteR

Skip counting around the room (SCATR) is a strategy that promotes numerical fluency and attention to number relationships. Variations of SCATR for students in K'grade 6 are shared.

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## The Footprint Problem: A Pathway to Modeling

By exploring an open-ended investigation involving proportional reasoning, students were able to walk through both problem solving and modeling.

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## Student-Generated Questions in Mathematics Teaching

Exploring even something as simple as a straight-line graph leads to various mathematical possibilities that students can uncover through their own questions.