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## The Opportunities of No-Solution Problems

When students encounter unusual situations or exceptions to rules, they can become frustrated and can question their understanding of particular topics. In this article, I share some practical tips.

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## Triangle Center Technology

The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.

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## Patterns on a Calendar

### big solutions to little problems

Solutions to a previous Solve It problem are discussed, and the procedures used with problem solving are explored.

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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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## Improving Preservice Secondary Mathematics Teachers' Capability With Generic Example Proofs

Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.

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## Mathematical Explorations: Visualizing Algebraic Rules for the nth Term

This article describes a visual method for finding the algebraic rule for the nth term using tile pictures. Activity sheets are included.

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## Music Cards

Students display a wide variety of creative mathematical thinking and misconceptions when they complete a classroom task that focuses on proportional reasoning.

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## Mysterious Subtraction

Conjecturing is central to the work of reasoning and proving. This task gives fourth and fifth graders a chance to make conjectures and prove (or disprove) them.

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## Cartoon Corner: Let's Talk Turkey

A cartoon that explores how much turkey to serve is coupled with a full-page activity sheet.

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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.