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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### Anne Quinn

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.

### Carolyn James, Ana Casas, and Douglas Grant

Encouraging students to justify earlier as they attempt to solve an open-ended task can lead to greater understanding and engagement.

## Patterns on a Calendar

### big solutions to little problems

### Jo Ann Cady and Pamela J. Wells

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

### Patrick M. Kimani, Dana Olanoff, and Joanna O. Masingila

The Mathematics Teaching Practices open the door to helping students engage with meaningful mathematics.

## Mathematical Explorations: A New Twist on Collaborative Learning

### classroom-ready activities

### Stephanie M. Butman

Research on students' learning has made it clear that learning happens through an interaction with others and through communication. In the classroom, the more students talk and discuss their ideas, the more they learn. However, within a one-hour period, it is hard to give everyone an equal opportunity to talk and share their ideas. Organizing students in groups distributes classroom talk more widely and equitably (Cohen and Lotan 1997).

## Mathematical Explorations: Find the Distance: No Formula Necessary

### classroom-ready activities

### Ryota Matsuura and Yu Yan Xu

This activity involves finding the distance between two points in a coordinate plane and emphasizes reasoning from repeated calculations, which is one of the mathematical practices specified by the Common Core State Standards for Mathematics.

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

### “when will I ever use this?”

### Fred Dillon and Kevin Dykema

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

### D. Bruce Jackson

Given two slices of bread—a problem and the answer—students fill in the fixings: their own mathematics reasoning.

### Jane M. Wilburne and Ashley Kulbacki

A sixth-grade teacher's word task uncovers higher-level thinking and engages her students in the Standards for Mathematical Practice.