As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.

# Browse

### Matt Enlow and S. Asli Özgün-Koca

Equality is one of the main concepts in K–12 mathematics. Students should develop the understanding that equality is a relationship between two mathematical expressions. In this month's GPS, we share tasks asking students one main question: how do they know whether or not two mathematical expressions are equivalent?

### Scott Corwin, Michelle Cascio, Katherine Emerson, Laura Henn, and Catherine Lewis

Our middle school mathematics department used lesson study to investigate how to introduce fractions division to our sixth-grade students. We highlight our learnings during the Study and Plan phases, describe our observations during the lesson, and provide tips for educators interested in using lesson study to study their own content.

### Jennifer A. Czocher, Diana L. Moss, and Luz A. Maldonado

Conventional word problems can't help students build mathematical modeling skills. on their own. But they can be leveraged! We examined how middle and high school students made sense of word problems and offer strategies to question and extend word problems to promote mathematical reasoning.

### Amber G. Candela, Melissa D. Boston, and Juli K. Dixon

We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.

### Ryan Seth Jones, Zhigang Jia, and Joel Bezaire

Too often, statistical inference and probability are treated in schools like they are unrelated. In this paper, we describe how we supported students to learn about the role of probability in making inferences with variable data by building models of real world events and using them to simulate repeated samples.

### Dr. Zandra de Araujo, Ms. Deborah Hanuscin, and Ms. Samuel Otten

In this paper we discuss different ways teachers can integrate science and mathematics into their curriculum. In particular, we focus on science and mathematics integration via the disciplinary practices.

### Erin E. Baldinger, Matthew P. Campbell, and Foster Graif

Students need opportunities to construct definitions in mathematics. We describe a sorting activity that can help students construct and refine definitions through discussion and argumentation. We include examples from our own work of planning and implementing this sorting activity to support constructing a definition of linear function.

### Krista L. Strand and Katie Bailey

K-5 teachers deepen their understanding of the Common Core content standards by engaging in collaborative drawing activities during professional development workshops.

### 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.