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.

### 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.

### Katherine Baker, Naomi A. Jessup, Victoria R. Jacobs, Susan B. Empson and Joan Case

Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

### 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.

### LouAnn H. Lovin

Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

### 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.

### Julie M. Amador, David Glassmeyer and Aaron Brakoniecki

This article provides a framework for integrating professional noticing into teachers' practice as a means to support instructional decisions. An illustrative example is included based on actual use with secondary students.

### Zandra de Araujo, Deborah Hanuscin and 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.