The authors introduce an activity involving “follow-up equations” to connect with ideas children have already expressed during fraction problem solving.

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### Victoria R. Jacobs, Susan B. Empson, Joan M. Case, Amy Dunning, Naomi A. Jessup, Gladys Krause, and D’Anna Pynes

### Victor Mateas

How trigonometry is used and portrayed differently in mathematics and physics textbooks highlights potential sources for student struggle, constraints on our trigonometry curriculum, and lessons learned when looking across STEM disciplines.

### Sandra J. Miles

This lesson uses the pH scale to build students’ understanding of the additive identity and inverse. It also gives suggestions for how to extend the lesson to multiplication.

### Travis Lemon

We can be catalysts for change in mathematics classrooms. One example shared, hopefully many more are inspired by these words.

### Jenna R. O’Dell, Cynthia W. Langrall, and Amanda L. Cullen

An unsolved problem gets elementary and middle school students thinking and doing mathematics like mathematicians.

### Akihiko Takahashi, Makoto Yoshida, and Introduction by: Dewey Gottlieb

From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.

### Rachel Wiemken, Maria Nielsen Stewart, Gabriel Matney, Timothy Folger, and Tami Matney

This department provides a space for current and past PK–12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

### Amanda T. Sugimoto and Heidi Meister

The authors draw on collaboration with a group of teachers to describe how three-act tasks could be (re)designed and implemented for online synchronous and asynchronous learning, identifying technological factors that teachers might consider.

### Lara K. Dick, Mollie H. Appelgate, Dittika Gupta, and Melissa M. Soto

A group of mathematics teacher educators (MTEs) began a lesson study to develop a research-based lesson to engage elementary preservice teachers with professional teacher noticing within the context of multidigit multiplication. Afterward, MTEs continued teaching and revising the lesson, developing an integrated process that combined lesson study with the continuous improvement model. This article introduces the continuous improvement lesson study process, shares an example of how the process was used, and discusses how the process serves as a collaborative professional development model for MTEs across institutions.

### Hyunyi Jung, Ji-Won Son, and Ji-Yeong I

Use a COVID-19 lesson as an example of how to apply a framework aligned with research recommendations to support students as they apply mathematics to real life.