The Trammel of Archimedes traces an ellipse as the machine’s lever is rotated. Specific measurements of the machine are used to compare the machine’s actions on GeoGebra with the graph of the ellipse and an ellipse formed by the string method.

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### George J. Roy, Matthew Cunningham, and Kenneth Rafanan

Teachers have the opportunity to make mathematics relevant. We leveraged the popularity of *Star Wars* to engage students in exploring and connecting two dimensions and three dimensions to careers in toy design.

### Arsalan Wares and David Custer

This pattern-related problem, appropriate for high school students, involves spatial visualization, promotes geometric and algebraic thinking, and relies on a no-cost computer software program.

### Kate Roscioli and Jennifer Suh

Learn how to engage students in geometry concepts through a real-world task that leverages GeoGebra to provide students with generalization and authorship opportunities.

### T. Royce Olarte and Sarah A. Roberts

Teachers can implement a mathematics language routine within in-person/hybrid and remote instructional contexts.

### Lara K. Dick, Amanda G. Sawyer, Margaret MacNeille, Emily Shapiro, and Tabitha A. Wismer

We investigate resources on TeachersPayTeachers and discuss how what is available affects our teaching practices.

### Margaret Rathouz, Nesrin Cengiz-Phillips, and Angela S. Krebs

Issues of equity in mathematics classrooms existed prior to COVID-19. For many students, however, meaningful participation in mathematical discussions became nearly impossible in online settings during the pandemic. In this study, we note the diversity in and nature of participation in mathematical discourse in an online course for preservice teachers (PSTs). We investigate the influence of implementing two support strategies for discussion: (a) establishing a “rough-draft/revision” orientation to mathematical tasks; and (b) providing time and structure (tasks and prompts) in an online discussion board for PSTs to post their initial thoughts, react to peers’ solutions, and collectively revise their ideas. In this article, we highlight several benefits of these support strategies to equitable PST participation in a unit on number theory. For example, as compared with oral discussions where only a few PSTs offered their ideas, the written discussion format encouraged every PST to post their ideas. Using a rough-draft/revision stance in the prompts fostered sharing and revealed diverse mathematical approaches, perspectives, and ideas. We argue that giving students opportunities to interact with one another and the mathematics in a variety of ways promotes equitable participation.

### Sheldon P. Gordon and Michael B. Burns

We introduce variations on the Fibonacci sequence such as the sequences where each term is the sum of the previous three terms, the difference of the previous two, or the product of the previous two. We consider the issue of the ratio of the successive terms in ways that reinforce key behavioral concepts of polynomials.

### Ruthmae Sears

This article describes how visual representations can help develop students’ reasoning and proof skills.

### Hanan Alyami

During a Desmos activity, students adjust the measures of angles in radians to reposition a laser and a mirror so the beam passes through three stationary targets. The Radian Lasers activity can be extended to simulate project-based learning.