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

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### 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.

### 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.

### WenYen (Jason) Huang

The author discusses “synthesizing" teaching practice, which encourages students to explore patterns and its underlying mathematics structure through technology.

### Michael S. Meagher, Michael Todd Edwards, and S. Asli Özgün-Koca

Using technology to explore a rich task, students must reconcile discrepancies between graphical and analytic solutions. Technological reasons for the discrepancies are discussed.

### Xi Yu

When learning is virtual and students’ webcams are turned off, the ways that we interacted in an in-person classroom fall short. These six strategies for hearing from all students during whole-group instruction and small-group work honor students’ need to keep their webcams off.

### Marina Goodman

Bridge the digital divide by teaching students a useful technological skill while enhancing mathematics instruction focused on real-life matrix applications.

### Maria de Hoyos

To ensure that technology use benefits all students, it must be accessible with respect to cost and ease of use. Moreover, technology needs to be integrated by considering it from the perspective of the curriculum.

### Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.