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## A Radian Angle Measure and Light Reflection Activity

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.

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## Exploring Sequences Related to Medial Triangles

Sequences are an important topic—not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns that can be discovered with the use of dynamic geometry software (DGS) such as GeoGebra or Web Sketchpad. In addition, exploring sequences with DGS allows learners to formulate and test conjectures, an important mathematical process. In this article, I describe how my students used GeoGebra and geometric reasoning to visualize, discover, formulate,

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## Sea of Cycles

This article presents an example of discovering an idea through creative play. After some trial and error, I drew a wonderful image, which I later learned was a two-dimensional view of a four-dimensional shape called tesseract.

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## Area of a Changing Triangle: Piecing It Together

Examining the covariation of triangle dimensions and area offers a geometric context that makes analyzing a piecewise function easier for students.

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## Non-Euclidean Geometry Lesson Promotes Mathematical Reasoning

A two-day lesson on taxicab geometry introduces high school students to a unit on proof.

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## Everybody Still Plays: Virtual Engagement without Webcams On

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.

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## Graphing Technology Helps Narrow the Digital Divide

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.

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## Puddle Play!

For the Love of Mathematics

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## Student Engagement with the “Into Math Graph" Tool

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.

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## Examining Errors and Framing Feedback

Engaging mathematics students with peers in analyzing errors and formulating feedback improves disposition, increases understanding, and helps students uncover and correct misconceptions while informing opportunities for targeted instruction.