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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### Alice Aspinall

This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.

### Elizabeth G. Arnold, Elizabeth A. Burroughs, Mary Alice Carlson, Elizabeth W. Fulton, and Megan H. Wickstrom

Ear to the Ground features voices from several corners of the mathematics education world.

### Paula Beardell Krieg

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.

### Xiaobo She and Timothy Harrington

Get familiar with this visual instructional tool to help students make sense of mathematical relationships and select suitable operations for word problems at varied grade levels.

### Megan H. Wickstrom

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.

### Jere Confrey, Meetal Shah, and Alan Maloney

Three learning trajectories and their connections show how to promote vertical coherence in PK–12 mathematics education.

### Caleb Goff

This article describes how using music and the TikTok platform can help students recall mathematical definitions in a whimsical and relatable way.

### Corinne Thatcher Day

This hands-on task, featuring differentiation and open-ended learning, sets up students to discover area models for themselves. Organized around NCTM’s eight teaching practices from *Principles to Actions*, this article describes the task’s setup and implementation.

### Jennifer Albritton

I have developed a deep appreciation for and love of mathematics by using famous works of art as a bridge to energize my mathematics teaching and inspire my students.