Two classic hands-on tasks address conceptual understanding of functions. The tasks center student discourse and rough draft mathematics as students grapple with the relationship between input and output.

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### Karen Zwanch and Bridget Broome

This game teaches algebraic generalizations through differentiated play in pairs, small groups, or as a whole class and uses manipulatives to bridge numerical and algebraic thinking.

### Nasim Chenari

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

### Katherine Baker, Scott A. Morrison, and Mirella F. Cisneros Perez

Integrating mathematics and nature offers students benefits for physical and mental health and enriches their learning.

### Dorothy Y. White

Use this activity to support students in working together, recognizing one another’s contributions, and leveraging their mathematical strengths to solve challenging problems.

### 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.

### Michael Daiga and Shannon Driskell

The two provided activities are geared for students in middle school to facilitate and deepen their understanding of the arithmetic mean. Through these activities, students analyze visual representations and use a special type of statistical thinking called transnumerative thinking.

### Jennifer Marshall

A series of tasks encourage students to reflect on the reasonableness of their number sense and use benchmarks to refine their estimations.

### Theresa J. MacVicar, Amy R. Brodesky, and Emily R. Fagan

A teacher uses formative assessment interviews to uncover evidence of students’ understandings and to plan targeted instruction in a mathematics intervention class. We present an example of a student interview, a discussion of the benefits and challenges of conducting interviews, and actionable suggestions for implementing them.

Over the past 100 years, technology has evolved in unprecedented fashion. Calculators, computers, and smart phones have become ubiquitous, yet school mathematics experiences for many children still remain without many powerful technological tools for the exploration of mathematics. We consider the evolution of some tools as we imagine a future.