One of the many benefits of teaching mathematics is having the opportunity to encounter unexpected mathematical connections while planning lessons or exploring ideas with students and colleagues. Consider the two problems in **figure 1**.

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### Lee Melvin M. Peralta

### Clayton M. Edwards, Rebecca R. Robichaux-Davis, and Brian E. Townsend

Three inquiry-based tasks highlight the planning, classroom discourse, positive results, and growth in one class's journey.

### Stephen Phelps

### Edited by Anna F. DeJarnette

A monthly set of problems targets a variety of ability levels.

### Jo Boaler

Engage your learners through tasks proven to significantly promote reasoning and problem solving, which touch on many of the Mathematics Teaching Practices in *Principles to Actions: Ensuring Mathematical Success for All*. These tasks are discussed in this article, another installment in the series.

### Lingguo Bu

The rise of dynamic modeling and 3-D design technologies provides appealing opportunities for mathematics teachers to reconsider a host of pedagogical issues in mathematics education, ranging from motivation to application and from visualization to physical manipulation. This article reports on a classroom teaching experiment about cube spinning, integrating traditional tools, GeoGebra (www.geogebra.org), and 3-D design and printing technologies. It highlights the rich interplay between worthwhile mathematical tasks and the strategic use of diverse technologies in sustaining sense making and problem solving with a group of prospective teachers.

### Low Chee Soon

Use freedom of choice to promote students' mathematical flexibility.

### Karen D. Campe

There is a distinction between using technology as a tool for doing mathematical tasks and using it to develop conceptual understanding (Dick and Hollebrands 2011). In this article, the table feature of the TI-84 Plus graphing calculator is used in the second role, enabling students to participate in the reasoning and sense-making process. This article showcases four classroom activities that use tables as a dynamic tool for inquiry, applying numerical representations to algebraic, graphical, and geometric phenomena. Although these activities are presented using the TI-84 Plus CE graphing calculator, other calculator and computer platforms can be employed; see the Teacher Guide in **more4U** for details.

### Peter Wiles, Travis Lemon, and Alessandra King

Students move from slides, flips, and turns into reasoning about the characteristics of rigid transformations.