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## Making Connections Between Representations

Three approaches to the Doughnut task highlight how representing functions in multiple ways can support student understanding in interpreting key features of functions within a context.

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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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## Parameters, Sliders, Marble Slides, Oh My!

Three different technological activities to explore parameters of quadratic functions each has its own pros and cons.

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## Visualizing Complex Roots of a Quadratic Equation

A quadratic equation was the basis for activities involving both concrete and technological representations.

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## Pythagoras, PVC Pipes, and Pianos

This practitioner article describes a lesson carried out in a high school classroom at the conclusion of a unit on exponential growth. Two teachers use a series of music-related activities to engage students in using and connecting multiple representations of exponential growth while exploring musical frequencies on a piano.

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## #WODB: The Power of Dynamic Representations

Dynamic representations situated within a “Which One Doesn’t Belong?” routine can extend students’ exploration of functions and can enable a focus on the variant and invariant characteristics of mathematical objects.

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## Escape Room Math: Luna's Lines

An escape room can be a great way for students to apply and practice mathematics they have learned. This article describes the development and implementation of a mathematical escape room with important principles to incorporate in escape rooms to help students persevere in problem solving.

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## Planning Questions to Help Surface Understanding

Dude Perfect has one of the most popular YouTube channels in the United States. An example mathematical activity connected to a Dude Perfect video is described along with the incorporation of assessing and advancing questions.

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## Triangle Center Technology

The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.

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## Equivalent Expressions Using CAS and Paper-and-Pencil Techniques

Designing activities to reconcile multiple representations supports students' focus and fluency.