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## Envelope Curves Unify Sinusoidal Graphing

Transferring fundamental concepts across contexts is difficult, even when deep similarities exist. This article leverages Desmos-enhanced visualizations to unify conceptual understanding of the behavior of sinusoidal function graphs through envelope curve analogies across Cartesian and polar coordinate systems.

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## Modeling a Bouncing Ball with Exponential Functions and Infinite Series

We modify a traditional bouncing ball activity for introducing exponential functions by modeling the time between bounces instead of the bounce heights. As a consequence, we can also model the total time of bouncing using an infinite geometric series.

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## Building a Strong Conception of the Number Line

This manuscript discusses two important ideas for developing student foundational understanding of the number line: (a) student views of the number sequence, and (b) recognizing units on the number line. Various student strategies and activities are included.

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## GPS: From Folding to Dynamic Geometry Environments

In this month's Growing Problem Solvers, we focused on supporting students' understanding of congruence and similarity through rigid motions and transformations. Initial understandings of congruence and similarity begin in first grade as students work with shapes in different perspectives and orientations and reflect on similarities and differences.

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## Learning Exponential Functions through Experiments

This article describes physical activities and modeling process through which–exponential patterns are understood and felt.

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## Problems to Ponder

Problems to Ponder provides 28 varied, classroom-ready mathematics problems that span grades PK-12, arranged in order of grade band. Links to the problem answers are available in this department.

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## Quick Blocks: Developing Spatial Sense

This article shares the importance of giving K-12 students opportunities to develop spatial sense. We explain how we designed Quick Blocks as an activity to engage our students in both spatial reasoning and number sense. Several examples of students thinking are shared as well as a classroom dialogue.