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## Student Engagement with the “Into Math Graph" Tool

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.

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## Using TileFarm to Support Emerging Multiplication

Symmetric dot patterns are a particularly powerful object for investigation, providing opportunities for foundational learning across PK–5. We found that second-grade students naturally used repeated addends to count symmetric dot patterns created using the new software TileFarm.

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## Partial Pies

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

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## Playing with Fractions

Constraints for social distancing require teachers to find creative ways to engage students. Consider this fun strategy for exploring fraction equivalence, addition, and subtraction in a game environment where students use self-made or digital manipulatives.

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## Technology Continues to Evolve

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.

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## Calculator Programming Engages Visual and Kinesthetic Learners

A programming activity helps students give meaning to the abstract concept of slope.

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## Generalizing: The Core of Algebraic Thinking

The meaningful use of symbols links context and generality.

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## Technology Helps Students Transcend Part-Whole Concepts

Explore a new app that allows students to develop a more sophisticated understanding of fractions.

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## Activities for Students: Soap and Slope: Mathematical Adventures in Fluid Dynamics

The mathematical concept of slope can be made real through a set of simple, inexpensive, and safe experiments that can be conducted in the classroom or at home. The experiments help connect the idea of slope with physical phenomena related to surface tension. In the experiments, changes in surface tension across the surface of the water, which correspond to greater slopes on the graph, lead to increased motion of the fluid. The mathematical content, targeted to middle school and high school students, can be used in a classroom or workshop setting and can be tailored to a single session of thirty to ninety minutes.

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## Sound Off!: The Myth of Differentiation in Mathematics: Providing Maximum Growth

After teaching high school mathematics in Maryland for three years, I began teaching sixth-grade mathematics in one of the best school districts in Pennsylvania (according to state test scores) and have been teaching there for the past six years. My high school teaching background led me to differentiate differently from my colleagues. I share my observations of the result of the differences in methodology and my conclusions from those observations, and I offer a plan to implement changes in the way that mathematics is taught.