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## April Showers Bring May Flowers

Given the numbers and data at our fingertips in this digital age, mathematical and digital literacy skills are imperative when it comes to understanding natural and social phenomena and making good decisions. As teachers we are responsible for helping students make sense of this information

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## Fostering Quantitative Reasoning Through a Question of Fairness

An instructional activity positions students’ quantitative reasoning as the central mechanism of problem solving based on the notions of fairness and reasonableness.

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## GPS: Replicating Patterns

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

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## The Hidden Beauty of Complex Numbers

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## Simple Mathematical Model for Designing a Corbeled Arch

This mathematical method can be used to find the size and shape of the bricks necessary to create a corbeled arch of nearly any shape. This method focuses on finding the minimum lengths of the bricks necessary to create a mathematically stable arch subject to certain constraints.

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## Teaching Angle as Turn Using a Code.org Lesson

Elementary school students use physical manipulatives (e.g., pattern blocks) to make sense of the geometry and measurement ideas in a Code.org block-based programming lesson.

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## Building Equitable Math Talk Classrooms

The power of Number Talks and extensions that can build to an equitable Math Talk Classroom

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## Chalk Talk: Engaging All Students in Visible Thinking

We share two examples of student engagement in visible, mathematical thinking through a Chalk Talk within the four walls of the classroom, as well as the connected spaces of online learning. Five steps for facilitating the Chalk Talk are outlined, with descriptions of teacher moves for each step.

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## Computer-Supported Assessment of Geometric Exploration Using Variation Theory

We report on an innovative design of algorithmic analysis that supports automatic online assessment of students’ exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic activity format for if–then propositions and implemented the activity on a platform that collects and analyzes students’ work. Finally, we searched for ways to use variation theory to analyze ninth-grade students’ recorded work. We scored and classified data and found correlation between patterns in exploration stages and the conjectures students generated. We demonstrate how automatic identification of mistakes in the early stages is later reflected in the quality of conjectures.

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## Crack the Code

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.