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## A Science Analogy for Understanding Mathematical Structure

This lesson uses the pH scale to build students’ understanding of the additive identity and inverse. It also gives suggestions for how to extend the lesson to multiplication.

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## Smiles: A Strengths-Based On-Ramp Mathematics Task

Use this activity to support students in working together, recognizing one another’s contributions, and leveraging their mathematical strengths to solve challenging problems.

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## GPS: How Does It Grow?

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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## Facilitating Student-Created Math Walks

An example of an after-school club activity gives educators some tools and suggestions to implement such an approach in their schools.

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## Improving Understanding of Mathematical Equivalence

Modify arithmetic problem formats to make the relational equation structure more transparent. We describe this practice and three additional evidence-based practices: (1) introducing the equal sign outside of arithmetic, (2) concreteness fading activities, and (3) comparing and explaining different problem formats and problem-solving strategies.

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## Focusing on Visual Representations in Mathematics

The authors outline the importance of using variety when teaching mathematics.

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## Fact Strategy Instruction + Meaningful Discourse = Student Understanding

This article provides actionable steps and tools for teachers to use to promote student discourse while teaching multiplication fact strategies.

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## Conditional Reasoning Online with Mastermind

As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.

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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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## GPS: Equivalent Expressions

Equality is one of the main concepts in K–12 mathematics. Students should develop the understanding that equality is a relationship between two mathematical expressions. In this month's GPS, we share tasks asking students one main question: how do they know whether or not two mathematical expressions are equivalent?