Teachers can more productively use board work to scaffold joint sense making.

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## Using Public Records to Scaffold Joint Sense Making

### Keith R. Leatham, Blake E. Peterson, Ben Freeburn, Sini W. Graff, Laura R. Van Zoest, Shari L. Stockero, and Nitchada Kamlue

## Prove It! Graph Theory and Induction: The Next Big Thing

### Jeffrey P. Smith

Eighth-grade students participated in a two-day lab exploring graph theory. In addition to learning about a completely new topic, they experienced a subtle introduction to proof by induction.

## GPS: Teaching Shapes Inclusively

### Samuel Otten, Tiffany J. LaCroix, Faustina Baah, and Rebekah Hanak

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.

## Teaching Is a Journey: From Apathy to Passion

### Taea Fonkert

This department provides a space for current and past PK-12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.

## Using Number Talks to Compare Fractions

### George J. Roy, Kristin E. Harbour, Christie Martin, and Matthew Cunningham

Using this strategy, a teacher facilitates a short conversation during which students verbally explain and justify reasoning. We have found that a coordinated series of number talks supports students’ reasoning when comparing fractions.

## Puddle Play!

### Deanna Pecaski McLennan

## Promoting Discourse: Fractions on Number Lines

### Susan Ahrendt, Debra Monson, and Kathleen Cramer

Examine fourth graders’ thinking about the unit, partitioning, order, and equivalence on the number line and consider ways to orchestrate mathematical discussions through the Five Practices.

## The Opportunities of No-Solution Problems

### Nicholas J. Gilbertson

When students encounter unusual situations or exceptions to rules, they can become frustrated and can question their understanding of particular topics. In this article, I share some practical tips.

## Seeing Algebraic Structure: The Rubik's Cube

### Amanda Milewski and Daniel Frohardt

Few high school students associate mathematics with playfulness. In this paper, we offer a series of lessons focused on the underlying algebraic structures of the Rubik's Cube. The Rubik's Cube offers students an interesting space to enjoy the playful side of mathematics, while appreciating mathematics otherwise lost in routine experiences.

## GPS: Working Backward with Data

### Matt Enlow and S. Asli Özgün-Koca

This month's Growing Problem Solvers focuses on Data Analysis across all grades beginning with visual representations of categorical data and moving to measures of central tendency using a “working backwards” approach.