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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## GPS: Teaching Shapes Inclusively

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

## 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.

## Positioning During Group Work on a Novel Task in Algebra II

### Anna F. DeJarnette and Gloriana González

Given the prominence of group work in mathematics education policy and curricular materials, it is important to understand how students make sense of mathematics during group work. We applied techniques from Systemic Functional Linguistics to examine how students positioned themselves during group work on a novel task in Algebra II classes. We examined the patterns of positioning that students demonstrated during group work and how students' positioning moves related to the ways they established the resources, operations, and product of a task. Students who frequently repositioned themselves created opportunities for mathematical reasoning by attending to the resources and operations necessary for completing the task. The findings of this study suggest how students' positioning and mathematical reasoning are intertwined and jointly support collaborative learning through work on novel tasks.

## Mathematical Explorations: A New Twist on Collaborative Learning

### classroom-ready activities

### Stephanie M. Butman

Research on students' learning has made it clear that learning happens through an interaction with others and through communication. In the classroom, the more students talk and discuss their ideas, the more they learn. However, within a one-hour period, it is hard to give everyone an equal opportunity to talk and share their ideas. Organizing students in groups distributes classroom talk more widely and equitably (Cohen and Lotan 1997).

## Developing the Area of a Trapezoid

### Agida G. Manizade and Marguerite M. Mason

When calculating the area of a trapezoid, students use a range of problem-solving strategies and measurement concepts.

## Mysterious Subtraction

### Amy F. Hillen and Tad Watanabe

Conjecturing is central to the work of reasoning and proving. This task gives fourth and fifth graders a chance to make conjectures and prove (or disprove) them.