Three instructional situations demonstrate the value of using an “unknown” student's work to allow the advancement of students' mathematical thinking as well as their engagement in the mathematical practice of critiquing the reasoning of others.

### Angela T. Barlow, Natasha E. Gerstenschlager and Shannon E. Harmon

### Chepina Rumsey, Jody Guarino, Jennie Beltramini, Shelbi Cole, Alicia Farmer, Kristin Gray and Morgan Saxby

Read about how the authors used many technological tools and platforms to engage a team of educators across the country in this collaborative project.

### Angela T. Barlow, Alyson E. Lischka, James C. Willingham and Kristin S. Hartland

A well-crafted opening problem can provide preassessment of students' fraction knowledge and assist teachers in determining next steps for instruction.

### Drew Polly and Chandra Orrill

To support mathematics educators as they consider implications of the Common Core State Standards for Mathematics (CCSSM) for instruction and assessment, Teaching Children Mathematics is publishing a series of feature articles. In this fourth installment, authors Polly and Orrill suggest implementation strategies for grades 5 and 6. A final, cohesive article will appear in the August 2012 issue. Authored by Susan Jo Russell, the last piece concentrates on the implementation of the eight Standards of Mathematical Practice (SMP) and the constellations of Practices and Standards.

### Jen Hawkins

The Who Wants Pancakes? problem, originally published in the May 2017 issue of TCM, uses a recipe as the context to explore representations of mixed-number multiplication. Students are encouraged to use visual images to explain their thinking and to determine answers as they work through the problem.

### Corey Webel, Erin Krupa and Jason McManus

Contextual tasks such as the Milk problem and the Cupcake problem can illuminate operations with fractions, but not all visual models align with the standards.

### Taajah Felder Witherspoon

Observe fourth graders' thinking in action as they connect the multiplication of whole numbers to arrays.

### Steven M. Schulman

Step in and out of an impromptu fifth-grade math lesson with an experienced teacher, and renew your appreciation for students' algebraic thinking.

### Andrew Izsák, Sybilla Beckmann and Torrey Kulow

This article explores teaching practices described in NCTM's *Principles to Actions: Ensuring Mathematical Success for All*. Common factors, common multiples, strip diagrams, and double number lines are discussed in this, the third installment in the series.

### Michelle Stephan and Jennifer Smith

To incorporate more classroom discussion, allow students to argue.