Elapsed-time problems are notoriously difficult for children (Monroe, Orme, and Erickson 2002). Instruction on techniques for teaching and learning elapsed time is not emphasized in current mathematics education literature. Nor is it addressed in *Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence* (NCTM 2006). This absence of instruction may be due to a position held by some mathematics educators that telling time and determining elapsed time are life skills rather than skills delegated to mathematics instruction. (See Editor's note.) However, time is addressed in the *Principles and Standards for School Mathematics* (NCTM 2000) Measurement Standards for both the pre-K–2 and 3–5 grade bands. And regardless of one's perspective on the delegation of time as a discrete content area, determining elapsed time is encountered during mathematics instruction by most children at some point and is often met with frustration. This is especially true when the start or end time falls between the hour and half hour. Children find it challenging to keep track of unit changes between hours and minutes. On a national assessment, only 58 percent of eighth-grade students were able to correctly identify that 150 minutes equals 2 1/2 hours (Jones and Arbaugh 2004). Elapsed-time instruction often focuses on converting units and keeping track of those conversions rather than on counting up or back from one time to another. This article examines how students are able to make sense of elapsed-time problems when instruction is connected to open number-line strategies. Adapting this technique–typically used for recording addition and subtraction counting strategies–provides a method for supporting students' thinking about elapsed-time problems.

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### Lisa A. Brooks and Juli K. Dixon

A second-grade teacher challenges the raise-your-hand-to-speak tradition and enables a classroom community of student-driven conversations that share both mathematical understandings and misunderstandings.

### Juli K. Dixon and Jennifer M. Tobias

Anticipate and address errors that arise when fractions are placed in context and illustrated with models.

### Amber G. Candela, Melissa D. Boston, and Juli K. Dixon

We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.

### Vanessa M. Battreal, Vanessa Brewster, and Juli K. Dixon

Using donuts to contextualize and enrich mathematical discourse can sweeten students' understanding of how to interpret the remainder in a division problem.

### Juli K. Dixon and Christy J. Falba

In the information age, middle school students must be intelligent consumers of information. to instill critical thinking with respect to statistical data, the interpritation and creation of graphs are essential. Although vast amounts of information can be gleaned from traditional text sources, the World Wide Web (WWW) offers information that is updated far more frequently than most printed materials. Because of the motivational aspects and expedient nature of using data from the Web, this article focuses on its use; however, each of the activities can be adapted for use with traditional, text-based media.

### Juli K. Dixon, Treshonda Rutledge, Jennifer C. Caton, and Edward C. Nolan

Constraints for social distancing require teachers to find creative ways to engage students. Consider this fun strategy for exploring fraction equivalence, addition, and subtraction in a game environment where students use self-made or digital manipulatives.

### Wendy S. Bray, Juli K. Dixon, and Marina Martinez

A series of lessons focused on development of invented strategies for measuring areas of irregular polygons in a fourth grade transitional language class. Of focus are strategies that teachers can use to engage students with limited English proficiency (LEP) in communicating and justifying mathematical ideas.

### Edited by Mary Ellen Hynes, Juli K. Dixon, and Thomasenia Lott Adams

The purpose of the “Investigations” department is to provide mathematically rich and inviting contexts in which children and their teachers solve problems, communicate, and reason. Investigations encourage students to make connections among mathematical ideas, as well as connections with contexts outside of mathematics. As students collaborate, experiment, explore, collect data, research various sources, and engage in activities during the investigation, they will have opportunities to represent their mathematical ideas in multiple ways.

### Edited by Juli K. Dixon, Thomasenia Lott Adams, and Mary Ellen Hynes

The purpose of the “Investigations” department is to provide mathematically rich and inviting contexts in which children and their teachers solve problems, communicate, and reason. Investigations encourage students to make connections among mathematical ideas, as well as connections with contexts outside of mathematics. As students collaborate, experiment, explore, collect data, research various sources, and engage in activities during the investigation, they will have opportunities to represent their mathematical ideas in multiple ways.