A humorous cartoon and related problems (and answers) about pi are coupled with a full-page activity sheet.

## Mathematical Explorations: Will It Terminate?

### classroom-ready activities

### Aliza Libman Baronofsky

An activity explores whether a fraction will terminate or repeat. Activity sheets are included.

### Edited by Stephen P. Smith and David Spangler

A cartoon involving pi (or 3.14….) is coupled with a full-page activity sheet.

### Scott A. Brown

The traditional technique for converting repeating decimals to common fractions can be found in nearly every algebra textbook that has been published, as well as in many precalculus texts. However, students generally encounter repeating decimal numerals earlier than high school when they study rational numbers in prealgebra classes. Therefore, how do prealgebra students in the middle grades convert repeating decimals to fractions without using the age-old algebraic process (multiplying and finding the difference of two “stacked” equations) or without applying the precalculus approach of treating repeating decimal digits as an infinite geometric series?.

### Kasandra Dickman and Laura Bofferding

This department explores a game used to help students learn about additive inverses, or “zero pairs.” Authors describe some common reasoning that students used while playing the game and provide activity sheets geared toward students in grades 5–7.

### Kristen Lew and Juan Pablo Mejía-Ramos

This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First, mathematicians believed that mathematical language should obey the conventions of academic language, whereas students were either unaware of these conventions or unaware that these conventions applied to proof writing. Second, students did not fully understand the nuances involved in how mathematicians introduce objects in proofs. Third, mathematicians focused on the context of the proof to decide how formal a proof should be, whereas students did not seem to be aware of the importance of this factor.

### Hagit Sela, Nicole Davis and Jennifer Hulse

Teachers reflect on how three dialogue protocols can promote meaningful and efficient communication and learning through social interactions.

### Benjamin Dickman

Explore three original problems, the thinking behind their formulation, how they can be solved, and related extensions.