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.

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### Sarah B. Bush, Karen S. Karp, Jennifer Nadler and Katie Gibbons

By examining ratios in paintings and using a free educational app, students can size up artists' use of proportional reasoning in their creations.

A cartoon exploring a problem about order of operations is coupled with a full-page activity sheet.

### Kami M. Dupree

Abandon mnemonics and make stronger connections between the operations and properties of arithmetic.

### Nicole Panorkou and Alan P. Maloney

Develop fifth-grade students' early expression of pattern relationships through instructional tasks.

## Odd Shape Out

### big solutions to little problems

### Jo Ann Cady and Pamela Wells

Solutions to a previous Solve It problem are discussed, and the procedures used with problem solving are explored.

### Sonalee Bhattacharyya, Nama Namakshi, Christina Zunker, Hiroko K. Warshauer and Max Warshauer

This activity engages students in problem solving while exploring key concepts of number theory, such as divisibility and divisibility tests, place value, fractions, and scale factors.

### Matt B. Roscoe and Joe Zephyrs

Pull on the threads of congruence and similarity in a series of lessons that explores transformational geometry.

### Sarah B. Bush, Judith Albanese and Karen S. Karp

Students engage in an activity of predicting, collecting, organizing, analyzing, and interpreting data by exploring the frequency of names that occur over three generations.

### Lincoln Peirce

A cartoon involving presidential birth dates is coupled with a full-page activity sheet.