Communicating reasoning and constructing models fold nicely into a geometry activity involving the building of nesting boxes.

### Kathy E. Prummer, Julie M. Amador and Abraham J. Wallin

A scaling task that incorporates rectangular prisms can net an increase in students' geometric understanding.

## Math for Real: Packaging Golf Balls

### “when will I ever use this?”

### Randy Hall

A package of three golf balls provides the real-world scenario for this ratio and area activity.

### Shirley M. Matteson

Use this visual tool to plan lessons and assessments, diagnose gaps in students' conceptual knowledge, and help you and your students see connections within a particular lesson objective.

### Kimberly Sipes Hartweg

Building a rod raft allows students to make mathematical connections among a model, a table, a formula, and a graph.

### Günhan Caglayan

The Platonic solids, also known as the five regular polyhedra, are the five solids whose faces are congruent regular polygons of the same type. Polyhedra is plural for polyhedron, derived from the Greek poly + hedros, meaning “multi-faces.” The five Platonic solids include the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. **Photographs 1a-d** show several regular polyhedra

### Edited by Brian Bowen

Do you recall the formula for the surface area of a cylinder? How about the surface area of a cone? Did you find one of these formulas more difficult to recall than the other? I have observed a difference in our students' understanding of these two formulas, and this has motivated me to think about a more conceptually based approach to learning geometric formulas.

### Timothy Deis

The Tiling Tubs task is a middle school activity published in NCTM's *Navigating through Algebra in Grades* 6-8. Students examine a drawing that shows a square hot tub with side length *s* feet. A border of square tiles surrounds the tub, with each border tile a 1-foot square. Students determine the number of border tiles required to surround the tub and express that number in as many ways as they can, thereby creating various equivalent algebraic representations. A valuable component of Tiling Tubs is its requirement that students contextually justify their algebraic representations. Students also realize that more than one correct representation and justification exists.

### Greg Snedeker

“Photon Translations” is a piece of installation art that incorporates all the disciplines of science, technology, engineering, art, and mathematics (STEAM) and is on display at the Stoneleigh-Burnam School in Greenfield, Massachusetts. Installation art is just what it implies: art that is created for the purpose of being installed at a particular location. Sometimes the artwork can be interactive, allowing audience members to participate in the experience in some dynamic way. Terry Marashlian of Northfield, Massachusetts, created this artwork. The author collaborated with Marashlian on creating the musical chimes.

Surface area and volume are explored with this cartoon, also containing an activity sheet.