Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…

Students' lack of understanding about the relationships between geometry in two and three dimensions led the author to a surprising source of inspiration--the ancient philosopher and geometer Plato. From a theoretical perspective, the author's approach embodies the four instructional strategies that Eggen and Kauchak (2001) suggest for engaging…

This article describes middle school mathematics activities that relate measurement, ratios, and geometric sequences to finger positions or the placement of frets on stringed musical instruments. (Contains 2 figures and 2 tables.)

Geometric pattern tasks can be a useful tool for developing students' capacities to reason algebraically and in helping establish classroom norms and practices at the beginning of the school year. In this article, the authors consider the mathematical and social purposes that pattern tasks can serve by examining one middle school's…

Presents an activity using the cardboard tube from a roll of bathroom tissue or paper towels to help students examine and extend their understanding of the geometric properties of parallelograms. (ASK)

This article discusses how paper folding can be used in the classroom to introduce the standard results of school geometry, such as the transversal and parallel lines results, along with results concerning angles in convex polygons and centres of triangles, for example. Angle bisectors, midpoints, perpendiculars are all straightforward…

Explores middle school students' understanding of area and perimeter. Concludes that students need to construct visual representations of figures with given areas and perimeters, generate related word problems, and justify properties to grasp the concepts of area and perimeter. (ASK)

Describes an activity in which students develop a conceptual understanding of the formulas of the circumference and area of a circle by exploring pi. (YDS)

Presents an activity in which students investigate geometric probability at a school fair. (YDS)

Uses the Paper Balloon origami form to help students discover the relationship between ratios of corresponding distance, area, and volume measures in similar solids. (YDS)

Presents an activity in which students explore properties of quadrilaterals using geoboards. (YDS)

Illustrates a way in which students can estimate the ratio of an area of a circle using the radius square. Discusses why the same value of pi appears in both the formulas for the circumference and the area of the circle. (YDS)

Describes the processes used by middle school students to expand their thinking about the formula for the area of a parallelogram by observing patterns in the operation of a flexible parallelogram. (YDS)

Presents a game designed to help middle school students think about geometric properties and the relationships among them. (ASK)

Poses a problem in which readers are asked to determine which pentomino pieces will form a square. (YDS)