Right triangles play a significant role in mathematics. In this favorite lesson, the authors help students understand variant and invariant properties by considering relationships among angle measures and side lengths in right triangles. Students explore these relationships using interactive mathematics software, changing one angle and observing…

We consider here a number of ideas for the classroom or lecture theatre associated with the mensuration of solids. In particular, the volumes of various tetrahedra are obtained in an indirect manner (by way of prisms and square-based pyramids). This activity develops problem-solving skills, spatial visualization and a from-first-principles…

"Setting the Stage with Geometry" is a new math program aligned with the National Council of Teachers of Mathematics (NCTM) standards that is designed to help students in grades 6-8 build and reinforce basic geometry skills for measuring 2D and 3D shapes. Developed by The Actuarial Foundation, this program seeks to provide skill-building math…

Using investigations in teaching mathematics has for many years become an established feature of most curricula around the world. Investigations can be a vehicle for enabling children to experience the genuine excitement that comes from mathematical discovery. The true spirit of inquiry and investigation lies in the mind-set that continually asks…

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

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.)

This article describes an alternate way to utilize a circular model to represent thirds by incorporating areas of circular segments, trigonometric functions, and geometric transformations. This method is appropriate for students studying geometry and trigonometry at the high shool level. This task provides valuable learning experiences that…

Children who learn math fundamentals in preschool and kindergarten have the best chance of later achievement in school--but too often, children don't get the effective early math instruction that makes all the difference. Now there's a core early childhood textbook that helps current and future educators teach the most critical math concepts to…

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)

Describes the fundamentals of dimensionality and the relationships of the elements in a four-dimensional coordinate system. Outlines a number of analogies between the elements and techniques for creating images of one-point perspective. Describes two of the ways in which realistic imagery can be used to illustrate the relationships in a…

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)

Some topics in mathematics are unique because they can be explored by learners from the early grades through the advanced grades. An example of such a topic is polygon rings. Presents activities on polygon rings that integrate problem solving, reasoning, and communication. (Author/ASK)

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)