In this article, the authors describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions. They list three major ways in which one can imagine the environment and problems being used by teachers. Among other things, they discuss how the environment could support teaching and learning, and how the…

In the mid-1800s, Englishman John Venn invented a type of diagram to help visualize logical relationships. A Venn diagram is simply a rectangular box with circular loops in it that overlap to show how objects are related. This article describes activities with Venn diagrams that can be a fun way to sharpen students' logic skills and develop number…

In this article, the author describes integrated science and mathematics activities developed for fourth-grade students to explore and investigate three-dimensional geometric shapes, Bernoulli's principle, estimation, and art with and through bubbles. Students were engaged in thinking and reflection on the questions their teachers asked and were…

Alf Coles and Barry Orr reflect on what it looked like when Alf taught a year 7 lesson. In this article, Alf was asked by Barry (student) if he would take a lesson with the Y7 class that he had taken over from another teacher in the department in order to see what someone else might do with his lesson plans. Alf describes what some moments with…

This article describes a hands-on project in which unusual fractal images are produced using only a photocopy machine and office supplies. The resulting images are an example of the contraction mapping principle.

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…

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…

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)

While exploring the subject of geometric proofs, boolean logic operators AND and OR can be used to allow students to visualize their true-or-false patterns. An activity in the form of constructing electrical circuits is illustrated to explain the concept.

Participants at the Summer Institute Pattern Exploration: Integration Math and Science in the Middle Grades used and developed a method treat arithmetic, algebra and geometry as one entity. The use of iterative geometric constructions is seen to reinforce the concepts of exponents, ratios and algebraic expressions for the nth stage of the…

This article describes a polyhedra construction project that illustrates how one activity can address several of the mathematics content standards in the NCTM Principles and Standards for School Mathematics.

This article discusses Pythagoras' theorem, typically, it is introduce to students in the junior years of secondary school. Students consolidate their understanding of the theorem by using it for finding missing sides of triangles and for checking whether a given triangle has a right angle. But the topic often seems to dry up rapidly once these…

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)