Chapter 11: Lessons and Activities

Activity Name Activity Description
The Tortoise and Hare Race Students step through the tortoise and hare race, based on Zeno's paradox, to learn about the multiplication of fractions and about convergence of an infinite sequence of numbers.
Cantor's Comb Students learn about fractions between 0 and 1 by repeatedly deleting portions of a line segment, also learning about properties of fractal objects. Parameter: fraction of the segment to be deleted each time.
Shape Explorer Students are shown shapes on a grid and asked to calculate areas and perimeters of the shapes.
Triangle Explorer Students learn about areas of triangles and about the Cartesian coordinate system through experimenting with triangles drawn on a grid.
Pythagorean Explorer Students find the length of a side of a right triangle by using the Pythagorean Theorem, and then check their answers.
Squaring the Triangle Students learn about how the Pythagorean Theorem works, through investigating the standard geometric proof. Parameters: Sizes of the legs of the triangle.
Surface Area & Volume Students manipulate dimensions of polyhedra, and watch how the surface area and volume change. Parameters: Type of polyhedron, length, width and height.

Lesson Name General Lesson Description
Perimeter Introduces students to the concept of perimeter.
Area Introduces students to the concept of area.
Length, Perimeter and Area Introduce students to length, perimeter and area.
Surface Area and Volume Introduces students to the concepts of surface area and volume.
Pythagorean Theorem Students learn how the Pythagorean Theorem works and how to apply it.
Introduction to Linear Functions designed to introduce the basic ideas needed for learning about linear functions