Rates of Change in Pick’s Theorem

Students will use a spreadsheet to investigate rates of change among various figures created on a geoboard. The coefficients of Pick’s Theorem are easily determined from these rates of change.

Pick’s Theorem as a System of Equations

Students will gather three examples from a geoboard or other representation to generate a system of equations. The solution will provide the coefficients for Pick’s Theorem.

Rediscovering the Patterns in Pick’s Theorem

Students will use a geoboard, geoboard interactive, or Geometer’s Sketchpad^® to help them discover the pattern of Pick’s Theorem.

Graphical Representations for the Number of Hits

Finding a rule for the number of hits is only the first step in exploring the Paper Pool game. Students can gain a deeper understanding of the patterns by considering graphical representations of the results.

Pedal Power

In this lesson, students investigate slope as a rate of change. Students compare, contrast, and make conjectures based on distance-time graphs for three bicyclists climbing to the top of a mountain. 

Finding the Area of Trapezoids

Students discover the area formula for trapezoids, as well as explore alternative methods for calculating the area of a trapezoid.

Components of a Vector

In this lesson, students manipulate a velocity vector to control the movement of a car in a game setting. Students learn that vectors are composed of two components: magnitude and direction.

Difference of Squares

This activity uses a series of related arithmetic experiences to prompt students to generalize into more abstract ideas. In particular, students explore arithmetic statements leading to a result that is the factoring pattern for the difference of two squares. A geometric interpretation of the familiar formula is also included. This lesson plan was adapted from an article by David Slavit, which appeared in the February 2001 edition of Mathematics Teaching in the Middle School.

Rates and Taxes

This activity allows students to become familiar with percents and taxes. Students learn how to determine the amount of tax a family will pay based on a certain income. This lesson was adapted from an article by Warren W. Esty, which appeared in the May 1992 edition of Mathematics Teacher.

Allow Me 2 Reiterate

In this grades 9‑12 lesson, students use a computer software program to assist them in determining the square root of 2 to a given number of decimal places. From this, they will be able to study the repeating-decimal phenomenon of rational numbers and explore the system property of irrationality of numbers, such as 2.