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Algebra

Building Connections

9-12
This lesson focuses on having students make connections among different classes of polynomial functions by exploring the graphs of the functions. The questions in the activity sheets allow students to make connections between the x-intercepts of the graph of a polynomial and the polynomial's factors. This activity is designed for students who already have a strong understanding of linear functions, some knowledge of quadratic functions, and what is meant by a polynomial function.
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Geometry

Counting Embedded Figures

6-8, 9-12
This grades 7-12 activity allows students to look for patterns within the given data. After looking at the pattern, the student should be able to form generalizations for the problem. Furthermore, this activity sharpens the algebraic skills of the students. The problem sharpens visualization skills.
Algebra

The Devil and Daniel Webster

9-12
Adapted from Navigating through Algebra in Grades 9–12, this lesson allows students to examine a recursive sequence in a game between the Devil and Daniel Webster.
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Data Analysis and Probability

Exploring Linear Data

6-8, 9-12
Students model linear data in a variety of settings that range from car repair costs to sports to medicine. Students work to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.
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Algebra

Allow Me 2 Reiterate

9-12
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.
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Algebra

Modeling Orbital Debris Problems

9-12
In this lesson, students examine the problem of space pollution caused by human-made debris in orbit to develop an understanding of functions and modeling. It allows the students an opportunity to use spreadsheets, graphing calculators, and computer graphing utilities.
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Algebra

Rates and Taxes

9-12
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.
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Algebra

Smokey Bear Takes Algebra

9-12
This lesson introduces students to the many factors that play a role in creating a forest-fire danger rating index. They will be looking at how we use a scale to quantify the abstract idea of forest fire danger. Using the real-world situation, students examine the meaning of the slope and intercepts of a line. To complete the activities related to these indexes, students should be comfortable with linear, quadratic and exponential functions and their graphs. Students’ facility with a graphing calculator is assumed. Students also use summation notation to do the activities relating to the Nesterov index. This lesson plan was adapted from the article "Smokey the Bear Takes Algebra," which appeared in the October 1999 issue of the Mathematics Teacher.
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Geometry

Euler Diagrams and Logic

9-12
This lesson focuses on using Euler diagrams to explore direct, indirect, and transitive reasoning. It was adapted from the article "A Visual Approach to Deductive Reasoning" by Frances Van Dyke, which appeared in the September 1995 issue of the Mathematics Teacher journal.
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Algebra

Light in the Ocean

9-12
In the first lesson, students make a conjecture about how the intensity of light changes as a function of the depth of the ocean. A video clip is used to prompt thinking, and students propose a graph that represents light intensity vs. depth.