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### 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.### 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.### 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.

### 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. ### 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.
### 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.### 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*.

### 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*.

### 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.

### 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.