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### 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*.

### Reflect On This

9-12

This lesson, adapted from an activity in *Navigating through Geometry in Grades 9‑12*, requires students to investigate reflections using hinged mirrors. With a kaleidoscope, students will examine the interior angles of regular polygons.

### 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*.

### Trigonometry for Solving Problems

9-12

This lesson offers a pair of puzzles to enforce the skills of identifying equivalent trigonometric expressions. Additional worksheets enhance students' abilities to appreciate and use trigonometry as a tool in problem solving. This lesson is adapted from an article by Mally Moody, which appeared in the March 1992 edition of *Mathematics Teacher*.

### Traveling Distances

9-12

In this lesson, students interpret the meaning of the slope and *y*-intercept of the graph of real-life data. By examining the graphical representation of the data, students relate the slope and

*y*-intercept of the least squares regression line to the real-life data. They also interpret the correlation coefficient of the resulting least squares regression line.

### 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.

### Bathtub Water Levels

9-12

This lesson is similar to Lesson One: Traveling Distances; however,
this lesson is designed so students examine real-life data that
illustrates a negative slope. Students interpret the meaning of the
negative slope and *y*-intercept of the graph of the real-life data. By examining the graphical representation of the data, students relate the slope and

*y*-intercept of the least squares regression line to the real-life data. They also interpret the correlation coefficient of the least squares regression line.

### My Graph Is…

9-12

This lesson is designed to allow students to select their own real-life
data to plot and interpret. Interpreting the meaning of the slope and *y*-intercept of their least squares regression lines will help reinforce the concepts introduced in Lessons One and Two of this Unit Plan. The students are then given the opportunity to display their work.

### Gallery Walk

9-12

This lesson is designed to allow students to view the work of other
students in the class and to explain their own work. Some teachers may
be tempted to skip this step in the Unit Plan, but it is very important
that students be given the opportunity to verbalize what the
mathematics means that they performed in Lesson Three.### Automobile Mileage: Year vs. Mileage

9-12

In this lesson, students plot data about automobile mileage and interpret the meaning of the slope and *y*-intercept in the resulting equation for the least squares regression line. By examining the graphical representation of the data, students analyze the meaning of the slope and

*y*-intercept of the line and interpret them in the context of the real-life application. Students also make decisions about the age and mileage of automobiles based on the equation of the least squares regression line.