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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.

When one end of a wooden board is placed on a bathroom scale and the
other end is suspended on a textbook, students can "walk the plank" and
record the weight measurement as their distance from the scale changes.
The results are unexpected— the relationship between the weight and
distance is linear, and all lines have the same x‑intercept. This investigation leads to a real world occurrence of negative slope, examples of which are often hard to find.

Students begin with a problem in a real-world context to motivate the need to construct circumcenters and then incenters of triangles and to make sense of these constructions in terms of bisecting sides and angles.

Students further explore square roots using the diagonals of rectangles. Using measurement, students will discover a method for finding the diagonal of any rectangle when the length and width are known, which leads to the Pythagorean Theorem.

This lesson helps students clarify the relationship between the shape of a graph and the movement of an object. Students explore their own movement and plot it onto a displacement vs. time graph. From this original graph, students create a velocity vs. time graph, and from there create an acceleration vs. time graph. The movement present and how to interpret each type of graph is emphasized through the lesson, which serve as an excellent introduction to building blocks of calculus.

Students explore the Fibonacci sequence, examine how the ratio of two consecutive Fibonacci numbers creates the Golden Ratio, and identify real-life examples of the Golden Ratio.

In this cooperative learning activity, students are presented with a
real-world problem: Given a mirror and laser pointer, determine the
position where one should stand so that a reflected light image will
hit a designated target.

This investigation allows students to develop several rational
functions that models three specific forms of a rational function.
Students explore the relationship between the graph, the equation, and
problem context.

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