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### Area of Parallelograms

6-8

This applet shows the relationship between the area of a parallelogram and the lengths of its sides.### Walk the Plank

6-8, 9-12

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.

### Hospital Locator

9-12

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.### Exploring Diagonals and the Pythagorean Theorem

6-8

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.### Varying Motion

9-12

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.### Golden Ratio

6-8

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.### Light It Up

9-12

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.

### The Giant Cookie Dilemma

6-8

Students explore two different methods for dividing the area of a circle in half, one of which uses concentric circles. The first assumption that many students make is that half of the radius will yield a circle with half the area. This is not true, and it surprises students. In this lesson, students investigate the optimal radius length to divide the area of a circle evenly between an inner circle and an outer ring.