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### One Step at a Time

9-12

In this lesson, students learn Polya's four-step problem solving heuristic and how to use metacognition. They practice these on simple word problems and equations, then apply the techniques to games and more complex problems. The problem solving heuristic can be applied to problems outside of mathematics and used for cross-curricular activities.### Logarithms Demystified

9-12

Before there were electronic calculators, there were logarithm tables and slide rules. In this lesson, students make and use slide rules to discover the properties of logarithms. The technique, analogous to number-line addition, reinforces the hierarchy among the operations of addition, multiplication, and exponentiation.### The Cantor Set

9-12

This lesson allows students to extend their idea of sequences beyond a list of numbers to mathematical objects like intervals by asking them to examine the infinite intersection of these sequences. This lesson works especially well just after students have worked with infinite geometric series. It even contains an unexpected application of geometric sequences and series.### Joking with Proofs

9-12

In the same way that supporting statements are used to reach a
conclusion in a paragraph-style proof, students modify a cliché or
common phrase to use as a punch line to a humorous story. This lesson
works well in aiding in the transition from two-column proofs to
paragraph-style proofs.### Polish Notation

9-12

Students sometimes have difficulty using the order of operations when
evaluating expressions. By converting these expressions into binary
expression trees before evaluating them, students gain a better
understanding of the order of operations. In addition, students learn
to represent algebraic expressions using prefix notation, which is
often called "Polish Notation," because of the nationality of its
inventor, Polish logician Jan Łukasiewicz.### Drug Filtering

9-12

In this lesson, students observe a model of exponential decay, and how kidneys filter their blood. They will calculate the amount of a drug in the body over a period of time. Then, they will make and analyze the graphical representation of this exponential function.### Computer Animation

9-12

In this lesson, students transform images through rotation, reflection, dilation, and translation using matrix multiplication. After digitizing images by representing the images as matrices, they multiply image matrices by various transformation matrices, producing transformed images.### Rolling Into Radians

9-12

Student groups collect height versus distance data for rolling objects of different sizes. Each group produces two sinusoidal graphs of the data, one in which both axes are measured in units, and the other in which both axes are rescaled and free of units. Students note that the amplitude and period of the unit-free graph are the same for all groups, and then discuss how their measurement opens a different way of describing points on a unit circle.### How Far Can You Go in a New York Minute

6-8, 9-12

In this lesson, students use proportions and similar figures to adjust
the size of the New York City Subway Map so that it is drawn to scale.
Students are asked to evaluate whether these changes are necessary
improvements.### Too Hot To Handle, Too Cold To Enjoy

9-12

Predicting the right time to take that first sip of any hot beverage is difficult. Unfortunately, the temperature of hot coffee does not decrease steadily (linearly) over time. If so, it would be easy to predict when to take that first sip. Which function best represents the rate at which coffee cools: linear, quadratic, square root, absolute value, exponential or logarithmic?