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.
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.
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?
9-12
This lesson allows students to explore the idea that
rainforest deforestation is occurring at an exponential rate. Students will use
provided research about Amazon deforestation and conduct their own research to
determine whether deforestation is occurring exponentially.
9-12
This
activity uses a 2009 study based on the book
The Joy of Cooking that found portion sizes in the iconic cookbook
had expanded 60% since 1936 and 33% since 1996. Students use linear functions
to create models of weight as a function of calories and time, then use the
models to make projections about what impact increased portion sizes may have on
weight.
9-12
In the third lesson, students identify a function that models the data. An interactive graphing tool can be used to determine a function that fits the data points.
6-8, 9-12
This lesson invites students to investigate the patterns when a "plus sign" (a cross-shaped arrangement of five squares) is placed on the board in various locations. Students will conjecture about the pattern of the five displayed numbers, the sum of the five numbers, and any other patterns that they notice. Students may also explore similar patterns when other shapes, such as a 2 × 1 rectangle, are placed on the hundreds board.
9-12
In this lesson, students will learn to read an antifreeze chart to determine the necessary mix of antifreeze and water for protection against various temperatures. Students will then numerically analyze a particular cooling system to determine how much fluid to drain in order to get the desired percent concentration of antifreeze. Finally, students will set up a system of equations to solve the same system.
9-12
Starting from the concrete notion of weights and balance and moving to symbolic expressions and representations of functions, this i-Math investigation has focused on some of the issues that arise along the way. In this part, this connection is extended to functions. More sophisticated tools allow for a greater diversity of investigations.
9-12
Students develop a delicious new drink by mixing various concentrations of a two-fold dilution series. Students calculate the percents of their mixtures, taste these differences, and visually observe their results.
