Illustrative Mathematics
Illustrative Mathematics: F Le Rising Gas Prices Compounding and Inflation
In this task, students explore exponential models in the context of a real-world problem. Students learn about price inflation for a single commodity and are introduced to the Consumer Price Index for measuring the inflation of a body of...
Illustrative Mathematics
Illustrative Mathematics: F Le Basketball Bounces, Assessment Variation 2
This task asks students to analyze a set of data about the height of a basketball for each time it bounces. They choose a model that reasonably fits the data and use the model to answer questions about the physical context. This second...
Illustrative Mathematics
Illustrative Mathematics: F Le Carbon 14 Dating in Practice Ii
This problem introduces Carbon 14 dating which is used by scientists to date certain organic material. This version is based on the ratio of Carbon 14 to Carbon 12, which decreases at a constant exponential rate after an organism dies....
Illustrative Mathematics
Illustrative Mathematics: F Le in the Billions and Exponential Modeling
For this task, young scholars examine world population data from 1804 to 2012 and investigate whether an exponential function is appropriate for modeling the relationship between the world population and the year. Aligns with F-LE.A.1.c.
Illustrative Mathematics
Illustrative Mathematics: F Le Carbon 14 Dating, Variation 2
In this task on exponential decay, students calculate what the amount of Carbon 14 left in a preserved plant will be as time passes and when one microgram will be all that is left. Aligns with F-LE.A.1.c.
Illustrative Mathematics
Illustrative Mathematics: F Le Newton's Law of Cooling
For this problem, students use an exponential equation to investigate the cooling of a cup of coffee and how long it would take for it to cool down to different temperatures. Aligns with F-LE.B.5 and F-LE.A.4.
Illustrative Mathematics
Illustrative Mathematics: F Le Carbon 14 Dating in Practice I
In this task, students learn about exponential decay by examining the amount of Carbon-14 left in a preserved plant with the passage of time after the plant has died. This provides a simple introduction to Carbon-14 dating but the actual...
Illustrative Mathematics
Illustrative Mathematics: F Le Rumors
In this task, students investigate the exponential growth of a rumor about a celebrity. Aligns with F-LE.A.2.
Illustrative Mathematics
Illustrative Mathematics: F Le, a Rei Population and Food Supply
In this task, students analyze the sizes of a country's population and of its food supply to determine when and if food shortages will occur. To solve it, they must construct and compare linear and exponential functions and find where...
Illustrative Mathematics
Illustrative Mathematics: F Le Snail Invasion
In this task, students investigate the power of exponential growth in this real-world example of an invasive species that was introduced to Florida in 1966, a giant snail. Aligns with F-LE.A.2 and F-LE.A.4.
Illustrative Mathematics
Illustrative Mathematics: F Le Linear or Exponential?
In this task, young scholars are asked to identify whether changes are linear or exponential. Aligns with F-LE.A.1.
Illustrative Mathematics
Illustrative Mathematics: F Le Illegal Fish
In this task, students learn about exponential functions when they investigate the exponential growth of an invasive fish population. Aligns with F-LE.B.5 and F-LE.A.1.c.
Illustrative Mathematics
Illustrative Mathematics: F Le Us Population 1790 1860
In this task, students are shown a table of U.S. population data between 1790 and 1860 and are asked to explore whether exponential functions would be appropriate to model relationships within the data. The purpose of the task is to help...
Illustrative Mathematics
Illustrative Mathematics: F Le Comparing Exponentials
In this task, students work with exponential functions in a real-world context involving continuously compounded interest. They will study how the base of the exponential function impacts its growth rate and use logarithms to solve...
Illustrative Mathematics
Illustrative Mathematics: F Le Us Population 1982 1988
In this task, students are shown a table of U.S. population data between 1982 and 1988 and are asked to explore whether linear functions would be appropriate to model relationships within the data. Aligns with F-LE.B.5 and F-LE.A.1.b.
Illustrative Mathematics
Illustrative Mathematics: F Le Exponential Functions
Students are shown the intersecting graphs of two exponential functions in the format of f(x) = a times b to the power of x, and are asked to explore their characteristics. They discover that the value of each function will increase by a...
Illustrative Mathematics
Illustrative Mathematics: F Le Equal Differences Over Equal Intervals 1
In this task, students prove that linear functions grow by equal differences over equal intervals, and notice that in this case, the equal differences have the same value as the slope. Aligns with F-LE.A.1.a.
Illustrative Mathematics
Illustrative Mathematics: F Le Identifying Functions
In this task, young scholars are shown a table with linear, quadratic, and exponential functions at various values of x and are asked to match the function type to each data set and explain their reasoning. Aligns with F-LE.A.1.b and...
Illustrative Mathematics
Illustrative Mathematics: F Le Sandia Aerial Tram
For this task, students examine data on the elevation and the minutes into a ride for a tram that is traveling up a mountain and write an equation for the function that models the relationship between the two variables. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: F Le Interesting Interest Rates
For this task, students work with simple and compound interest rates to determine which bank offers the best return on a deposit. Aligns with F-LE.A.1.
Illustrative Mathematics
Illustrative Mathematics: F Le Taxi!
In this task, students explore the linear relationship between distance traveled and taxi fare cost. Aligns with A-REI.D.10 and F-LE.B.5.
Illustrative Mathematics
Illustrative Mathematics: F Le in the Billions and Linear Modeling
In this task, students are shown a table of world population data and asked to explore whether linear functions would be appropriate to model relationships within the data. Aligns with F-LE.A.1.b.
Illustrative Mathematics
Illustrative Mathematics: F Le Basketball Rebounds
The purpose of this task is to introduce students to an exponential decay function in the form f(x) = abx, with a concrete interpretation of the decay factor b. A table shows the rebound height of a basketball for each successive bounce....
Illustrative Mathematics
Illustrative Mathematics: Roll & Build
The purpose of this task is to give students practice representing two-digit numbers with concrete objects to reinforce the meaning of the tens digit and the ones digit. Directions and materials needed are included in the lesson.