Illustrative Mathematics
Illustrative Mathematics: F Le Boiling Water
Students are shown two tables of data showing the approximate boiling point of water at different elevations. Both data sets can be modeled by linear functions but with different slopes. When the tables are combined, however, students...
Illustrative Mathematics
Illustrative Mathematics: F Le Choosing an Appropriate Growth Model
The goal of this task is to examine some population data for large cities from a modeling perspective. Students are asked to decide if the population data can be accurately modeled by a linear, quadratic, and/or exponential function, and...
Illustrative Mathematics
Illustrative Mathematics: F Le Do Two Points Determine an Exponential Function?
In this task, students investigate whether exponential functions will always be determined by two points. It complements the task "Do two points always determine a linear function?" Aligns with F-LE.A.2.
Illustrative Mathematics
Illustrative Mathematics: F Le a Valuable Quarter
The context of this task is that a quarter was put into a bank account in 1901 and students are asked to calculate its value in 2013 at two different interest rates. Those amounts are compared to the appreciation rate of a rare and...
Illustrative Mathematics
Illustrative Mathematics: F Le Basketball Bounces, Assessment Variation 1
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 variant...
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 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
For 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 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 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: F Le Two Points Determine an Exponential Function Ii
In this task, young scholars are shown a graph of an exponential equation, with two points labeled with their coordinates, and are asked to find the values of a and b in the equation. Aligns with F-LE.A.2.
Illustrative Mathematics
Illustrative Mathematics: F Le Two Points Determine an Exponential Function I
This is a simple task where students are shown a graph of an exponential equation, with two points labeled with their coordinates, and are asked to find the values of a and b in the equation. Aligns with F-LE.A.2.
Illustrative Mathematics
Illustrative Mathematics: F Le Algae Blooms
This problem examines the growth of algal blooms in Chesapeake Bay. Students build an exponential function modeling algae concentration based on the information provided, and gain an appreciation for the exponential growth exhibited...
Illustrative Mathematics
Illustrative Mathematics: F Le Do Two Points Determine a Linear Function Ii?
In this task, students investigate the relationship between linear equations and linear functions. Aligns with F-LE.A.2.
Illustrative Mathematics
Illustrative Mathematics: F Le Do Two Points Always Determine a Linear Function?
For this task, students explore linear functions and whether they can always be determined by two points on the coordinate grid. It focuses on producing an explicit function f(x) in the case where the line is not vertical. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: F Le Finding Parabolas Through Two Points
For this task, students are asked to find the quadratic functions that pass through two given points on a coordinate grid and to describe how their graphs are related. Aligns with F-LE.A.2.
Illustrative Mathematics
Illustrative Mathematics: F Bf Temperatures in Degrees Fahrenheit and Celsius
In this task involving temperature conversions, students construct a linear function given two input-output pairs, investigate the inverse of a linear function, and reason about quantities and/or solving a linear equation. Aligns with...