This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below is a table showing the approximate boiling point of water at different elevations: Elevation (meters above sea level)Boiling Point (degrees Celsi...

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below are population estimates for the larger metropolitan areas of Paris (France), Shenzhen (China), and Lagos (Nigeria) for each decade between 1950 ...

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

In this task students have the opportunity to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

This lesson unit is intended to help teachers assess how well students are able to: articulate verbally the relationships between variables arising in everyday contexts; translate between everyday situations and sketch graphs of relationships between variables; interpret algebraic functions in terms of the contexts in which they arise; and reflect on the domains of everyday functions and in particular whether they should be discrete or continuous.

The task is an introduction to the graphing of exponential functions. The first part asks students to use technology to experiment with the two parameters defining an exponential function, with little guidance. Since it is important for the second part, teachers should encourage students to try a wide range of values, and in particular, values of b both less than and greater than 1. The task includes a Desmos app, in which students can make use of sliders to more viscerally see the effect of changing a and b separately.

Students groups act as aerospace engineering teams competing to create linear equations to guide space shuttles safely through obstacles generated by a modeling game in level-based rounds. Each round provides a different configuration of the obstacle, which consists of two "gates." The obstacles are presented as asteroids or comets, and the linear equations as inputs into autopilot on board the shuttle. The winning group is the one that first generates the successful equations for all levels. The game is created via the programming software MATLAB, available as a free 30-day trial. The activity helps students make the connection between graphs and the real world. In this activity, they can see the path of a space shuttle modeled by a linear equation, as if they were looking from above.

This is a Desmos Activity that reviews linear, quadratic, and exponential models.  It also includes applications such as perimeter, area, and rate of change. 

Students will look to make connections between vertex form, standard form and intercept form for quadratic equations.

This lesson unit is intended to help teachers assess how well students are able to: interpret a situation and represent the constraints and variables mathematically; select appropriate mathematical methods to use; make sensible estimates and assumptions; investigate an exponentially increasing sequence; and communicate their reasoning clearly.

This resource was created by the Washington Office of Superintendent of Public Instruction. 

This resource was created by the Washington Office of Superintendent of Public Instruction. 

This is a very open-ended task designed for students to develop some of the basic ideas surrounding exponential growth. While implementations will vary (as discussed below), the core idea is that each fold of the piece of paper doubles the height of the stack. Combined with an estimate of the original thickness of the paper and the distance to the moon, this is enough information to deduce the minimum number of folds to get there. The solution uses the estimate of 0.1 mm for the thickness of paper and 385,000 km for the distance to the moon.

In this task students construct and compare linear and exponential functions and find where the two functions intersect. One purpose of this task is to demonstrate that exponential functions grow faster than linear functions even if the linear function has a higher initial value and even if we increase the slope of the line. This task could be used as an introduction to this idea.

The PhET Activities Database is a collection of resources for using PhET sims. It includes hundreds of lesson plans, homework assignments, labs, clicker questions, and more. Some activities have been created by the PhET team and some have been created by teachers.

The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real world problem with ties to developing financial literacy skills.

The task provides an opportunity for students to engage in Mathematical Practice Standard 4: Model with mathematics.

The purpose of this task is to give students experience modeling a real-world example of exponential growth, in a context that provides a vivid illustration of the power of exponential growth, for example the cost of inaction for a year.

Temperature conversions provide a rich source of linear functions which are encountered not only in science but also in our every day lives when we travel abroad. The first part of this task provides an opportunity to construct a linear function given two input-output pairs. The second part investigates the inverse of a linear function while the third part requires reasoning about quantities and/or solving a linear equation.