Take the mystery out of linear functions. Provided an image with no scale, learners guess where the line that connects them might cross the y-axis. After providing the coordinates of the points, they realize scale is an important...

Smells like learning! Young scholars collect data on the length of time a stick of deodorant lasts. After modeling the data with a graph and function, they make predictions about deodorant use over time.

Your algebra learners write linear, exponential, and quadratic equations containing the same two graph points in this collaborative task.

Examine trends in student-to-teacher ratios over time. Building from the first task in the two-part series, classes now explore the pattern of student-to-teacher ratios using a non-linear function. After trying to connect the pattern to...

What's so special about slope? Pupils first match cards with slope and y-intercept to graphs of linear equations. They continue the lesson by matching equations in slope-intercept form to the same graphs.

A graph not only tells us who won the bike race, but also what happened during the race. Use this resource to help learners understand graphs. The commentary suggests waiting until the end of the year to introduce this topic, but why...

This exercise is an opportunity for algebra learners to understand the connection between the slope of a line and points found on the line. Use similar triangles to explain why slope m is the same between any two points. Discuss with the...

A mail truck travels the same amount of miles per day. It will be up to your algebra learners to find an equation for this mailman’s truck. One needs a good understanding of rate of change and the initial value for this model. The...

Your movie fans will be interested in this resource. They will compare video streaming plans. One plan charges a set rate per month and a reduced viewing fee, and the other has a flat rate per each video viewed. Unfortunately, learners...

What is the financial benefit for attending a community college for the first two years before transferring to a four-year college? The second part of the educational lesson asks young scholars to explore this question through data...

Create a technical report explaining the components of a medical plan through a function. The project-based learning activity gives a medical insurance scenario that young mathematicians model using piecewise functions. Their analyses...

Your learners will write quadratic functions whose graphs include specific points and explore how these graphs are related to each other.

How can baseball and skeet-shooting be modeled mathematically? Sports lovers and young mathematicians learn how to use quadratic equations and systems of equations to model the flight paths of various objects.

How many nurses does it take to support one doctor? A project-based activity asks learners to analyze state data to answer this question. Classes create polynomial functions from the data of doctors and nurses over a seven-year...

Verify the rule of thumb for finding the time of death. The project-based learning task asks pupils to determine when the rule of thumb process of finding the time of death is appropriate. Learners develop a function for the rule and...

Design and build a rover ... then eat it? This activity has groups of two design and build Mars rovers. The teams determine what instruments they want to include with their rover and plan a budget. They calculate the cost of the body of...

Make the most of your prom—with math! Pupils write and use a quadratic model to determine the optimal price of prom tickets. After determining the costs associated with the event, learners use a graph to analyze the break even point(s).

Draw a graph that shows the qualitative features of a function that has been described verbally. Make sure learners understand where time is zero and the distance is zero. It may take them some time to understand this concept, so working...

A very simple example of a functional relationship between depth of water and time is shown here. In fact, it might be more useful to use a coastal tide book to better illustrate this real-world experience. Pupils are to count the number...

Algebra learners explore, analyze and build an exponential equation given its form and a specific point that exists on the function in this task. The last question asks learners to apply their ideas to an exponential equation given two...

An interesting example of a discrete function and how it is applies to the real world. This could easily make a good collaborative lesson with an environmental science class. Practice reading a table and drawing a scatter plot make up...

Learners rewrite a general quadratic function by completing the square to see a new form of the function that more easily identifies the x-coordinate of the vertex and the two roots of the function.

Tell the story of the math. Given a graph of a linear system, learners write a story that models the graph before crafting the corresponding functions. Graphs intersect at an estimated point, allowing for different variations in the...

This activity guides learners through an exploration of common transformations of the graph of a function. Given the graph of a function f(x), students generate the graphs of f(x + c), f(x) + c, and  cf(x) for...