The concept of slope gets an approachable, yet theoretical, treatment in a comprehensive algebra lesson. The use of functional notation and problem-solving techniques keep the material rigorous, but detailed teaching notes and lots of...

Learners consider the rate of filling a cone in the 23rd installment of this lesson series. They analyze the volume of the cone at various heights and discover the rate of filling is not constant. The lesson ends with a...

Learners investigate average rates of change for linear functions and connect the concept to slope. They then determine average rates of change in quadratic and exponential functions.

In this function worksheet, students read word problems and write functions. They determine the instantaneous rate of change and identify intervals. This three-page worksheet contains approximately 20 problems.

Explore functions with non-constant rates of change. The first installment of a 12-part module teaches young mathematicians about the concept of a function. They investigate instances where functions do not have a constant rate of change.

Students calculate the rate of change. In this algebra lesson, students identify the slope and discuss the different properties of lines as they relate to rate. A discuss doubling time, zero slope and being in two places at once.

Your class will be very interested in the results of this activity. How long does it take a MP3 and video game player to charge?  Sam only has an hour and the MP3 player only has 40% of its battery life left. Plus, his video player...

Students observe and calculate slopes. In this algebra lesson plan, students graph equations and determine the pace at which the slope is changing. They use the navigator to see the change as they graph the lines around.

If mathematicians know the secret to compound interest, why aren't more of them rich? Young mathematicians explore compound interest with exponential functions in the twenty-seventh installment of a 35-part module. They calculate future...

Graph polynomials and identify the end behavior of each polynomial function. The class differentiates between linear, quadratic, and other polynomial equations.

An inquiry-based algebra lesson explores real-world applications of linear functions. Scholars investigate four different situations that can be modeled by linear functions, identifying the rate of change, as well as the...

Your young microbiologists will interpret and solve exponential equations in this real-world context task set in a hospital research scenario. Learners think in terms of the functions as well as their rates of change. 

Using this resource, scholars develop graphs that model situations by showing change over time. They answer 15 questions based on information from charts that show growth in weight. They extend the concepts to an assessment section of...

Context is the key to understanding slope. A real-world application of slope uses a weight loss scenario with a constant rate of change to introduce the concept of slope of a line, before it makes a connection to the ordered pairs...

Explore linear functions! In this Algebra I lesson, mathematicians graph data in a scatter plot and use a graphing calculator to find a linear regression and/or a median-median line. They use the model to make predictions.

Inquiry-based learning and investigations form the basis of a deep understanding of quadratic functions in a very thorough unit plan.  Learners develop recursive and closed methods for representing real-life situations,...

In this Algebra I/Algebra II worksheet, students examine the slope of line as the rate of change between the dependent and independent variables.  The one page worksheet contains two multiple choice questions.  Answers are...

Scholars model the height of water in a container with an exponential function and apply average rates of change to this function. The main attraction of the lesson is the discovery of Euler's number. 

Students analyze the patterns in polygons and relate it to the rate of change. In this algebra lesson, students discuss the relationship between the data and the graph of the data.

Eleventh graders solve problems dealing with rate of change. For this algebra lesson, 11th graders graph their rate of change problems and analyze it comparing their data with each other. They solve problems dealing with percent and rate...

Students solve problems with slopes. In this algebra activity, students identify the slope of a line and relate it to the rate of change.  They graph their lines on the TI and observe changes in the lines.

Swimming is more fun with quantities. The short assessment task encompasses finding the volume of a trapezoidal prism using an understanding of quantities. Individuals make a connection to the rate of which the pool is filled with a...

Move on into trigonometry. An informative eBook takes the content of a College Algebra course and adds more relating to trigonometry and trigonometric functions. The content organization allows pupils to build upon their learning by...

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...