Learn about the relationship between position and velocity for a model rocket during launch and in free-fall. Experiment with rocket mass, rocket thrust, and rocket burn time to understand the connection of velocity and position. Uncover more about this physics concept with four more examples.

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Student groups use a "real" 3D coordinate system to plot points in space. Made from balsa wood or wooden dowels, the system has three axes at right angles and a plane (the XY plane) that can slide up and down the Z axis. Students are given several coordinates and asked to find these points in space. Then they find the coordinates of the eight corners of a box/cube with given dimensions.

Using Avida-ED freeware, students control a few factors in an environment populated with digital organisms, and then compare how changing these factors affects population growth. They experiment by altering the environment size (similar to what is called carrying capacity, the maximum population size that an environment can normally sustain), the initial organism gestation rate, and the availability of resources. How systems function often depends on many different factors. By altering these factors one at a time, and observing the results, students are able to clearly see the effect of each one.

Students observe four different classroom setups with objects in motion (using toy cars, a ball on an incline, and a dynamics cart). At the first observation of each scenario, students sketch predicted position vs. time and velocity vs. time graphs. Then the classroom scenarios are conducted again with a motion detector and accompanying tools to produce position vs. time and velocity vs. time graphs for each scenario. Students compare their predictions with the graphs generated by technology and discuss their findings. This lesson requires assorted classroom supplies, as well as motion detector technology.

In this exercise, questions provide practice with coordinate plane word problems. Immediate feedback is given and hints or a video are available if needed.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Gain an understanding of how to solve systems of equations by graphing by viewing an example and a video lesson. [2:49]

From the University of Georgia, this tutorial provides exercises and problems using Heron's Formula for the area of a triangle, makes use of several problem representation methods, including a graph.

Interactive multiple-choice assessment in which a graph is given and the properties of the graph must be observed. Such properties include zeros of the function, positive and negative intervals of the function, and monotonically increasing and decreasing intervals.

An in-depth lesson which teaches you how to graph exponential equations. Examples are worked through step by step and explained in detail for different exponential equations.

Practice graphing points on a coordinate plane and identifying the quadrant or axis where they are located. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Complete step-by-step investigation of quadratic functions, allowing the user to input the function. Each step, from solving f(x) = 0 to graphing and finding extreme points, is covered in depth, via links for each step (requires JavaScript). The latter part of the resource looks at how to recognize whether a quadratic equation is needed for solving a word problem and goes through some example problems.

Many of today's popular sports are based around the use of balls, yet none of the balls are completely alike. In fact, they are all designed with specific characteristics in mind and are quite varied. Students investigate different balls' abilities to bounce and represent the data they collect graphically.

This site contains basic information on rational functions. Gives definition, how to find domain and roots, and how rational functions apply to asymptotes and holes in the graph.

Students build and use a very basic Coulter electric sensing zone particle counter to count an unknown number of particles in a sample of "paint" to determine if enough particles per ml of "paint" exist to meet a quality standard. In a lab experiment, student teams each build an apparatus and circuit, set up data acquisition equipment, make a salt-soap solution, test liquid flow in the apparatus, take data, and make graphs to count particles.

Graphing can be made fun and hands-on with different real world "tools" - like snacks!

This lesson demonstrates how to solve linear inequalities by graphing them on a coordinate plane. Includes short quiz. [8:36]

Students apply pre-requisite statistics knowledge and concepts learned in an associated lesson to a real-world state-of-the-art research problem that asks them to quantitatively analyze the effectiveness of different cracked steel repair methods. As if they are civil engineers, students statistically analyze and compare 12 sets of experimental data from seven research centers around the world using measurements of central tendency, five-number summaries, box-and-whisker plots and bar graphs. The data consists of the results from carbon-fiber-reinforced polymer patched and unpatched cracked steel specimens tested under the same stress conditions. Based on their findings, students determine the most effective cracked steel repair method, create a report, and present their results, conclusions and recommended methods to the class as if they were presenting to the mayor and city council. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.

Absolute value is basically the distance between "number" and "zero" on a number line. You will learn more about this concept in this video. You will also learn how to express absolute value functions as piecewise functions. [10:47]

Linear inequalities can be represented both graphically and algebraically. In this video, you will learn how to express linear inequalities as an equation and on a number line. [8:15]

In this lesson, we will learn how to find the quadratic function when we are given the graph of a parabola. Worked examples and a video are included. [8:22]