Students learn about an important characteristic of lines: their slopes. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero or undefined. Students get an explanation of when and how these different types of slope occur. Finally, they learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another.

Explore the world of lines. Investigate the relationships between linear equations, slope, and graphs of lines. Challenge yourself in the line game!

Students analyze their social networks using graph theory. They gather data on their own social relationships, either from Facebook interactions or the interactions they have throughout the course of a day, recording it in Microsoft Excel and using Cytoscape (a free, downloadable application) to generate social network graphs that visually illustrate the key persons (nodes) and connections between them (edges). The nodes in the Cytoscape graphs are color-coded and sized according to the importance of the node (in this activity, nodes are people in students' social networks). After the analysis, the graphs are further examined to see what can be learned from the visual representation. Students gain practice with graph theory vocabulary, including node, edge, betweeness centrality and degree on interaction, and learn about a range of engineering applications of graph theory.

Students are introduced to graphing on the coordinate plane, in the first quadrant, using (x, y) coordinates.

Students will learn about NASA's Radiation Belt Storm Probes (RBSP), Earth's van Allen Radiation Belts, and space weather through reading a NASA press release and viewing a NASA eClips video segment. Then students will use simple linear functions to examine the scale of the radiation belts and the strength of Earth's magnetic field. This activity is part of the Space Math multimedia modules that integrate NASA press releases, NASA archival video, and mathematics problems targeted at specific math standards commonly encountered in middle school textbooks. The modules cover specific math topics at multiple levels of difficulty with real-world data and use the 5E instructional sequence.

This task addresses an important issue about inverse functions. In this case the function f is the inverse of the function g but g is not the inverse of f unless the domain of f is restricted.

This task requires students to recognize the graphs of different (positive) powers of x. There are several important aspects to these graphs. First, the graphs of even powers of x all open upward as x grows in the positive or negative direction. The larger the even power, the flatter these graphs look near 0 and the more rapidly they increase once the distance of x from 0 excedes 1.

This exploration can be done in class near the beginning of a unit on graphing parabolas. Students need to be familiar with intercepts, and need to know what the vertex is.

This short video and interactive assessment activity is designed to teach fourth graders about greater or less than comparisons of length (english units).

This short video and interactive assessment activity is designed to teach fourth graders about greatest common factor.

This short video and interactive assessment activity is designed to teach third graders about forming largest and smallest numbers (even and odd).

This short video and interactive assessment activity is designed to teach fourth graders about forming the largest or smallest possible number.

This short video and interactive assessment activity is designed to teach third graders about grouping with illustrations - word problems.

This short video and interactive assessment activity is designed to teach second graders about understanding grouping with illustrations.

This short video and interactive assessment activity is designed to teach fifth graders about finding the remainder - long division word problems.

This short video and interactive assessment activity is designed to teach fourth graders about finding the total number: given remainder and number needed.

This task adds some rigor to the activity of growing bean plants. By collecting growth data, students practice measuring and recording length measurements.

This task is designed to make students think about the meaning of the quantities presented in the context and choose which ones are appropriate for the two different constraints presented. In particular, note that the purpose of the task is to have students generate the constraint equations for each part (though the problem statements avoid using this particular terminology), and not to have students solve said equations.

This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.