Algebra can be hard to visualize. Learning to show relationships between symbolic expressions and their graphs opens an avenue to really seeing algebraic patterns. According to the NCTM *Standards*, at the middle school students move from plotting points to exploring the graphs of lines, including slope and intercept.

**An Introduction to the Coordinate Plane**

This is a fun but serious introduction to Cartesian coordinates. Students work interactively online to plot points of integer pairs, to deal with changing the scale of a graph, and to consider “tricky” graphs.

**Coordinate Graphing**

Another site on the basics of coordinate graphing with opportunities to practice plotting points. This is actually a complete lesson on the subject—introduction, objectives, procedures, and extensions—plus excellent interactive games for students to practice their point-plotting skills.

**Lines and Slope**

At this site, students learn to draw a line and find its slope. Joan, a cartoon chameleon, is used throughout the tutorial to demonstrate the idea of slope visually. Background information on solving equations and graphing points is laid out clearly, followed by a step-by-step explanation of how to calculate slope using the formula. Students also observe the slope of horizontal, vertical, parallel, and perpendicular lines, not a usual topic at a beginning level. Finally, the slope-intercept form (y = mx + b) is carefully set out.

**Grapher: Algebra (Grades 6-8)**

Using this online manipulative, students can graph functions of their choice—including functions with square roots, exponents, and fractions. In fact, they can graph up to three functions in the same window, a useful capability when considering points of intersection. Also, they can zoom in on a region of the graph and trace the function paths to find particular coordinates. A powerful tool for exploring graphs!

**We Want Your Feedback**

We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our

**Middle School Portal 2**publications. You can also email us at msp@msteacher.org. Post updated 11/08/2011.

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