Both students and teachers agree that the best activities are fun ones. Sometimes creating fun ideas means stepping out of the textbook box. Games and visually creative activities help engage students who don't usually think of math as fun. Activities with practical applications are great for students who are a little bored with working lists of problems.
Plotting a Path
Create worksheets with simple mazes drawn on a coordinate grid. Have students write down the series of coordinates for traveling on the path through the maze. Or, for an overnight project, have them create mazes and paths themselves, as well as tables of points. Use all four quadrants.
Graphing Linear Equations -- Full Body Style
Lynne Haman, a middle school math teacher, developed an activity called "Graphing Linear Equations -- Full Body Style." Use blue painters' tape to mark off an x- and y-axis on the floor of the classroom. Many classoom floors have one-foot square tiles. Using these as a guide, label the axes with numbers. If your classroom does not have square tiles, you can use sidewalk chalk to lay out a grid. Ask for volunteers or select groups of three or four students. Give the students the equation for a line. One student stands at the y-intercept of the line. The rest fill in by matching the slope. Once they are in place, they can hold their arms straight out to make a solid line. Then the teacher can ask the students to show what would happen with a change in slope or y-intercept.
Utilities frequently have a base rate and then a usage rate. The bill is usually calculated by multiplying the usage rate by usage and then adding the product to the base rate. If you graph the bill against usage, you get a straight line with the base rate as the y-intercept, and the usage rate as the slope. Have students graph their own electric, gas and water bills in slope intercept form and state which is which.
Stained Glass Windows
Have students graph many criss-crossing lines on a sheet of graph paper and label each line with its equation. Then they will fill the spaces between the lines with different colors creating a stained glass window effect. The graphed lines form the leading between the pieces of glass, and look best in a dark, thick line. To make this activity a little more advanced, include polynomial curves.
Have students collect data for making scatterplots. They will need to pick two quantifiable characteristics, one for each axis. Stress variables that are likely to have a linear relationship, which the students can try to estimate and graph. Some ideas for vital statistics to collect from friends and family include ages, heights, weights, shoe sizes, and lengths of fingers and arms. Any of these could be graphed against any other. Some practical ideas include total miles driven in cars versus their age, water bill versus area of lawn, or heating bill versus size of house. For comparison, some tables of vital statistics are available at the CDC website.
Have students plan their dream trips around the world by picking cities to visit in a particular order. Using a Mercator projection map, have them plot the courses between cities as lines on the map. Each pair of cities corresponds to two points, each with a latitude and longitude coordinate. Students will use these two points to determine the equation for the line. Then they will write up a series of navigation instructions for the trip in terms of a series of lines.
- Centers for Disease Control and Prevention: Growth Charts
- Citizens Utility Board: Making Sense of Your Electric Bill
- Water Sense: Understanding Your Water Bill
- Digitallessons.com: Stained Glass Window Graphing Project
- Map Lab: Get to Know a Projection: Mercator
- Teaching Channel: Graphing Linear Equations -- Full Body Style
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