Hide a prize somewhere on the campus and devise a series of math problems that will serve as a “treasure map” when solved. For example, one problem could require students to find the number of paces and compass directions by calculating the area and interior angle of a regular polygon. An octagon with an area of 42 square inches and an interior angle of 135 degrees would signify “walk 42 paces southeast.” You can easily adapt this activity to your students’ skill level.
Where possible, have students work together to find creative solutions to math problems. If you’re teaching a lesson on estimating the area of irregular shapes, choose an irregularly-shaped state on a U.S. map and discuss methods of breaking it down into a collection of regular shapes. Then group students into teams and let them choose their own tools -- such as geometrical stencils or graph paper -- and their own methods of solving the problem based on the map’s distance scale and the standard formulas for calculating the area of squares, rectangles and triangles. Treat any method that comes within 80 percent of the correct answer as a success. Award a prize to the team that comes closest to the state's actual area.
Activities in which students use their own bodies as measuring devices can personalize math concepts and help them stick. In one relatively simple exercise, students use the length of their shadows to calculate the height of a much taller object. Select a streetlight or flagpole on the campus and ask students to estimate its height by comparing the length of its shadow to the length of their own shadows. To solve this problem, the student must base his calculations on his own height with the following proportion equation: Student’s height/length of student’s shadow = height of pole/length of pole’s shadow.
Students tend to remember lessons that explain the math behind activities they enjoy. As an example, board games that use dice or a spinner provide a fun way to explain probability. Break students into small groups and give each group the same board game. Have each group conduct 25 tests to identify the most common landing space on the first spin or throw. Afterward, explain how to calculate probability for the dice or spinner. For two dice, 6 of 36 possible combinations add up to 7. This is a probability of 6/36 or 17 percent, so the seventh space should be the most common landing point. Individual groups will typically see some variation; but when you combine all of the groups’ data, they should come closer to the expected results in accordance with the law of large numbers. As an additional exercise, have students consider whether mechanical factors -- such as a bent spinner or unbalanced dice -- skewed their results.