The mathematical concept of slope can be made real through a set of simple, inexpensive, and safe experiments that can be conducted in the classroom or at home. The experiments help connect the idea of slope with physical phenomena related to surface tension. In the experiments, changes in surface tension across the surface of the water, which correspond to greater slopes on the graph, lead to increased motion of the fluid. The mathematical content, targeted to middle school and high school students, can be used in a classroom or workshop setting and can be tailored to a single session of thirty to ninety minutes.
Jamie-Marie L. Wilder and Molly H. Fisher
Our favorite lesson is a hands-on activity that helps students visually “tie” (pun intended) the concepts of rate of change and y-intercept together in a meaningful context using strings and ropes. Students tie knots in ropes of various thicknesses and then measure the length of the rope as the number of knots increases. We provide clothesline, twine, bungee cord, and other ropes found at local crafts, sporting goods, and home stores. We avoid very thin string, such as thread or knitting yarn, because the knots are small and the string length does not change enough to explore a rate of change. A variety of thicknesses is important because this allows for variability in the rates of change.
Virtual worlds, such as the one inhabited by the players of World of Warcraft, can serve as sampling grounds for students who are video gamers.
Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month the editors consider photographs of African bowls made of recycled telephone wire. The mathematics involves trigonometry, parametric equations and their graphs, and linear regression.
Marla A. Sole
Using bivariate data, students investigate the ingredients in pasta sauce.
“Mathematical Lens” uses photographs as a springboard for mathematical inquiry and appears in every issue of the Mathematics Teacher. All submissions should be sent to the department editors. For more background information on “Mathematical Lens” and guidelines for submitting a photograph and questions, please visit http://www.nctm.org/publications/content.aspx?id=10440#lens.
Students bring the real world into the classroom by studying speeding data collected on two Pennsylvania highways.
Arnulfo Pérez, Bailey Braaten, and Robert MacConnell
A hands-on, project-based modeling unit illustrates how real-world inquiry deepens student engagement with function concepts.
Students analyze items from the media to answer mathematical questions related to the article. The mathematics involved in this month's articles includes exponents, exponential equations, logarithmic equations, data analysis, linear functions, and regression.
Gemma F. Mojica, Christina N. Azmy, and Hollylynne S. Lee
Concord Consortium's Common Online Data Analysis Platform (CODAP), a free Web-based data tool designed for students in grades 6-12 and higher, is continuously being updated and developed for diverse projects in data science, science education, and mathematics/statistics education (https://codap.concord.org/). Teachers and students can access CODAP without downloading software or registering for accounts. Although some Web-based technology tools provide certain features for free and require users to pay a fee to use additional features, CODAP has no hidden costs. Devices need only be connected to the Internet using an updated Web browser (Chrome is preferred). CODAP is not optimized (yet) for use on such touchscreen devices as tablets or iPads®.