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March 2012, Volume 17, Issue 7

 FEATURES Cleared for Takeoff: Paper Airplanes in FlightStacy L. ReederMath and science, as well as mean, median, and mode, made smooth landings during a three-day data-collection unit. Second Look:Measures of Central Tendency Alice in the Real WorldTom ParkerA computer application promotes programming knowledge and allows students to create their own worlds through mathematical problem solving. Students’ Strategies Can Take Us Off GuardJane M. KeiserThese students produced incorrect answers, but their teacher helped them ultimately become more proficient with computation by skillfully leveraging their prior understanding. Hunger Games: What Are the Chances?Sarah B. Bush and Karen S. KarpThe mathematics found in the popular adolescent book and movie gives students another way to view probability. From Arithmetic Sequences to Linear EquationsRyota Matsuura and Patrick HarlessAlerting a class to a connection between two familiar topics will help students become more agile with each of them. Continuation of activity sheets in “From Arithmetic Sequences to Linear Equations”

 Departments Informing PracticeInforming Practice: Fraction Multiplication from a Korean Perspective Cartoon CornerCartoon Corner: The Math Police Solve It!Solve It!: Relatively Speaking Palette of Problems/Menu of ProblemsPalette of Problems - March 2012 Window on ResourcesWindow on Resources: Books Math for RealMath for Real: Firewood by the Cord

 Second Look - Measures of Central Tendency Mathematical Exploration: Mean, Median, or Mode: Which One Is My Pencil?Students measure pencils and explore mean, median, and mode in the process. Contemporary Curriculum Issues: Statistics in the Middle Grades: Understanding Center and SpreadUnderstanding center and spread in statistics is the focus of this issue's Contemporary Curriculum Issue. A lesson is described that involves formulating a question that can be answered with data, collecting data to address the question, analyzing the data and interpreting the results. The mean is viewed as a balancing point to discuss variability in dot plots and box-and-whisker plots. This regular department provides a forum to stimulate discussion on contemporary mathematics curricular issues across a K-12 audience. It’s a Fird! Can You Compute a Median of Categorical Data?Students need time and experience to develop essential understandings when they explore data analysis. In this article, the reader gains insight into confusion that may result as students think about summarizing information about a categorical data set that is attempting to use, in particular, the median. The authors highlight points to consider in helping students unpack these essential understandings. Illuminations Lesson: Building HeightStudents will use a clinometer (a measuring device built from a protractor) and isosceles right triangles to find the height of a building. The class will compare measurements, talk about the variation in their results, and select the best measure of central tendency to report the most accurate height. Data Analysis and Probability Standard for Grades 6-8In grades 6–8, teachers should build on this base of experience to help students answer more-complex questions, such as those concerning relationships among populations or samples and those about relationships between two variables within one population or sample. Toward this end, new representations should be added to the students' repertoire. Box plots, for example, allow students to compare two or more samples, such as the heights of students in two different classes. Scatterplots allow students to study related pairs of characteristics in one sample, such as height versus arm span among students in one class. In addition, students can use and further develop their emerging understanding of proportionality in various aspects of their study of data and statistics.