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| Home > Teacher Resources > Newsletter Table of Contents > March/April 2002 Newsletter |
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March/April 2002 Newsletter
PwaP evaluation ... Please help! PwaP Evaluation...Please Help! We are preparing a report for our funder, the National Science Foundation, about the ways in which the Problems with a Point website is being used, and the kinds of people who are using it. We are eager to get your input. Please use the online evaluation form:http://www2.edc.org/mathproblems/evaluateB.asp (or, from the PwaP web site, click on Contact Us to find the link to the evaluation form) and tell us what you think of Problems with a Point. Each person who sends us a completed evaluation form by June 15, 2002 will receive a $10 gift certificate to Amazon.com. Featured problem: "A winning connection" Correlation of data is an oft-reported result of data, but what does it mean? In this problem set, students look at selected statistics from Major League Baseball with the intent of predicting which teams won more games. They first compare a table of data (which includes the "games won (%)" category). Then they are given plots of games won versus other statistics, with the question of which of those statistic would be best to use to estimate which teams won more games and how confident one can be in such an estimate. The concept of correlation is introduced, and students rank three unrelated graphs from strongest to weakest correlation.Although correlation is so important to statistical analysis, the basic idea behind it—how well the variables are connected—is often lost in a sea of numbers and calculations. Without discussing actual number values, students consider the strength of a correlation on a more general level, in terms of how useful one variable is in predicting relative positions for another variable. This problem is useful as an introduction to correlation, before students are exposed to the numerical coefficient. It can be used as a springboard to a general discussion about the usefulness of the concept as well as the usefulness of a quantitative measure (the coefficient). For students who find abstract mathematical formula daunting, approaching from a more qualitative perspective may be helpful in understanding the utility of the formula (rather than focusing on the mechanics of calculation). http://www2.edc.org/mathproblems/getp.asp?name=ekcorrelate Here is a sample of the new problems available on our site: FITTING POLYNOMIALS http://www2.edc.org/mathproblems/getp.asp?name=ekPolyFit Students learn a method for fitting a polynomial of degree n to n+1 points. They compare the method to solving a system of equations. MULTIPLES OF GAUSSIAN INTEGERS http://www2.edc.org/mathproblems/getp.asp?name=ekGaussMult Students consider multiples of Gaussian integers, complex numbers a + bi in which a and b are both integers. As with multiples of integers on the number line, these numbers are regularly spaced on the complex plane. Students describe and generalize the locations of the corresponding points. MATRICES AND CANCELLATION http://www2.edc.org/mathproblems/getp.asp?name=ekInvMatrix In this problem set, students see that, unlike the real numbers, matrices do not have the cancellation property—because not every matrix (even excluding 0) has an inverse. Students should be able to multiply matrices and solve systems of linear equations. STAR LIGHT, STAR BRIGHT http://www2.edc.org/mathproblems/getp.asp?name=ekNGrams Students explore features of regular n-grams (n-pointed stars, also called star-polygons). The problem set connects geometry and number theory (modular arithmetic, for example). WHEN GOOD SHOWS GET CANCELLED http://www2.edc.org/mathproblems/getp.asp?name=ekNielsen Students collect different size samples, first from a small population (to get a feel for the process) and then from a large population (using a spreadsheet). They consider how closely these samples give the actual percentages and how large a sample is needed to give reliable results. MAP COLORING http://www2.edc.org/mathproblems/getp.asp?name=ekMapColor This problem set introduces vertex-edge graphs through one useful application: map coloring. Students color maps, with and without converting to graphs, to find the fewest number of colors required. TRIANGLES ON A SPHERE http://www2.edc.org/mathproblems/getp.asp?name=ekSphere Students reason about triangles on spheres instead of in a plane, including angle sums and a congruency test (AAS). PASCAL PATTERNS http://www2.edc.org/mathproblems/getp.asp?name=nmapascal Students will generate entries and discover patterns found in Pascal's triangle. FIBONACCI MATRICES http://www2.edc.org/mathproblems/getp.asp?name=ekMatrixFib Students try to find a way to reasonably quickly find any term in the Fibonacci sequence. Using powers of a matrix is presented as one such way. The Problems with a Point Web site is a searchable
and well-indexed collection of problems and orchestrated problem sets
designed to help students in grades 6 through 12 develop both deep conceptual
mathematical understandings and technical skills. Accessible to teachers,
students, and parents over the Web, this resource includes problems and
problem sets for development, practice, assessment, and integration of
concepts and skills, classified by categories such as topic, difficulty
level, and use of technology. To sign up for the Problems with a Point newsletter, or
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