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| Home > Teacher Resources > Newsletter Table of Contents > May 2002 Newsletter |
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May 2002 Newsletter
Get an Amazon.com gift certificate! Get an Amazon.com gift certificate! (PwaP Evaluation Update) As mentioned in last month's newsletter, we are preparing a report for our funder, the National Science Foundation, about the ways in which the Problems with a Point web site is being used, and the kinds of people who are using it. We thank those of you who have already completed the survey; you will soon be receiving your Amazon.com gift certificates. We would like to collect more input from newsletter subscribers. Please use the online evaluation formhttp://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: "Spinning wheel 1" This problem set introduced radian as a unit of measure using the location of an air valve on a bicycle wheel as motivation. First, students consider the distance that a wheel of radius 1 "spoke" has traveled when it's made a full revolution, and then quarter and half revolutions. Measuring an angle by the length of the corresponding arc of the wheel is introduced, and students connect the distance traveled with these arcs. Building on that concept, the radian unit is defined. A few problems have students apply this definition to angles defined by revolution and the distances the wheel has traveled. Students come up with a process for converting between degrees and radians. Finally, they apply the concept to a 26-inch bicycle wheel.Although most trigonometry and pre-calculus students can tell you that 2(pi) radians define a circle, few make (and keep) the connections among radian, radius, and the formula for the circumference. By spending time building the concept, they may be able to see the connection and remember it in the future. This problem set serves well as a precursor to unit circle trigonometry, or to angular velocity. The problem sets, Spinning wheel 2 and Spinning wheels—faster! are useful follow-up sets for these topics. See the full problem on the Web at http://www2.edc.org/mathproblems/getp.asp?name=ekBikeWheels1 Here is a sample of the new problems available on our site: THE CIRCLE AND ITS COUSINS http://www2.edc.org/mathproblems/getp.asp?name=ekConics By generalizing the formula for a circle, students create several graphs of ellipses and hyperbolas. They compare the parameters that form the graphs and summarize the results. GRAPHING IN 3D http://www2.edc.org/mathproblems/getp.asp?name=ek3Dgraph In this introduction to 3D graphing, students work with a linear function with two independent variables and consider what a three-dimensional graph of such a function would look like. They also match other function forms with given graphs. THE PERFECT SHUFFLE http://www2.edc.org/mathproblems/getp.asp?name=ekShuffles Motivated by the results of a "perfect" shuffle, students consider the orbits of 16-card and 52-card decks and find how many shuffles will return each deck to its original state. (In addition to being fun, this makes a good introduction to algebraic permuations.) TAXICAB FIGURES http://www2.edc.org/mathproblems/getp.asp?name=ekTaxi This problem set introduces the classic "taxicab" geometry and has students find the analogues to conic sections (circle, parabola, ellipse, and hyperbola) in the new geometry. AREA FORMULAS http://www2.edc.org/mathproblems/getp.asp?name=ekAreas Students get practice with simple integrals (of linear equations) and algebraic skills as they reinforce the connection between the integral of a function and the area between the function and the x-axis. PARTYGOERS' GEOMETRY http://www2.edc.org/mathproblems/getp.asp?name=ekPartyGeom This problem set presents a non-Euclidean geometry in which people are points and lines are created by following an acquaintance chain. (That is, who knows whom in "six degrees of separation" style.) Circle and triangles are defined, and the triangle inequality is considered for this geometry. VOLUMES OF CONES AND SPHERES http://www2.edc.org/mathproblems/getp.asp?name=ekVolRev1 Students derive the volume formulas for cones and spheres (and square pyramids as well) using cylinders to approximate the objects. They use the sum of the volumes of n cylinders to approximate the volume of the original object, and then consider what happens when n goes to infinity. Some experience with finite and infinite series (particularly summation notation) is helpful. TRANSFORMATIONS IN ART http://www2.edc.org/mathproblems/getp.asp?name=ekTransArt Students look at designs (including strip designs) to see what transformations can create the design from a single basic element. They also have an opportunity to create their own design. (Note, this requires that they know how to draw the transformation of a figure.) WEB SEARCH OPERATIONS http://www2.edc.org/mathproblems/getp.asp?name=ekWebSearch This problem set uses the context of Web searches to introduce Boolean values and operations. Students evaluate simple and complex Boolean expressions, using all three operators (AND, OR, and NOT). A question about De Morgan's formulas is presented as a challenge. WHERE'S THE (DECIMAL) POINT? - PART 1 http://www2.edc.org/mathproblems/getp.asp?name=sbdecimalmult Students work through and explain an algorithm for multiplying decimal numbers (without a calculator): first ignore the decimal points, then multiply the resulting whole numbers, then put the decimal points back. Next, they investigate an analogous method for multiplying integers ending in several zeros. Then, they develop a similar method for multiplying numbers expressed in scientific notation. 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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