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Volume 3, Number 9

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2 March 1998                                   Vol. 3, No. 9

 Math Parent Handbook | MathWorld Interactive |
Integer Pairs MATH PARENT HANDBOOK - GRADES K-6 A Guide to Helping Your Child Understand Mathematics An introduction to contemporary math, including technology in the classroom, with teaching strategies to help children become mathematical thinkers; resources and ideas for working with your child; quick and easy math games (no special equipment is needed); math activities for when you're out and about at the grocery store, in restaurants, or shopping; "refrigerator math" (games that can be posted on the fridge for the whole family to participate in); and a list of books for grades K-2 and 3-6 to read with your children. This guide was developed for parents of children using the Houghton Mifflin mathematics program, but almost all of the information presented can be used by anyone wanting to explore mathematics with a child. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- MATHWORLD INTERACTIVE - Carolynn S. Mortensen Breakfast cereal usually comes with the weight listed on the box. Sometimes when you open the box it does not seem full to the top. Do you think you have been cheated? Can you explain why the box is not full but there is still the correct weight of cereal? Is weight a good way to sell cereal? Is there a better way? Participating students from all over the world work on this and other MathWorld Interactive Challenges, open-ended word problems at four levels: Grades K-3 (ages 5-8) Grades 4-6 (ages 9-11) Grades 7-8 (ages 12-14) Grades 9-12 (ages 14+) Challenges are issued every nine weeks and students are asked to follow a specific format: - write what you know about the problem (the facts) - write what you are looking for (the questions) - write all your problem-solving strategies - write your solutions (the answers) - explain how you checked your work - extend the problem by writing a new problem based on the original Participants use an on-line form or the MathWorld Interactive Message Boards to submit their solutions. Students receive e-mail awards highlighting their strengths and achievements, and the results are also posted online in the MathWorld Interactive Hall of Fame. Find these areas and others at: -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- DUMB LUCK... AND INTEGER PAIRS - geometry-puzzles A recent conversation on the newsgroup geometry-puzzles, which began with an investigation of how to derive an equation for the radius of the circle that will circumscribe a general triangle of sides a, b, and c. Monte Evans found two triangles with sides 10,11,12 and 10,7,4 that could both be circumscribed by a circle with radius 40/sqrt(39), and asked, "Does anyone know of any other pair of triangles, each side being an integer, that is circumscribed by one circle?" After many interesting posts, Evans commented: ... To John Conway, Pat Ballew, Helena Verrill, and Don Gilmore - Many thanks for the interest shown in this problem! I am rapidly learning that my amazing coincidence wasn't quite as unusual as I thought. Pat and his energetic students jumped right on this problem and came up with 3 pairs of such triangles, and John Conway came up with a triple! If I correctly understand Conway's last entry, we can have a circle with as many integer-sided triangles in it as we desire. It may be a rather large circle, by the time the rescaling is through. My request for an analytical approach has been answered in spades! WOW... To find all the relevant threads, use the searcher to look for the words integer triangle : For more about geometry-puzzles, including how to join, see: -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum Ask Dr. Math Problems of the Week Internet Resources Join the Math Forum Send comments to the Math Forum Internet Newsletter editors _o \o_ __| \ / |__ o _ o/ \o/ __|- __/ \__/o \o | o/ o/__/ /\ /| | \ \ / \ / \ /o\ / \ / \ / | / \ / \

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