*************************************** MathMagic Cycle 10: Level 10-12 Regular *************************************** The mathematical concept of ISOMORPHISM (mathematical equivalency) is a very important concept. Basically it means that you can often solve a problem by transforming it to an isomorphic one that already has been solved, or you know how to work. HOT|FORM|WOES Consider now this game: By taking turns two players ----+----+---- can use these listed words and cross them out, each one TANK|HEAR|WASP trying to get a horizontal, vertical or diagonal line ----+----+---- with three words that have the same letter in common. TIED|BRIM|SHIP 1) What common isometric problem can be used here? 2) Can you create another set of nine words that can be used for this game? **************************************** MathMagic Cycle 10: Level 10-12 Advanced **************************************** Circus and Zoo Algebra. Mr. Schenck's Algebra II students were told to visit the zoo or the circus and bring to class some problems related to algebra. Two stu- dents were then called to share their problems. Harvey said, "I went to the zoo and saw a cage where giraffes and ostriches live together. I first counted 44 legs, then right after some thunder, I counted 14 pairs of eyes." - Can you figure out how many animals were there? Chris and his librarian mom Helen went to the circus. His report: "We saw a number of horses and riders. Between them there were 50 feet and 18 heads. Also, the circus had some jungle animals that had, altogether, 11 heads and 20 feet. In this group, there were twice as many four- footed jungle animals as there were two-footed creatures." - Can you figure how many horses, riders and jungle animals were in the circus? (Challenges based on Martin Gardner's "aha!") ========= Good Luck