Crossmatics – Math Madness! The buzzword in G3 is “Crossmatics,” a challenging set of 45 difficult math puzzles designed for 7th to 12th graders. After the class had learned multiplying and dividing fractions, completed their first TWO SINGAPORE MATH PACKETS, and had successfully solved 15 ALPHAMATH brainteasers, they were ready for this “Big Challenge.” The first bunch of students to qualify consisted of about six or seven enthusiastic learners. I handed each a pack of 12 puzzles and told them to collaborate to solve the first 8 puzzles. I expected the students to struggle through the first Crossmatics puzzle for at least a day or two, perhaps three, before beginning Puzzle #2. Most, amazingly, went home that night with nearly all of puzzle #1 done. The next morning when I unlocked the door to our class, I saw the excitement in their eyes. Ela was waving her packet of Crossmatics above her head – she had completed the first TWELVE. Most of that first bunch had completed about four puzzles. To my delight, they became obsessed – obsessed with hard math. This motivated the others in class to qualify for the challenge. It has been a week now (November 25th) since they started, and more students have qualified. Ela just completed Puzzle 26; Carlie, 24; a handful are in the teens. To my delight, my students have became obsessed Math Maniacs – obsessed with hard math, a teacher’s dream. Every spare moment between lessons, I see them working on those puzzles. Their enthusiasm is contagious, and others are madly finishing their Singapore Math and Alphamath requirements to begin their grueling journey through “7th -­‐12th grade math.” History of Crossmatics in G-­‐3 About twenty years ago, a parent of my brightest student, Mrs. Wells, found the Crossmatics publication during a trip to California and gave it to me, “Mrs. Fukumoto, can you tell Michael (her son) to do this. If I tell him, he’ll refuse. But he’ll do it for you.” I thumbed through the pages and doubted whether 5th graders, even my brightest, could solve these puzzles. However, I asked Michael to try. He struggled through them, and finally completed #3, barely. I put the “book” on the shelf for another two years, until I taught another very bright student. He only completed #2. Convinced that the math was too difficult for 5th graders, I shelved it again – until I attended a National Math Conference and bought the big idea “Algebra for All.” I decided to try again, but this time use “collaboration” as my major teaching strategy. I had read the research that Lev Semyonovich Vygotsky, the Russian Linguist, had conducted with third graders and how he got them to do work two academic years beyond their level through collaboration. I, hence, incorporated strategic grouping and collaboration, allowing my kids to collaborate up to puzzle #8. The results: the lowest student finished #12, and many finished all 45. Amazing!!!! Our principal agreed to spotlight students who completed all 45 Crossmatics at our Awards Assembly at the end of the year. This allows the 4th graders to anticipate this challenge in 5th grade. Other teachers in Grade 5 have also made Crossmatics a part of their math curriculum. For the past two years, many of my students complete Crossmatics BEFORE the end of the year. This prompted me to design a sequel – I call it “Double Crossing Math-­‐Trix” (cross-­‐math-­‐tricks) which incor-­‐ porates all stands of math (Probability, Data Analysis, Geometry, Singapore Math Mode Drawing, Measurement, etc.). So far, I completed 12 of these puzzles, but my plan is to compose at least 24 and market it. Those who finish all 45 Crossmatics, try their skills at completing even one of my Double Crossing Math-­‐Trix. So far no one has been able to go beyond my puzzle # 3. This year, however – someone may. It could be your child ☺. I inserted “Double Crossing Math-­‐Trix” #1 below to let you see the high level of difficulty these puzzles present and the vast math vocabulary involved. DOUBLE-CROSSING MATH-TRIX
MATHTRIX
1 2 6 8 9 10 11 13 14 17 20 18 21 25 26 3 4 5 7 12 15 19 16 22 23 24 28 29 30 31 32 33 34 35 Double-Crosser 1
ACROSS: (a= across; ex. 3-­‐a = 3-­‐across) 1. Divisible by 3, 6, and 9 3. Square root of 11-­‐d 4. 9th prime number 6. Square of first digit in 30-­‐a 7. 30 cm snow falls each hour, how much in 110 min. 10. Half of double 34-­‐a 15. Neither odd nor even 16. A baker’s dozen 17. Mean of 4-­‐a; 4-­‐d; 1-­‐d 18. Greatest Prime number under 90 19. Sum of degrees in 3 triskaidecagons +700 22.1/5 the sum of degrees in 4 dodecagons 25.Subtract 6 from the largest 2-­‐digit prime number 28. 7/9 of 22-­‐a 29. 2/3 of 27-­‐d 30. 250 x 11-­‐d 33. Zeros in 1 Septendecillion 34. Forty times a millennium x 1/10 2 plus 82 35. Cube root of 2197 27 This one will rip the smile off your face.. . . oouch! DOWN: (d= down; ex. 3-­‐d = 3-­‐down) 1. Sum of digits in 3-­‐d 2. Double 9-­‐a, times half of half-­‐a-­‐dozen 3. Highest total of right angles in 72 right trapezoids +10 4. Largest odd factor of 216 5. Number of digits in volume of cube with edge of 7 u 8. Square of 9-­‐d 9. Number of digits in 108 11. Square of 3-­‐a 12. 1/9 of 1-­‐a 13. Common factor of all even numbers only 14. Two Scores and four years divided by 11 20. Largest 1-­‐digit factor of 216 21. Digits in Area of a Circle with diameter of 600 u 22. (Sum of the squares of ten, eleven, and thirty) + 3 26. Number of sides in an hendecagon plus 5 27. Subtract 27,801 sec. from seconds in 1/3 of a day 28. Zeros in a googol plus years in ¾ Century 31. Thousands’ digit of 110x120x130x160x190x110 32. Cube Root of 12,167