Math Crosswords A Lesson in the Math Fun

Math Crosswords A Lesson in the “Math + Fun!” Series Dec. 2004 Math Crosswords 1

About This Presentation This presentation is part of the “Math + Fun!” series devised by Behrooz Parhami, Professor of Computer Engineering at University of California, Santa Barbara. It was first prepared for special lessons in mathematics at Goleta Family School during the 2003 -04 and 2004 -05 school years. The slides can be used freely in teaching and in other educational settings. Unauthorized uses are strictly prohibited. © Behrooz Parhami Dec. 2004 Edition Released First Dec. 2004 Revised Math Crosswords Revised 2

How Are Crosswords Made? Start with a blank pattern Number the squares 1 6 Fill squares with words Backtrack if stuck Design the clues For example: Across: Down: 1. Not fresh 1. Smart 6. Residences 2. Sum Dec. 2004 7 9 11 S H A 2 T O A A P L 4 M E S A S ? S E O T S 8 10 L 5 E T R Math Crosswords 3 3

Crossword Puzzle Patterns Standard: no isolated square, symmetric Fancy Nonstandard: many single squares (easy to design) Dec. 2004 Math Crosswords 4

Computer-Generated Crosswords http: //www. pdos. lcs. mit. edu/cgi. bin/theme-cword The MIT Web site listed at the top allows you to enter a few words into a blank pattern and then generates a crossword or replies that it could not do it. For example, when I entered the two highlighted entries, I got this result Dec. 2004 M A G I + + W A N + + E F T S A D E N + S A L E S + T A R O L A R D + T I A R A + A V I D I M M O L A T I O N S + O P S + + + O A R + + + T E A R + + + C I R C L E + G A E L I C + R A N + S E P I A + R A T I O P R O C + T I T U S + N I L E M A C A W + C O L A S + S I R + T U S H E S + S T I G M A + + + L E A R + + + I L L + + + B O A + M O T I V A T I O N S O A T H + D A V I T + T H E A W H E E + E R A S E + C I S T S U D S + + A N A + + H O S E Math Crosswords 5

Making a Math Crossword Words to use: RECTANGLES TRIANGLE BAR GRAPH HUNDRED CIRCLE ARC ADD SUB TEN SIX Dec. 2004 S C I T R C U I B A R G R A R R E C T N A N G D L N P H L H U N D R E D Math Crosswords L T E E S I X 6

Another Math Crossword http: //www. puzzle-maker. com/CW/ This simple crossword was generated by a computer program at a Web site (named at the top) after entering these words and clues: CIRCLE/Rim of a plate, usually SQUARE/Shape of most tiles ARC/Part of a circle TRIANGLE/Three-sided shape Dec. 2004 2 1 T S Q U A R E I A 3 4 A R C Math Crosswords I N G R C L E E 7

Activity 1: Making a Math Crossword 1 3 Across: 4. _____________ 5. _____________ 7. _____________ 10. _____________ 4 6 5 8 9 7 10 Down: 1. _____________ 2. _____________ 3. _____________ 6. _____________ 8. _____________ 9. _____________ Dec. 2004 2 S C U B A R G R R E C T A D H U N D Math Crosswords I R N R T R I A N G L E T C L E N P H L E S I D X 8

Activity 2: Solving Some Other Types of Math “Crosswords” So far, we have covered math crosswords that are just like regular crosswords but use math terms. Here are some other types. Use digits 1 through 9 in the squares to make the result for each row or column equal to 10 Dec. 2004 Fill the circles with numbers so that the operations inside box arrows are valid Math Crosswords Fill in the missing letters so that each row and column has all the letters M A T H S 9

Crossnumbers: “Crosswords” with Numbers Across Down 1. 30 + 13 3. 52 + 32 6. 18 – 7 8. 69 – 20 10. 43 – 24 12. 47 – 26 14. 94 – 6 16. 79 – 47 19. 16 + 8 21. 52 – 29 23. 62 + 12 25. 4 + 21 27. 48 + 4 28. 13 – 3 2. 78 – 47 4. 54 – 10 5. 50 – 9 7. 21 – 9 9. 45 + 45 11. 95 + 3 13. 23 – 10 15. 78 + 4 17. 50 – 28 18. 5 + 12 20. 51 – 9 22. 73 – 43 24. 30 + 15 26. 79 – 28 Dec. 2004 4 3 1 1 2 Math Crosswords 1 3 2 2 3 0 10

Activity 3 Solve this crossnumber puzzle Do the math next to the clues and enter numbers into the grid only after you have checked to see that the digits match Dec. 2004 Math Crosswords 11

Activity 4 9 8 9 2 4 Solve like an ordinary crossword puzzle. Example for 1 across: 79, 224 + 19, 700 98, 924 Dec. 2004 Math Crosswords 12

Across Down 1. 189 + 433 4. 305 + 375 7. 612 / 6 10. 215 + 206 12. 445 + 305 14. 5 + 6 15. 570 / 5 17. 11 + 3 18. 29 + 184 20. 29 x 4 23. 302 + 198 25. 39 + 294 27. 124 + 287 29. 7 + 5 30. 324 + 187 32. 17 + 13 33. 26 + 79 34. 528 – 18 2. 633 / 3 3. 13 + 7 5. 719 + 168 6. 627 + 214 8. 291 – 90 9. 250 + 54 11. 27 + 185 13. 405 + 11 15. 9 + 4 16. 425 – 15 19. 193 – 90 21. 201 – 97 22. 35 + 296 23. 375 + 126 24. 305 x 2 26. 15 + 306 28. 156 – 26 30. 12 + 43 31. 23 – 8 Dec. 2004 Activity 5 Math Crosswords Solve this crossnumber puzzle 13

Activity 6: A Challenging Crossnumbers Puzzle Across 1. The cube of a whole number. 5. The number of square inches in a square yard. 6. The number of cubic inches in a cubic foot. 7. The number of millimeters in a meter. Down 1. A number which is unchanged if the digits are reversed. 2. A prime number. 3. The number of feet in a mile. 4. The number of seconds in an hour. Dec. 2004 Math Crosswords +-----+-----+-----+ |1 | |2 |3 |OOOOO|4 | | |OOOOO| | +-----+-----+-----+ | |OOOOO|5 | | |OOOOO| | | +-----+-----+-----+ |6 | | | |OOOOO| | +-----+-----+-----+ | |OOOOO|7 | | |OOOOO| | | +-----+-----+-----+-----+-----+-----+ |1 | |2 |3 |OOOOO|4 | | 3 | 7 | 5 |OOOOO| 3 | | |OOOOO| | +-----+-----+-----+ | |OOOOO|5 | | | 1 |OOOOO| 1 | 2 | 9 | 6 | | |OOOOO| | | +-----+-----+-----+ |6 | |OOOOO| | | 1 | 7 | 2 | 8 |OOOOO| 0 | | |OOOOO| | +-----+-----+-----+ | |OOOOO|7 | | | 3 |OOOOO| 1 | 0 | 0 | | |OOOOO| | | +-----+-----+-----+ 14

Activity 7: Make a Crossnumbers Puzzle Use no more than 7 black squares Across: __________ __________ __________ _____ Dec. 2004 Use +, -, x, / in clues Down: __________ __________ __________ _____ Math Crosswords 15

Activity 8: Make a Crossnumbers Puzzle Use no more than 7 black squares Across: __________ __________ __________ _____ Dec. 2004 Down: __________ __________ __________ _____ Use substitutions based on a = 3, b = 11, c = 8 (e. g. , use 2 b – c for 14) Math Crosswords 16

Cross-sums Puzzle Use only digits 1 to 9, each no more than once per puzzle entry. Numbers above the diagonal show the sum of digits in spaces to the right. Numbers under the diagonal show the sum of digits in spaces below. Dec. 2004 Math Crosswords 17

A Cross-sums/products Puzzle The product p and sum s for digits of each entry are given. Example: For 324, p = 24 and s = 9 1 Across: # p s 1 18 10 Down: # p s 3 1 4 3 32 12 2 48 14 4 40 13 3 0 6 7 8 8 10 7 9 30 10 Dec. 2004 2 4 5 5 9 5 12 5 7 35 12 8 6 15 6 7 8 9 5 Math Crosswords 18

A Very Special Crossnumber Puzzle All the clues in the following puzzle are the same, but no number is repeated in it. Across and down clue: The square of a number. 1 2 3 4 5 6 Dec. 2004 7 Math Crosswords 19

Next Lesson Thursday, January 6, 2005 Example to think about: Amy says that she was 10 years old the day before yesterday and that she will turn 13 next year. How is this possible? Dec. 2004 Math Crosswords 20