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

2. Dec. 2004Math CrosswordsSlide 2 About This Presentation EditionReleasedRevised FirstDec. 2004 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

3. Dec. 2004Math CrosswordsSlide 3 How Are Crosswords Made? Start with a blank pattern Number the squares 1234 6 5 78 9 11 10 Fill squares with words Backtrack if stuck STALE P R A HMES Design the clues For example: Across: 1. Not fresh 6. Residences Down: 1. Smart 2. Sum O L A T S E S ? OT S A

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

5. Dec. 2004Math CrosswordsSlide 5 Computer-Generated Crosswords 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 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

6. Dec. 2004Math CrosswordsSlide 6 Making a Math Crossword Words to use: RECTANGLES TRIANGLE BAR GRAPH HUNDRED CIRCLE ARC ADD SUB TEN SIX L E R T A N I HRGPRBACICLE D DHUNRD R T N RECTANGLESI XU S

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

8. Dec. 2004Math CrosswordsSlide 8 Activity 1: Making a Math Crossword Across: 4. __________________________ 5. __________________________ 7. __________________________ 10. _________________________ Down: 1. __________________________ 2. __________________________ 3. __________________________ 6. __________________________ 8. __________________________ 9. __________________________ L E R T A N I HRGPRBA CICLE D DHUNRD R T N RECTANGLES I X U S 12 3 4 5 6 7 89 10

9. Dec. 2004Math CrosswordsSlide 9 Use digits 1 through 9 in the squares to make the result for each row or column equal to 10 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. Fill the circles with numbers so that the operations inside box arrows are valid Fill in the missing letters so that each row and column has all the letters M A T H S

10. Dec. 2004Math CrosswordsSlide 10 Crossnumbers: “Crosswords” with Numbers AcrossDown 1. 30 + 13 2. 78 – 47 3. 52 + 32 4. 54 – 10 6. 18 – 7 5. 50 – 9 8. 69 – 20 7. 21 – 9 10. 43 – 24 9. 45 + 45 12. 47 – 2611. 95 + 3 14. 94 – 613. 23 – 10 16. 79 – 4715. 78 + 4 19. 16 + 817. 50 – 28 21. 52 – 2918. 5 + 12 23. 62 + 1220. 51 – 9 25. 4 + 2122. 73 – 43 27. 48 + 424. 30 + 15 28. 13 – 326. 79 – 28 4 3 11 21 32 23 0

11. Dec. 2004Math CrosswordsSlide 11 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

12. Dec. 2004Math CrosswordsSlide 12 Solve like an ordinary crossword puzzle. Example for 1 across: 79,224 + 19,700 98,924 Activity 4 9 8 9 2 49 8 9 2 4

13. Dec. 2004Math CrosswordsSlide 13 AcrossDown 1. 189 + 433 2. 633 / 3 4. 305 + 375 3. 13 + 7 7. 612 / 6 5. 719 + 168 10. 215 + 206 6. 627 + 214 12. 445 + 305 8. 291 – 90 14. 5 + 6 9. 250 + 54 15. 570 / 511. 27 + 185 17. 11 + 313. 405 + 11 18. 29 + 18415. 9 + 4 20. 29 x 416. 425 – 15 23. 302 + 19819. 193 – 90 25. 39 + 29421. 201 – 97 27. 124 + 28722. 35 + 296 29. 7 + 523. 375 + 126 30. 324 + 18724. 305 x 2 32. 17 + 1326. 15 + 306 33. 26 + 7928. 156 – 26 34. 528 – 1830. 12 + 43 31. 23 – 8 Activity 5 Solve this crossnumber puzzle

14. Dec. 2004Math CrosswordsSlide 14 Activity 6: A Challenging Crossnumbers Puzzle +-----+-----+-----+-----+-----+-----+ |1 | |2 |3 |OOOOO|4 | | | | | |OOOOO| | | | | | |OOOOO| | +-----+-----+-----+-----+-----+-----+ | |OOOOO|5 | | | | | |OOOOO| | | | | | |OOOOO| | | | | +-----+-----+-----+-----+-----+-----+ |6 | | | |OOOOO| | | | | | |OOOOO| | | | | | |OOOOO| | +-----+-----+-----+-----+-----+-----+ | |OOOOO|7 | | | | | |OOOOO| | | | | | |OOOOO| | | | | +-----+-----+-----+-----+-----+-----+ 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. +-----+-----+-----+-----+-----+-----+ |1 | |2 |3 |OOOOO|4 | | 3 | 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 | 0 | | |OOOOO| | | | | +-----+-----+-----+-----+-----+-----+

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

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

17. Dec. 2004Math CrosswordsSlide 17 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.

18. Dec. 2004Math CrosswordsSlide 18 A Cross-sums/products Puzzle #ps 11810 33212 44013 678 8107 93010 The product p and sum s for digits of each entry are given. 12 34 6 5 78 9 Across: Down: #ps 145 24814 309 5 125 15 73512 865 Example: For 324, p = 24 and s = 9

19. Dec. 2004Math CrosswordsSlide 19 A Very Special Crossnumber Puzzle 234 6 5 7 All the clues in the following puzzle are the same, but no number is repeated in it. 1 Across and down clue: The square of a number.

20. Dec. 2004Math CrosswordsSlide 20 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?