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Math Games and Puzzles (Level III Math Teacher Resource) Draft (NSSAL) C. David Pilmer ©2011 (Last Updated: December 2013) This resource is the intellectual property of the Adult Education Division of the Nova Scotia Department of Labour and Advanced Education. The following are permitted to use and reproduce this resource for classroom purposes. Nova Scotia instructors delivering the Nova Scotia Adult Learning Program Canadian public school teachers delivering public school curriculum Canadian nonprofit tuition-free adult basic education programs The following are not permitted to use or reproduce this resource without the written authorization of the Adult Education Division of the Nova Scotia Department of Labour and Advanced Education. Upgrading programs at post-secondary institutions (exception: NSCC) Core programs at post-secondary institutions (exception: NSCC) Public or private schools outside of Canada Basic adult education programs outside of Canada Individuals, not including teachers or instructors, are permitted to use this resource for their own learning. They are not permitted to make multiple copies of the resource for distribution. Nor are they permitted to use this resource under the direction of a teacher or instructor at a learning institution. Table of Contents Introduction (for Instructors) ……………………………………………………………… ii 3 by 3 KenKen Puzzles (A to D) …………………………………………………………. 1 4 by 4 KenKen Puzzles (A and B)………………………………………………………… 5 5 by 5 KenKen Puzzles ……………………………………………………………………. 8 KenKen Puzzles: Signed Numbers ……………………………………………………… 9 Magic Squares ……………………………………………………………………………. 12 Addition Pyramids: Whole Numbers …………………………………………………….. 13 Addition Pyramids: Decimal Numbers …………………………………………………… 15 Addition Pyramids: Signed Numbers …………………………………………………….. 16 Row Factors and Column Factors ………………………………………………………… 17 Whole Number Cross Word Puzzles (A to D) …………………………………………… 18 Signed Numbers Cross Word Puzzles (A and B) ………………………………………… 22 RAD Puzzles: Whole Numbers …………………………………………………………... 24 RAD Puzzles: Signed Numbers ………………………………………………………….. 27 Connect Four Whole Number Addition Game (A and B) ……………………………….. 30 Connect Four Whole Number Subtraction Game (A and B) …………………………….. 32 Connect Four Whole Number Multiplication Game (A to D) …………………………… 34 Connect Four Whole Number Division Game …………………………………………… 38 Divisibility or Prime Connect Four Game ……………………………………………….. 39 Connect Four Fraction Decimal Equivalency Game …………………………………….. 40 Connect Four Adding Decimal Numbers Game (A and B) ……………………………… 41 Connect Four Subtracting Decimal Numbers Game (A and B) …………………………. 43 Connect Four Fraction Percent Equivalency Game ……………………………………… 45 Connect Four Percentage Game …………………………………………………………. 46 Connect Four Adding Signed Numbers Game …………………………………………… 47 Connect Four Subtracting Signed Numbers Game ………………………………………. 48 Connect Four Multiplying Signed Numbers Game ……………………………………… 49 Connect Four Dividing Signed Numbers Game …………………………………………. 50 Connect Four Squaring and Cubing of Signed Numbers Game …………………………. 51 Connect Four Time Ahead Game (A and B) …………………………………………….. 52 Connector ………………………………………………………………………………… 54 Fraction Fury Puzzles (A and B) …………………………………………………………. 55 Math Logic Puzzles ………………………………………………………………………. 59 Answers ………………………………………………………………………………….. 60 NSSAL ©2011 i Draft C. D. Pilmer Introduction (for Instructors) One of the ongoing concerns for teachers, instructors, and professors, who teach secondary and post-secondary mathematics courses, is poor arithmetic skills (and related estimation skills) displayed by some learners. These educators are attempting to teach higher level mathematical concepts to their learners but, in some cases, these efforts are impeded when learners have poor arithmetic and estimation skills. These learners waste valuable time and effort and/or fail to understand underlying concepts because of deficiencies in this area. For example, how can a learner factor a trinomial by inspection, if one does not know their whole number math facts? Similarly, how can a learner simplify a rational expression, if they have difficulty working with fractions? In the past, the approach to fostering strong arithmetic skills was to have learners complete a variety of "drill-and-kill" questions, usually in a timed situation. Examples of such questions are shown below. Complete the following questions within the next ten minutes. 3 2 7 (a) 39 85 (b) 6 1 (c) Convert 2 to a decimal. 8 3 16 (d) 2945 8 (e) 45.8 + 682.3 4 1 (f) 2 1 5 6 (g) 563 28 6137 6 15 12 (h) 31 4 7 (i) 6 5 7 8 1 2 3 2 Learners who were unable to correctly answer 80% of the questions during the allotted time would often be expected to return at lunch time or after school to make the necessary corrections. For those adults schooled during the 1960s and 1970s, this was a common practice. Although this practice did result in stronger arithmetic skills and in some cases stronger estimation skills, they were two shortcomings associated with it. 1. The focus was primarily on the mastery of specific algorithms. Instead of thinking flexibly about mathematics, learners were largely expected to follow the same rules to answer questions. Therefore this feeds the misconception that mathematics is a rule-driven noncreative discipline. 2. A timed test, with lunch hour or afterschool corrections, was not fun anyone. Who enjoys math when the only reward is avoiding a correction session (i.e. detention). Also, learner perception was that the only thing valued by the math teacher was the right answer; all the work that preceded it was moot if the learner made a careless mistake in their last step. The "all-that-counts-is-the-final-answer" misconception is fostered by this practice. Does that mean that we never expose our learners to these types of "drill and kill" questions? No, but we must recognize that these questions are only one tool for improving arithmetic skill and that they must be used judiciously. NSSAL ©2011 ii Draft C. D. Pilmer Are there non-threatening and engaging means of improving arithmetic skills that also foster more flexible thinking? Yes, and this can be accomplished using mathematical games and puzzles. Hence we have created the following outcome for our Level III Math course. Learners will be expected to develop efficient strategies, high levels of automaticity, and flexible thinking skills as they pertain to arithmetic skills in the context of whole numbers, decimal numbers, fractions, and signed numbers through the ongoing use of games and puzzles. In this accompanying Level III Math resource, instructors can find a variety of games and puzzles that range from Level I to Level III. This being said, not all puzzles and games are appropriate for all learners. Therefore the material in this resource should not be viewed as a unit that a learner completes from "stem-to-stern" within an allotted time; rather, this is an instructor resource where activities are gradually, yet regularly, distributed based on the instructor's professional judgment. NSSAL ©2011 iii Draft C. D. Pilmer 3 by 3 KenKen Puzzles (A) Insert the numbers 1, 2, and 3 into the grid such that: no number is repeated in the same row or column, and the numbers in the cages produce the target number using the indicated operation (e.g. 2 : find two numbers when multiplied give you 2). (a) 2 4+ 5+ (b) 9 6 3+ 3+ 6 (c) 6 4+ (d) 12 5+ 4+ 3 (e) 3+ 6 4+ (f) 6 3+ 2 NSSAL ©2011 3 3+ 5+ 3 3 1 Draft C. D. Pilmer 3 by 3 KenKen Puzzles (B) Instructions: Insert the numbers 3, 4, and 5 into the grid such that: no number is repeated in the same row or column, and the numbers in the cages produce the target number using the indicated operation (e.g. 12 : find two numbers when multiplied give you 12). (a) 12 (b) 15 8+ 4 12 9+ 15 (c) 5 15 7+ 4 (d) 8+ 12+ 7+ 12+ 12 8+ 20 (e) 20 9+ (f) 12 11+ 15 8+ 14+ 12 5 NSSAL ©2011 2 Draft C. D. Pilmer 3 by 3 KenKen Puzzles (C) Instructions: Insert the numbers 5, 6, and 7 into the grid such that: no number is repeated in the same row or column, and the numbers in the cages produce the target number using the indicated operation (e.g. 35 : find two numbers when multiplied give you 35). (a) 35 (b) 42 13+ 5 11+ 12+ 42 (c) 30 11+ 30 19+ (d) 17+ 7 35 11+ 18+ 13+ (e) 7 42 11+ 5 13+ 13+ 35 NSSAL ©2011 42 (f) 17+ 30 3 Draft C. D. Pilmer 3 by 3 KenKen Puzzles (D) Instructions: Insert the numbers 7, 8, and 9 into the grid such that: no number is repeated in the same row or column, and the numbers in the cages produce the target number using the indicated operation (e.g. 72 : find two numbers when multiplied give you 72). (a) 72 16+ 8 (b) 9 15+ 63 15+ 63 (c) 56 17+ 56 24+ (d) 17+ 72 56 23+ 72 16+ (e) 72 15+ (f) 63 25+ 17+ 72 22+ 56 NSSAL ©2011 4 Draft C. D. Pilmer 4 by 4 KenKen Puzzles (A) Insert the numbers 1, 2, 3, and 4 into the grid such that: no number is repeated in the same row or column, and the numbers in the cages produce the target number using the indicated operation (e.g. 8 : find two numbers when multiplied give you 8). (a) 8 12 4+ 1 (b) 3 6+ 6+ 4 6 6 12 (d) 6+ 1 2 NSSAL ©2011 3 7+ 3 9+ 8+ 4+ 8 1 12 4 7+ 6 6+ (c) 2 4 3+ 24 1 2 5 Draft C. D. Pilmer 4 by 4 KenKen Puzzles (B) Insert the indicated numbers into the grid such that: no number is repeated in the same row or column, and the numbers in the cages produce the target number using the indicated operation (e.g. 8 : find two numbers when multiplied give you 8). (a) 1, 2, 3, 4 Puzzle 3 (b) 1, 2, 3, 4 Puzzle 8 6 6 12 5+ 5+ 12 4 3+ 8+ 12 15 5+ 9+ 2 12+ 6+ 6+ 10 8 6+ NSSAL ©2011 3 (d) 2, 3, 4, 5 Puzzle 20 15 3+ 5+ (c) 2, 3, 4, 5 Puzzle 8 5+ 6 8+ 5 6 Draft C. D. Pilmer (e) 3, 4, 5, 6 Puzzle 24 (f) 3, 4, 5, 6 Puzzle 7+ 8+ 11+ 30 18 10+ 15 15 (g) 4, 5, 6, 7 Puzzle 11+ 30 42 4 28 20 4 17+ 20 15+ 13+ 35 11+ (i) 5, 6, 7, 8 Puzzle 48 NSSAL ©2011 42 4 (j) 6, 7, 8, 9 Puzzle 15+ 30 13+ 56 72 15+ 14+ 35 12+ 10+ (h) 4, 5, 6, 7 Puzzle 11+ 12+ 11+ 8+ 30 11+ 12 11+ 56 42 17+ 63 14+ 7 Draft C. D. Pilmer 5 by 5 KenKen Puzzles Insert the numbers the appropriate numbers into the grid such that: no number is repeated in the same row or column, and the numbers in the cages produce the target number using the indicated operation (e.g. 8 : find the numbers when multiplied give you 8). (a) 1, 2, 3, 4, 5 Puzzle 8 20 4+ (b) 2, 3, 4, 5, 6 Puzzle 6 15 5 18 4 4 2 5+ 42 4 35 6+ 9+ 11+ 5+ NSSAL ©2011 24 (d) 5, 6, 7, 8, 9 Puzzle 30 9 40 40 48 13+ 9+ 7 30 3 19+ 48 6+ 14+ 8+ 15+ 11+ 6 9+ (c) 4, 5, 6, 7, 8 Puzzle 32 8 3+ 5 12+ 54 63 45 20+ 10+ 42 6 72 13+ 8 Draft C. D. Pilmer KenKen Puzzles: Signed Numbers Insert the numbers the appropriate numbers into the grid such that: no number is repeated in the same row or column, and the numbers in the cages produce the target number using the indicated operation (e.g. -8 : find the numbers when multiplied give you -8). (a) 1, -2, 3 Puzzle -2 (b) -1, 2, -3 Puzzle 4+ 3 -1+ -1+ -6 -20 -4+ -1+ -12 3 -6 -3 4 48 -20 14+ -1+ -1+ -30 -5+ -12 8+ 24 1+ (h) 7, -8, 9 Puzzle -7 1+ (f) -4, 5, -6 Puzzle 5 (g) 6, -7, 8 Puzzle NSSAL ©2011 8 (e) 3, -4, 5 Puzzle 15 -56 1+ -2 (d) -3, 4, -5 Puzzle (c) 2, -3, 4 Puzzle (i) -7, 8, -9 Puzzle 63 -7+ -72 16+ -56 -25+ -56 1+ 9 Draft C. D. Pilmer (j) 1, -2, 3, -4 Puzzle -4 8 4+ -2 (k) 2, -3, 4, -5 Puzzle -6 -1+ -5 -20 -3+ -1+ -18 (m) 4, -5, 6, -7 Puzzle -30 15 -42 -5 -12 48 7 -1+ -1+ -72 -1+ 35 -7 -42 -1+ -1+ 5+ -40 NSSAL ©2011 -20 (o) 6, -7, 8, -9 Puzzle 6+ -56 6 24 (n) 5, -6, 7, -8 Puzzle -30 -1+ -28 -10+ -20 -1+ -1+ 15 2 (l) 3, -4, 5, -6 Puzzle -1+ -12 -1+ 1 8 63 48 10 Draft C. D. Pilmer (p) 1, -2, 3, -4, 5 Puzzle -6 -20 15 (q) 2, -3, 4, -5, 6 Puzzle -18 -5+ -12 -1+ -3+ -1+ -10 -8 -14+ -8+ 3 -10 -12 NSSAL ©2011 -42 8 -30 -30 45 -1+ -54 -42 -4 8+ (s) -5, 6, -7, 8, -9 Puzzle -7+ 3+ 5+ 4 -28 12+ 8 3+ 3+ (r) -4, 5, -6, 7, -8 Puzzle 48 6+ 12 5 1 1+ 15 -5 63 -72 -42 9+ -40 -40 8 -16+ -12+ 11 Draft C. D. Pilmer Magic Squares In a magic square, the numbers in each column, row, and diagonal all add up to the same number. For example, with the magic square on the right, the numbers in each column, row, and diagonal all add up to 30. 7 14 9 12 10 8 11 6 13 Complete each of the magic squares below. (a) (b) 3 5 (c) 6 3 7 2 7 6 7 (d) 5 (e) 5 (f) 4 4 10 8 6 1 8 (g) 5 (i) 4 12 7 NSSAL ©2011 7 8 7 (h) 2 3 12 5 9 4 10 3 12 9 8 6 Draft C. D. Pilmer Addition Pyramids: Whole Numbers With addition pyramids, the two numbers in adjoining boxes add to give the number in the box immediately above. 8 18 3 5 7 34 11 5 2 14 9 5 4 20 9 11 1 8 3 Insert the missing numbers in each of the following addition pyramids. 1. 2. 4 6 13 5 3. 10 4. 8 3. 9 6. 14 2 9 9 7. 8 8. 9. 9 7 2 10. 9 10 3 6 11. 18 2 12. 4 19 11 3 8 13. 14. 7 21 12 3 NSSAL ©2011 10 1 7 15. 9 2 14 4 13 6 8 Draft C. D. Pilmer 16. 17. 18. 30 16 10 7 6 0 5 8 19. 2 7 1 5 20. 13 21. 12 7 12 3 8 9 22. 2 23. 9 11 14 6 22 12 6 2 40 20 10 NSSAL ©2011 3 24. 17 3 7 10 5 Draft C. D. Pilmer Addition Pyramids: Decimal Numbers Complete the following addition pyramids. With addition pyramids, the two numbers in adjoining boxes add to give the number in the box immediately above. 1. 2. 3. 3.8 1.2 0.4 2.1 1.7 2 0.8 4. 5. 1.4 6. 3.4 1.4 1.1 0.9 7. 0.2 0.3 0.9 0.7 8. 3.1 0.6 9. 4.3 2.3 1.3 0.4 1.4 10. 1.4 1.8 0.8 1.1 11. 12. 2.7 1.2 0.3 1.4 0.9 13. 0.9 2.1 0.3 14. 3.4 2.6 3.2 0.2 2.7 1.7 1.8 0.4 0.3 17. 9.7 0.1 15. 1.8 16. 0.8 0.6 5.7 1.6 18. 4.3 5.3 4.6 2.4 2.5 0.9 NSSAL ©2011 1.3 0.7 1.1 15 1.6 0.9 0.4 Draft C. D. Pilmer Addition Pyramids: Signed Numbers Complete the following addition pyramids. With addition pyramids, the two numbers in adjoining boxes add to give the number in the box immediately above. 1. 2. 3. 2 -6 -5 4. 2 -6 -4 5. 4 -2 -4 6. -2 -3 -6 -1 7. -4 -5 9. -2 -6 -6 6 3 -3 10. -1 11. -2 12. -2 -5 -1 3 -3 7 -2 4 -4 13. -8 -2 14. 15. -8 1 -4 -5 16. 6 3 -4 18. -3 -1 2 2 -6 -1 -5 NSSAL ©2011 -5 -3 17. -4 -3 3 -6 -2 5 4 8. 3 -3 -6 16 -1 2 4 Draft C. D. Pilmer Row Factors and Column Factors In each question you have been provided with a chart that is missing four numbers. These numbers are the factors of the numbers found to the right of each row, and factors of the numbers found at the bottom of each column. Find the missing numbers. Example: 35 Answer: 15 5 3 15 28 7 4 28 35 12 12 Questions: (a) 10 (b) 18 12 8 6 27 (e) 60 24 18 (h) (k) NSSAL ©2011 30 35 (l) 14 32 28 (n) 28 56 40 72 7 8 20 30 54 40 42 16 (m) 21 (i) 54 18 27 3 4 18 15 24 28 45 10 (j) 30 (f) 20 20 36 8 8 9 (g) 12 6 7 21 20 2 15 (d) (c) 16 (o) 35 6 21 16 17 27 15 63 Draft C. D. Pilmer Whole Number Crossword Puzzle (A) A B C F H D E G I J K L M O R N P S Q T V U W Across: Down: A. Next even number after 384 B. 8 10 C. 22 + 10 + 10 D. 2000 + 100 + 30 + 9 G. one thousand, four hundred twenty E. 337 - 10 I. 5 more than 228 F. 8 90 J. Double 25 H. 7 less than 470 L. The product of 4 and 8 K. Next number in the following sequence. 70, 74, 78, 82, ____ O. 196 + 231 Q. 143 - 87 R. 5 times 7 T. The number of minutes in 1 hour and 34 minutes M. 3 sets of 9 N. increase 734 by 20 P. 11 + 5 + 3 + 9 S. Next number in the following sequence. 63, 60, 57, 54, ____ V. 42 W. A number between 10 and 20 that is divisible by both 5 and 3 NSSAL ©2011 U. The number of cents in 2 quarters, 1 dime, and 1 nickel 18 Draft C. D. Pilmer Whole Number Crossword Puzzle (B) A B C F H D E G I J K L M O R N P S Q T V U W Across: Down: A. 50 9 B. The next odd number after 51 C. 5 more than 81 D. six thousand, four hundred thirty-nine G. 4000 + 800 + 10 + 5 E. 213 rounded to the nearest tens I. increase 153 by 30 F. Next number in the following sequence 394, 399, 404, 409, ____ J. 63 - 29 L. ____ 7 = 4 O. The number of minutes in 6 hours and 4 minutes Q. A number between 10 and 20 that is divisible by 2, 3, 6, and 9 R. decrease 70 by 7 T. The product of 2 and 7 V. 5 + 10 + 2 + 30 H. 156 + 316 K. 72 M. Double 12 N. 1542 3 P. 6 sets of 11 S. 6 less than double 20 U. Next number in the following sequence 60, 54, 48, 42, ____ W. The even number before 88 NSSAL ©2011 19 Draft C. D. Pilmer Whole Number Crossword Puzzle (C) A B C F H D E G I J K L M O R N P S Q T V U W Across: Down: A. 70 8 B. 6 + 20 + 2 + 40 C. Triple 6 plus 1 D. nine thousand, seven hundred twelve G. 7558 rounded to the nearest hundreds E. Next number in the following sequence 886, 890, 894, 898, 902, ____ F. 15 23 I. increase 361 by 40 J. Number of cents in 3 quarters and 2 dimes L. 9 times 6 O. 800 + 70 + 4 Q. 37 + 56 R. 581 7 T. Double 13 H. The next multiple of 5 that follows 130 K. 8 sets of 4 M. 82 N. Number of minutes in 3 hours and 16 minutes P. 161 - 87 V. Next number in the following sequence 50, 47, 44, 41, ____ S. 39 decreased by 6 W. ____ 6 = 8 U. A number between 20 and 30 that is divisible by 2, 4, 7, and 14 NSSAL ©2011 20 Draft C. D. Pilmer Whole Number Crossword Puzzle (D) A B C F H D E G I J K L M O R N P S Q T V U W Across: Down: A. The next odd number after 769 B. 87 decreased by 9 C. 6 sets of 3 D. 8000 + 600 + 20 + 9 G. six thousand, three hundred seven E. 746 increased by 60 I. Next number in the following sequence 338, 344, 350, 356, ____ F. 50 less than 784 J. 444 6 H. Number of minutes in 2 hours and 37 minutes L. 25+47 K. triple 8 plus 4 O. 1 + 30 + 4 + 100 + 50 M. Next number in the following sequence 107, 104, 101, 98, ____ Q. 6 times 7 R. ____ 9 = 4 T. Number of cents in 2 quarters and 3 dimes V. A number between 40 and 50 that is a multiple of 3, 5, 9, and 15 N. 24 35 P. 92 S. Double 32 U. 119 - 37 W. The product of 8 and 9 NSSAL ©2011 21 Draft C. D. Pilmer Signed Number Crossword Puzzle (A) A B C F H D E G I J K L M O R S V N P Q T U W Across: Down: A. -6 7 B. -5 (-8) C. 24 + (-3) D. -90 (-20) G. 90 2 I. -20 + 650 E. 300 - (-100) F. Next number in the following sequence -44, -49, -54, -59, ____ J. (-3) + 3 9 H. Decrease -46 by 2. L. 78 - 2 (-1) K. 12 less than double 5 O. 8 sets of -2 M. 6 + (-5) (-4) Q. -10 + 40 + (-20) N. -22 + 3 R. 8 - 15 P. 2 S. 40 2 + (-8) T. 10 less than -1 V. 30 more than -10. W. 3 + 5 (-2) NSSAL ©2011 2 10 U. -5 (-3) - 4 (-3) 22 Draft C. D. Pilmer Signed Number Crossword Puzzle (B) A B C F H D E G I J K L M O R N P S Q T V U W Across: Down: A. -3 8 B. -40 (-7) C. 15 - 18 D. 3400 + (-200) G. Double 120 plus -5 E. 8 sets of -7 H. 40 more than -10 F. 5 + (-50) I. -70 (-6) K. The number between 0 and 20 that is divisible by both -6 and -9. J. 2 decreased by 7 L. Find the next number in the sequence. 16, 10, 4, -2, ____, … M. 4 5 9 N. 56 7 1 P. -5 times -5 S. 4 9 1 2 T. How many times does -4 go into -120? O. -24 - (-3) Q. 10 2 10 R. -18 - (-5) 3 V. 3 4 2 W. 2 4 NSSAL ©2011 U. (-3) 4 + 8 2 23 Draft C. D. Pilmer RAD Puzzles: Whole Numbers Using the numbers in the table below, correctly complete each puzzle. (a) 11 (b) - + = = - + + - = + 10 = - + - 12 = = = = = = 16 = = = + 0 = = 6 = = 8 = = = + = = = = = = = = - + - - 0 + 1 2 4 4 30 32 = 2 4 2 6 = 2 7 3 8 + 3 8 1 + 3 = 3 4 10 21 0 1 4 4 48 60 1 5 2 5 (c) = 2 5 2 6 + 2 6 3 9 3 24 (d) = = + + 28 + = = - + - = = = = 7 = 40 = - = = = = 6 = = = = = = = = = = 36 = = = 4 = 9 2 = + = 1 + + - 2 2 3 3 4 4 4 4 5 7 10 10 21 30 31 34 36 41 42 80 NSSAL ©2011 - 0 1 6 6 45 54 24 - 5 = 1 9 1 9 2 9 + = + 3 9 3 4 5 11 40 42 Draft C. D. Pilmer (e) (f) = - = 72 - - + + = - - 6 = = + = = = 40 2 + + + 1 2 7 7 60 70 = 63 3 7 = 9 = = = = 24 = = = = = = = = = = + - + + = 3 8 + 4 5 6 6 10 20 21 49 0 1 6 6 36 48 (g) 32 + 3 = 8 = = 3 7 = = 2 8 = 20 = 2 8 3 4 4 6 6 10 12 19 23 30 (h) + = - = = = = 1 21 + 1 2 7 7 24 56 NSSAL ©2011 28 = = = = = = + + 4 2 = = 2 - = = = = = - = = = 18 = = = = - 36 + = 2 8 = = = 3 8 3 8 + - = + 3 9 4 4 6 14 17 19 - = = - 9 2 2 3 3 4 5 6 7 8 9 10 11 13 15 24 27 28 30 50 81 25 Draft C. D. Pilmer (i) (j) - + = 6 = + = = = = = = 30 + 53 1 = = = = + = + + = = = 2 = = = + = = = = 48 = - 1 = = = = - + - 36 7 + 1 2 5 7 42 60 = 2 7 2 8 - = 3 3 3 4 5 10 14 16 18 30 0 1 6 7 49 85 (k) = 2 7 2 8 = 2 2 3 4 6 6 10 12 18 30 36 (l) - = + = 5 3 + + = = - + 7 = 10 = - = = = = 64 = = = 4 = = = = = = = = = 32 = = = = = = 48 + 7 + = = 1 1 2 6 8 8 8 8 8 9 10 11 12 16 22 40 42 72 84 88 NSSAL ©2011 - 1 2 6 6 64 72 26 = 2 8 8 = + 2 3 3 4 4 6 12 13 16 24 36 61 Draft C. D. Pilmer RAD Puzzles: Signed Numbers Using the numbers in the table below, correctly complete each puzzle. (a) (b) + = = - - 8 + = - - 13 = = = = = = 20 -1 - + + = -9 -7 -6 -2 -2 -1 19 24 -6 2 -8 = = = + = + 25 = 1 = = = -6 = = = + -2 = = = = = = = = + + + - + = -5 6 -4 8 + -4 9 -4 -3 10 11 -8 -8 -2 -1 42 48 (c) = -7 1 -6 2 = -4 2 -4 3 -3 4 -1 -2 -2 14 21 (d) + = = + = = + 22 = = - 52 = + = = = -4 = = = -6 3 = = = = = = = - - - + = = = = = -9 = = = 28 2 + + = -9 -9 -8 2 3 4 36 44 -7 8 NSSAL ©2011 = -6 9 - + -6 -2 -1 1 11 15 24 30 = 16 = -4 -8 -5 -4 -3 -3 -1 -1 2 3 5 7 15 16 19 20 25 33 45 72 76 27 Draft C. D. Pilmer (e) (f) + = = + = - = - -1 = -3 = - = = = = 25 = = = = = = 3 28 = = = = = = -7 = -8 + = = = -6 -5 -5 1 2 5 60 75 -4 6 -3 9 = 21 = = 15 = + + 14 -3 -3 -1 -1 10 15 24 50 + -9 -7 3 3 21 63 (g) = -5 4 + -5 4 = -4 7 -2 7 + + -1 9 2 3 13 14 (h) = - = + - 10 -4 + + = - = + 9 = -6 = = = = = 48 = = = + = -8 -8 -7 4 4 5 40 50 -6 8 = = = = 0 NSSAL ©2011 = = 64 + = = = = 12 = = = - -1 = = = + - 8 + + + -5 -3 -2 -1 2 10 12 22 25 33 -9 -6 0 1 30 36 28 = -5 2 -4 2 = -3 2 -3 3 -3 6 -2 -2 11 14 Draft C. D. Pilmer (i) (j) + = = - + 1 + = - = - -9 = = -2 = = 18 16 -5 = = = = - 40 = = = 8 = = = = = = = = = = = = = + + + + - + - = -9 -6 -6 -2 -1 0 16 36 -6 1 = -5 1 -4 2 -4 2 -3 -5 = -3 5 -2 9 -8 -8 0 2 20 35 -7 3 -7 4 (k) = -5 5 -4 5 -2 7 -2 -1 12 15 (l) = = 3 = = + + - - + - - = = = = = = = = = = -7 45 = = + = = = 14 = = = -5 = = + -1 = -9 -8 -8 -2 2 4 18 28 -4 5 NSSAL ©2011 = -3 6 + + -3 -2 -2 -2 10 10 13 16 -9 -6 6 6 30 43 29 = = 7 + = = 3 -5 = -6 9 = 2 -4 -3 -2 -1 2 5 10 12 14 15 19 20 Draft C. D. Pilmer Connect Four Whole Number Addition Game (A) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers on the Addend Strip whose sum is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate sum. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same sum but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Addend Strip. They then mark the square with that sum using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the addend strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 10 12 7 13 8 11 9 11 10 12 6 13 6 14 9 11 10 9 8 11 12 7 14 11 13 10 8 6 9 10 9 7 14 10 12 8 6 7 Addend Strip: 3 NSSAL ©2011 4 5 30 Draft C. D. Pilmer Connect Four Whole Number Addition Game (B) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers on the Addend Strip whose sum is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate sum. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same sum but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Addend Strip. They then mark the square with that sum using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the addend strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 12 11 18 14 16 14 15 14 13 16 12 13 16 12 15 10 14 17 15 17 14 18 15 13 13 10 13 16 11 18 15 12 11 17 14 10 Addend Strip: 5 NSSAL ©2011 6 7 8 9 31 Draft C. D. Pilmer Connect Four Whole Number Subtraction Game (A) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same difference but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that difference using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 3 2 5 4 6 4 7 4 6 2 3 5 6 0 1 0 5 6 3 5 3 7 2 4 4 3 2 4 1 0 1 7 0 5 3 6 Value 1: 13 NSSAL ©2011 Value 2: 12 11 10 9 6 32 7 8 9 Draft C. D. Pilmer Connect Four Whole Number Subtraction Game (B) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same difference but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that difference using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 3 5 4 5 6 5 6 8 7 9 10 7 9 7 6 3 5 9 7 10 5 7 8 4 8 6 9 4 9 3 4 7 8 10 5 6 Value 1: 15 NSSAL ©2011 Value 2: 14 13 12 5 33 6 7 8 9 Draft C. D. Pilmer Connect Four Whole Number Multiplication Game (A) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers on the Factor Strip whose product is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Factor Strip. They then mark the square with that product using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the fraction strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 6 45 27 5 45 8 10 0 36 18 20 15 36 8 12 4 0 36 2 18 45 27 6 12 20 4 15 0 10 9 27 12 3 6 36 20 Factor Strip: 0 NSSAL ©2011 1 2 3 4 34 5 9 Draft C. D. Pilmer Connect Four Whole Number Multiplication Game (B) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers on the Factor Strip whose product is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Factor Strip. They then mark the square with that product using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the fraction strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 18 2 30 8 12 24 9 54 12 18 10 6 24 5 8 6 54 20 10 30 18 5 24 3 24 4 20 12 2 18 12 54 9 30 5 8 Factor Strip: 1 NSSAL ©2011 2 3 4 5 35 6 9 Draft C. D. Pilmer Connect Four Whole Number Multiplication Game (C) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers on the Factor Strip whose product is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Factor Strip. They then mark the square with that product using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the fraction strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 14 63 6 28 15 30 42 12 30 63 14 10 8 21 54 18 54 21 35 15 8 28 42 12 18 54 14 63 6 35 10 28 42 12 21 18 Factor Strip: 2 NSSAL ©2011 3 4 5 6 36 7 9 Draft C. D. Pilmer Connect Four Whole Number Multiplication Game (D) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers on the Factor Strip whose product is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Factor Strip. They then mark the square with that product using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the fraction strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 42 12 16 8 24 48 6 72 45 54 15 18 56 24 21 16 56 20 14 30 10 40 6 27 54 18 36 12 42 21 15 72 27 14 35 10 5 6 Factor Strip: 2 NSSAL ©2011 3 4 37 7 8 9 Draft C. D. Pilmer Connect Four Whole Number Division Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate quotient (i.e. Value 1 divided by Value 2). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same quotient but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that quotient using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 6 24 12 15 12 2 8 3 6 30 4 15 18 12 10 9 8 12 6 8 2 24 6 9 30 4 15 12 4 3 6 18 9 2 10 18 Value 1: 30 NSSAL ©2011 Value 2: 24 18 12 6 1 38 2 3 Draft C. D. Pilmer Divisibility or Prime Connect Four Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place one paperclip on the Tens strip and one paperclip on the Ones strip. They have now generated a two digit number. That two digit number is either divisible by a single digit whole number greater than 1 (i.e. 2, 3, 4, 5, 6, 7, 8, 9), or the number is a prime. The player captures a single square that describes the number. For example if the two digit number is 14, it is divisible by 2 or 7 (of the choices we are given), then the player can capture either a square with a 2 on it, or a square with a 7 on it. If the number is prime, then a square marked P can be captured. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on either the Tens or Ones strip. They then mark the square that describes that number using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 6 4 7 2 6 3 P 9 6 8 P 2 5 3 P 5 4 9 4 8 9 7 3 2 7 2 4 6 8 P 6 P 9 3 2 5 Tens Strip: 1 NSSAL ©2011 Ones Strip 2 3 1 2 39 4 5 6 8 Draft C. D. Pilmer Connect Four Fraction Decimal Equivalency Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. The square with a specified decimal is captured by creating the equivalent fraction using the numerator and denominator strips at the bottom of the page. One paperclip is placed on each strip to do so. For example, if one chooses 3 on the numerator strip and 4 on the 3 denominator, then they can capture one square labeled 0.75 ( is equivalent to 0.75). They 4 either mark the square with an X or place a colored counter on the square. Only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with the equivalent decimal using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 0.4 1 0.2 0.4 1 0.5 0.6 0.2 0.3 0.25 0.3 0.4 0.25 0.1 0.75 0.8 0.3 0.6 0.75 0.2 0.4 0.8 0.2 1 0.2 0.8 0.25 0.1 0.5 0.4 0.1 0.5 0.3 0.75 0.6 1 Numerator (Top) Strip: 1 NSSAL ©2011 2 3 Denominator (Bottom) Strip: 4 4 40 5 10 Draft C. D. Pilmer Connect Four Adding Decimal Numbers Game (A) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers on the Addend Strip whose sum is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate sum. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same sum but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Addend Strip. They then mark the square with that sum using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the addend strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 0.8 1.4 1.3 2 0.8 1.1 1.1 0.5 0.9 1.5 1.2 0.9 1.4 1.6 0.8 1.1 0.5 2 1.2 0.7 1.4 1.7 1.6 0.8 0.8 1.3 2 0.5 1.3 1.4 1.4 1.7 1.1 0.9 1.5 0.7 Addend Strip: 0.2 NSSAL ©2011 0.3 0.5 0.6 41 0.9 1.1 Draft C. D. Pilmer Connect Four Adding Decimal Numbers Game (B) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers on the Addend Strip whose sum is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate sum. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same sum but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Addend Strip. They then mark the square with that sum using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the addend strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 3.8 3 4.8 2 1.6 3.4 2.2 2 2.6 4.8 0.8 3 2.6 4.2 5.2 3.8 4.4 5.2 0.8 3.4 4.4 3 1.6 4.2 2 2.6 3.8 2.2 3.4 2.6 4.4 1.6 3 5.2 4.8 2.2 2 2.4 Addend Strip: 0.2 NSSAL ©2011 0.6 1.4 42 2.8 Draft C. D. Pilmer Connect Four Subtracting Decimal Numbers Game (A) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same difference but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that difference using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 2.5 0.6 1.8 0.1 1.9 0.9 0.1 2 1.2 2.5 0.8 2.7 1.9 2.6 2.8 1.4 2.3 1.7 1.6 0.9 1.7 1.8 2 1.6 2 2.7 1.4 2.6 0.9 2.5 1.7 0.8 2.3 1.2 2.8 0.6 Value 1: 3 NSSAL ©2011 Value 2: 2.8 2.2 1.9 1.1 0.2 0.3 0.5 43 1 Draft C. D. Pilmer Connect Four Subtracting Decimal Numbers Game (B) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same difference but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that difference using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 2.4 1 1.4 1.2 3.2 0.8 0.4 2.2 0.8 2.6 1.4 1 2 3.2 1.6 1.8 2 2.4 1.8 0.6 3 2.8 1.2 0.4 0 1.2 1.4 0.8 0.6 2.6 2.8 1.6 2.2 0 3 1.8 Value 1: 3.6 NSSAL ©2011 Value 2: 3 2.4 2.2 1.6 0.4 0.8 1.2 1.6 44 Draft C. D. Pilmer Connect Four Fraction Percent Equivalency Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. The square with a specified percent is captured by creating the equivalent fraction using the numerator and denominator strips at the bottom of the page. One paper clip is placed on each strip to do so. For example, if one chooses 3 on the numerator strip and 4 on the 3 denominator, then they can capture one square labeled 75% ( is equivalent to 75%). They 4 either mark the square with an X or place a colored counter on the square. There may be other squares with that same difference but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with the equivalent decimal using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 40% 10% 20% 100% 40% 50% 25% 100% 25% 80% 60% 20% 30% 60% 40% 50% 30% 40% 75% 20% 30% 25% 80% 100% 20% 80% 75% 10% 20% 40% 10% 50% 100% 60% 30% 75% Numerator (Top) Strip: 1 NSSAL ©2011 2 3 Denominator (Bottom) Strip: 4 4 45 5 10 Draft C. D. Pilmer Connect Four Percentage Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two strips below; one on the "Percentage" strip and one on the "Of" strip. Take the percentage of that number and capture the appropriate square (e.g. 20% of 40 allows one to capture an "8" square). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same value but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that value using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 10 16 10 12 8 20 30 8 3 24 15 10 2 5 18 4 25 30 25 20 10 6 16 8 6 4 12 2 3 5 18 24 15 20 12 4 Percentage: Of: 10% 15% 20% 25% NSSAL ©2011 20 46 40 80 100 120 Draft C. D. Pilmer Connect Four Adding Signed Numbers Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers on the Addend Strip whose sum is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate sum. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same sum but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Addend Strip. They then mark the square with that sum using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the addend strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: -6 -14 7 -10 -2 -8 0 3 -8 -4 -6 16 -12 16 -2 -14 2 1 2 1 -10 9 -4 0 -4 7 -6 0 -12 -8 1 -14 9 3 -6 -2 1 8 Addend Strip: -7 NSSAL ©2011 -5 -1 47 Draft C. D. Pilmer Connect Four Subtracting Signed Numbers Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same difference but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that difference using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: -1 1 2 -4 -1 -7 12 -4 7 -10 9 12 -7 2 6 -2 -1 15 -1 4 -10 -7 1 7 15 7 -2 12 -4 6 -4 9 -7 -10 4 -1 Value 1: 10 NSSAL ©2011 Value 2: 2 -3 -6 4 48 1 -2 -5 Draft C. D. Pilmer Connect Four Multiplying Signed Numbers Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers on the Factor Strip whose product is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Factor Strip. They then mark the square with that product using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the factor strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 18 -30 -54 36 25 -12 9 10 4 -15 18 -54 4 -6 81 9 -12 -54 45 -15 25 -30 -27 25 -12 -27 4 45 10 18 -30 18 -15 36 -6 81 Factor Strip: -9 NSSAL ©2011 -5 -2 3 6 49 Draft C. D. Pilmer Connect Four Dividing Signed Numbers Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate quotient (i.e. Value 1 divided by Value 2). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same quotient but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that quotient using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: -8 -12 9 -5 2 4 -9 15 -4 6 10 -3 -15 2 6 -8 9 12 -6 -3 10 -9 -4 -5 12 -4 -8 -5 15 6 9 -15 -6 4 6 -12 Value 1: Value 2: -30 24 -18 12 NSSAL ©2011 -3 50 -2 2 6 Draft C. D. Pilmer Connect Four Squaring and Cubing of Signed Numbers Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paperclips on the two strips; one on the Base Strip and one on the Exponent Strip. Once they have chosen the values, they can capture one square with that appropriate value. For example, if the base value is -3, and the exponent is 2, then the player can capture a 9 square 3 9 . They either mark the square with an X or place a colored counter on the 2 square. Only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that value using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one paperclip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 4 125 25 -64 27 -1 -27 -8 4 -1 9 125 9 27 16 -27 -64 -8 -64 25 125 4 8 1 8 9 -1 27 25 4 4 -27 1 -8 16 9 Base Strip: -4 NSSAL ©2011 Exponent Strip: -3 -2 -1 2 3 51 5 2 3 (square) (cube) Draft C. D. Pilmer Connect Four Time Ahead Game (A) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place paper clips on the strips below; one on the Start Time Strip and one on the Minutes Ahead Strip. If the player chose 3:30 (start time) and 45 (minutes ahead), then they could capture a square labelled 4:15. They either mark the square with an X or place a colored counter on the square. There may be other squares with this same time but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that time using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 5:00 4:30 6:00 4:15 3:30 5:45 3:45 5:15 4:00 4:45 3:45 4:30 4:45 5:45 3:15 5:00 4:00 5:15 3:15 4:00 5:30 4:15 6:00 3:45 4:15 5:00 4:45 5:15 3:15 5:30 5:30 3:30 4:30 3:45 5:00 4:15 Start Time Strip Minutes Ahead Strip 3:00 3:30 4:00 4:30 5:00 NSSAL ©2011 52 15 30 45 60 Draft C. D. Pilmer Connect Four Time Ahead Game (B) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place paper clips on the strips below; one on the Start Time Strip and one on the Minutes Ahead Strip. If the player chose 2:45 (start time) and 30 (minutes ahead), then they could capture a square labelled 3:15. They either mark the square with an X or place a colored counter on the square. There may be other squares with this same time but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that time using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 3:45 3:00 4:15 3:15 4:00 3:30 3:15 4:30 2:30 3:30 2:45 3:45 2:45 4:00 3:15 3:45 3:30 4:15 3:45 3:30 4:15 3:00 4:00 3:15 4:30 3:00 3:45 3:15 2:30 3:30 3:15 2:45 3:30 4:00 3:45 3:00 Start Time Strip Minutes Ahead Strip 2:15 2:30 2:45 3:00 3:15 3:30 NSSAL ©2011 53 15 30 45 60 Draft C. D. Pilmer Connector In this two or three player game, your objective is to obtain as many points as possible by connecting numbers in straight lines vertically, horizontally, or diagonally on the playing board below. The point values are shown below. (The points are calculated at the end of the game.) 2 points for 2 in a row 4 points for 3 in a row 7 points for 4 in a row 10 points for 5 in a row 14 points for 6 in a row How do you capture a number? It involves rolling three six-sided dice. You use the three numbers rolled and the operations of addition, subtraction, multiplication, division, and exponentiation to capture one desired number. For example, if you rolled the numbers 2, 5, and 6, here are some of the possible numbers you could capture. 1 because 2 5 6 1 3 because 2 6 5 3 7 because 2 6 5 7 15 because 6 2 5 15 28 because 6 5 2 28 31 because 52 6 31 The first player rolls and captures a single number that they desire. That number should be marked with a symbol or color specific to that player. Then the next player rolls, captures, and marks their desired number. This process continues until it becomes difficult to complete the remaining numbers on the board. Tally the points at the end to determine the winner. 1 8 2 3 9 4 5 6 10 7 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 NSSAL ©2011 54 Draft C. D. Pilmer Fraction Fury Puzzles (A) With the fraction fury puzzle, your mission is to use the six 4 6 1 indicated numbers to create the desired nine fractions. However, 5 3 2 you are not permitted to repeat a number in a row or column (They can be repeated in a diagonal.). Hints are provided so that 1 5 4 you can figure out which fraction (proper or improper) belongs in each of the nine squares. If we look at the completed puzzle on 3 2 6 the right, the hint for the first square (top left) could have been " 1 0.2 ." There is only one possible solution based on this hint 2 1 5 4 6 4 3 and it is . For the second square (top center), the hint could 5 6 4 2 4 have been "Simplifies to 2." The possibilities are , , or . The can be eliminated 3 2 1 2 because we already used the 4 in the previous square (Can't repeat the same number in a row or 6 2 column.) At this point, you are unable to determine whether or belongs in square two. 3 1 You will have to look at the hints provided for the other squares before determining which of the two possible answers is appropriate for square two. Please note that you must be comfortable with fractions, decimals and percentages to complete these puzzles. (a) 1, 2, 3, 4, 5, 6 Puzzle Whole Number 60% 2 - 0.75 300% (b) 2, 3, 4, 5, 6, 7 Puzzle Equal to 6 NSSAL ©2011 of 3 9 1.2 14 3 2 5 1 2 1 16 3 6 Little > 1 2 5 2.5 150% 16 55 5 3.5 - 2.75 14 Between 1 and 2 Equal to Between 0.5 and 1 Double 1 3 7 10 Draft C. D. Pilmer (c) 3, 4, 5, 6, 7, 8 Puzzle 1 3 1 1.5 (d) 4, 5, 6, 7, 8, 9 Puzzle 1 Little > 2 7 Little < 1 Equal to 2 2 1 1 1 8 2 Between 1.5 and 2 of 150% 6 of 3.5 8 Little < 1 2 NSSAL ©2011 Equal to 9 14 2 Equal to 3 8 2 - 0.2 3 1 1 7 175% Little < 2 1 3 14 8 1 Equal to 3 8 12 (f) 2, 4, 5, 6, 8, 9 Puzzle 1 1 3 5 450% 2 Little > 1 10 3 Little > 1 4 (e) 1, 2, 3, 5, 7, 9 Puzzle 1 1 Little < 9 1 Between 0.5 and 1 2 5 1 1 4 8 Between 1 and 2 9 of 300% 3 sets of 2 Equal to 4 Little > 2 1 4 56 3 Equal to 2 0.8 1 2 Equal to 2 3 Draft C. D. Pilmer (g) 1, 3, 4, 5, 8, 9 Puzzle (h) 1, 2, 5, 6, 7, 8 Puzzle 2 5 1 6 2 Between 1 and 1.5 Close to 0 160% 2.25 Whole Number 50% of 1.2 Equal to 2 7 18 5 3 4 1 3 Little > 1 11 12 Equal to 1 1 Equal to 2 1.5 7 3 20 5 1 3 7 3 Whole Number Little > 1 Between 0.5 and 1 Equal to 4 Equal to 1 4 125% 250% 3 2 Between 1 and 1.5 (j) 2, 5, 6, 7, 8, 9 Puzzle 2 8 Equal to 1 12 Between 2 and 3 NSSAL ©2011 Close to 1 18 (i) 3, 4, 5, 6, 7, 8 Puzzle 1 of 0.8 Little > 1 1 20 3 16 57 5 16 Between 1 and 1.5 Little < 1 Between 1 and 1.5 Equal to 75% 50% of 4 9 Draft C. D. Pilmer Fraction Fury Puzzles (B) All of the puzzles on this page use the numbers 1 through 8. 1. 2 3 11 3 5 21 7 8 1 21 Equal to 2 3 7 1 8 8 2. 2 1 3 4 1 4 Double 2 3 1 3 1 Little > 6 2 1 Equal to 7 2 sets of 2 5 1 5 4 Whole Number >4 2 - 1.6 Between 2.5 and 3 2 Equal to 5 1 6 3 7 6 3 Equal to 16 120% Between 2.7 and 3.6 600% 3 - 1.25 21 8 21 Whole Number >4 Equal to 1 2 NSSAL ©2011 58 1 1 3 8 Equal to 1 - 0.6 1 Triple 2 1 5 14 1 6 9 1 14 4 of 1 1 6 1 3 1.75 1 of 3 4 1 Between 1.5 and 2 3. Equal to 4 2 160% Double 2 1 3.5 4 80% 8 sets of Equal to 75% 2 4 of Equal to 1 - 0.75 Equal to 3 Whole Number <6 18 10 One part of six 1 9 16 11 16 Equal to 2 2 Draft C. D. Pilmer Math Logic Puzzles For each, find the numbers represented by the symbols , , and . Hint: For each of the puzzles, one of the equations, not necessarily the first equation, allows you to solve for a symbol very quickly. Puzzle 1: -=2 +1=6 +=8 Puzzle 4: -=3 + + = 10 4 = 8 Puzzle 7: -3= + = 2 14 = 2 Answers (in no particular order) = 4, = 6, = 2 = 14, = 6, = 4 = 2, = 5, = 3 NSSAL ©2011 Puzzle 2: Puzzle 3: +=8 +=6 +=7 Puzzle 5: +=8 3 = 6 + = 10 Puzzle 6: -2=7 + + = 17 = 18 Puzzle 8: -=5 ++=9 += Puzzle 9: ++2= 3=4 -=6 24 = ++1=9 + = 3 = 6, = 4, = 12 = 11, = 3, = 8 = 4, = 2, = 5 = 6, = 2, = 9 = 7, = 5, = 1 = 1, = 7, = 4 59 Draft C. D. Pilmer Answers 3 by 3 KenKen Puzzles (A) (page 1) (a) (b) 2 1 3 3 1 2 1 3 2 2 3 1 3 2 1 1 2 3 (c) (d) 1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2 (e) NSSAL ©2011 (f) 3 1 2 3 2 1 1 2 3 2 1 3 2 3 1 1 3 2 60 Draft C. D. Pilmer 3 by 3 KenKen Puzzles (B) (page 2) (a) (b) 4 5 3 3 5 4 3 4 5 4 3 5 5 3 4 5 4 3 (c) (d) 5 3 4 3 4 5 4 5 3 5 3 4 3 4 5 4 5 3 (e) NSSAL ©2011 (f) 5 4 3 4 3 5 3 5 4 3 5 4 4 3 5 5 4 3 61 Draft C. D. Pilmer 3 by 3 KenKen Puzzles (C) (page 3) (a) (b) 5 6 7 7 5 6 7 5 6 6 7 5 6 7 5 5 6 7 (c) (d) 6 5 7 6 7 5 5 7 6 5 6 7 7 6 5 7 5 6 (e) NSSAL ©2011 (f) 7 6 5 5 7 6 5 7 6 6 5 7 6 5 7 7 6 5 62 Draft C. D. Pilmer 3 by 3 KenKen Puzzles (D) (page 4) (a) (b) 8 7 9 9 7 8 9 8 7 7 8 9 7 9 8 8 9 7 (c) (d) 7 9 8 9 8 7 9 8 7 8 7 9 8 7 9 7 9 8 (e) NSSAL ©2011 (f) 8 7 9 7 9 8 7 9 8 8 7 9 9 8 7 9 8 7 63 Draft C. D. Pilmer 4 by 4 KenKen Puzzles (A) (page 5) (a) (b) 2 3 1 4 3 1 2 4 4 1 2 3 2 4 3 1 3 2 4 1 4 2 1 3 1 4 3 2 1 3 4 2 (c) NSSAL ©2011 (d) 1 2 4 3 2 1 3 4 3 4 2 1 4 3 1 2 4 1 3 2 3 4 2 1 2 3 1 4 1 2 4 3 64 Draft C. D. Pilmer 4 by 4 KenKen Puzzles (B) (pages 6 and 7) (a) 1, 2, 3, 4 Puzzle (b) 1, 2, 3, 4 Puzzle 1 3 4 2 2 3 1 4 4 1 2 3 4 1 2 3 2 4 3 1 3 2 4 1 3 2 1 4 1 4 3 2 (c) 2, 3, 4, 5 Puzzle NSSAL ©2011 (d) 2, 3, 4, 5 Puzzle 4 5 2 3 5 3 4 2 2 3 5 4 3 2 5 4 5 4 3 2 2 4 3 5 3 2 4 5 4 5 2 3 65 Draft C. D. Pilmer (e) 3, 4, 5, 6 Puzzle (f) 3, 4, 5, 6 Puzzle 6 4 3 5 4 3 6 5 5 6 4 3 6 4 5 3 3 5 6 4 5 6 3 4 4 3 5 6 3 5 4 6 (g) 4, 5, 6, 7 Puzzle NSSAL ©2011 (h) 4, 5, 6, 7 Puzzle 4 6 5 7 7 4 6 5 7 5 4 6 5 6 7 4 5 7 6 4 4 7 5 6 6 4 7 5 6 5 4 7 66 Draft C. D. Pilmer (i) 5, 6, 7, 8 Puzzle (j) 6, 7, 8, 9 Puzzle 8 6 7 5 7 9 6 8 5 7 8 6 6 8 7 9 6 8 5 7 9 6 8 7 7 5 6 8 8 7 9 6 5 by 5 Ken Ken Puzzles (page 8) (a) 1, 2, 3, 4, 5 Puzzle (b) 2, 3, 4, 5, 6 Puzzle 2 5 4 1 3 6 3 5 4 2 4 3 5 2 1 4 2 3 6 5 5 1 3 4 2 2 4 6 5 3 1 4 2 3 5 3 5 4 2 6 3 2 1 5 4 5 6 2 3 4 NSSAL ©2011 67 Draft C. D. Pilmer (c) 4, 5, 6, 7, 8 Puzzle (d) 5, 6, 7, 8, 9 Puzzle 4 7 6 8 5 9 5 8 7 6 8 4 5 7 6 6 8 9 5 7 6 5 8 4 7 8 7 6 9 5 7 6 4 5 8 5 9 7 6 8 5 8 7 6 4 7 6 5 8 9 KenKen Puzzles: Signed Numbers (pages 9 to 11) (a) 1, -2, 3 Puzzle (b) -1, 2, -3 Puzzle (c) 2, -3, 4 Puzzle -2 1 3 -3 -1 2 2 4 -3 1 3 -2 2 -3 -1 -3 2 4 3 -2 1 -1 2 -3 4 -3 2 (d) -3, 4, -5 Puzzle (e) 3, -4, 5 Puzzle (f) -4, 5, -6 Puzzle -5 -3 4 3 5 -4 5 -4 -6 4 -5 -3 -4 3 5 -4 -6 5 -3 4 -5 5 -4 3 -6 5 -4 NSSAL ©2011 68 Draft C. D. Pilmer (g) 6, -7, 8 Puzzle (h) 7, -8, 9 Puzzle (i) -7, 8, -9 Puzzle 6 8 -7 -8 9 7 -9 -7 8 -7 6 8 7 -8 9 8 -9 -7 8 -7 6 9 7 -8 -7 8 -9 (j) 1, -2, 3, -4 Puzzle (k) 2, -3, 4, -5 Puzzle -4 3 1 -2 -3 2 -5 4 1 -2 3 -4 -5 -3 4 2 3 -4 -2 1 4 -5 2 -3 -2 1 -4 3 2 4 -3 -5 (l) 3, -4, 5, -6 Puzzle (m) 4, -5, 6, -7 Puzzle -4 3 -6 5 -7 -5 4 6 3 -6 5 -4 6 -7 -5 4 5 -4 3 -6 -5 4 6 -7 -6 5 -4 3 4 6 -7 -5 NSSAL ©2011 69 Draft C. D. Pilmer (n) 5, -6, 7, -8 Puzzle (o) 6, -7, 8, -9 Puzzle 5 -8 -6 7 8 -9 -7 6 -6 7 -8 5 6 8 -9 -7 -8 5 7 -6 -7 6 8 -9 7 -6 5 -8 -9 -7 6 8 (p) 1, -2, 3, -4, 5 Puzzle (q) 2, -3, 4, -5, 6 Puzzle 3 -4 5 1 -2 6 -3 -5 2 4 -2 5 1 -4 3 -5 4 2 6 -3 1 3 -2 5 -4 -3 2 6 4 -5 -4 1 3 -2 5 4 6 -3 -5 2 5 -2 -4 3 1 2 -5 4 -3 6 (r) -4, 5, -6, 7, -8 Puzzle (s) -5, 6, -7, 8, -9 Puzzle 5 -6 -8 -4 7 8 -7 6 -9 -5 -4 -8 5 7 -6 -9 6 -7 -5 8 7 5 -6 -8 -4 -5 8 -9 -7 6 -8 -4 7 -6 5 6 -9 -5 8 -7 -6 7 -4 5 -8 -7 -5 8 6 -9 NSSAL ©2011 70 Draft C. D. Pilmer Magic Squares (page 12) (a) (b) (c) 8 1 6 3 8 1 7 2 9 3 5 7 2 4 6 8 6 4 4 9 2 7 0 5 3 10 5 2 9 4 9 4 11 10 3 8 7 5 3 10 8 6 5 7 9 6 1 8 5 12 7 6 11 4 5 10 3 6 11 4 12 5 10 4 6 8 5 7 9 7 9 11 9 2 7 10 3 8 8 13 6 (d) (e) (g) (f) (h) (i) Addition Pyramids: Whole Numbers (pages 13 and 14) 1. 4 3. 6 9 5 4. 10 8 NSSAL ©2011 2. 10 2 3. 4 14 71 10 3 6. 9 5 13 9 8 1 Draft C. D. Pilmer 7. 8. 21 9 7 10. 9 12 2 10 3 4 13. 8 8 14. 16. 11 6 6 0 19. 13 8 8 7 5 22. 2 12 5 17 3 NSSAL ©2011 4 6 10 11 5 72 3 2 6 22 18 6 10 8 40 12 2 13 5 24. 8 6 7 20 19 3 8 2 8 28 15 6 13 5 2 21. 39 9 1 20 7 3 23 9 3 19 10 7 10 3 8 6 30 9 15 23. 36 4 18. 6 27 14 10 50 12 3 5 1 20. 25 13 2 0 24 5 7 3 6 6 15. 16 10 5 7 26 18 5 13 1 7 17. 19 12 2 9 4 5 12. 11 9 29 2 21 12 3 4 6 10 9 7 29 18 19 7 3 11. 11 7 16 9 6 18 9. 18 1 10 12 5 7 3 Draft C. D. Pilmer Addition Pyramids: Decimal Numbers (page 15) 1. 6.3 2.5 0.4 2. 3.8 2.1 4. 0.4 1.7 0.5 7. 2.3 1.9 1.4 0.1 10. 0.4 1.4 9.3 4 1.7 0.3 13. 3 0.9 6 3.4 0 0.8 1.1 0.6 1.9 0.4 NSSAL ©2011 0.9 2.1 15. 1.7 0.7 0.5 1.2 73 0.6 2.5 2.1 1.4 1.6 0.7 0.9 0.3 5.3 4.6 1.1 2.7 1.8 18. 2.5 0.7 6.2 1.8 0.8 0.8 0.1 3.5 1 4.3 1.8 0.7 0.6 3.2 0.4 1.6 0.8 1.3 8.9 3 2.4 1.5 0.7 5.4 4.3 2.1 0.6 1.4 1.1 3.7 0.9 1.4 17. 9.7 0.7 12. 0.3 2.5 0.2 1.5 5.7 2.6 1.6 16. 1.2 14. 1.8 1.6 0 2.1 2.5 1.8 1.5 1.2 0.8 4.3 2.4 2.7 1.4 0.6 9. 5.1 5.3 1.4 0.3 2.3 11. 2.3 0.9 0.7 0.8 0.6 2.3 1.1 2.2 2 1.4 6. 4.5 1.7 1.3 0.4 0.2 0.4 8. 3.1 1.8 3.4 0.3 3.8 1 0.8 5. 0.8 1.4 3. 1.2 2.2 0.9 2.2 1.2 2.8 1.9 0.9 0.4 0.5 1.4 Draft C. D. Pilmer Addition Pyramids: Signed Numbers (page 16) 1. -14 -11 -6 2. -3 2 8 5 -2 -8 6 10. 9 4 13 -3 7 13. -2 -6 -2 -14 -4 -3 -7 -8 -3 -8 -3 -10 NSSAL ©2011 -4 -4 2 74 6 13 -11 19 23 -4 -5 1 -6 3 -5 -2 -3 8 -7 2 5 -2 3 6 3 -5 4 18. -1 -6 -11 -3 -6 -5 -1 -5 -3 -9 -5 8 -6 3 17. 2 7 -7 -7 -1 -5 15. -3 -4 -5 0 -8 -7 -2 -1 -13 -10 1 16. 3 -9 -2 12. -5 14. -2 -2 0 -4 5 -1 -5 3 1 -6 3 -7 -1 5 4 9. -3 -3 11. 5 -10 -4 -6 8 -6 -10 -3 -1 12 -5 8. -4 6. 7 -4 3 2 -4 -9 -7 -2 -2 -2 -1 7. 6 5. -3 -9 2 -6 4 7 3. 0 -5 4. 2 4 -1 -9 2 8 -6 Draft C. D. Pilmer Factor Rows and Factor Columns (page 17) (a) 2 5 10 4 3 12 8 15 3 9 27 7 1 7 21 9 9 2 18 4 5 20 36 10 3 8 24 9 2 18 27 16 9 6 54 8 5 40 72 30 (d) (g) (j) (m) NSSAL ©2011 (b) (e) (h) (k) (n) 6 3 18 1 2 2 6 6 6 10 60 4 2 8 24 20 3 6 18 5 9 45 15 54 5 4 20 6 7 42 30 28 7 8 56 3 2 6 21 16 75 (c) (f) (i) (l) (o) 4 5 20 2 6 12 8 30 4 7 28 1 3 3 4 21 8 5 40 1 7 7 8 35 7 2 14 4 8 32 28 16 5 7 35 3 9 27 15 63 Draft C. D. Pilmer Whole Number Crossword Puzzle (A) (page 18) 3 8 6 0 7 4 2 6 3 5 5 1 2 2 1 3 0 2 4 3 4 3 4 3 2 7 9 8 2 7 7 5 8 9 0 6 6 4 6 6 1 5 Whole Number Crossword Puzzle (B) (page 19) 4 5 0 3 4 4 1 7 2 3 3 4 NSSAL ©2011 6 6 7 6 4 8 4 8 3 6 8 2 8 3 1 0 9 4 2 5 4 1 1 5 9 8 4 3 8 76 6 Draft C. D. Pilmer Whole Number Crossword Puzzle (C) (page 20) 5 6 0 8 3 1 4 3 5 9 3 3 7 9 7 0 5 4 8 8 1 9 6 1 0 6 2 3 6 1 4 9 4 2 0 2 3 6 8 2 4 8 Whole Number Crossword Puzzle (D) (page 21) 7 7 1 8 7 1 3 5 7 7 6 4 NSSAL ©2011 8 1 5 8 6 6 4 2 1 3 1 8 3 2 0 6 9 2 9 8 5 4 8 7 8 2 0 8 7 77 2 Draft C. D. Pilmer Signed Number Crossword Puzzle (A) (page 22) - 4 2 0 - - 6 4 8 2 7 2 1 1 8 3 4 0 - - 2 4 1 0 0 0 0 - 2 - 6 1 4 - 0 2 0 9 0 2 - 7 Signed Number Crossword Puzzle (B) (page 23 ) - 3 2 4 8 - 0 4 - - 3 4 NSSAL ©2011 2 5 9 3 2 2 5 8 - - - 3 0 5 6 0 1 - - 1 9 8 0 3 0 1 78 4 Draft C. D. Pilmer RAD Puzzles: Whole Numbers (pages 24 to 26) (a) 11 (b) - 3 = 8 = 6 + 2 60 6 = 10 = 2 5 + - + - + - + - 21 1 2 4 3 12 0 2 1 0 = = = = = = = = = = 6 48 32 2 = 16 = 10 + 6 = 8 = 3 + 5 = = = = = = = = = = 4 0 4 30 7 24 2 3 4 9 + - + - - 1 2 8 2 = 4 = 3 + (c) 10 + 3 = 5 = 1 + 4 + 3 = 45 = 9 5 (d) 3 = 30 = 2 + 28 42 + - + - 4 31 5 21 4 7 2 9 0 1 = = = = = = = = = = 7 6 40 - 34 = 6 = 42 6 = 36 = 9 4 = = = = = = = = = = 80 36 10 41 4 54 11 40 9 1 - - + + - - + 3 9 2 NSSAL ©2011 2 = 4 = 1 + 79 - 5 = 4 = 1 + 3 Draft C. D. Pilmer (e) 10 (f) 7 = 70 = 72 - 2 36 + 12 = 48 = 6 8 - - + - - + 6 4 7 8 5 6 8 2 3 0 = = = = = = = = = = 7 6 60 + 3 = 63 = 9 4 = 24 = 3 8 = = = = = = = = = = 40 2 3 6 49 6 23 4 30 6 + + + - + + 7 1 20 + 1 = 21 = 3 (g) 32 + 19 = 20 = 10 2 8 = 3 = 30 - 27 (h) + 24 = 56 = 7 8 24 - + + 8 17 2 2 4 4 2 6 15 3 = = = = = = = = = = 2 28 4 7 = 28 = 14 - 10 = 18 = 2 9 = = = = = = = = = = 1 21 19 6 3 4 50 36 13 81 + + + - - 1 7 3 NSSAL ©2011 3 = 9 = 8 + 80 - 5 = 2 = 11 - 9 Draft C. D. Pilmer (i) 18 (j) - 4 = 14 = 7 2 6 + 2 = 8 = 7 + 1 + + + + + 3 1 16 53 1 2 2 6 7 0 = = = = = = = = = = 2 12 6 5 = 30 = 60 4 = 48 = 49 - 1 = = = = = = = = = = 42 8 3 30 7 36 10 30 85 2 - - - + - 5 3 7 + 3 = 10 = 2 (k) 9 6 = 18 = 36 2 12 = 36 = 6 6 (l) - 1 = 8 = 40 5 3 + + + - + 8 7 8 10 11 61 6 4 3 10 = = = = = = = = = = 16 64 72 - 8 = 64 = 4 2 = 32 = 2 16 = = = = = = = = = = 12 1 22 88 8 72 2 4 48 13 + + - - + 2 8 6 NSSAL ©2011 7 = 42 = 84 81 1 = 8 = 24 3 Draft C. D. Pilmer RAD Puzzles: Signed Numbers (pages 27 to 29) (a) -6 (b) + 8 = 2 = 10 - 8 3 14 = 42 = 21 2 - - + - - + -4 11 -4 19 -7 -2 13 -7 25 -4 = = = = = = = = = = 1 -6 24 -3 = -8 = -9 + 1 = -6 = -4 + -2 = = = = = = = = = = 20 -1 -2 9 6 48 -3 -8 -2 -1 - + + + + - + -5 -8 -4 + -2 = -6 = -1 + (c) -8 4 = -2 = 2 -1 3 = 45 = 20 + 25 (d) + 44 = 36 = -6 -6 15 + + - 4 22 -9 30 1 5 -1 -5 52 33 = = = = = = = = = = -6 3 -2 2 = -4 = 24 -3 = -9 = 72 -8 = = = = = = = = = = -1 11 28 3 9 -1 16 7 76 2 + - - - + 15 -3 2 + NSSAL ©2011 -9 = -7 = 8 - 82 + 19 = 16 = -4 -4 Draft C. D. Pilmer (e) -6 (f) + 1 = -5 = 15 -3 7 9 = 63 = 21 3 + - - -4 -1 -5 60 -1 4 13 -9 14 -3 = = = = = = = = = = 3 28 24 - -1 = 25 = 75 -4 = -7 = 7 -1 = = = = = = = = = = -3 9 50 15 6 2 3 -5 21 4 - + + + + -3 14 -8 + 10 = 2 = 5 + (g) 2 -7 = -2 = 3 + -5 + 0 = -4 = 2 -2 (h) 25 = 50 = 5 10 -4 - + - + - + -3 33 -2 -7 -6 -9 -3 -3 9 -2 = = = = = = = = = = 4 36 -6 -8 = 48 = 12 3 = 12 = 11 - -1 = = = = = = = = = = -1 64 8 22 0 6 8 -2 14 1 + + - + + + + - 4 30 -5 NSSAL ©2011 -8 = 40 = 10 83 -5 = -6 = -3 2 Draft C. D. Pilmer (i) -1 (j) + -2 = -3 = -4 + 1 -8 -2 = 4 = 20 - 16 - + - - 9 0 -6 -9 1 -5 -7 12 -5 -8 = = = = = = = = = = 2 40 -9 -2 = 18 = 36 5 = 8 = -4 -2 = = = = = = = = = = -5 1 16 -6 5 5 0 15 3 2 + + + + - + - -3 35 -4 -2 = 2 = -6 (k) -3 -5 = -7 = 7 -1 10 = 20 = 14 + 6 (l) -2 = 6 = 18 3 2 + - - + - - 13 -2 -8 -9 10 43 19 -4 9 -6 = = = = = = = = = = -7 45 10 + 4 = 14 = -2 -9 = -5 = 5 -1 = = = = = = = = = = -5 5 28 16 -3 3 -6 7 30 -2 + + + - -4 15 -2 NSSAL ©2011 -1 = 2 = -8 84 + -3 = 12 = 6 2 Draft C. D. Pilmer Fraction Fury Puzzles (A) (pages 55 to 57) (a) 1, 2, 3, 4, 5, 6 Puzzle 2 3 1 5 4 5 6 4 3 6 6 1 4 3 (c) 3, 4, 5, 6, 7, 8 Puzzle 7 6 3 5 7 6 8 4 5 9 2 3 7 NSSAL ©2011 5 4 8 8 9 6 7 6 9 2 2 2 5 2 4 8 85 4 6 4 1 5 9 5 5 9 9 (f) 2, 4, 5, 6, 8, 9 Puzzle 9 1 7 4 7 3 3 8 7 5 6 2 5 5 8 7 7 7 6 6 (e) 1, 2, 3, 5, 7, 9 Puzzle 1 6 6 9 4 3 4 4 3 5 2 (d) 4, 5, 6, 7, 8, 9 Puzzle 8 8 4 3 2 5 4 5 3 2 3 7 7 5 4 2 5 1 2 6 (b) 2, 3, 4, 5, 6, 7 Puzzle 8 6 5 9 Draft C. D. Pilmer (g) 1, 3, 4, 5, 8, 9 Puzzle 4 1 3 8 5 8 9 5 1 2 9 3 7 1 4 8 7 8 3 4 6 8 2 5 4 2 9 7 7 7 8 2 8 5 5 7 6 5 3 5 9 3 6 6 (j) 2, 5, 6, 7, 8, 9 Puzzle 6 7 7 1 6 (i) 3, 4, 5, 6, 7, 8 Puzzle 5 2 1 4 1 6 8 8 5 8 5 3 4 9 (h) 1, 2, 5, 6, 7, 8 Puzzle 6 7 5 8 5 8 2 6 9 Fraction Fury Puzzles (B) (page 58) 1. 2 8 5 1 7 5 7 6 6 1 4 8 4 4 8 2 5 6 6 2 7 2 8 3 1 3 3 NSSAL ©2011 4 5 7 3 1 86 Draft C. D. Pilmer 2. 6 4 1 3 7 2 7 4 8 4 5 3 5 4 6 7 6 1 7 5 1 3 5 6 3 2 2 4 4 8 1 7 7 3 6 1 1 7 2 3 6 1 8 5 2 5 7 6 3 6 3 2 NSSAL ©2011 4 1 8 8 5 8 5 3. 2 8 4 8 2 87 Draft C. D. Pilmer