Math Games and Puzzles

Transcription

1 Math Games and Puzzles (Level III Math Teacher Resource) Draft (NSSAL) C. David Pilmer 20 (Last Updated: December 203)

2 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.

3 Table of Contents Introduction (for Instructors) ii 3 by 3 KenKen Puzzles (A to D). 4 by 4 KenKen Puzzles (A and B) by KenKen Puzzles. 8 KenKen Puzzles: Signed Numbers 9 Magic Squares. 2 Addition Pyramids: Whole Numbers.. 3 Addition Pyramids: Decimal Numbers Addition Pyramids: Signed Numbers.. 6 Row Factors and Column Factors 7 Whole Number Cross Word Puzzles (A to D) 8 Signed Numbers Cross Word Puzzles (A and B) 22 RAD Puzzles: Whole Numbers 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) 4 Connect Four Subtracting Decimal Numbers Game (A and B). 43 Connect Four Fraction Percent Equivalency Game 4 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. 0 Connect Four Squaring and Cubing of Signed Numbers Game. Connect Four Time Ahead Game (A and B).. 2 Connector 4 Fraction Fury Puzzles (A and B). Math Logic Puzzles. 9 Answers.. 60 NSSAL i Draft

4 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 (a) 39 8 (b) 6 (c) Convert 8 3 (d) (e) (f) to a decimal. (g) (h) (i) 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 960s and 970s, 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.. 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 ii Draft

5 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 iii Draft

6 3 by 3 KenKen Puzzles (A) Insert the numbers, 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 + (b) (c) 4+ 6 (d) (e) 4+ 6 (f) NSSAL Draft

7 3 by 3 KenKen Puzzles (B) Instructions: Insert the numbers 3, 4, and 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 8+ (b) (c) 4 (d) (e) 2+ + (f) NSSAL 2 Draft

8 3 by 3 KenKen Puzzles (C) Instructions: Insert the numbers, 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. 3 : find two numbers when multiplied give you 3). (a) 3 3+ (b) (c) (d) (e) 42 (f) NSSAL 3 Draft

9 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) (b) (c) (d) (e) + 72 (f) NSSAL 4 Draft

10 4 by 4 KenKen Puzzles (A) Insert the numbers, 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) (b) (c) 6 2 (d) NSSAL Draft

11 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), 2, 3, 4 Puzzle (b), 2, 3, 4 Puzzle (c) 2, 3, 4, Puzzle (d) 2, 3, 4, Puzzle NSSAL 6 Draft

12 (e) 3, 4,, 6 Puzzle (f) 3, 4,, 6 Puzzle (g) 4,, 6, 7 Puzzle (h) 4,, 6, 7 Puzzle (i), 6, 7, 8 Puzzle (j) 6, 7, 8, 9 Puzzle NSSAL 7 Draft

13 by 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), 2, 3, 4, Puzzle (b) 2, 3, 4,, 6 Puzzle (c) 4,, 6, 7, 8 Puzzle (d), 6, 7, 8, 9 Puzzle NSSAL 8 Draft

14 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), -2, 3 Puzzle (b) -, 2, -3 Puzzle (c) 2, -3, 4 Puzzle (d) -3, 4, - Puzzle (e) 3, -4, Puzzle (f) -4,, -6 Puzzle (g) 6, -7, 8 Puzzle (h) 7, -8, 9 Puzzle (i) -7, 8, -9 Puzzle NSSAL 9 Draft

15 (j), -2, 3, -4 Puzzle (k) 2, -3, 4, - Puzzle (l) 3, -4,, -6 Puzzle (m) 4, -, 6, -7 Puzzle (n), -6, 7, -8 Puzzle (o) 6, -7, 8, -9 Puzzle NSSAL 0 Draft

16 (p), -2, 3, -4, Puzzle (q) 2, -3, 4, -, 6 Puzzle (r) -4,, -6, 7, -8 Puzzle (s) -, 6, -7, 8, -9 Puzzle NSSAL Draft

17 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 Complete each of the magic squares below. (a) 6 (b) 3 (c) (d) 4 (e) 4 (f) (g) (h) 4 (i) NSSAL 2 Draft

18 Addition Pyramids: Whole Numbers With addition pyramids, the two numbers in adjoining boxes add to give the number in the box immediately above Insert the missing numbers in each of the following addition pyramids NSSAL 3 Draft

19 NSSAL 4 Draft

20 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 NSSAL Draft

21 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 NSSAL 6 Draft

22 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: Answer: Questions: (a) 0 (b) 8 (c) (d) 27 (e) 60 (f) (g) 8 (h) 8 (i) (j) 24 (k) 20 (l) (m) 4 (n) 6 (o) NSSAL 7 Draft

23 Whole Number Crossword Puzzle (A) A B C D E F G H I J K L M N O P Q R S T U V W Across: A. Next even number after 384 C G. one thousand, four hundred twenty I. more than 228 J. Double 2 L. The product of 4 and 8 O Q R. times 7 T. The number of minutes in hour and 34 minutes V. 4 2 W. A number between 0 and 20 that is divisible by both and 3 Down: B. 8 0 D E F H. 7 less than 470 K. Next number in the following sequence. 70, 74, 78, 82, M. 3 sets of 9 N. increase 734 by 20 P S. Next number in the following sequence. 63, 60, 7, 4, U. The number of cents in 2 quarters, dime, and nickel NSSAL 8 Draft

24 Whole Number Crossword Puzzle (B) A B C D E F G H I J K L M N O P Q R S T U V W Across: A. 0 9 C. more than 8 G I. increase 3 by 30 J L. 7 = 4 O. The number of minutes in 6 hours and 4 minutes Q. A number between 0 and 20 that is divisible by 2, 3, 6, and 9 R. decrease 70 by 7 T. The product of 2 and 7 V W. The even number before 88 Down: B. The next odd number after D. six thousand, four hundred thirty-nine E. 23 rounded to the nearest tens F. Next number in the following sequence 394, 399, 404, 409, H K. 7 2 M. Double 2 N P. 6 sets of S. 6 less than double 20 U. Next number in the following sequence 60, 4, 48, 42, NSSAL 9 Draft

25 Whole Number Crossword Puzzle (C) A B C D E F G H I J K L M N O P Q R S T U V W Across: A C. Triple 6 plus G. 78 rounded to the nearest hundreds I. increase 36 by 40 J. Number of cents in 3 quarters and 2 dimes L. 9 times 6 O Q R. 8 7 T. Double 3 V. Next number in the following sequence 0, 47, 44, 4, W. 6 = 8 Down: B D. nine thousand, seven hundred twelve E. Next number in the following sequence 886, 890, 894, 898, 902, F. 23 H. The next multiple of that follows 30 K. 8 sets of 4 M. 8 2 N. Number of minutes in 3 hours and 6 minutes P S. 39 decreased by 6 U. A number between 20 and 30 that is divisible by 2, 4, 7, and 4 NSSAL 20 Draft

26 Whole Number Crossword Puzzle (D) A B C D E F G H I J K L M N O P Q R S T U V W Across: A. The next odd number after 769 C. 6 sets of 3 G. six thousand, three hundred seven I. Next number in the following sequence 338, 344, 30, 36, J L O Q. 6 times 7 R. 9 = 4 T. Number of cents in 2 quarters and 3 dimes V. A number between 40 and 0 that is a multiple of 3,, 9, and W. The product of 8 and 9 Down: B. 87 decreased by 9 D E. 746 increased by 60 F. 0 less than 784 H. Number of minutes in 2 hours and 37 minutes K. triple 8 plus 4 M. Next number in the following sequence 07, 04, 0, 98, N P. 9 2 S. Double 32 U NSSAL 2 Draft

27 Signed Number Crossword Puzzle (A) A B C D E F G H I J K L M N O P Q R S T U V W Across: A C (-3) G I J. (-3) L (-) O. 8 sets of -2 Q (-20) R. 8 - T. 0 less than - V. 30 more than -0. W. 3 + (-2) Down: B. - (-8) D. -90 (-20) E (-00) F. Next number in the following sequence -44, -49, -4, -9, H. Decrease -46 by 2. K. 2 less than double M. 6 + (-) (-4) N P S (-8) U. - (-3) - 4 (-3) NSSAL 22 Draft

28 Signed Number Crossword Puzzle (B) A B C D E F G H I J K L M N O P Q R S T U V W Across: A C. - 8 G. Double 20 plus - H. 40 more than -0 I. -70 (-6) J. 2 decreased by 7 L. Find the next number in the sequence. 6, 0, 4, -2,, O (-3) Q R (-) 3 V Down: B. -40 (-7) D (-200) E. 8 sets of -7 F. + (-0) K. The number between 0 and 20 that is divisible by both -6 and -9. M. 4 9 N. 6 7 P. - times - S T. How many times does -4 go into -20? U. (-3) W NSSAL 23 Draft

29 RAD Puzzles: Whole Numbers Using the numbers in the table below, correctly complete each puzzle. (a) (b) - = = + = 0 = = 6 = + 6 = 8 = = = = = (c) = = = = = 6 = = 36 = = = + - = = + (d) NSSAL 24 Draft

30 (e) (f) = = = = = 63 = 9 = 24 = = = + = 20 = (g) (h) 32 + = = = = = 28 = 2 - = 8 = = = + - = = NSSAL 2 Draft

31 (i) - = = + = = + (j) = 30 = = 48 = = = = = (k) - = = 3 = = (l) = 64 = 4 = 32 = = = = 8 = NSSAL 26 Draft

32 RAD Puzzles: Signed Numbers Using the numbers in the table below, correctly complete each puzzle. (a) (b) + = = - 8 = = = -8 = + = -6 = = = + = = (c) + = = = = + (d) = -4 = -6 3 = -9 = = = - + = 6 = NSSAL 27 Draft

33 (e) + = = = = (f) = 2 = 3 28 = -7 = = = + 4 = = (g) = = = = (h) = 48 = = 2 = = = = = NSSAL 28 Draft

34 (i) + = = + = = - 6 (j) = 8 = 40 = 8 = = = -3 - = = (k) = = 3 = = + (l) = 4 = -7 4 = - = = = + = = NSSAL 29 Draft

35 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:. 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: Addend Strip: NSSAL 30 Draft

36 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:. 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: Addend Strip: NSSAL 3 Draft

37 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:. 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 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 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: Value : Value 2: NSSAL 32 Draft

38 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:. 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 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 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: Value : Value 2: NSSAL 33 Draft

39 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:. 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: Factor Strip: NSSAL 34 Draft

40 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:. 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: Factor Strip: NSSAL 3 Draft

41 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:. 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: Factor Strip: NSSAL 36 Draft

42 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:. 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: Factor Strip: NSSAL 37 Draft

43 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:. 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 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate quotient (i.e. Value 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: Value : Value 2: NSSAL 38 Draft

44 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:. 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 (i.e. 2, 3, 4,, 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 4, 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: P P 2 3 P P 6 P Tens Strip: Ones Strip NSSAL 39 Draft

45 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:. 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 denominator, then they can capture one square labeled 0.7 ( 3 is equivalent to 0.7). 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: Numerator (Top) Strip: Denominator (Bottom) Strip: NSSAL 40 Draft

46 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:. 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: Addend Strip: NSSAL 4 Draft

47 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:. 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: Addend Strip: NSSAL 42 Draft

48 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:. 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 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 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: Value : Value 2: NSSAL 43 Draft

49 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:. 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 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 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: Value : Value 2: NSSAL 44 Draft

50 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:. 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 denominator, then they can capture one square labeled 7% ( 3 is equivalent to 7%). 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% 0% 20% 00% 40% 0% 2% 00% 2% 80% 60% 20% 30% 60% 40% 0% 30% 40% 7% 20% 30% 2% 80% 00% 20% 80% 7% 0% 20% 40% 0% 0% 00% 60% 30% 7% Numerator (Top) Strip: Denominator (Bottom) Strip: NSSAL 4 Draft

51 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:. 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: Percentage: 0% % 20% 2% Of: NSSAL 46 Draft

52 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:. 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: Addend Strip: NSSAL 47 Draft

53 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:. 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 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 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: Value : Value 2: NSSAL 48 Draft

54 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:. 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: Factor Strip: NSSAL 49 Draft

55 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:. 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 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate quotient (i.e. Value 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: Value : Value 2: NSSAL 0 Draft

56 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:. 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 2 square 3 9. They 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 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: Base Strip: Exponent Strip: (square) 3 (cube) NSSAL Draft