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#### Square Dance

##### (MathPickle, 2016)

This mini mathematical universe is used to get your students generating and discussing true and false conjectures. Make sure to reward true AND false conjectures. If students are hesitant to come up with false conjectures you should suggest your own or prod them into making one.

After you look at the slide show above you might be interested in seeing Andy Juell’s numerical pattern that describes the 160 patterns that appeared in the second to last slide:

1 (9, 7, 5, 3, 1) 2 (9, 7, 5, 1, 1) 3 (9, 7, 4, 2, 3) 4 (9, 7, 4, 1, 2) 5 (9, 7, 3, 1, 1) 6 (9, 7, 2, 3, 2) 7 (9, 7, 1, 1, 1) 8 (9, 6, 4, 5, 1) 9 (9, 6, 4, 1, 3) 10 (9, 6, 3, 5, 2) 11 (9, 6, 3, 1, 2) 12 (9, 6, 2, 5, 1) 13 (9, 6, 1, 4, 1) 14 (9, 6, 1, 2, 3) 15 (9, 6, 1, 1, 2) 16 (9, 5, 3, 1, 1) 17 (9, 5, 2, 4, 3) 18 (9, 5, 1, 4, 2) 19 (9, 5, 1, 1, 1) 20 (9, 4, 5, 1, 2) 21 (9, 4, 2, 3, 1) 22 (9, 4, 1, 3, 2) 23 (9, 4, 1, 2, 1) 24 (9, 3, 5, 2, 2) 25 (9, 3, 4, 2, 1) 26 (9, 3, 1, 3, 1) 27 (9, 3, 1, 1, 1) 28 (9, 2, 5, 1, 2) 29 (9, 2, 4, 1, 1) 30 (9, 2, 3, 2, 1) 31 (9, 1, 3, 1, 1) 32 (9, 1, 1, 1, 1) 33 (8, 6, 7, 3, 1) 34 (8, 6, 7, 1, 1) 35 (8, 6, 4, 2, 5) 36 (8, 6, 3, 1, 3) 37 (8, 6, 2, 3, 4) 38 (8, 6, 1, 5, 1) 39 (8, 6, 1, 2, 4) 40 (8, 6, 1, 1, 3) 41 (8, 5, 7, 4, 1) 42 (8, 5, 7, 2, 3) 43 (8, 5, 7, 1, 2) 44 (8, 5, 3, 1, 2) 45 (8, 5, 2, 6, 2) 46 (8, 5, 1, 3, 4) 47 (8, 5, 1, 1, 2) 48 (8, 4, 7, 1, 1) 49 (8, 4, 5, 6, 2) 50 (8, 4, 5, 1, 3) 51 (8, 4, 2, 6, 1) 52 (8, 4, 2, 3, 2) 53 (8, 4, 1, 5, 1) 54 (8, 4, 1, 2, 2) 55 (8, 3, 7, 4, 1) 56 (8, 3, 7, 2, 1) 57 (8, 3, 5, 6, 1) 58 (8, 3, 5, 2, 3) 59 (8, 3, 4, 6, 2) 60 (8, 3, 4, 2, 2) 61 (8, 3, 1, 4, 1) 62 (8, 3, 1, 2, 3) 63 (8, 3, 1, 1, 2) 64 (8, 2, 7, 3, 1) 65 (8, 2, 7, 1, 1) 66 (8, 2, 5, 2, 4) 67 (8, 2, 5, 1, 3) 68 (8, 2, 4, 5, 2) 69 (8, 2, 4, 1, 2) 70 (8, 2, 3, 5, 1) 71 (8, 2, 3, 2, 2) 72 (8, 1, 6, 3, 1) 73 (8, 1, 6, 1, 1) 74 (8, 1, 4, 5, 1) 75 (8, 1, 4, 1, 3) 76 (8, 1, 3, 5, 2) 77 (8, 1, 3, 1, 2) 78 (8, 1, 2, 5, 1) 79 (8, 1, 1, 4, 1) 80 (8, 1, 1, 2, 3) 81 (8, 1, 1, 1, 2) 82 (7, 5, 6, 1, 4) 83 (7, 5, 3, 6, 4) 84 (7, 5, 2, 6, 3) 85 (7, 4, 6, 3, 5) 86 (7, 4, 6, 1, 3) 87 (7, 4, 2, 6, 2) 88 (7, 4, 2, 5, 3) 89 (7, 4, 1, 5, 2) 90 (7, 3, 6, 2, 3) 91 (7, 3, 4, 6, 3) 92 (7, 3, 1, 4, 2) 93 (7, 2, 6, 5, 1) 94 (7, 2, 6, 2, 4) 95 (7, 2, 6, 1, 3) 96 (7, 2, 4, 5, 3) 97 (7, 2, 3, 5, 2) 98 (7, 2, 3, 4, 3) 99 (7, 1, 6, 4, 1) 100 (7, 1, 6, 2, 3) 101 (7, 1, 6, 1, 2) 102 (7, 1, 5, 2, 4) 103 (7, 1, 5, 1, 3) 104 (7, 1, 2, 5, 2) 105 (7, 1, 2, 4, 3) 106 (7, 1, 1, 4, 2) 107 (6, 7, 5, 1, 4) 108 (6, 7, 3, 4, 5) 109 (6, 7, 3, 1, 2) 110 (6, 7, 1, 5, 2) 111 (6, 7, 1, 3, 4) 112 (6, 7, 1, 1, 2) 113 (6, 4, 2, 5, 2) 114 (6, 4, 1, 5, 1) 115 (6, 3, 1, 4, 1) 116 (6, 3, 1, 3, 2) 117 (6, 2, 3, 5, 1) 118 (6, 2, 3, 4, 2) 119 (6, 1, 5, 3, 4) 120 (6, 1, 5, 1, 2) 121 (6, 1, 4, 5, 3) 122 (6, 1, 2, 5, 1) 123 (6, 1, 2, 4, 2) 124 (6, 1, 1, 4, 1) 125 (6, 1, 1, 3, 2) 126 (5, 7, 4, 1, 2) 127 (5, 7, 2, 4, 3) 128 (5, 7, 2, 3, 2) 129 (5, 7, 1, 2, 2) 130 (5, 6, 1, 4, 3) 131 (5, 3, 6, 4, 3) 132 (5, 2, 6, 2, 2) 133 (5, 1, 3, 4, 2) 134 (4, 7, 5, 3, 4) 135 (4, 7, 5, 2, 3) 136 (4, 7, 1, 4, 1) 137 (4, 7, 1, 2, 3) 138 (4, 7, 1, 1, 2) 139 (4, 6, 3, 5, 3) 140 (4, 6, 1, 4, 2) 141 (4, 5, 6, 2, 2) 142 (4, 5, 1, 4, 1) 143 (4, 5, 1, 3, 2) 144 (4, 2, 6, 2, 3) 145 (4, 2, 6, 1, 2) 146 (4, 2, 5, 4, 2) 147 (4, 1, 5, 2, 3) 148 (4, 1, 5, 1, 2) 149 (4, 1, 3, 4, 1) 150 (3, 7, 5, 1, 3) 151 (3, 7, 4, 1, 2) 152 (3, 7, 2, 2, 3) 153 (3, 7, 2, 1, 2) 154 (3, 5, 6, 1, 2) 155 (3, 5, 2, 3, 2) 156 (3, 4, 6, 2, 2) 157 (2, 7, 3, 1, 2) 158 (2, 7, 1, 1, 2) 159 (2, 5, 2, 4, 2) 160 (2, 5, 1, 3, 2)

#### Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

##### MP1 Toughen up!

This is problem solving where our students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

##### MP3 Work together!

This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

##### MP6 Be precise!

This is where our students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

##### MP7 Be observant!

One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.