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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!

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

##### MP2 Think abstractly!

Students take problems and reformat them mathematically. This is helpful because mathematics lets them use powerful operations like addition.

##### MP3 Work together!

Students discuss their strategies to collaboratively solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

##### MP4 Model reality!

Students create a model that mimics the real world. Discoveries made by manipulating the model often hint at something in the real world.

##### MP5 Know the tools.

Students master the tools at their fingertips - whether it's a pencil or an online app.

##### MP6 Be precise!

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!

Students learn to identify patterns. This is one of the things that the human brain does very well. We sometimes even identify patterns that don't really exist 😉

##### MP8 Be lazy!?!

Students learn to seek for shortcuts. Why would you want to add the numbers one through a hundred if you can find an easier way to do it?