Take 10 II

Investigation number 12:
Take Ten Cards (I am not sure now where I got it from, but it makes an excellent low floor/high ceiling activity, and is capable of many, many What Ifs...Give students the numbers one to ten from a pack of cards, Ace counts as one.  Place those ten cards in this configuration so that no consecutive cards are adjacent to each other, this goes for up-and-down, side-to-side and diagonally. Initially students just skirmish and are happy to find a solution, if you give each student the whole page of 6 solutions they will get the idea that you expect more than one answer. Once many answers are found, ideas develop about which card position(s) is important, and why. If they can articulate this, then you know they have been using algebraic thinking. If they don't automatically say something about how many different solutions are possible, question them - don't give it away.
What If... many students change the configuration of the cards,then test to see if solutions are possible. A lovely twist is to make 10 and 1 "wrap-around" so they are considered as consecutive.
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