FROM THE FILEAuthor(s): John GoughSource: The Arithmetic Teacher, Vol. 41, No. 8 (APRIL 1994), p. 498Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41196060 .

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FROM THE FILE

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J Spatial Thinking

DOTTY SQUARES This activity reinforces the concept of a square with a challenging spatial-visualization strategy game. It is an alternative to tic-tac-toe or to go moku (five-in-a-row). Playing is similar to tic-tac-toe, but the

winning formation is a square of circles or of crosses instead of the standard line-of-three.

Grade level: 3-8 0 . Objective: Students will develop spatial thinking and game strategies. ^ ^ Materials: Each pair of students will need a sheet of square dot paper ^ ^

and a pencil. • (•) • X • • • Alternative materials: V •••••• (a) a Peg-Board and pegs in two colors or ^ (b) a sheet of square grid paper and counters in two colors.

Students play a game, one player using circles, the other using crosses. They take turns "capturing" a dot by drawing their cross on, or their circle around, any dot that has not yet been "captured." Alternatively, players "capture" by placing a peg of their color in any empty peg hole or by placing a counter of their color into any empty square in the grid. The winner of the game is the player who first completes a pattern by forming the four corners of a square with his or her circles or crosses. The

edges of a winning square may contain extra dots "captured" by the opponent; this situation does not prevent the square from winning. The square may be of any size and may be oriented diagonally, but it must be precisely "square" (i.e., have right-angled corners and equal-length sides). Of course, players may attempt to block one another. In the diagram shown, the player using crosses has just completed a tilted square. Does the reader see that it is actually square?

From the file of John Gough, Deakin University, Malvern, Victoria, Australia 3144

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498 ARITHMETIC TEACHER

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