# Last Square Standing and Squares that End in 5

After the children solved the Locker Problem last week and determined that the ten open lockers were all square number 1,4,9,16,25,36,49,64,81,and 100, I decided to further explore square numbers. I was disappointed that there were no games on the internet that promoted the learning of square numbers so I created my own. I called it “Last Square Standing.”

The object of the game is to be able to always place your square on the game board and identify the square area. The One Die Version of Last Square Standing is played on a 16 x 16 board and the first move is made on the perimeter. If you roll a 5, you create a 5 x 5 square adjacent (next to) to the perimeter and write 25 inside of the square. The next person rolls and if she rolls a 6, has to create a 6 x 6 square adjacent to the 5 x 5 square. The objective of the game is to prevent the other person from being able to create their square. If they are unable, they lose. The best strategy is to create your squares to take up the greatest space frustrating the other player. You can play this game with 1 or more players.

There is a Two Dice Version of Last Square Standing played on a 32 x 32 board so if you roll double sixes your square is 12 x 12 and you create a 144 square area. The same rules apply as in the One Die Version.

Please see the rule and game boards attached.

For all of the 2nd through 6th graders we also explored squares that end in 5 and looked at the patterns created. I also developed an algorithm for these squares. I looked at 5^2 or 5 squared, 15^2 = 225, and 25^2 = 625 and found that all squares that end in 5  end in 25 and the 100s place is alway the product of the 10s digits and the next consecutive integer; for example,  95^2 you would multiply 9 x 10 and tack on 25 to the end so 995^2 is 9,025. 95^2 is 9900 with a 25 tacked on so 990,025. 9995^2 is 99,000,025. Believe it or not, 995^2 or 995 x 995 is incredibly easy as you simply multiply 99 x 100 which of course is 9900 and then tack on a 25, so 990,025 is your answer. There are many other patterns in this sequence of numbers: 25, 225, 625, 1225, 2025, 3025, 4225, 5625, 7225 and so on.

AttachmentSize
Last_Square_Standing_Game.pdf653.42 KB
Squaring_Numbers_that_end_in_5.pdf27.51 KB