This puzzle is one that will enable you and/or your students to discover some of the history of Halloween. It’s a mathematical history . . . and "the doer(s)" will be the one(s) supplying the arithmetic. Don’t despair! Each of the expressions to be evaluated can either be done mentally, or with minimal pencil-work. Each of the expressions DOES have at least one square to be evaluated, and some elementary adding and subtracting will come into "play." There are some numbers that end in five to be squared. These can be scratched out . . . or the mental method that I've given below (and in the puzzle explanation) can be used/taught. The problems are not at all that difficult, and the facts, learning, short cut mental math, and "Scottish saying solution" will be appreciated by fifth graders through adult.
Whenever you square a number ending in 5, there’s any easy way to perform the calculation mentally. Consider 45 squared . To perform the square mentally, take the number in the ten’s place (that’s 4) and add one to it (getting 5). Now multiply those two numbers together (getting 20, I hope), and put a 25 on the end of that . . . 2025. That’s it, 45 x 45 = 2025. 65 squared = ? Add one on to the 6 getting 7, 6 x 7 is 42, slop a 25 on the end to get 4225. It even works with a number like 115 squared . . . but you have to be slick, and then you have to know what 11 x 12 is. Of course if you do, you know that 115 squared is 13225.
History Halloween,Halloween by the Numbers,Practice and Fun Squaring numbers
by Value Added Publishing
is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License