Here is a timely, informative, and helpful extra credit opportunity for the enterprising student who wants to know more! This puzzle, along with most of the other puzzles that I write, is a mental exercise in integrating, reviewing, and blending. I want to integrate more than one subject in a learning activity, cross-curricular learning as it were. All of life’s experiences are integrated activities. I want to review previous material a student (puzzle doer) has been exposed to. We get better at tasks in life by repetition. I want to blend a learning experience with as many other learning situations as I can. Few life experiences are isolated happenings.
This puzzle blends the basic arithmetic of exponents and order of operations found in early algebra with finding out some interesting facts about some mothers throughout history. (oldest, youngest, most children, etc.)
In the introduction that accompanies the puzzle I DO explain a process to square numbers ending in five mentally, for the student (puzzle doer) who needs some take home assistance or review. They will only have to use it four or five times in the puzzle . . . but it's a handy thing to know. The next paragraph IS that explanation.
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.
Armed with this mental math trick, and a recall of basic exponents and order of operations the student, or puzzle-doer, will find some astounding mother facts . . . and a truism.
Mothers by the Numbers, A Mothers' Day Math Essay
by Jay Waggoner, Value Added Publishing
is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License