This prime set of Neat Numbers is intended to supplement work with learning essential number properties and operations at all levels in el-hi education . . . from First Grade to Calculus.
Two of my major goals in teaching math have always been, first, to show how what we’re learning can be used and, second, to blend the “topic for the day” with other subjects whenever possible (integrate subjects and teach cross-curricularly, as it were). To that end, each of the 71/73 Neat Numbers is neat because it is significant in history, literature, or science. The 876 expressions to simplify that follow were designed to achieve mathematical understanding while planting seeds of history, literature, and science. As such they should be quite palatable for both student and teacher. Each of the 876 problems has been created to be done with no calculator. I’m absolutely certain that teachers will come up with other ways to use the expressions but I have used the problems as class openers/closers, test questions for “No Calculator” parts of tests (and given bonus points for being able to identify the significance of the number they’ve simplified), and as problems for students to do on white boards or blackboards (for schools which still have them.)
For each of the 71/73 numbers that follow I’ve created twelve different expressions such that when evaluated/simplified will yield the number at the top of the page. There are 71 different Neat Numbers; I repeated two of them. The problems on each page are arranged, for the most part, in order of increasing difficulty. Of course, that difficulty may well vary from teacher to teacher according to the order that various material has been presented. At the end of each set of twelve expressions to be simplified you will find three comments on the Neat Number at the top of the page, and a math fact. The first comment is the significance of the number, the second comment is a statement on if/when the number is considered a date what was happening mathematically on that date, the third is a comment on something that happened “exactly x years prior to, or from, that date”. The math fact is a fact that I try to tie in with my second comment
. . . though I’m not always successful.
Generally speaking, my problem number ones are number patterns that are to be added. I tried to get patterns pleasant to a primary student’s eye, but I also tried to work in numbers that add to ten. In the problem number twos, I tried to encourage the use of the commutative property to group “things that add to a multiple of ten” together. The number threes are meant to encourage a little more difficult additions as well as some mental subtraction where the numbers, though larger, can be subtracted mentally . . . with practice. The number fours are meant to develop the order of operations when adding, subtracting, and multiplying, to learn how to keep track of the zeros when multiplying multiples of ten, and to set up squaring powers of ten. The numbers from five to eight are to help middle school student with learning order of operations and powers and roots. The squares of the numbers work their way from 1 through 25, the cubes from 1 through 12. Problems nine and ten encourage exponent and root work for the numbers from 1 through 5 raised to the fourth and fifth powers. Problem number eleven works in some fractional exponents, some logs, and some trig functions. And problem number twelve has all of the above . . . with an occasional definite integral to evaluate.
The intent of A Substantial Prime Number of Neat Numbers is to help with awareness of math facts and properties that will help with ANY pre-college test taker . . . grade level requisite exams, graduation exams, SATs, ACTs, quiz bowls, math counts. A “companion volume” to this will follow in a couple weeks which will aim to help in sharpening the skills of those who’d like to increase mental math speed. It will work with various math short cuts and “tricks.” It’s title might be Dang You’re Fast at Math! Time will tell.
Should you be interested in buying both companion volumes, it can be done at a discount from buying each individually. Please type in "Neat Numbers, Dang" in the Search Rectangle if you are interested. THANK YOU!!
Substantial Prime Number Neat Numbers,order of operation,exponents,mental math
by Value Added Publishing
is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License