The Importance of Addends

In the course of the last few years, I have taken on students of every skill level and age you can imagine, from 3 to 83, from those who could not count yet to those who just needed some brush up in preparation for calculus. A recurring theme among those students who are getting the poorest grades and saying they aren't "getting it" is the inability to make tens (or nines).

Seems basic enough, but you'd be surprised how many students come to me because they are failing algebra who cant add fractions, multiply quickly and easily in their heads or answer simple questions like 6 plus what makes 10? Seriously, they don't know their addends and their parents are mystified that their smart little 14 year old isn't doing well in algebra, or worse expect they won't do well because they themselves didn't do well, as if poor math skills can "run in the family" due to poor math genes.

The problem especially for girls is once they start getting bad grades in math ALL the grades suffer; not always but certainly often enough and although it is not specific to females it is more pronounced. When I was traveling the nation I heard that story over and over again from women of all ages: they could point to the year that they got their first failing grade in math as the year that their academic careers either came to an end or as the year that marked beginning of the end. Studies from the University of Women and others have borne this anecdotal evidence out.

There have been long dissertations written as to why this is but the point is that it is a fact not just my opinion and it is beyond the scope of this essay. Let it suffice to say males preserve their ego by thinking there is something wrong with math or the teacher if they don't "get it" while women tend to think "there must be something wrong with me" if they don't get it. This leads to all manner of self esteem issues and to students who graduate high school and then go on to college asking important questions like "what kind of degree can I get out of this university without taking much math?"

Recently I started doing some work at a local intermediate school, grades 6 through 8, where I am exposed to larger groups of students and can notice some trends and commonalities. I set it up so that I was allowed to work with "honors" and "accelerated" students sometimes labeled gifted and talented ("GT" for short) as well as the students who were "challenged" or receiving "F's".

Without exception the F students were unable to easily answer questions like "what does four need to make ten?", or "what does five need to make nine?" Even some of the GT kids were slow to answer or needed the aid of their fingers.

To some this is stunning. I had a parent sit in on their students first lesson. The parent was mortified to see that when asked some basic addends like those already mentioned and also ones past ten like "what's 6 + 7?" or "8 + 5?" their child either responded incorrectly or took quite a bit of time to arrive at an answer. When presented with a simple fractions problem 1/2 + 1/3 the expression was one of horror. 2/5 was the sheepish reply...

Gee, why are they having trouble in algebra?

I see it all the time. So I simply get back to basics as part of my tutoring. I remind students and parents of the five basic concepts, and make simple addition and subtraction part of the session every time.

The 45 addends are foundational math. It has been said that you can do all math with just addition and subtraction...it just takes longer. Multiplication is just adding repeatedly, division can be thought of as subtracting repeatedly although I personally don't teach it that way. I find that concept based teaching makes learning math much easier but students will still run into trouble if they get bogged down in computation while they are trying to figure out what to do to solve a problem. This applies to all areas of math... whether it's algebra or calculus or just percentages and fractions.

I can teach them what to do, but they still have problems with how to do it because they lack the most basic skill sets. The good news is these skill sets are easily learned and with a little practice easily mastered.

Any student who does not suffer from serious learning disabilities (and even then) can learn to add 3 + 7 to get 10. I have one student who is considered severely disabled but if you ask him any of the combinations for 10 he can tell you without hesitation, and certainly faster than the "normal" students twice his age at the intermediate school.

Knowing all the addends but at leaste the two digit combinations for nine and ten are quite useful for adding any two numbers with ease. Very young students can now see that adding 7 + 5 to get 12 and adding 57 + 5 to get 62 is basically the same problem with some extra tens along for the ride... 7 + 5 is always 12; the way I teach them do this is 7 needs 3 to be ten so it takes the 3 out of the 5 and there are 2 left over: 7 + 5 = 7 + (3 + 2) = (7 + 3) + 2 = 10 + 2 = 12 that process takes a long time to type out but takes a fraction of second in your head, once you understand what you are doing.

The next step is subtracting, which the way I teach it is just small addition. I taught a couple of 13 year old girls how to make change for 100.00 They were quite pleased with themselves once they figured out all they had to do was make three nines and a ten. Suddenly a problem like this took seconds:

100.00
-64.57
----------

The way they did it (and this make take you a few seconds to "get") was 6 needs 3 to make 9, 4 needs 5 to make 9, 5 needs 4 to make 9, and 7 needs 3 to make 10. We did it from left to right, not right to left and we didn't count backwards, borrow or otherwise consternate ourselves.

100.00
-64.57
----------
35.43

After just a little practice I have students who can tell me the answers to these kinds of problems as fast as I can write them on the board. Often exclaiming "WOW, that's EASY!" Another student exclaimed, "I've never felt so smart in my life!" after knocking out five or six in a row.

Then we can move on to problems like this:

34
-7
----

We can't "take 7 out of 4" (subtract 7 from 4) so we take it out of one of the 10s...so skipping a step we just add 3 to 4 and get 27. Instead of counting backwards, we just turned it into a small addition problem...we didn't do 14 minus 7, we did 3 plus 4...ask any kid which is easier.

34
-7
----
27

Parents and teachers often have a hard time with this one even after they see it a few times, and see more examples. The point is knowing your addends makes subtraction easy and fast once you know how.

It also makes integers easy, negative numbers and their differences are a snap.

I have developed a FREE iPhone app that helps students practice the combinations for nines and tens, go to the iApp store and search Crewton Ramone... or go to my website for CREWTON RAMONE'S ABSOLUTELY AMAZING ADDENDS. Just give me your email address and I'll send you a link where you can play with it online, or download it to your Mac or PC for FREE.

In another article I will go on to show how knowing your addends makes learning multiplication much easier too. Addends along with simple patterning make multiplication simple, and multiplication is the first "milestone" in the mathematics because it allows you to count very, very quickly.