Mt. Pleasant Classical Academy

We’ve run into math problems this year, or rather problems with math concepts this year in Pre-Algebra.   First we needed to spend weeks on the concept of adding and subtracting with negative numbers.    Finally though we passed that hurdle and adding and subtracting with negative numbers became “easy.”   What a happy day it is when I hear Mark utter those words while we do math.

We reviewed factoring, prime numbers, greatest common multiple, converting mixed numbers to improper fractions, and then adding and subtraction with negative mixed numbers, before moving onto linear equations.   That’s solving for x-type equations.

Stumbling area for sure.   The first time through our very first example it looked as though Mark got all the concepts and this would be a no-brainer.  Then Mark said, “I don’t get where they came up with that equation. Where did it come from?”   I smiled, reached down inside for some patience, and started over.     Mark caught on quickly to the concept that what you do one side of the equation you must do to the other side.  Maybe that’s because he had heard me say this so frequently to Michael over the years.  But what you did, adding or subtracting, dividing or multiplying just wasn’t understood.  He would ask, ‘why do you do one, one time and then something different the next time?’   Legitimate questions and I took the adage that if my student is not understanding what I am teaching then I need to change my approach.   Particularly when I’ve taken a similar approach day-after-day-after-day.

Oftentimes when this happens with homeschoolers the first avenue to try is to switch  math programs and I will admit that in a way that is the approach I took.   I pulled Key to Algebra off the shelf and paged through it to see how they approached linear equations.  It was the same approach I had been using with the Pre-Algebra by Mary Dolciani book.   Still searching I watched the Khan Academy math video on linear equations.  As I listened I heard a simple word that he used and thought that I’d give it a try.

Yesterday as we looked at the problem 2x = 18,  I pointed to the 2 I said “Let’s multiple by the inverse of 2.  What is that Mark?”  He answered “1 over 2.”  It was a breakthrough!   We worked through 2 more problems, with me saying  “Let’s multiple by the inverse of…”  and soon Mark exclaimed, “This is easy.”   YES!  Music to my ears!  We moved onto 2x - 5 =19 type equations.   And again instead of asking whether we should add or subtract I said,   “Let’s add by the opposite of -5″  Mark caught on and quickly volunteered the opposite of each number whether it was a positive or negative, he knew how to add the opposite of a positive or negative number.

As I’m writing this Mark is working through his math lesson, taking equations such as 3/5x + 2/3=2&2/3 and solving for x.  The only questions I’m getting are the ‘would you check this one mom?’  Not bad, not bad at all, and of course I will!

A simple word change did the trick.  Again.  I saw this earlier in the year too when I replaced that negative sign with the simple word ‘OWE’ and changed it all over to a money concept.  And now, by replacing that question of whether to multiple or divide by some number in order to isolate the unknown, by using the simple word of ‘INVERSE’ , and eliminating the constants in the equation by using ‘OPPOSITE’ did the trick.  No new math program needed, just a slight change in word-use and a math teacher willing to search for the approach that will work with the child.  Oh, a bit of patience thrown in too.