How Does A Couponer Teach Factoring To A Visual Learner?

If ya'll have been following my facebook page, you will notice I've been mostly gone these past couple weeks.  Where have I been?  Helping Mike with Algebra.  

Now, first, I'm going to tell you that I kept telling him that it was too fast paced for him in the summer.  His words..."I already know this, I just failed the final last time." 

FAMOUS. LAST. WORDS.

 So, he's pulling out what little bit of hair he has left, and I'm on the edge of pulling mine out.

And now we get to...

FACTORING!

And how does he respond to this??? 

Not well.  And, this semester, I decided that I'm not going to argue with him over this.  When he starts arguing with me or raising his voice, or just agreeing with me to get to the next question without the understanding, I have walked out, until he calms down and asks for my help again.

(Yes, there's a story to why I'm walking out and making him calm down!)

So, now we get to the hard question tonight...Ready???

a⁶ – 3a⁵ + a – 3

How can you teach a visual learner how to factor this when there's that tricky invisible 1 next to that last a?

We tried writing it down on paper...we tried factoring the first part and then instead of the parenthesis just substituting an x...we tried just about every trick I knew.  He started agreeing with me...yep...whatever you say.  I walked out in tears, and he's slamming things around.

Then it came to me.

VISUAL...he has to see it.

Soooooo....I asked him to come to the living room and brought out all my little shampoos and conditioners that I had been able to get. And...I put them down like this.

Doesn't this look like the problem.  Imagine the red bottles are invisible 1's and the bottles up top are the exponents.  This was the problem.  Now to break it down to how he could understand it.

 

   

I needed to put it to where he could see the parenthesis and the invisible 1.
So it was broken into two different equations to factor. This one is
a⁶ – 3a⁵

 
This was the second half of the equation which was

a – 3

Now the trick was to show him how AND why there were not TWO of the a - 3

He kept wanting to take the a of the second equation, and I'm pulling out my hair to try and show him why he couldn't do it that way.  Soooo....now that I broke it down into visible items that he could see, he was with me this far.  So, I then proceeded to factor.

I proceeded to take out the

a⁵

^{And that left him with the} 

a – 3

^{So, he could see it with the invisible 1's there...those are the red bottles.}

^{And for this one, I had to factor out the invisible 1's.  This was all to show a point which he just wasn't grasping.}

^{So, now we had a problem that he could semi-understand.}

a⁵(a – 3) + 1(a – 3)

Yes, this is what kept tripping him up...Why was there NOT two of the 

(a – 3)?

I then showed him that even though I took the

(a – 3)  out of both sides, it was still attached to a variable on each side.  And that was what was catching him.  He could factor if it was just one number or one variable, but the parenthesis messed him up...until I showed him with all these bottles.  And this is the final outcome.

^{After TWO frustrating hours, it took 20 minutes of me showing him with bottles of shampoo and conditioner how to do factoring.  And this is how the answer looks with the numbers instead of the bottles.}

 

(a⁵ + 1)(a – 3)

And there was a light bulb that was shining so bright above his head, a smile on his face, and understanding in his eyes.  

And, this my friends is how you teach factoring to a visual learner!!!!!  

A simple Thank You made him smile

Today, I was driving home from Houston, and came across a car that was from Indiana (I think...couldn't see the plate too well).  You could tell he was a soldier because he had the little oval tags for Iraq and Afghanistan in the back window.  As he passed me, he looked over at me and he seemed a little sad the way he looked at me.  Then it hit me...I'm going to tell him Thank You while driving down the road.  So, I took out my military dependents ID card and held it up to where he could see it.  Then I signed "Thank You" in sign language, while also saying it with my lips.  

He SMILED, and signed "Welcome" in sign language.  He also seemed a little more upbeat in the way he sit in his car driving down the road.  His head was no longer down a little bit, he looked up with pride.  I'm pretty sure he was headed to Fort Hood because he took the 190 exit off of 59 N.  

This little act of kindness made me feel better because I brought a smile to someone, who really appeared a little beat down.  And I know it made him feel just a little better that someone would actually say "Thank You" while driving down the road.  

Soooo...I know this is a bad picture, but there was a lot of traffic, but if anyone knows this guy, tell him I am glad I made him smile.  

P.S.  He waved to me as he was taking the 190 exit.  It's amazing what such a little thing as a "Thank You" can do!!!  

What does Memorial Day mean to you?

This weekend is a holiday weekend.  Most people care about the 3-day weekend, and BBQ picnics.  In our family, we remember.  My husband, Mike, usually sits by himself and reflects on the past.  Mike is haunted by the past.  He has survivors guilt.  Constantly wondering why he didn't die also.  

I have no answers for that.  I don't even know why, except that he is here, and one of his soldiers isn't. 

Memorial Day is defined as a day of remembering the men and women who died while serving in the United States Armed Forces.  But for those who lived it, that's every day.  They don't forget.  

(Here's my two cents worth coming in now)  I think that the reason Mike's PTSD keeps getting worse is because of the survivors guilt.  I don't think he deserves to have a family when his soldier didn't get that chance.  

There are certain days of the year when I know to leave Mike alone.  I have given up so much to be with him.  Because of his PTSD, he avoids crowds, he doesn't go anywhere, and he really doesn't sleep anymore.  I told him yesterday he reminded me of my grandpa, who served during the Korean War.  I don't ever remember him sleeping with my grandma, he had his own room.  He would never leave the house, and he hardly ever slept.  He would be up at nights when we visited and just sit on the porch.  That's about how Mike is now.  I can't remember the last time he came to bed with me...though at times he comes in later.  

Would most wives be supportive of their husband staying up all night because they can't sleep?  Would most wives be supportive of their husband playing a video game all the time?

Would most wives be supportive of their husband just walking off by themselves?

I support all of these!  These are the quirks that I've learned to live.  I listen to him talk about a game I have no interest in...it's his escape.  His "therapy".  I've given up many things for him.  The PTSD has gotten so bad that we hardly go to sports games anymore...even if we could afford it.  

While I'm on that thought...while you're enjoying your weekend, and ALL THOSE SALES AT THE STORES...please REMEMBER that there are soldiers that are still appealing their disability...still going month to month eating beans and rice.  YES...that's what we've been eating for about a month now!  Still calling the VA to try to get things rolling...which with this system takes forever.  

What I wouldn't give to have just one week where we didn't have to worry about ANYTHING!! Where we can have an enjoyable week, doing anything...which for Mike right now would be camping and fishing.  Hey, I would take that because that means that it's a vacation.  A week without worrying, without him watching out the front window.  A week of relaxing.  A week of enjoying a lot of food, without worrying if we're going to have money at the end of the month.  A week to see a smile on his face.  

So, while you're having a great weekend, and shopping those sales.  Please, please....remember people like Pfc. Jesse D. Mizener, who was my husbands soldier who didn't make it back.  This young man, whom I've never met, has impacted my life so profoundly.  We do think of him and his family on a regular basis.