The 2 Things You Need for Solving Algebra

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Before I was an accountant, I was the daughter of a math teacher.  You could just imagine my younger days, as a humble math prodigy, with a busy schedule of winning math competitions, solving the latest algebra problems  with my fellow geeky friends, arguing math hypothesis with my dad….

Well, that never happened.

I spent my childhood finding cool ways to make Lego people with my limited blocks instead of solving algebra.  (Years later, I discovered Lego mini figures and was floored!)

My avoidance came to a halt in college when I was forced to do calculus!  I spent many classes in a state of frustration and anger.  I was livid as I watched a young prodigy sail through the exams while I failed consistently.  (I got back at him in Spanish class though.  It was oddly satisfying to see him stumble as he tried to conjugate a verb.  Ha! Stick with your numbers, kid!).

Both my mother-in-law and my father were high school math teachers for many years.  Yeah, they were that kid.  And they grew up to be strict teachers who exhausted themselves teaching others like me.  Numerous times, their former students, older and wiser, found them on social media or at a wedding or a funeral parlor (ah, such is life!) and thanked them for their math & life lessons.

I can’t be the first teacher’s daughter to wrestle with solving algebra and higher level equations.

Usually, I avoid my daughter’s homework by planning my dinner prep at that very moment each day.  Oops, sorry, I’m sautéing the chicken, have to stand here and watch it sizzle….

A few weeks ago, Rita was chatting (drilling) my daughter about school.  I wasn’t paying attention and the conversation led to her writing up an instructional sheet on how to add monomials versus how to multiply them.  What did I miss?  She then patiently explained it to myself and my daughter while I pretended to follow along.

I didn’t know why adding/multiplying in solving algebra would be such a big deal.

Until this summer.  Maybe Rita was working her math magic.

This past July, I finally bought these popular Summer Bridge activity books I’d heard of.  They promised a good refresher of the past year and to also slowly introduce your child to new concepts.  It was an inexpensive purchase and THERE IS AN ANSWER KEY, FOLKS!

Each week, I was the all-knowing wizard, raising my wand over my daughter’s work and putting proud little checks on her correct answers.  We were rolling along nicely!

It wasn’t meant to last. One day, I realized my daughter had the wrong answers for an entire page.  My euphoria quickly vanished – reluctantly, I sat down with her and we attempted to work it out together.

Suddenly I remembered what my mother-in-law had tried to explain to me before.  And wouldn’t you know, it was exactly what my daughter was confused about!  Rita’s worksheet about monomials glared at me from the corner of my desk.

After reading this, you might never know what a monomial is either or need to look for it hiding in your kitchen cupboards.  (Don’t worry, it’s not.)

BUT you are going to help your child clear up an often confused math concept in solving algebra and they’ll thank you for it….maybe before they graduate from high school.  Hang in there.

 SO WHAT’S THE BIG DEAL?

Have a look at these equations – which of the following are correct?

 (The multiplication sign is replaced with a middle dot · so you can tell the difference between multiplication sign and the x.  It’s genius but I didn’t learn math that way so it looks like a different language!).

Hey, guess what?  They’re all wrong.

And why should you care?

Because it’s an easy fix and you can help make the rest of your middle schooler’s math journey less formidable in one lesson.

ADDING MONOMIALS

To add monomials, think about how we calculate the perimeter of something – we add the lengths of the sides.

1 meter + 1 meter + 1 meter = 3 meters

Let’s get fancy:

1m + 1m + 1m = 3m

or:

m + m + m = 3m

Same thing, right?  Just shorter and to the point.

And since math teachers love to use ‘x’ as the variable, let’s do the same:

1x + 1x + 1x = 3x

or:

x + x + x = 3x

Remember that when you’re ADDING, you’re grouping all the variables (x) by their whole numbers or co-efficient (1x + 1x + 1x) and ending up with one nice, neat combination (3x).

Here’s a slightly more difficult one:

x2 + x2 = 2x2

Don’t let that little mini ‘2’ throw you off – that’s the exponent and nothing to be afraid of.  When you add monomials, you add the whole numbers and keep the exponents just the way they are.

Take the time to let this sink in – solving algebra takes repetition but it will become second nature.

MULTIPLYING MONOMIALS/WORKING WITH EXPONENTS

To multiply monomials, you will need to work with exponents, such as  x2 above, the 2 being the exponent.

Think about how we calculate the AREA of something – we multiply the lengths of two sides, right?

1 meter  ·  1 meter = 1 square meter

Or written more concisely:

m  ·  m = m2

Wait!  Shouldn’t it be  m · m = 2m?  Nope.

When you multiply, you express the answer as the base variable (m) and write the sum of occurrences as the exponent.  

Here’s another example:

m3 · m3 = m6

Students would look at this and think the answer is 2m3 or even m9 but they would be wrong.

It’s like saying m ·  m ·  m ·  m ·  m ·  m = m6   but all you had to do is keep one ‘m’ and add the exponents.  The base variable stays the same – only the exponents change.

Another thing to repeat to yourself: when we multiply monomials, we ADD the exponents, not multiply them.

Now, if you see a problem with whole numbers in the mix, don’t worry – here’s how you handle it:

3a ·  2a = 6a2

The answer is not 5a.  Neither is it 6a.

You think of it as:

 3  ·   2   ·   a  ·  a =  6a2

Multiply the whole numbers, write the base variable ONCE and list the number of times it occurs as the exponent.

When in doubt, stretch it out and see what you have.

THINK YOU GOT IT? 

3a + 2a = 5a

3a ·  2a = 6a2

These are both correct.

And if you’re curious, here are the correct answers from our trick question:

Solving algebra doesn’t have to break you – spend a few minutes going over a few problems with your child and it will be worth it!  They’re a child prodigy in the making – just brush up on that Spanish too, eh?

Cute graphics courtesy of Scrapbook Gems.