# Football, Absolute Value and A Life Size Number Line Too: A Middle School Math Hands-On Lesson

Updated on September 12, 2012

Janine is a published author in Only Trollops Shave Above the Knees, appears on The Huffington Post and at Confessions of A Mommyaholic.

The New York Giants football team started on the 30 yard line and fell back into the 19 yard line. Which represents their change or position? So I set up the problem for the my Do Now problem of the day for my students and was the way I opened up my class discussion on the day that the aim read, "What is Absolute Value?"

So I asked my students as the Do Now problem to calculate this problem. Most came up with the answer of -11.

Now I pulled out a ruler and asked if you could find any negatives on my ruler. One brave hand went up and answered, "No!"

And that is correct, so how then did most everyone come up with -11. Well, simple they calculated and said 30 - 11 = 19 and clearly they lost 11 spaces so it has to be negative, right?

Well, not so and let's see why!!

## What is Absolute Value?

Absolute Value, quite simply is the distance a number is away from zero.

If you think of a number line that has both positive and negative numbers on it, then let us take a look at the +5 and -5. If you were to stand on an actual number line and walk from zero to five, how many steps would you have taken? If you answered five, you would be correct! Now stand back on the number line, start at zero again and walk to -5. How many steps did you now take to get to -5 from your original spot on zero? If you answered five again, you would still be correct! Whether you are walking to a positive number or a negative number, you still would be walking a positive distance, because DISTANCE IS NEVER A NEGATIVE NUMBER!!! So from the Do Now, we now know why the 11 is not negative, because of this!

So the absolute value can never be negative. Therefore the absolute value of +5 = 5. And the absolute value of -5 = +5. Absolute value and distance too are never negative and always positive!!

In my classroom, when I taught this, I had an actual number line taped to the floor to demonstrate this exact problem that I just laid out for you to introduce this topic, plus for the problems that are about to follow here. The kids were able to assume the role of a number and walk on the actual number line. It was a way for my students to see the problem visually, as well as a nice way to get some much needed classroom participation (a thing that many students don't want to do in math class). Hey, I was allowing them to get out of their seat and move around in their math classroom, most kids had their hands up willing to participate for this activity.

## So how do we start to solve absolute value problems?

Now I throw the kids a bit of a curve ball and ask a volunteer to start at -3 instead of zero.

Then I ask the student to move 5 spots away from -3. The student will most likely walk towards 5 steps towards the positive numbers and land on +2.

Then I ask if that is the only position that would be 5 steps away from -3? The student may need to think for a moment and I direct them to return to -3 and now instead of moving towards the positive direction ask them to think about walking 5 places towards the negative numbers. The student should then be able to walk 5 places to -8. But how can we get a negative number? Mrs. Huldie, you said absolute value was never negative? Yes, because the distance of 5 is positive in either direction even though when we walk 5 spaces to the negative side we clearly get -8. The answer or where we stop on the number line may be negative, but the distance or absolute value is 5 and is still clearly positive!

## How do we write absolute value?

This symbol denotes absolute value ||. So when we are finding the absolute value of the original problem of the distance of 5, we can write is as: | 5 | = 5 or | -5 | = 5. See whether we are finding the absolute value of +5 or -5, the answer with still be +5!

So now let's throw some good old algebra in. We need to solve for x or our favorite letter!! Yes students can usually follow me this far, but usually most hate seeing the dreaded "x" or algebra added in.

So how do we find the absolute value of x. Let's take a look, shall we. |x| = 6. So how do we solve for x? Remember the number line? All this is saying is let's find all the distance 6 spaces away zero! So another student will come up and show us that 6 places away from zero could be both +6 and -6 too. So |x| = 6 is x = {6, -6}.

## More Solving with Absolute Value:

The next problem I throw out there is |x + 2| = 3. How will we solve this? Let's again use our number line!!

So we always started at zero before this, because quite simply x was by itself, but now x has a 2 added onto it. So how are we going to find where to start on our number line?

In order to get rid of the 2, we need to subtract it from the original zero (this has us using a bit of prior knowledge that the opposite of addition is indeed subtraction). So to subtract it from zero, means to move 2 places towards the negative side, so we end up on -2 and that is our new starting point for this problem.

So now what does the 3 mean? This is our distance remember distance is always positive and the answer to the absolute value problem (see the three is after the equals sign and not in the actual absolute value bars!!)

So on our number line, I have a student start at the number -2 and model both spots that are the distance 3 spots away to show us that x = {1 and -5}.

## So now that we talked and walked the problem out, let's see how to solve it algebraically:

We again work with the previous problem:

|x + 2| = 3

1. Get rid of the absolute value bars: x + 2

2. Then set up 2 equations to solve (remember we always got two answers walking on our number line!):

a. x + 2 = 3

b. x + 2 = -3

3. Solve for x:

a. x + 2 = 3

x = 3 - 2 or x = 1

b. x + 2 = -3

x = -3 - 2 or -3 + -2 (leave, change, opposite, which is prior knowledge of adding/subtracting negative numbers), x = -5.

There you have it x = {1 and -5}. Same as we got before!!

## Summing Up This Lesson...

I love this lesson, because it is another hands-on lesson utilizing football (which most young kids have some background knowledge about) as the lead in motivation for this topic that can definitely be a bit boring and even a bit of a difficult concept for kids to grasp, plus it allows the students to move around the classroom during this activity to see hands on what Absolute Value actually is. This topic truly can be very tedious and cumbersome for young kids to learn and grasp, but having the students walk on the physical number line has them see first hand that absolute value can truly never be negative. And if they learn nothing else from this lesson I hope that they at least walk away grasping that from the hands on visual here. However, I also love the fact as I previously stated that this activity truly gets the whole class involved and participating, because most students don't want to pass up the opportunity to be able to actually get out of their seat and move around a bit in class. Let's face it on a good day, I think I got asked if they could go to the bathroom, the nurse or some other activity that allowed them not to have to sit still. So this activity allowed and required for these kids to actually move around and not stay seated for the class duration. Also, participation from young kids can be something that is not in high demand during math class and I loved how this activity reinforced and promoted classroom participation for the entire class.

So my hope in teaching this lesson on a more complex math topic is that my students will leave my class remembering absolute value and the hands on number line for years to come even after this topic and test are long over and behind them. And as a teacher that is truly something you hope for that the student takes away something from your lesson and doesn't just forget it once the test is long gone! Anyone who has read any of my other math teaching articles previously will know from them that I am a strong believer in using stuff that interests middle school students to help them learn many of the basic concepts that are a requirement. I truly enjoy engaging my students and showing them how we can use math in everyday life and believe this lesson is another one that does just that.

Janine is a freelance writer and mom of two. She is known for being a certified and licensed professional Math Teacher through NY State and has taught in both the middle and high school levels. You can checkout her profile and more real-life Math articles here.

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• Logangal1

8 days ago

This is a spot-on example! Brilliant concept! Thanks for sharing!!!

• AUTHOR

Janine Huldie

7 years ago from New York, New York

My pleasure and thank you for your kind words!! :)

7 years ago

What a nice topic you have written? Thanks you.

• AUTHOR

Janine Huldie

7 years ago from New York, New York

Linda, now you sound like Kevin!! Seriously, thanks for the share and just always being you, too!!

• Linda Bilyeu

7 years ago from Orlando, FL

As you aware, numbers and I do not get along well, but I do like football! :)

• AUTHOR

Janine Huldie

8 years ago from New York, New York

Thank you so very much girishpuri for your lovely comment, very much appreciate it!!

• Girish puri

8 years ago from NCR , INDIA

It is great to learn, absolute value in your class, useful hub,thanks

• AUTHOR

Janine Huldie

8 years ago from New York, New York

Wow, Glimmer Twin Fan that sounded like an awesome activity and definitely a great motivator. I will have to keep that in mind hopefully when I teach again in my future classroom. Thank you seriously for your kind words here and do agree that football is also a great motivator for young kids. Thank you also for your votes.

• Claudia Mitchell

8 years ago

Football is a great motivate for kids! I subbed in a 1st grade class once and they had a field on the board and the kids were lined up in teams and one by one had to answer math questions. The football had velcro on it and would move closer to the goal or further depending on the correct answer or not. They loved it. Voted up and useful!

• AUTHOR

Janine Huldie

8 years ago from New York, New York

Keith, thank you so very much for saying that I try to find fun and interesting ways to teach math to kids. I truly tried my darnedest to use everyday life when I was teaching to try to relate the subject of math as much as I could. Thank you also for your continued support and votes too :) :)

• KDuBarry03

8 years ago

You always find very fun and interesting ways to teach students! ALways a great way to teach when you can relate a school subject to an everyday experience :) Voted up!

• AUTHOR

Janine Huldie

8 years ago from New York, New York

Dianna, I too wis I could have had more students like you too with all your enthusiasm and willingness to learn. Seriously thank you for the comment and votes too!!

• Dianna Mendez

8 years ago

As I have mentioned before, I wish I would have had you for a math teacher when I was in junior high. I understand your methods so well, but alas, it is too late for me. Voted way up!

• AUTHOR

Janine Huldie

8 years ago from New York, New York

Oh Docmo, from the bottom of my heart thank you for saying such beautiful things about my teaching and article. I can't say enough how much I truly do appreciate your continued support and thank you do also bookmarking this and do hope you can put this to use with your kids' homework in the future. I am a math teacher though and might have a bit of trouble helping out with hyperboles thoug, lol!! Seriously thank you so much!!

• Mohan Kumar

8 years ago from UK

This is totally awesome. I am bookmarking this for my kids homework. I understand the concept of absolute numbers but no one ever had taught Maths with such clarity, creativity and gentle guidance. You are the BEST maths teacher I've ever known. If only I could recommend you for some kind of award.. I will. Cuz this totally blew me away! You really are an incredibly good teacher. I can't stop with my hyperbole ... help!

• AUTHOR

Janine Huldie

8 years ago from New York, New York

Thank you so much Julie for saying that. I definitely am interested in in doing just that, but of course I need to take a better look into what it entails and have yet to get there, but do hope to in the future. Seriously I very much appreciate all your help and support!!

• Blurter of Indiscretions

8 years ago from Clinton CT

Awesome Awesome Awesome! Your math hubs are incredible. You maybe should think about an e-book someday. You have lots of great math ideas!

• AUTHOR

Janine Huldie

8 years ago from New York, New York

Rema, think you from the bottom of my heart for saying that for your enthusiasm on my latest article and math I general. No worries, I loved the caps and seeing that you were indeed being emphatic and excited here made my day. Seriously thank you and for sayi g that you will come back when I publish more of these hands on math lessons. I never know if people truly enjoy these, because I know how many do feel about math, but I loved teaching in this way ands haring them has been pleasure. Thank you again truly :)

• Rema T V

8 years ago from Chennai, India

Mrs. Huldie,

May I sit in your class from tomorrow and participate in the math activities along with your other students?

JANINE,

THIS IS ABSOLUTELY GREAT! I have learned Absolute value but NEVER THIS WAY. I mean this is so enjoyable. I want to learn math from my first grade now. I have fallen in love with the subject :)

Sorry about the caps if that annoyed you. I had to do it to emphasize my point. Thanks a lot and keep more of these classes coming. My attendance will be 100%. Cheers, Rema.

• AUTHOR

Janine Huldie

8 years ago from New York, New York

Michelle, I am the same as you with loving using what others do love and enjoy to get them motivated when teaching. I think that is the teacher in both of us. Thank you seriously for the compliment and share too!!

• Michelle Liew

8 years ago from Singapore

I love using what people love and turning it into a great lesson, and you've done so here! Thanks for sharing, Janine!

• AUTHOR

Janine Huldie

8 years ago from New York, New York

Bill, I could see using baseball statistics for math and love that idea, if I ever do teach again, I am definitely going to steal that idea from you :) Thank you so much seriously for your continued kindness and support. It truly is so very appreciated!!

• Bill Holland

8 years ago from Olympia, WA

I used to use baseball statistics for math; same theory and so obviously I bow to your creativity. Great math lesson....pertinent to the kids and valuable to their learning. Great job as always Janine!

• AUTHOR

Janine Huldie

8 years ago from New York, New York

Joseph, yet again thank you for your kind words and for saying that you can see how much I cared about how I presented my lessons on concepts that could be very tedious and quite difficult for many to comprehend. You know I did take a graduate course on the history of math believe it or not in my training, but seriously don't really remember hearing how they actually came up with this symbol. Thank you again for your kindness and sharing this all over. So very appreciated!!

• Joseph De Cross

8 years ago from New York

Wonderfully done Janine. Nobody can't doubt of your dexterity as a math teacher. The graphics are right on target for the bored mind. This is essential read for Middle high school. Was wondering how did they come out with the darn Symbol! But I was there as a 13-14 years old facing these problems with an obsolete system. Thanks so much for your efforts and hope these hubs get lots of viewss. Sharing all over. Thanksfor your constant initiative and unique methods. Didactic and appealing! Lol! to Rcrumble!

• AUTHOR

Janine Huldie

8 years ago from New York, New York

Linda, you are not alone in your feelings of math. I told you my own husband cringes at the thought of using math, but LI and behold I found him calculating some very large number last night on hisnIPad calculator, when I asked what he was doing he told me he was trying to make sure the graphic boxes he was designing for a clients new website were all the same dimensions. Seriously he hates math, but had to concede that he needed it for his work last night. So there you have sometimes math is a necessary evil, lol!! Thanks seriously Linda!!!

• AUTHOR

Janine Huldie

8 years ago from New York, New York

Richard, I promise to warn you the next time, I swear lol!! Seriously, I tried my best to get certain complex and dull topics across by using stuff that the kids could truly relate to and stuff that they indeed knew about or even liked, so Football seemed a natural use to me here. Do hope I didn't ruin the sport too much for you this morning, but sometimes you got to do what you got to do and as a teacher I learned that lesson fairly quick!! Thanks seriously for your comment and continued support :)

• Linda Bilyeu

8 years ago from Orlando, FL

I think I have mentioned before that math, numbers and I never got along well. That's still true. I'm with Rich about watching football and imagining absolute value.

Still can't believe that all the players on our Pick'em game chose the Giants except for my friend Amanda who chose the Cowboys!!

Excellent hub teach!:)

• Rich

8 years ago from Kentucky

Janine - Well, at least I didn't gain any weight in this hub. However, I'll never be able to watch football again without thinking of absolute value.

Please, don't do one on basketball! Or, warn me so I don't see it! It's the one sport left that I truly love! lol

Another great job! The kids don't have a chance but to learn the way your teach!

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