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My Battle with the Integers

9/26/2011

17 Comments

 
I have very strong opinions about manipulatives.  I like them.  I really do, as long as they are natural, demonstrate a clear pattern, or give students an alternative way to work out a problem.  To me this seems obvious. Why would you have students work with manipulatives if they do not clearly illustrate and support the objective of the lesson?  Unfortunately in BC our curriculum is trying to shoehorn manipulatives into the curriculum.  I get their effort to make things more concrete, but I feel as if manipulatives should be a supplement, not a requirement.  Regardless of this opinion, I still have to find ways to make these manipulatives accessible, clear, and engaging, and this is my effort to do so.

The Battle of the Integers (Army Men kick inergers chips arses)

Ok, yes I am a loser.  I just need to get that out of the way, but hey it works!  How do I do this in class?  Here goes.

Start the video: The opening sequence is enough time to hand out bags of army men.  I hand them out one ziploc bag per pair, and worksheet/notes per student.
integer_addition.docx
File Size: 104 kb
File Type: docx
Download File


Then I press pause when "Integer addition" shows up on the screen.  This is the easy part.  We talk about what happens in war.  In integer war they always kill each other off in pairs (zero pairs to be specific).  Kids catch on to this pretty quick.  So we can begin with our first example.  This is our basic addition example.  Have students start with three positive army men, then add three more.  Easy peasy!  I play the video for a few seconds to let those three positive guys come in.  Now we have six, so ask the students what if the 4 red guys came to the battle scene?  The students recreate the battle scene, write down there answer, and then view it on the video!  (This involves pausing and playing, and you really have to know where to stop it).

Then students work out their own examples, they can use the army men, and they plot their actions on a number line.  I have tried to make the work sheet one that slowly removes steps (I think I saw Jason Buell do this, and I love it).  By the end students get a pretty good grasp of integer addition. It is just practice (I pick integer addition war, or a  pre-alg with pizazz that I snagged from Dan Meyer).

Where battle starts getting tough... (AKA Subtraction, and its difficulties...)

The next day we start with some small activity (probably war), and then we jump into subtraction.  I remember when I was a kid, and learning about subtracting a negative number I felt a little like this...
Picture
Subtracting negative integers is not intuitive (to me at least) in the slightest.  In fact it was not until my modern algebra class in third year university, that I actually understood why a negative times a negative is a positive.  It is thus not a surprise that this was the hardest part for me to teach, but after a few tries I finally got it.

I start by asking the students to make a battle situation that will result in a zero, but uses ten men (in total).  Students work through it, and with a little bit of help and guiding questions, they get 5 red and 5 blue.  I then introduce them to the idea of retreat.  Subtraction is like retreating, so I tell them,"from this battle, retreat (or subtract) +3 guys.  What do we have left?"

Students show me and tell me, "Negative 3!  You have -3 left!"  I get them to write this down (I am working on a worksheet still, but for now blank paper will do).  So I decided to pull out my infinite cloner from my Smart notebook, and get them to show me on the board.
battle_of_the_integers.notebook
File Size: 100 kb
File Type: notebook
Download File

We reset to zero and build it up, make bigger battles, and try questions like 0-(+5), 0-(+10), it doesn't take long to get that subtracting a positive, is like adding a negative.  Then I have them reset to zero, and this time, with out removing any men, they have to make the battle scene (I haven't thought of a better name than battle scene) equal to +2.  In this case they should have 7 positive guys, and 5 negative guys. I ask them the same thing, "now remove 3 positive guys, (+2) - (+3)," students get really used to recognizing how it helps.  The basic steps are as follows (you can do it for any number).

  1. Reset to zero
  2. For the first number of the equation, add those army men (start with zero, go to positive, then go to negative).
  3. Subtract the number (in battle terms, tell which side should retreat, start with positive, work to negative).
  4. Fight the battle, see what remains.
  5. Repeat

Go through the combinations, and keep asking students, "Do you notice patterns?" Follow along on the smartboard.  Here is an example of what it looks like on a Smartboard.

Move on Soldier!

It took me at least three full lessons of falling flat on my face (having kids more confused than when we started), but this way finally worked.  Students could see the patterns and the rules clearly.  Kids who could memorize the rules did, those who didn't could make the battle with the army men.  I was happy, but now I have to do multiplication.  I have some ideas, but nothing that I feel inspired by, whereas I am proud of this.  Any tips?  I'd love to hear them...

A completely pointless epilogue

Just for fun, I created this, and put it up in my class using block posters. 
Picture
17 Comments
LSquared
5/6/2012 06:12:18 am

This is totally awesome.

Reply
Rachael
12/4/2012 09:49:55 am

Wow! Way to go! I love this.

Reply
Andrea
7/25/2013 11:00:54 pm

This is awesome! I teach 6th grade, so I plan on adding in some scaffolding. Technical question: where did you buy your army men? :)

Reply
Timon Piccini
7/25/2013 11:06:56 pm

Dollar stores usually Carr some form of them.

Reply
Mrs. O'Brien
7/29/2013 01:59:33 pm

So cool! Can't wait to share with my 5th graders. Thanks!

Reply
Ashley Rust
7/29/2013 03:07:36 pm

Can't wait to use this use! My 7th graders are going to love it!

Reply
Andrea
8/11/2013 01:11:27 am

Hey Tim, I don't have smartboard software. Would you mind posting the integer subtraction as a word doc?

Thanks!

Reply
Timon Piccini link
8/19/2013 04:26:27 am

Hey Andrea,

Sorry about the long response. All the smart board file was, is what you can see on the video. Nothing really to convert.

I have started playing around with this handout...

https://www.dropbox.com/s/qn9gq3nrmvpyrc5/Integer%20Subtraction%20refining.docx

Tell me what you think. It is just a draft.

Reply
katie
10/20/2013 03:52:06 am

I think this is wonderful, but I just wanted to let you know that you switched your signs in your smartboard activity, In the movie the fighters in red are negative ( which I think is great cause it relates to accounting and what not) but in your smartboard activity the red are positive. Just wanted to let you know. Otherwisem I think the whole idea is wonderful.

Reply
Timon Piccini
10/20/2013 04:07:37 am

Katie, thanks. I know exactly what happened. I made the video before I looked at my textbook, and the textbook swapped it. So I had to start the class off by telling them the video lied (stupid textbooks, why do I even use them?!?!).

Reply
Anna
7/16/2014 10:38:10 am

Timon,

I am teaching summer school and integers were really not going well so I was searching for a new way of explaining it and this was awesome. Thank you! I like the way you showed subtraction but, I was thinking and I came up with this idea....

For something like 5 - (-3), start with 5 positive guys and equate subtraction to being a traitor.... So there are 5 green and 3 red and those red desert their side and join the green. I did this on the smart board by using the pen to color them in green.

Again, thank you!!

Reply
Sandi Berg
11/19/2014 05:51:04 am

I think this is a great activity for students. Last year while I was browsing youtube for integer activities for teaching multiplication, I saw this video: https://www.youtube.com/watch?v=RAb2PR4lKvY

Basically, you look at (+3) x (+2) as adding 3 (+3) groups of (x) positive 2 (+2).
(-3) x (+2) would be stated as removing 3 (-3) groups of (x) positive 2 (+2).

The adding groups of concept is easy regardless of whether you are adding groups of positive or negative numbers.

The removing groups of concept is easy as long as you've done the pre work of preloading your battle field with "zero pairs" which your students would easily understand based on your current lesson.

Dividing requires backwards thinking but works well as long as they've built the solid multplication background.

I have used this with students and it makes sense for them! It's all in the phrasing. I could easily see combining this process with your army concept.

I definitely recommend watching the video.

Reply
Ani link
9/16/2015 04:40:48 pm

Have you heard of Mr. Multiplivison? He really helped my 7th graders last year!

Reply
Amy Zimmer link
9/27/2015 05:35:42 pm

Loved how this inspired Clopen https://clopendebate.wordpress.com/2015/09/14/army-men-adding-negatives/ without the tech.

Nice!

Reply
Alexander James link
6/5/2017 08:25:05 am

You could easily model subtracting negatives as movement on a number line... not as 'fun' as this army man situation, but for those of you not doing project based learning...

Conversely you can talk about losing debt, though not the same thing as adding, it at least gets them going in the right (see what I did there?) direction.

Reply
Amber link
7/13/2017 08:43:42 am

I LOVE this! Thank you for the great resource! I just bought a large bag of army men on Amazon to use for this!

I've found the added link I've included to be a good resource for the concept of negative times a negative. For the army men, you could use each side as "fleets" of men- so 4 "fleets" of 5 "negative" army men would be 20 negative men in the battle.

Reply
Alex Roman
6/26/2019 06:32:57 pm

What brilliant idea!

Reply



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