Adding and Subtracting Integers Using The Number Line Dance

Studies have proven again and again that students learn best when they are interacting with the material that they are learning.  Not all of the material is open to the possibilities but here is a tried and true method for teaching and practicing adding and subtracting integers. 

It is possible to complete this activity in the hallways of the school or out in pavement or concrete courtyard.  The supplies vary a little bit for the two variations but are easily accessible.  The most important part of this activity is that the students understand what they are supposed to be practicing which starts with the teachers seamless explanation.  I gave a lot of examples on my number line at the front of my classroom and on the smart board with a stick man before I ever sent the out to do their trial problems.  I found that with the 10 to 13 age group the crazier I acted the closer they paid attention.  So when I was demonstrating the number line dance, it started with the bunny hop and did some salsa steps and what ever other crazy dance came to my head at that moment when I was moving between the numbers.  

Supplies For in the School 

• Masking tape: about 5 m per group 
• dark coloured dry erase markers:1 or 2 per group (Tip: don’t use red and some greens as for some reason they don’t come off as easy) 
• a question sheet 

Supplies for Outside

• side walk chock: 1 or 2 for each group (any chock will work, in my school we had boxes left over from the ages of the black board and I used that because it was free) 
• a question sheet 

As you can see there isn’t much required for this activity but it requires a lot of enthusiasm on the part of the teacher.  First I will explain how to do The Number Line Dance and then I will give you the instructions that worked for me.  The “Dance” itself is very simple but it fosters skills to assist students in understanding addition and subtraction of integers which they struggle so much with.  

We will start with something all your students should know the answer to and progress from there.  

Example 1:  4 + 2
If your students were to see this, they should know to start at 4 on the number line and count up 2 which takes them to 6.  

So to do the number line dance for this, they start by standing on the 4.  When we are adding and subtracting, we know that we already have the first value that shows up in the expression so that is where we need to start on the number line.  When we are adding things, we know that the sum should be getting larger, hence we face the  positive side of the number line because the operation is addition.  

The Number Line Dance 

We are adding positive two, so they are going to move forward by two.  Most students understand that they are getting larger by two and don't need the number line to complete this question but it is a good starting point for the deeper understanding when we are adding negatives.  

Resulting in them standing on the 6.  

I always begin with simple addition because students know how it is supposed to work and it assists in the understanding of the number line dance that they are going to be learning.  It is also a question where they can build their confidence to work in this system.  

We will still do another one that they usually find simple, though some still struggle. 

Example 2: (-3) + (-4)
Again, we start on the first number (-3).   The operation is addition, so we are going to face the positive end of the number line because when we add we are getting larger.   

We are adding negative four, so we are going to take 4 steps backwards to represent the negative four.  If students think through this intuitively there is usually a number of different rationalizations they have but I find the most common one is that the number is getting larger by negative four, which has the same result as getting smaller by 4.  

Leaving us standing on negative seven.   

Now lets get into what the students really struggle with…subtracting!  The only real difference with subtraction is that we are getting smaller, so when we position ourselves on the number line we are going to face the smaller end of the number line, or the negative side.  

Example 3: 3 - 5 
We start on the number line at three, but this time we are going to face the negative side of the number line because we are subtracting and as our students should know subtraction means the solution should get smaller.   

We then take 5 steps forwards to represent the positive five that we are getting smaller by. 

Landing at (-2) Which we know to be the answer.    

Finally, we will subtract a negative, the one students find the hardest to understand.  

Example 4: 1 - (-2) 
We begin standing on the number line at one, facing the negative end of the line because we are subtracting.   

Then we take two steps backwards to represent the (-2), which makes sense if you are following the rules of the number line dance however some students are going to need a little more explanation.  I would talk about subtracting negatives as the opposite of subtracting positives.  We know when we subtract a positive we get a smaller number, thus the reverse is true for subtracting negatives.  When we subtract a negative the result should get bigger because we are taking away things that are negative.  

Leaving us standing at 3.  

There is a lot of teacher annotation that needs to happen in order to make this activity meaningful to the students but having them up out of their desks does great things for their memories.  Many students will also need help transitioning from doing the number line dance to being able to add and subtract integers on a number line without walking along it.  

Here are the instructions I sent with the students to work with, after I had given verbal instructions as well as shown them examples both on the number line at the front of my classroom as well as the smart board.    

Instructions: 

1. Lay your tape in a straight line or draw a straight line with your chock. 
2. Find where the centre of your line is approximately and mark this zero.  
3. Use either your foot or your partners foot to measure and label the ticks on the number line (if time constraint is an issue, I have then use a pair of shoes as the measuring tool and one person goes each way)
1. place your heel on zero facing the positive end of the number line 
2. make a mark where your toe is
3. label the mark one
4. place your heel on one
5. make a mark where your toe is 
6. label this mark two
7. continue in the positive direction until you reach … (enough so they can complete the practice problems you have created for them) 
8. place your heel on zero facing the negative end of the number line 
9. make a mark where you toe is 
10. label the mark negative one
11. continue in the negative direction until you reach …
4. take turns doing the number line dance to complete your sample problems. 

Tips:
It is more efficient if you set up the number lines a head of time for certain groups of students.  If you are able to leave the number lines on the ground for a little while, they can be reused for multiplication of integers.  

I always follow this activity with practicing on the number line with your fingers as the person dancing the number line.  For student’s who really struggle with the concept, I would often give them a lego man so they could face them the correct direction and walk them along the number line they have in front of them.  (I had a number of laminated number lines that I could hand out to the kids at any time so that they could use then without destroying them. They could also use dry erase markers on them to help solve problems) 

The number line dance allowed me to get my students out of their desks and when weather permitted, out of the school doing math which in itself was a novelty.  They had fun and there was a lot of great learning that went on.  I would see them a year or two later pulling out their number lines to add and subtract integers.  Good luck and feel free to send me any questions.