Multiplying 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/practicing multiplying integers.  

​The Number Line Dance.

It is possible to complete this activity in the hallway or out on pavement or concrete.  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 practiced a lot on my number line at the front of my classroom and showed them on the smart board with a stick man before I ever sent the out to do their trial problems.  I found that with this age group the crazier I could be the closer they paid attention.  So when I was demonstrating the number line dance, it started with the bunny hop I did some crazy leaps and what ever else could make the distance 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 (this ensures easy clean up, 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 often 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 Hop for multiplication and then I will give you the instructions that worked for my classes.  The “Hop” itself is very simple but it fosters skills to assist students in understanding multiplication of integers which they struggle so much with.  

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

Example 1:  4 x 2

If your students were to see this, they should know to start at 0 on the number line and count up by two, four times which takes them to 8.  

To do the number line hop for this, start by standing on the 0.  When we are multiplying positive numbers, we know that the values get larger.  We face forwards because we have positive four.  

Then we hop forward two units at a time because we have positive two in each of the four groups. 

Resulting in standing on the 8.

 I always begin with simple multiplication because most students know how it is supposed to work if not it is a good review. 

The next example is one that they struggle a little more with, but this gives them a better idea of what is going on.  

Example 2: (-3) x (2)

Again, we start on the zero.  This time we are going to face the negative end of the number line because the first number is a negative.   

This time, we hop forward, because its positive,  2 units three times.

The result is landing on -6.

Logically you can have your student think that if you have negative three groups of 2 they make six.

Or you can look at it the other way, two groups of negative three

Example 3: (2) x (-3)

You begin at zero and face the positive side of the number line to represent the positive of the two.   

Your hop would be three units backwards twice if you conceptualized it that way. 

Resulting in the same negative six as before.

Finally, the hard one to figure out…negative times negative.  

Example 4: (-4) x (-2)

Just as before, we start on zero.  We are going to face the negative end of the number line to represent the negative four.  

Then, we are going to hop backwards, to represent the negative, two units four times.

Resulting on us landing on positive eight.

I intentionally use the same numbers for example 1 and 4 because it helps the students begin to see the patterns when multiplying negative numbers.  I try to have them come up with the pattern them selves of two negatives multiply to make a positive and if the signs are different it will be a negative.  

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.

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 hop to complete your sample problems. 

Tip: If you have students who need a little extra help, it is more efficient if you set up the number lines a head of time for certain groups.

I always follow this activity with practicing on the number line with your fingers as the person hoping 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 hop them along the number line they have in front of them.  (I had a class set of laminated number lines that I could hand out and use with dry erase markers on them to help solve problems) 

I found that they key to multiplying integers was having the students recognize the patters for them selves.  This was a great activity to follow the Number Line Dance for adding and subtracting integers.  As long as it didn’t rain the number lines would stay on the ground they were useable again, as well as the instructions were a lot easier to follow. 

Good luck! Send me a comment if you have any questions.