What are we really doing when we are adding / subtracting positive / negative numbers?

To tune into our learning of adding / subtracting positive and negative numbers, we began by thinking about the sizes of negative numbers.

        Which number is smaller:   -4   or   -6  ?

        How many different ways can we explain why?

We used the think-pair-share routine and came up with some interesting reasons:

We then looked at our number line and with our partners tried to solve the following:

Sharing different answers we got, students were invited to share their reasons using our number line.

It's important that we can gain an understanding of what we are actually doing when adding / subtracting positive /negative numbers.

So after each, we came up with real life examples that would illustrate what we are doing with each number sentence.

When it came to adding or subtracting a negative number, a lot of head scratching took place to determine why.

We thought of an analogy that a negative number is 'magnetically' pulled back towards its negative number family. But sometimes, its pull isn't powerful enough.

Eventually we were able to think of a real life situation for:

                                          6 + ( - 3 ) = 3

Then we thought of possible ways to think of a real life situation for this number sentence: 

( -3 ) - ( - 5 )

We played around with different ideas such as going up and down in a lift with negative floors, but that didn't make sense. 

Someone else suggested we could look at it using temperature, but when we tried that it didn't seem to help.

So, we went back to owing people money and came up with this:

When learning new skills like these, its really important that children are given opportunities to think of real life applications.

I think we came up with some fabulous ideas today.




Using this conceptual understanding, we then played a game.

A student volunteered acting out how a toddler learns to walk.

During her performance we noticed she took steps forward BUT also took some steps back.

How is this related to positive / negative numbers?

We draw a toddler on a bit of paper and with our table partners, we draw a positive / negative number line.


Partners were given two dice like so:

Partner A rolls both dice to get a value.

Eg,   - 4

Rolls the + / - die only to determine whether they should add or subtract.

Eg,    +

Rolls both dice to get a second value.

Eg,  + 6

They then wrote their number sentence and solved it.

Eg,    - 4 + 6 = 2

Then they moved their babe on the number line where it belonged. ie how many steps forward and backwards did their baby take.

Partner B would do the same and this was repeated for 5 minutes.

At 5 minutes, whoever's baby was in the lead on the number line was deemed the champion. 

           

We had a lot of laughter cheering on a toddlers!

Children were also helping each other to understand how to add / subtract positive /negative numbers.

At 5 minutes, we shared where our toddlers were on the number line.

We thought it was funny to find out what the champion baby holders had done and what those in last place were doing wrong.

We played a second time.

As each student shared, we recorded and solved the number sentence to practise adding / subtracting some more.

Eventually, we were able to determine our super-baby and a baby perhaps in need. 


To get kids excited whilst adding / subtracting positive / negative numbers is quite a feat I think!