Addition and Subtraction of Integers

This past Friday, I introduced the addition and subtraction of integers.  I tried teaching it a different way than I usually do.  Ordinarily, I would use number lines to show how it works, talk about adding if you have two negatives or two positives and subtract if the signs are different.

In fact, one of the kids contributed that to the discussion but they are in this particular math class because they struggle with the basic concepts.  From previous experience, I know they have issues translating the visual when done with number lines to applying it to numbers.

One issue is the idea that on a number line, the positive and negative represent directions when they are used to thinking of those signs as indicating addition or subtraction.  This time, I tried introducing it a different way.

I told them that addition of integers is actually combining numbers with the same signs.  I didn't talk about adding, I used combining.  Then we talked about a can of soda where one student drank two ounces then drank another three ounces.  The students were able to see the situation could be represented by the equation -2 + -3 = -5 because each time they drank something it was removing the liquid from the soda can.

Another situation we discussed was giving money to friends. First one student gave two dollars to a friend and three dollars to another friend so he gave away $5.00 total.  They said it was minus $5.00 because he no longer had the $5.00.

When I introduced subtractions, I explained with the number line that it was finding the difference between two numbers for instance 5 - 7 = -2.  The example I used was the high temperature of the day was 5 degrees but that night it dropped seven degrees so the temperature was -2 degrees.  The second example used was you had $5.00 in your account and used your debit card to buy $7.00 worth of stuff at the store but you'd overspent by $2.00 or you were -$2.00 in the hole.

Of course when we hit the minus a negative number, I reverted to explaining 3 - (-4) is actually 3 + -1*-4 or 3 + 4 = 7.  Its hard to explain in any other terms because my students are ELL and I do not believe the science they get allows me to explain any scientific situations on this type of topic.

What I loved most was the mathematical discussion it evoked.  Most of the time, I get total silence when trying to involve them in a discussion but this one, they volunteered ideas on situations that matched the problems.  I would say this is one of the best lessons I had.

Let me know what you think, I'd love to hear.  Have a great day.