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Integers are probably my most favorite thing to teach! There are soooooo many great tools, activities, and games to use when teaching integers. The following is the best way I’ve found to teach adding integers.
To begin, the students are grouped in pairs so that they can easily view what others are doing to make sure they are correct. I give each pair a handful of two-color counters.
I explain that the red side is negative and the yellow side is positive. I write a problem on the board, example: -6 + 4. I explain that we are going to make a model of this problem. I ask them how we would model -6 and then have them do it. I then say that we are going to add four positives and how would we do that. I explain what zero pairs are and show them that the cancel each other out and that we remove them from our model. I then ask them how many they have left over. We do several examples of this in all of the different ways you can add integers. Then I give them a colored sheet of paper (I always like to use colored paper when I want them to write down important notes, because I feel like the think it is more important if they get special paper for it). I take up the counters and tell them that now we are going to do the same thing only drawing the model instead of using the actual counters. A circle with a negative sign in it represents a negative and a circle with a positive sign in it is a positive. I give them examples and have them write down the problem and then draw a model of the problem and crossing out the zero pairs.
Of course by this time, several students will have seen the pattern and will be able to do it in their head. I always tell them not to tell the others our secret if they’ve figured it out. Then I give them a big number like -450 + 25. They start griping about having to write all of those circles. I ask them if they saw any pattern in the other examples that would help them do the problem without drawing all of those circles. I ask them to imaging drawing 450 negative circles and then twenty-five positive circles. I ask them how many they would be able to cross out. They usually get it by now and can easily answer. I then ask them what they would be left with, and they would answer 425 negatives. I give them a few problems that I ask them not to draw circles for. After each problem, we talk about the steps we take. For instance, -2 + -5, I would say “What would I have drawn for the -2?” and then “What would I have drawn for -5? Would I have any zero pairs to cancel? If I don’t have any zero pairs to cancel, what do you have?” If they were different signs, I would ask, “Which did you have more of, the positives or the negatives?” After making sure they understand the why and how comes of adding integers, I introduce the song. I always make a big deal of the Integer Song. I pick song leaders and let them make their own beats and what have you. If you look on the side bar, under links, you can find a couple of my classes that performed the song. The words to the song go like this:
Same signs add and keep.
Different signs subtract.
Take the sign of the higher number, then it’ll be exact.
One game we play for “Adding Integers.” :
1. Integer War: This game is very common for integers, and you can play it with all operations except for division. I put them in groups of two. Pass out a deck of cards for each group. Here are the values of the cards:
Red cards= negative numbers
Black cards = positive numbers
Ace = 1, Jack = 10, Queen = 11, King = 12
Each student needs a piece of paper. They are to draw a line down the center of the paper and place their name on one half, and their partner’s name on the other half. One person deals out all of the cards. Both students turn over two cards out of their pile. On the first line of their paper, they need to write down their problem and their partner’s problem in the appropriate places. Each person works both problems and they check their answers when finished. They each put a star next to the answer with the highest value. This also strenghthens their ability to compare integers.
I will discuss some different games in later posts.