We’ve learned comparing and ordering integers as well as adding and subtracting integers, so we’re on to multiplying integers. I teach multiplying and dividing integers in the same fashion as I do adding and subtracting integers. I didn’t actually hand out the counters, but I used the counter magnets on my white board to demonstrate. Here is a picture of those.
For multiplying integers, here is how I show them:
1. 1(3) means one group of three positives. I show them one group of three yellow counters on the board. You are left with three positives.
2. 1(-3) means one group of three negatives. I show them one group of three red counters on the board. You are left with three negatives.
3. 2(3) means two groups of three positives. I show them two groups of three yellow counters. You are left with six positives.
4. 2(-3) means two groups of three negatives. I show them two groups of three red counters. You are left with six negatives.
5. -1(3) means the opposite of one group of three positives. It is important to explain that negative actually means “the opposite of.” Even in the second problem 1(-3), you could say that means one group of the opposite of three positives. With this one, I say “the opposite of one group of three positives.” One group of three positives is three, so the opposite of that is three negatives.
6. -1(-3) means the opposite of one group of three negatives. Again, you would thing of one group of three negatives, and then the opposite of that which is three positives.
7. -2(3) means the opposite of two groups of three positives. Two groups of three positives is six positives, so the opposite is six negatives.
8. -2(-3) means the opposite of two groups of three negatives. Two groups of three negatives is six negatives, so the opposite is six positives.
I tried to keep from teaching them my integer song, but my Pre-AP students were still having a hard time of remembering how it went, so I went ahead and broke down, and taught them the song.
The second verse of the integer song is to the tune of “Row, Row, Row Your Boat.” It goes like this:
Multiply or divide
It’s an easy thought.
Same signs are positive,
Different signs are not.
The next thing we did was play “I Have/ Who Has.” My students LOVE this game. I make sure that all of my students work each problem as we go. I make sure that they are given a few seconds to work the problem before the “answer person” stands up and reads their card. I have them record the problem and answers if their math spiral notebook. If someone doesn’t stand up and answer within a good little bit of time, I start slowly kind of explaining the answer. It would go something like this, “are the signs the same or different? So the answer would be positive or negative? __ times__ is ? So your answer would be?” I go about it slowly in the hope that someone will stand up before I get to the end. My students will do thirty-one integer expression without one bit of disgruntle. Try giving them an assignment to take home and see if you get 100% participation and return like you do when you play this game.
The “I Have/ Who Has” set that I made for integers is a bundle of all operations. It costs $4.00, and can be bought here on my blog or in my Teachers Pay Teachers store.
Notice the cute “fish eye” lens on some of my pictures? I think it gives the pictures a little character. It was a great Iphone app.
Buy this set of adding, subtracting, multiplying, and dividing integers I Have/ Who Has cards for only $4.00. I promise, your students will thank you. Buy them here or in my Teachers Pay Teachers store.
Playing the “I Have/ Who Has” game first gives students the confidence to play any additional games with partners. One game that I let the students play is “Integer War” with a deck of playing cards. I have them find a partner and give them a deck of playing cards. I write the following on the board:
red = negative
yellow = positive
Ace = 1
Jack = 10
Queen = 11
King = 12
In their math spiral notebooks, I have them put the title “Integer Multiplication War.” They make two columns down their paper and head one column with their name, and the other column with their partner’s name. At the same time, both students will flip over two cards each. They work both their problem and their partners problem. The problem is formed by their two cards. For example: if player A flips over a red nine and a black six, the problem is -9(6). They write both problems in the appropriate columns in their notebook, and find the answer. The student with the highest value wins that round. Play continues until the teacher calls time, or until they have run out of all their cards.
In one of my classes, I had more students than I had decks of cards. Because of this, I modified the rules. I placed them in groups of three. Points were assigned to greatest value down to least value. If the students answer was the greatest value, that student was awarded three points. Second highest was awarded two points, and the least was awarded one point. The student with the most points at the end of game wins.
To give them additional practice, and to give them some independent practice, I also have them “make” their own problems using a spinner I made and a twelve-sided dice. They spin the spinner to decide the sign of the first number and then roll the dice to get the actual number. They do this twice in order to form two numbers, then they multiply those numbers together. I have them work twenty problems (or however many you see necessary). Students get a kick out of getting to role the dice. Throw some dice into anything, and they’ll love it, especially if they’re not the normal six-sided dice. I printed them out, laminated them, and cut them out. Students use a paper clip with a pencil through the center to spin the spinner.
Click on the picture below to download the pdf of the spinner to be able to make your own. You could also use them for adding and subtracting integers as well.