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Multiplying Positive and Negative Integers

A Negative Times A Positive is Negative

When it came to deciphering negative and positive integers, the bottom line from my student days was always, "Remember the rule." This can be helpful when problem solving but understanding is always better.

Let's think about a negative number multiplied by a positive number. The rule is that a negative times a positive is negative. Great, but what exactly does this mean? Did anyone watch the Super Bowl? Okay, maybe that's a dumb question, but here is a way to use the Super Bowl as an example of multiplying negative and positive numbers.

Supposed you bet your friend $5 that San Francisco would win the Super Bowl. Guess what? You lost that bet, but since you bet one friend $5, that's all you lost. 

1 X $5 = $5

or since you are losing $5 call it,

1 X (-5) = -5

Had you made this bad bet with three friends, you'd be out three times the amount because . . .

3 X (-5) = -15

A Negative Times a Negative is Positive

But what if you won that bet? In that case, you are taking away the possibility of losing $5, so . . .

(-3) X (-5) = 15

-3 is the amount of times you could have paid a bad bet if you made one, 
while -5 represents the amount you could have lost.

Therefore, congrats! You made $15!
This worksheet is part of my Positive and Negative Integers Bundle. Sorry but, $5 is a little more than you would need to pay to buy this resource. Not a bad price for all that you get!

Next time you want to teach that a negative times a positive is a negative, try explaining this to your kids It's certainly better than telling them to just memorize the rules.

       Positive and Negative Integer Operations with Word Problems

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See you next week when we look at ways to make the classroom a kinder place.

Monday Music Moves Me

This week's theme is songs with names in the title, so I'm starting with a song by Kiss that is dramatically different from any other song this band has ever written, "Beth."

My next song was sung at the first concert I ever attended at Red Rocks in Colorado. I've always loved, "Amie" by Pure Prairie League!

Finally, this is an old song that we always sang to our daughter, Judy. Plus, it is totally goofy! Please listen to "Judy in Disguise" by John Fred and His Playboy Band.

Double Negatives and Musical Selections

Double Negatives

The English teacher hates when students write using double negatives because a double negative changes the meaning of what is said. Although the math teacher may not have a problem with double negatives, he or she knows that when you put them together you have a positive.

The rule states that minus a negative is adding. Other than memorizing a meaningless rule, this can be a tough concept to teach. However, if you are teaching minus a negative to seventh graders, you'll probably do better than when I taught this concept to gifted and talented fifth graders.

Let's think of minus a negative as taking away debt! Suppose a student borrowed a dollar from his friend's mom to get a goody at the bake sale. When the student went to pay the friend's mother back, she told him not to worry about it. So in a sense, the boy made a dollar.

$0 - (-$1) = $1

She took away the dollar debt, thus giving the boy a dollar.

Let's look at this another way, from the viewpoint of the English teacher. If I held a pencil in my hand and said, "I don't have nothing in my hand," would this be true?

Yes. I don't have nothing in my hand. I have something . . . a pencil!

The big question, however, is whether or not this argument works in an ethical debate. If I did a wrong and apologized for it, did I take away the wrong? Maybe or maybe not.

Good luck explaining this to your students. The older they are, the more likely they are to understand because once again, this is a Piaget sort of concept!

If you are interested in a resource for teaching middle school math, check this out!

Positive and Negative Integer Operations with Word Problems

Tune in next week for my last math post, multiplying integers. 

If you'd like to receive freebies along with my posts, sign up for my email list! Although my email posts are similar to my blog posts, people on the email list often receive free resources with my articles. You can, too, simply by signing up to have my emails delivered. Plus, by signing up, you get the free product pictured below. So what have you got to lose? Nothing!

Click HERE to receive a FREE teaching resource.

Monday Music Moves Me

Since I mentioned the ethics of taking away a wrong through an apology, I decided to post these songs about apologizing

First up is Linda and Paul McCartney with Uncle Albert/Admiral Halsey. I actually had an Uncle Albert; but if anyone should apologize, I'd say it should be him. He was awful to my Dad . . . but that's another post. I'm glad Paul McCartney has fond memories of his Uncle Albert and is apologizing for his generation's treatment of the older generation.

Here's another great song. Elton John with 

Sorry Seems to be the Hardest Word.

What's even more important than the apology is what someone does to change. That's why I chose this next song, Man in the Mirror, by Michael Jackson.