Sunday, August 29, 2010

Math Manipulatives for Multiplying Negatives and Positives

I was working with my oldest son on the distributive property in algebra, last week, and noticed he was still weak on the concept of multiplying negative, and positive numbers.

I never struggled with a negative multiplied by a negative being a positive. If I don't have none, I have some.

But, to make it more concrete, for my son, who is a tactile learner, I set up an exercise, based on an idea from a Canadian teacher, here.

I started by cutting a door in the side of a box. Kind of a girly box, but that's what happens when you have sisters in the house. The door is marked positive, for entering...

...and negative for exiting.

Inside, and outside are sets of blue construction paper "ice cubes", and black construction paper "coals". Ice cubes represent negatives, and hot coals represent positives.

When given a multiplication problem like (-2) x (-3), the negative two means you will exit the box twice. The negative three means each time you exit the box, you will carry out three ice cubes.

Removing six ice cubes from the box will raise the temperature in the box, six degrees, or positive six.

If the problem was (+2) x (-3), you would make two trips into the box, carrying three ice cubes, each time. So, the temperature of the box would get colder by six degrees, or -6.

Again, if the problem was (+2) x (+3), you would take three coals into the box, twice, raising the temperature by 6 degrees, or +6.

Really, by the time I had finished explaining the idea to my son, he had the whole concept of multiplying positives, and negatives down, but I think I'll keep the box handy for when we hit equations dealing with division.

I'm linking this to Math Monday at Joyful Learner, where you can find math activities for younger children, as well.

It's great to be a homeschooler.


  1. Okay that is totally too cool.

    I remember when I was learning this concept loving to go through and change all the negatives to positives because of canceling each other out.

  2. That is VERY concrete! It makes sense in a real world sense. It would be cool to show this on the thermometer as temperature goes up or down depending on whether heat is added or taken away. Thanks for this though. I'll have to keep this in mind when we get to that point.

  3. I think I finally get this now. Putting it in terms of temperature helped me to understand why. :) On a side note - my most elaborate "showing" studies on math were never appreciated by my son. He always had them figured out before I finished explaining, then never used my handy hand made tool . . . . sigh.

  4. I wish I would have thought of something like this when I was trying to explain algebra to Papa, when he was in college. I don't think he ever got it figured out.

  5. um.... I think maybe you were over my head... ;) well.. almost! I hate Math! I will be relying on Math DVD's as my munchkin gets older... sad but true!

  6. That is very cool. Fantastic idea! I wish math was taught like this when I was in school. Maybe I would like it! Unfortunately, I could feel that twinge in my stomach - the math twinge - while reading this post. I was always good at math (honors classes) but it made my stomach turn, I hated it. It still turns my stomach. I'm trying to keep that fact hidden from my kids.

  7. WOW. Wow. I am amazed at all the ways you make things easier for your children! This is so concrete!

  8. Oh man, I think I now understand the whole + and - concept now- I struggle with that for a while when I was in school too...

  9. This is a pretty interesting way to explain multiplication of positive and negative. I would have never thought of this. I admit that even though I understand the rules perfectly, negative numbers were always very abstract to me. Big kudos for making them so real.

  10. Oh my gosh! I love it! Thank you for this very neat idea.

  11. Great way to show it concretely. I'm adding your post to my website to share. Thanks!