Tag: addition

  • Two Reasons to Memorize Math Facts

    Two Reasons to Memorize Math Facts

    I learned my math facts by “singing” them while looking at flashcards.

    Having these facts ingrained with chanting or singing isn’t a bad idea. It might not “feel right” because we’re so into experiential learning these days. But if a kid can’t immediately access and use things like 8 x 7 = 56, he’s going to be slower than if he can.

    And if he’s slower, he might get frustrated and start to think that he’s not good at math.

    Also, knowing these cheap and dirty math facts helps with confidence. Even if a kid’s struggling with other things in math, knowing that he has this one thing (the “facts”) will help out.

    I fight this battle often. Some people feel that math facts shouldn’t be memorized. But there’s so much value in it.

    How about you? Which side of the fence are you on?

  • Teaching Math without Rules: Addition of Positive and Negative Numbers

    Teaching Math without Rules: Addition of Positive and Negative Numbers

    I’ve discovered many ways of teaching math through the years and the most interesting one was the addition of numbers with opposite signs. I learned this from a teacher who said that he never understood the rules – so he made up his own method.

    He “breaks” the bigger number into two pieces so it can be cancelled. Here it is:

    What do you think? Can you teach it this way? Share your thoughts in the comments.

  • Quick Addition Tip – Adding 5 to Larger Digits

    Quick Addition Tip – Adding 5 to Larger Digits

    For some reason I have trouble adding 5 to the larger digits (like 7, 8 and 9). I noticed at some point that the last digit of that addition is the same as if you subtracted 5 from that number. Like this:

    • 7 + 5 = 12
    • 7 – 5 = 2

    and

    • 8 + 5 = 13
    • 8 – 5 = 3

    and

    • 9 + 5 = 14
    • 9 – 5 = 4

    So now when I add them, I merely subtract them and slap on a 1 at the beginning!

    (Oh, yeah, and there is a good reason this happens – it has to do with 5 being half of 10. And 10 is the base of our number system. Maybe one of the other math blogs can do a proof of this using base n…?)

  • How to Never Find a Common Denominator Again

    How to Never Find a Common Denominator Again

    Do you keep struggling to teach common denominators? Do your kids just not “get it”?

    Well, it’s time to quit.

    Yep! You can teach (and do) fractions without ever finding a common denominator.

    The key is in the definition of addition for rational numbers. If you have two numbers  and  the sum of them is .

    Granted there is the technical issue of reducing, but using a little prime factorization will get you there without an issue. (And you don’t really HAVE to reduce, which I will discuss in a later post.)

    Here is an example:

    Here’s one with an obviously easy common denominator that works just fine with this method. In it I explain a little about why you would want to do it this way:

    You might argue that finding a common denominator is an important learning experience. And you’re right. In the same way that learning about death through the loss of a pet is an important learning experience. But if you can avoid all that pain, why wouldn’t you?

    If you teach this method first, kids will get annoyed with having to do so much reducing and discover the common denominator method for themselves. And that’s really what learning math is all about.

    What do you think? Can you teach fractions this way? Share your thoughts and experiences in the comments.

    Thanks to @padgets for our conversation about teaching fraction on #mathchat a few weeks ago. You inspired this post!