Christine asked me via twitter for some resources for Cuisenaire Rods and teaching fractions.
Of course I can’t pass the opportunity up to do some fun things with my rods!
Christine, I hope this helps. Let me know what’s next.
Anyone else? What would you like to see done with fractions and/or Cuisinaire rods?
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!
Multiplying fractions provides an interesting challenge. Put some mixed number into the situation and you could be facing a real bear.
Here’s one way to work the problem by converting it to mixed numbers:
Or you can use the handing dandy distributive property (or as some might recognize it – FOIL):
Here’s one more for fun:
Thanks to NapNinja4 on MyMathForum for this question.
This isn’t something you do everyday. Therefore it would be helpful to know how to remember it long term.
The mixed number really means .
Notice the PLUS sign? That’s the big key to doing this.
This video shows the long expanded way that most people won’t show you. You wouldn’t really convert this way, but it helps to see it in the long form. This way you know what your teacher is showing you isn’t some pixie dust magic:
Now that you can do that, you can probably go the other way too:
And how about checking your work? Nevermind the devil box (aka the calculator), the more you check your own work by hand, the more your confidence in your own math abilities will be. Try doing this:
What do you think? Will this help you remember? Do you have another way to remember? Share it in the comments.
