I'm Bon Crowder and the photos above are both of me - in 1989 and today. I'm a Generation X mom of Generation Z kids.

I began peer tutoring in high school in 1984. MathFour.com is the 2015 version of me helping peers be comfortable in math.

If you're a Gen-X parent, you're in the right place!

### Adding Fractions with Cuisenaire Rods

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! Continue Reading

### One Response to Adding Fractions with Cuisenaire Rods

1. Manuel says:

Too confusing.
I’ll try something more utilitarian.

So you think you HAVE to find a common denominator when adding fractions? Well, not really. Especially if you want to inspire kids to really think like a mathematician and do some inventing! Continue Reading

### 5 Responses to Why It's Okay to Add Denominators when Adding Fractions

1. Hi Bonnie,

I’m not sure I’m with you on this method. Having children explore mathematics to discover how it all works is a great idea, of course. But wouldn’t they become confused if they try adding the way you describe here, and possibly never straighten it out?

Love to hear what you think!

• Bon says:

I guess you’d have to judge the kid before doing something like this. I would say, though, that if the child was confident in exploring and looking at a variety of things in different ways, then it wouldn’t be a problem.

This is an exercise in seeing things differently as well as noticing how you don’t HAVE to do things in math like you’re told. If you want to build a bridge, you MUST do things like we’ve agreed on, but when you’re experimenting and playing, then the world of math is your own.

The biggest frustration having people say, “There’s only one way to do math” or “there’s only one answer in math.” If teachers continue to count problems wrong if they’re merely done differently (or the result is in a different form) than the teacher prefers, then we will continue to have only algorithmically minded kids. If we help children see that they really can do anything they want, then we’ll encourage them down the path of creative and mathematical thinking.

The “mediant,” which is what you get by adding numerators and adding denominators is actually a very useful thing in some contexts, but I have not tried it in teaching kids to add fractions.

I usually teach kids to add fractions by finding the LCD as the LAST step, because it is so much faster and simpler than the traditional method. If we insist that kids must find the LCD first, they cannot get started on problems like 11/42 + 5/48. If we allow the kids to find the LCD *after* they find the answer’s numerator, life is so much simpler.

3. donna says:

hmmm!

• Bon says:

Your curiosity, Donna, makes me curious!

### Practicing Math Skills Early in Life Is a Brain Changing Event

New research by Stanford Medical’s Dr. Vinod Menon shows that children can develop math skills and cognition early and quickly – with differences shown in as little as one year! Here is a way to start math learning early. Continue Reading

### 6 Confusing Terms in Mathematics

Here’s how to understand and explain some of the top confusing terms in mathematics – pain free. Continue Reading

### 5 Responses to 6 Confusing Terms in Mathematics

1. 1. Why is a negative number times a positive number equal a negative number?

2. Is a Quadratic an exponential function?

• Bon says:

As to your second question, a quadratic is a polynomial or polynomial function of degree 2. Which means that there are only x’s and squares of x’s along with numbers all added together.

An exponential function has exponents of variables.

So a quadratic is like x^2 (x squared) where an exponential is like 2^x (2 to the x power). See?

2. I’ve found that looking us the Latin roots of these terms helps. For example: Quadratus is Latin for square = x^2 is the highest degree. Also, domus is Latin for home, hence the domain is the where the function is found.

Math has a rich history that is not taught but would go far to putting the subject into perpective.

Marcus du Sautoy had a fantastic BBC 4 part show “The Story of Maths” that detailed where and how math developed. http://en.wikipedia.org/wiki/The_Story_of_Maths

• Bon says:

Thanks so much, Will!

I took Latin in high school because I wanted to learn more about the roots of our language. Alas, “The farmer loves the girl” didn’t end up helping that much.

I’ll look into that BBC series. Maybe it’s time to get Netflix again.

3. Ilana Horn says:

I would definitely add the terms ‘cancel’ and ‘borrow’ to this list. Neither is an adequate mathematical description. Thanks for this post!

### Adding Fractions: Why Avoiding Common Denominators Works

I wrote this post showing that adding fractions can be done using the algebraic definition of addition of rationals: MathHeadInc (via twitter) has requested a video showing why this works. I aim to please. Here is the video showing why adding fractions using a common denominator is the same as the definition of addition of… Continue Reading

### 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… Continue Reading

### 11 Responses to How to Never Find a Common Denominator Again

1. You can teach fractions this way. But I would not make a fetish out of it. Talk first of equivalent fractions. Later let the kids choose. Addition of fractions is not about the formula a/b + c/d = (ad + bc)/bd or its LCD variant. It’s about finding a common unit of measurement. If kids understand that, i.e. is not much difference about the unit selection. Choosing for them just one possibility is hardly the best practice.

• Bon says:

Thanks for the comment, Alexander.

The problem with teaching math to kids and using phrases like “it’s about finding a common unit of measurement” is that they don’t care about that. They care about fun. And cupcakes.

Make fractions about fun or cupcakes and you’re in. Later they can figure out how it all works together.

2. Interesting idea. I have taught fractions this way before and told the kids this is called the ‘macarena method’. See my blog post for explanation of this fab way of remembering the method. http://www.greatmathsteachingideas.com/2011/02/18/adding-fractions-the-macarena-method/

I find that the later method is understood by the kids and still retains the main concept that equivalent fractions are the same size. By ‘coming at it backwards’, by starting by adding fractions with like denominators then using equivalent fractions to find fraction sums with different denominators I find that the kids understand better when we start going the other way….

• Bon says:

I LOVE the Macarena Method! I’m not so sure about that star thing. Looks like it takes a lot of effort. But I’m all about many methods for one task – everyone connects to different things.

The key is to get them to connect to anything first. After which they will more easily connect to all the other things.

Thanks for the comment and links, Will.

3. Alternate ways of doing things are wonderful, esp when they help kids get more to the root of what the tricks actually DO!

(Yeah, you and I are going to have fun talking about algorithms tomorrow night! 😉

• Bon says:

Yep, Siggi. If they can’t get in through the front door, offer them the back door. If that still doesn’t work, try ever window in the house. And if they still can’t get in – by golly drill a hole in the roof!

4. I agree that the experience is painful at best of times, but providing students with another “one-size-fits-all” memory cue takes the meaning out of it. This looks very attractive only when compared to the algorithms that are usually taught. This in no way builds undersatnding. Yes it works, and the simple generalization in your recent video shows that, but it is does not enlighten adding fractions. I think teachers should strive to show students why we need common demominators, rather than try to show them tricks to side step them.

• Bon says:

Teaching this method alongside finding common denominators will enhance them both. If a student then chooses to use this method instead of finding a common denominator, then it works. Indeed it shouldn’t be a “one-size-fits-all” method and I mightn’t have labeled it this way.

Instead of teachers trying to show why we need things, they can show a multitude of different ways to arrive at the same thing. English classes do this all the time when they say, “Compare and contrast the …” A teacher can’t know what’s going to click with a student. Even homeschool parents can’t always know what’s going to cause understanding. Instead of explaining, they (we) can offer various ways of experimentation or methods to help them explain to themselves.

5. bd is the common denominator. It may not be the LEAST common denominator, but it is A common denominator.

• Bon says:

Good point, Maria. Although, you didn’t have to find it before coming up with the answer. So perhaps the title of the article should be “how to never find a common denominator before getting to the answer, again.”

Although one could argue that we never “found” a common denominator. We actually just arrived at the final answer and the denominator of that final answer happens to be one of the many possible common denominators.

6. Although this does find a common denominator, it always leads to non-reduced answers if the two denominators are not relatively prime.

I use a different method, one that finds the LCD as the LAST step in a very easy and algorithmic way.

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Calming generation X in math since 1985.

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