Let's Talk About FRACTIONS
FRACTIONS!
What happened in your mind when you read that word? Probably one of two things: either a visceral fear/hatred or a total excitement. That’s the thing with fractions. The concept is completely polarizing.
People seem to have a very fixed mindset (about math in general but specifically…) when it comes to fractions. Either we get them…or we don’t. But the truth is that fractions are as easy to understand as whole numbers. At the end of the day, they are numbers too!
But there are some things we bring into our classrooms that hold students back from conceptually understanding fractions.
Only using shape representation
When students only see fractions like this
They can carry on a misconception that fractions are just shapes. But like we already discussed, fractions are actually numbers, rational numbers to be exact. Check your academic standards - fractions aren’t under the geometry strand (although they relate!). Fractions are with number! They are the numbers that exist between our whole numbers. They can be represented with shapes in the same way that whole numbers can.
Like this!
So just like we use multiple representations when helping students come to know whole numbers, we need the same for fractions!
Using “out of” language (alone)
1/2 is “one out of two”, right? So many of us say and teach it that way. And it is true but it does little to help students understand fractions as the number system they are. We use this language when we are teaching division/dividing, which is essentially what fractions are…but if that was all then why would we have a whole separate unit dedicated to fractions? Again, fractions are a part of our number system. They are all the beautiful numbers that exist between our whole numbers. This is why using fraction number lines and unit fraction activities is so important. I sometimes hear teachers who say they “hate” the fraction number line lessons, or even worse, skip them altogether.
If you won’t help kids make fraction number lines, then don’t use whole number lines.
It sound silly, right? To NEVER use number lines. And in my case, I’m not talking about number lines as a crutch but building/analyzing number lines as a tool and a concept. The mental number line that we are always striving for kids to build.
We want the same thing for kids. ALL the stuff we want them to do with number (order, more/less, counting, comparing, joining, separating, representing, etc.) we want with fractions.
This is basically just a mindset shift. If we can shift our mindset about what fractions are, it will translate out to our students. If students can understand and work with whole numbers, they can (at the right developmental time/stage) work nicely with fractions.
Fractions don’t rely on size or shape
This is a big one. Many of us teach kids that 1/2 is always bigger than 1/4…but what if we are talking about half of your house to 1/4 of the The White House?
In that case, the 1/4 is bigger.
This is why teaching fractions as static “pieces” or “parts” can carry so many misconceptions. Yes, fractions are pieces and parts but they are not dependent on size or shape.
Half is half no matter what is is half of.
Just like one is one no matter what ONE is (one elephant vs. one ant…it’s all one!)
For example, the fourth part of The White House is bigger than half of your house BUT the half of your house related to your whole house is bigger than the fourth of the White House compared to the whole White House. The part is still a bigger piece related to its whole. (I know, complicated). But this is why fractions are rational numbers. Rational - Ratios
Fractions are ALWAYS comparing to a whole. A whole can be anything and it may change the “size” or “shape” of the fraction but the fraction is still the fraction.
If that confused you, you may now understand why kids need a lot of representation and manipulatives with fractions. It’s a deep concept, but not unreachable.
You may also see how fractions are directly related to percentages. If you have 100 dollars and your friend has 1,000 dollars, 25 percent of yours is 25 bucks and theirs is 250 bucks (1/4). They have more money but you both have the same percentage of your money. If you got out 75 percent (3/4) then you would still have less money but you would have a larger percentage of your money. 3/4 is still a larger fraction than 1/2 even though your piece still seems “smaller” (sucks, right?)
I hope this might help you begin a different relationship with your fraction unit. Because evaluating and deepening your own relationship with math content translates straight to your students.
Always remember, math is natural. AND HAPPY TEACHING!
