Welcome back! If you have been following this series of blog posts all about fractions and improving our fraction instruction and learning, I welcome you to day 3! If you are new to the series, feel free to snoop around at POST 1 and POST 2 when you have time for more foundation information about teaching fractions.

Today I want to focus on something I briefly touched upon in that first post–the fact that fractions can be so challenging because they appear in so many different formats and contexts. Whether you teach in a Common Core state or any other state/country with rigorous standards, we need to strive for a balanced approach to teaching fractions.

When we learn whole numbers, three means three. You can have 3 dogs. You can eat 3 chocolates. You can read 3 books. We can count 3 on our fingers. We can pound a drum three times. This makes sense. We can see it and hear it.

When we talk about fractional amounts, the game changes a little bit, especially for students who may struggle with math concepts. As I mentioned in the first post, consider the concept of “1/2”. I love to start a math class by sitting back and patting my stomach and telling my students that I ate half a pizza for dinner last night. Inevitably, they laugh and make comments about how much I love pizza, and so on. I play it up a little bit and hope (usually it happens!) that someone finally says…

“Wait…how big WAS that pizza?”

And then we begin.

### Fractions of Wholes

Or what about this. “Here is 1/4 of a cake. What would the entire cake look like?”

Here is what we might expect to see (with the original fourth shaded)…

But what about these? Wouldn’t these “atypical” examples work as well?

### Fractions of Sets

Providing these constructivist experiences builds so much more understanding than merely teaching students the algorithm. Does the algorithm work? You bet–but it will make so much more sense after they have seen WHY it works. Eventually, we can tie those counters to more abstract things…1/4 of 12 counters could REPRESENT 1/4 of 12 math problems on a test.

I love the Skittles activity I do with students that really gets them thinking about how fractions can be parts of sets. It’s one of the activities in my fraction unit if you are interested in checking that out.

### Fractions with Units of Measure

### Students Need to “DO” Fractions!

Interested in my fraction unit?

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