After working with students for 10 years, the same mistakes surfaced every time we introduced area and perimeter formulas for circles:

**Messing up the order of operations. **Take the traditional area formula, A=πr². Let’s say the radius is 3. Then students multiply π by 3, square that result, and get an incorrect answer.

**Confusion over the meaning of π.** “It’s a constant,” we tell them, or, “It’s just a number.” But consider: it’s a symbol, a Greek letter, that represents a ratio of two measures of a circle — in other words, it’s far from intuitive. It looks more like a variable than a number.

When calculating circumference, students will probably be successful since multiplying left to right works if we’re *approximating* π. But if we want students to give an *exact* answer in terms of π, they need to pluck π out of the middle of C=2πr, then take care of their multiplication, then throw π back on.

## Let’s fix the formulas

What if we **just put π at the end?**

Now if you put a value in for *r*, just square it and you have an exact answer! The circumference formula gets the same treatment:

The only objection from teachers I’ve heard is this: But π is a number, and numbers are coefficients, and coefficients must go the left of the variable! Is it worth it to adhere to this convention if it creates confusion for students?

I say: Try it. See what your students think.

If removing ambiguity is an important principle of mathematics, then let’s teach students formulas that do just that.