I work with students at different levels; I mean vastly different levels.  I have students in Algebra 2, Pre-Calculus and Algebra.  It's rewarding, engaging, amazing, and CHALLENGING!  Sometimes, I just want to plan a whole class activity, but because I have students at different levels, it can be difficult.  For Pi Day, I decided we would have a little fun with an oldie but a goodie.  This visual version of irrational and rational numbers (which included 3 activities) was a big hit.

First, we talked a little about the definition of irrational numbers and rational numbers.  Students knew the definitions but really hadn't thought about how that looks different.

Rational numbers are real numbers that can be written as a fraction such as
3, 3/4, 1.57, 3.66666666
or we can think of them as: integers, decimals that repeat or decimals with that terminate (i.e. end).

Irrational numbers are real numbers that can't be written in fraction form.  I think of them as decimals that never repeat.  Some of the more famous irrational numbers include Pi, the square root of two and e (Euler's number).  See some examples here (scroll down the page).

Mathsteps has a pretty good diagram of how rational and irrational numbers fit in the big scheme of numbers here.

After a brief discussion, I explained that we were going to "show" an irrational number of our choice.  This is just one of the visual/kinesthetic activities students could choose from:

1. The Beads: We took a variety of beads (you need at least 10 unique beads) and set up a code for the bead as a representative of a number.

In the photo above, you can see that there was a round purple bead for 5, an orange bead for 9, etc.

2. Select an irrational number: Then each student selected an irrational number to make such as pi or root 2.

3. Build your number: Students strung the beads on a string in the order of the numbers of the irrational number.  I let the students decide how many beads (numbers) to put on but gave a minimum of 25.

While the students were working, we continued our discussion about types of numbers and even briefly introduced the cube root of numbers and imaginary numbers.  As one of the students said upon finishing her necklace: "I'm wearing Pi".  Another student reflected that now she completely understands what it means when a number is an irrational number versus a rational number.

You can find the complete lesson plan here which includes 2 other activities for building rational and irrational numbers as well as student handouts.