Happy Numbers Activity

This Happy Numbers Activity is a fun lesson which introduces students to the concept of happy numbers and sad numbers. I have used this activity with students of various ages. Any student who understands the concepts of square numbers and addition can participate in this happy numbers fun!

I originally ran across the concept of happy numbers when I had one of those days after state testing when I needed to fill class time but still wanted to engage students in some mathematical thinking. I actually ended up giving this activity to students without trying it out myself.

It turns out to be an amazing activity that I have done with many students and presented to teachers in workshops/training.

The actual website I downloaded the Happy Numbers Activity from no longer exists, so I have uploaded the file at the bottom of this post.

The thought of having to complete this process for 100 numbers sounds SCARY, INTENSE, NEVER-ENDING.  There has to be a short-cut, right???

There is.  Just don’t tell your students what it is.  Let them discover it for themselves.

We read through the example on the handout.  Some students were extremely confused by this, so we had to go over it multiple times.

One of my classes was really struggling with getting started.  I worked this example on the board with them as a class.

It turns out I should check my students’ arithmetic as we go and not just write down whatever answer they call out.  Can you see where we made a MAJOR mistake???  Oops…

Here are some pictures of student work:

As you can, see this activity definitely kept my students BUSY!

But, it kept them more than just busy.  It sparked great conversations and great thinking.  I did have to urge a few students to seek out a short cut because they were working each number individually.  But, most of my students found the short cut on their own.

Students did seem to gravitate toward referring to the numbers as “good” and “bad” instead of “happy” and “sad.”

* Hasn’t the color coding already been done for us on this worksheet?  (Oh, child.  Not coloring both the happy numbers and sad numbers is NOT going to fly.  Nice try, though.)

* Is this going to make a design?  (At least one student asked this each class period.  I think this is a result of doing so many logic puzzles before this.  I told them they would have to wait and see!)

* This is depressing.  So many sad numbers.  Why can’t all the numbers be happy?

* When I started, I thought all the prime numbers were going to be sad.  But, I realized that wasn’t the case when I started working.

* Since we are squaring the numbers, I wonder if there’s a shortcut to determine if they are happy or sad by taking the square root.

* Oooh!  Changing the order of the digits doesn’t actually change the problem.  If 19 is happy, 91 has to be happy.  (I’m sad to admit that I didn’t find this shortcut.  This could have saved me some definite time!)

* With all the cancer there is in the world, why are mathematicians wasting their time studying happy and sad numbers?  They should be trying to find a cure for cancer!

This activity is a definite keeper!  I’m just trying to figure out where it would best fit into my school year.  Maybe as a beginning of year activity?

Free Download of Happy Numbers Activity

Happy Numbers Student Handout (PDF) (929 downloads )