Digit Cells Puzzle

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I want to share the Digit Cells Puzzle I had my students tackle on my first ever day of being a teacher.

Day 1 went pretty much as I had planned. I explained the concept of bell work to my students.  I don’t think any of them have ever had a class before where they were expected to begin working on something before the bell rang.

Even though I had the instructions on the white board, many of the students still needed my prompting to get started.

When I put up my first problem of the year, the students were not too thrilled about it.  Several asked me why we had to do this since it was the first day of school.  Here’s the problem we solved:

I learned about this puzzle through the Ohio Digital Mathematics Project. Back when I started teaching, they had a different website called “Stella’s Stunners.”

You can still access an archived version of the old Stella’s Stunners site, but it does appear that all of the puzzles have been since moved over to the Ohio Digital Mathematics Project site.

Most of my students had no clue where to start with the digit cells puzzle. But, I encouraged them to just try something and see if it worked.

There was instant frustration, but I told the students I was going to let them struggle with the problem on their own for a few minutes.

We had some great discussions about why you couldn’t just put ten zeros or a nine followed by nine zeros.

For the first six class periods, I let the students try by themselves for a few minutes, then I directed them to the board where we solved it together as a class.

I chose one student to give us a number to start with. Then, as students found a problem with the number on the board, they would raise their hand. I would call on a student to tell me what to change, and I would change it on the board.

This problem led to so many great conversations. A lot of students wanted to give up. They would even announce that they were giving up and put down their marker. But, soon they would have marker in hand and be trying another strategy.

My last period of the day is an 8th grade Algebra 1 class. My school district buses over the 8th graders each day to take Algebra 1 at the high school. I love the excitement and zeal for math that these students bring to my classroom.

After letting the class struggle for a minute or two with the problem, I started to work the problem out on the board together.

But, everyone was so excited to see how we could edit our number and try to make it work that they ended up requesting to keep working by themselves. I had several students arrive at the solution by themselves.

They would raise their hand to have their solution checked. I would start checking to see if they had the proper number of each number. As soon as I found a problem, the student would begin correcting and working again without any prompting.

One student announced: “I like this.  It’s so hard, it’s fun.” Another eighth grader told the class that this was his favorite class that day because it was the only class where they had done something other than listen to rules.

I love this digit cells puzzle. It’s a definite keeper.  It’s the type of problem that students will take one look at deem impossible.  The excitement on their faces when they finally find the solution is so worth it!

Puzzle Solutions

I intentionally do not make answers to the printable math puzzles I share on my blog available online because I strive to provide learning experiences for my students that are non-google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.

However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.

If you are a teacher who is using these puzzles in your classroom, please send me an email at sarah@mathequalslove.net with information about what you teach and where you teach. I will be happy to forward an answer key to you.

Tori

Monday 26th of July 2021

Why can't it have a 9 and then 9 zeros?

Sarah Carter

Monday 26th of July 2021

9000000000 would say that it had 9 zeros, 0 ones, 0 twos, 0 threes, 0 fours, ... 0 nines. But that can't be true because the number has one nine in it.