Twos to Nines Challenges

Day one and two are in the books! I’ll share a bit more about what I did with my classes on the first two days in a later post, but I want to go ahead and share the mathematical challenge I used with my students on the first day since I have got several questions about it on twitter.

This summer, my husband and I ran across a treasure trove of puzzle books at Goodwill. We *had* to buy them. As Shaun was driving us home, I flipped through the books and would occasionally pose puzzles for us to solve together in the car. We had a lot of fun with this, and in the process I found some puzzles that would be PERFECT for use in the classroom.

One of my favorite new puzzle books from this Goodwill trip is 100 Numerical Games by Pierre Berloquin. If you don’t believe me that this book is awesome, just take a look at who wrote the foreword. THE Martin Gardner!

You can a free peek at some of the puzzles in the 100 Numerical Games book by using the “Look Inside” feature from Amazon.

One particular set of puzzles which is sprinkled throughout the book really caught my eye.  This version was based on the number two, but the book also featured puzzles for the numbers three through nine.

The task is to use exactly four twos (or threes, fours, etc) to make each target number. Add arithmetical symbols between the numbers to make every equation true. You may use plus, minus, times, and divide symbols, as well as parentheses and brackets for grouping.

Originally, I thought about turning this into a puzzle for my puzzle table, but I never got around to it. Fast forward to this past week. I needed an activity to do on day one, and I decided I wanted to do something a bit different than what I’ve done in the past. For reference on past activities, check out my post on 30+ Ideas for the First Week of School!

One of the messages I communicate to my students on the first day of school is that we do math everyday. I can’t just say this. I also have to give them math to do on day one.

Yes, there were some groans. We carried on anyway.

My students are arranged in six groups of five, so I decided to set up six challenges around the room. The book featured challenges using the numbers between 2 and 9, so this meant that I had not used the challenges based on the numbers 8 and 9.

To introduce the task, I threw the Eights Challenge up on the TV.  (It’s going to take me a while to get used to saying TV and not SMARTBoard!)

After a quick overview of the rules, I gave them a few target numbers to work towards.

Students quickly got to work. Some grabbed paper and a writing utensil. Others got out their graphing calculator or phone calculator. Still others just sat and thought about the task.

Within a couple of minutes, a student in each period would announce that they had found the answer to 10. I asked them to read me their solution so I could write it on the board.

Almost every single time, I ended up hearing 8 + 8 / 8 + 8 = 10. So, I would tell them that we needed to check their work. This was when I asked them what the order of operations says that we need to do first. Unanimously, the class would say divide. Then, a bit of panic would set in. 8/8 is 1. So, 8 + 1 + 8 is 17, not 10.

Without me saying a word, the class would start to suggest either a different way to solve the problem OR a way to salvage this attempt. It usually wasn’t long before someone would suggest that we could use PARENTHESES! So, from this, I learned that we do know our order of operations. We’re just a bit rusty, but I can deal with that.

After the class found a few of the solutions for the Eights Challenges, I decided to change things up a bit. I told them that now that they understood how the puzzle’s structure worked, it was time to try a

Around the room, I had marked off six four-foot sections of white board space so that each group of students could have their own space for working problems throughout the year.

At each station, I had posted a challenge based on a different number.

I typed up the instructions for each challenge. My students didn’t really need this since we had done part of the eights challenge as an example, but I did see a few groups reference it. One group used their dry erase marker to actually write symbols between the numbers. Good thing I laminated them!

Then, I typed up the target numbers that students had to find. I thought about making them into magnets so the students could move the target numbers around, but I wasn’t sure where all magnets were. Let’s just say that moving classrooms sucks. I can’t find anything right now!

I ended up just taping them to the dry erase board. This worked just fine. Most groups left the numbers stationary and just wrote their solutions next to the appropriate number. A few groups did move the numbers around.

The tape stayed sticky, so they were able to change the number positions without any issues. Since this activity went SO well, I think I will definitely add magnets at some point.

Each table group chose a different number based challenge to work on. They instantly got to work, and the room was soon abuzz with awesome conversations. Students were excited and joyful as they found various solutions.

Students were checking other students’ ideas and pointing out any issues. Lots of parentheses were being used. Were all their answers perfect? Nope. But, it’s day one, and it gave me a great snapshot of where my students are starting from.

It was the first day of school and every kid was engaged. In fact, I would say this was the most engaged my students have ever been on the first day of school. This was my favorite first day of teaching EVER.

Check out this awesome group work!

Each group was given one dry erase marker and one graphing calculator to encourage collaboration. Every few minutes, I would announce “SWITCH!” This meant that the person holding the marker needed to pass it to another person in the group. The calculator person did the same thing.

Every once in a while, I would introduce a new twist. About five minutes into the activity, I had the groups pause and look at me. I instructed them to nominate one volunteer from each group. This person was to hold their hand up so I could ensure that I had one volunteer from EVERY group. They asked what they were volunteering for. I just said “You’ll find out soon.”

Once one hand was up from every group, I informed the class that these students would be rotating one group clock-wise. So, each group would lose one member and gain a different member. There were a few groans with this announcement, but students complied.

I was excited to try this strategy since each group was working on the same type of challenge, but no two groups had the same problems to solve. This meant that the new group member could bring STRATEGIES from their previous group, but they could not just bring ANSWERS.

After a few times of rotating a single group member, I changed things up yet again with having the entire group rotate to the next station. I did run into a few issues that I hadn’t figured out how to handle beforehand.

The groups assigned to the challenges based on lower numbers (2s, 3s, and 4s especially) were sometimes able to completely finish their challenge. When this happened, I did one of two things. In my smaller classes, there was often a challenge that had not yet been started. In these classes, I sent the finished group to this untackled challenge. In my larger classes, I had the finished group split apart and join other groups.

The Sevens Challenge ended up being the most difficult for my students to tackle. Often, there would only be two or three target numbers solved by the end of the class period.

Digital Adaptations of the Twos to Nines Challenge

Google Slides

The Twos to Nines Challenge has been turned into a Google Slides activity by Meghan Smeenk. Check it out here.

KellyLove shares a slightly different Google Slides version.  

Desmos Activity Builder

Scott McEwen has created Desmos versions of this activity as well. Each challenge is a separate Activity Builder.