**Modeling Monday** was born when the math teachers in my school district decided that it would be a valuable exercise to have **ALL of the students from grades six through twelve complete the same math problem on the same day.**

Recently, all of the students in my district’s two middle schools and one high school worked on a **math problem titled, “110 Years On.”** In this post I will share with you the purpose of Modeling Monday and some interesting takeaways that our math teachers experienced as we implemented Modeling Monday in our classrooms.

I will also share with you a** link to the problem** itself, a** YouTube video** that captured the essence of the Modeling Monday event in our district, and some **pictures of student work** in the event that you decide to give Modeling Monday a try in your own classroom.

By the way, all of the math teachers in our district were given a **Modeling Monday t-shirt** to wear during the three or four days that we set aside as Modeling Mondays this school year. The picture above is a **close up of the front of my t-shirt**.

The Common Core State Standards discuss “modeling” as follows:

Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. (Click here for more about modeling.)

### The Purpose of Modeling Monday

From my point of view the purpose of Modeling Monday was to allow all students in our district to try the same problem in order to create an interesting math event that would **promote mathematical conversations** between siblings, colleagues, teachers, parents, and students.

The problem requires higher level thinking but it is does not require complex mathematical procedures that our younger students would be unable to implement.

We also hoped that teachers and students would witness a **variety of problem solving methods** as well as the inclusion of a **number of different variables** that students might consider as they solved this problem.

### The Problem – 110 Years On

The problem that we used came from a British website at bowlandmaths.org. The task shows a picture that is 110 years old and tells you that the descendants of one of the girls in the picture are meeting for a party in the present time, 110 years later. **Students are asked to determine the number of her descendants who will be present at the party.** A few other supporting facts are given to help students think through some of the variables in the problem. A pdf file of the actual problem can be downloaded here.

### My Classroom Setup

To prepare my class to solve the Modeling Monday problem, I first divided my students into** groups of four**. I had them spread out around the room and directed them to have two people sit on each side of one of our classroom tables to facilitate discussion among group members.

We read and briefly discussed the 100 Years On problem and then I turned the students loose to discuss and work on solving the problem with each other. I recommend **not directing students too much during the brief introduction**. I found it helpful to clarify the term “descendants” with them and to also talk about the term “generation.” After that I wanted to see where my students would go on their own.

Some classes at the high school (with 55 minute periods) solved the problem and then had some student presentations within that one class period. I gave my students most of what remained of my 45 minute minute math period and then we followed up with student presentations during the next few days. Each group had been given a piece of poster paper and a marker to prepare for their presentations.

### My Observations During Student Work Time

**Students were very engaged in the process** of solving this problem. With our limited time, I found that most of my students were tightly focused on the task at hand. I think they enjoyed working together on the task.

One of the most interesting and exciting parts of this Modeling Monday problem was **seeing what assumptions were made** that students then used to solve the problem. Students in various grades sometimes considered historical events like the Great Depression, the impact of wars, and even disease. Others discussed the length of a generation, the average lifespan, or the number of children that families were likely to have during different historical periods of time.

In the video you will see that one of the descendants (in one group) did not survive because he was **run over by a wagon**. Somewhat random or “silly” details like this enabled the students to personalize their experience with the problem and have fun with it as they worked.

I think the real beauty of this problem was that students were free to make various assumptions about the descendants of the girl in the picture. However, they later had to **justify or explain their answer in light of the assumptions** that they made.

Since this problem is open-ended there is no right or wrong answer. There are only answers that can be defended and answers that are not supported by student assumptions. Since this problem **does not have one “correct” answer**, it** challenged students who think of math as a linear process** that always leads to THE CORRECT ANSWER.

(By the way,** we did not accept** the answer that the original girl in the picture died and had no children and so there were **zero people** at the party.)

### Student Presentations and Student Work

The other part of Modeling Monday (in addition to student thinking) that I highly valued was the **presentations that were made by the students** after their group work. During the presentations, students were exposed to a wide variety of ideas and variables that they might not have considered in their own group. The **presentations deepened student thinking** and gave them a chance to practice communicating their mathematical ideas and explanations.

Here are **three examples of student group** work and the **final answers** from my classes:

(Click on the pictures to enlarge them. Click the back button to return to the post)

### The 110 Years On Video

For a summary of our Modeling Monday, please **check out the awesome video** created by Robert Ostmann to chronicle the event. You can view it below or search for Modeling Monday on YouTube (and view it at home) if your site software blocks the YouTube feed below.

**I showed the video below to each of my math classes** after we had all completed the activity and the video had been compiled. I think it was fun for my 6th grade math students to see 8th graders and even high school students working on the same problem that they had tackled. There were similarities and differences in the ways that students of different ages approached the task.

### Conclusion – It’s All Here for You

My hope in writing this post is that you (my middle school math teacher colleagues) might **discover a new activity that you can use with your students**. You don’t have to make it a district or even a school-wide activity. You might just want to try 100 Years On in your classroom.

You have a description of **my experience**, **student samples**,** links** to** key resources**, and a **video** that captures the essence of our Modeling Monday event. That’s all that you need.

If you do try 100 Years On in your classroom, or if you have other questions, I’d love to hear about it in the comments section below. I will make every effort to display and respond to your comment or question within a day.

Wishing you all the best!

Mark

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