Here’s the biggest problem with my early math projects: **they emphasized calculations over thinking**. I’d write out dozens and dozens (and dozens) of steps for my students to follow. I wanted to be VERY clear what they to do next. I was desperate to avoid confusion.

The problem? **I was merely creating giant, step-by-step worksheets!**

I realized that it’s actually **imperative for students to have moments of confusion**. They need to stop and wonder… *wait, what should I do next?* If we don’t do this, we’ll create dependent students who cannot think their way through a problem.

You’ve seen the signs of this! Incredibly bright kids raise their hands and ask, **“What do I do next?”**

A good math project is not about computing right answers. It’s about figuring out which math tool to use to solve a problem. **I want to emphasize thinking, not calculating.**

I want to be careful not to do all of the thinking for my students. I want to leave gaps, ambiguity, and points where there is no best, obvious next step. **My favorite term for this is an ill-defined problem** (as opposed to a well-defined problem). I want a math project that’s more like a jungle path than a perfectly paved road. I want to leave room for kids to think.

### Four Qualities

With that preamble out of the way, I’ll walk through a sample project. Looking backwards, there are four qualities I often strive for when developing math projects:

- Juicy Data
- Interesting Conflict
- Expert Perspective
- Awesome Product

### 1. Starting With Some Data

A project has to have some kind of juicy data to get things going. I consider this the “seed” of the project. Here are a handful of sample places for data:

- IKEA furniture – Lots of measurements and price data.
- Census Data – Info about the people of the united states.
- Box Office Mojo – Revenue and ticket sales for movies.

But juicy data doesn’t always mean tables of numbers. Sometimes, a single image is enough to satisfy this requirement: satellite photographs, a diagram from an article, or a photo of a stadium.

**Sample Data:** Here’s a table of US census data I was looking at:

There are a whole lot of numbers (you can download the data here), **but where’s the interesting drama to draw our students in?**

### 2. Find the Conflict!

In the 2010s, I lived (and taught) in California but frequently traveled to Texas for consulting work. So when I noticed that California was the top state by population and Texas was in second place, **I knew I had a hook!**

I graphed the census data, looking for something that might interest my Californian students:

Bingo! **Texas is catching up!** That’s our conflict. Notice that it *immediately* gives us an obvious and pressing question: **when will Texas catch up!?** Or, how fast must California’s population grow to keep Texas at bay? I’m sure you can come up with several variations.

The important part is that, **once you find the conflict within the data, you’ll see the hook to pull students in**. We’re not aiming for “challenging” here. We want an authentically interesting question.

(Note: the graph and chart are all for *my own use*. I’m not going to give my kids that information. Remember, I want them to think! I want them to stumble on the same interesting conflict that I did. Of course, I’ll set the stage, but I won’t do all of the thinking for them.)

Now, let’s look for an expert’s perspective to further develop this project.

### 3. Think Like An Expert

I like to **give students a specific lens to view the conflict through**. Think of it as adding the Think Like An Expert technique.

This is important because it clarifies the direction I’m going to take students. **Different experts will ask different questions about the same data.** If I frame the conflict through the lens of a politician, we might be creating a message that appeals to the changing demographics. But if I frame it from a state’s tourism board, I’ll have a totally different lens. Historians might see the changing populations in a third way, looking for causes and parallels across time.

I went with the tourism board!

So, here’s how I’d set it up:

California’s board of tourism is concerned with Texas’ growing population. You’ve been hired to analyze the states’ population data and then increase the demand to move to California.

First, students will develop their own multiline graph to see the changing populations of Texas and California (I’m not giving them mine!). They should look for patterns and draw conclusions.

Next, they would follow the pattern, and **determine about how long California has until Texas takes the crown**.

We could also ask students to show Texas’ population each year as a percent of California’s. **These specific math requirements are up to you**.

Then, students would **determine how to highlight California’s best features to convince people to move**, ensuring The Golden State’s dominance over Texas.

Digging into this idea, students could cross disciplines and use:

- geographical points of interest
- weather and climate information
- locations of historical importance

Notice how much room there is for students to go in different directions? This is not a giant worksheet. **I’m not giving students step after step after step.** They will not be on auto-pilot! They get to apply mathematical concepts in interesting ways.

### 4. Awesome Product

The icing on the cake is to give students an interesting product to communicate their findings

Depending on their skills and interests, students might create:

- a website
- a commercial (either a skit or a video)
- a brochure

In the end, be sure to give your students a chance to show their classmates what they’ve created, and display it proudly appropriately around the class.

### A Flexible Pattern

Maybe you’re a Texan. **This project could easily be framed around helping Texas quickly catch up to California’s population.** In a smaller state? You could make it work there also. Maybe your conflict is breaking into the top ten or catching up to the state above you.

These four steps are a nice, flexible framework for developing math projects for the needs of your advanced learners. While they’re off working independently, you are free to spend time helping the rest of your class with grade-level materials.

Finally, expect to change these projects around every year. At the least, your product options should be modified to reflect changing technology and the unique interests of your students.

Good luck, and let me know if you come up with something juicy!

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