Citizen Math lessons are conversational. As teachers and students progress through them, the experience should feel like a group of people hanging out with one another and using math to discuss something interesting in the world. It's like a Socratic dinner party, just without the grub (or hemlock).

To support folks in having an exemplary experience, each Citizen Math lesson comes with three components: a student handout; a detailed teacher guide; and an online interactive with videos, graphs, and other elements that accompany the lesson. The more familiar teachers are with how each component works, the more powerful the classroom conversation will be.

It's a handout. For students. On paper. No big surprises here.

When teachers use Citizen Math lessons (or as some say, on "Citizen Math days"), they'll often have students work in small groups on each question, then discuss the question as a class before moving on to the next. This is a great idea. Still, even when students are working in groups, we recommend providing everyone with his/her own handout. Not only will this ensure that they have a record of their work, but it'll give them something to look back on twenty years from now. "Gosh," they'll say to themselves in their old-timey kind of way. "Math class sure was interesting!"

Let's be honest: Teacher guides can be pretty boring. Not ours! We think you're going to love our teacher guides. Not only are they beautifully designed. (Thanks, Sullivan Branding.) They're also exceptionally helpful and provide actionable tips to help teachers facilitate a successful classroom discussion.

The front page of each lesson guide includes the real-world takeaways that students should remember as well as the mathematical objectives that will be addressed. It also provides a quick summary of each question and estimated timings.

In addition to the front-page overview, each Citizen Math teacher guide offers a detailed explanation for every question in the lesson. These explanations highlight the type of work that students might do to answer each question. In situations where students might answer a question in different ways -- for instance by using a table, graph, or equation -- we'll typically include an example of each approach. This gives teachers a helpful heads-up about what to expect and can help them plan their instructional moves accordingly.

Math is dynamic. The more students can visualize mathematics, the more deeply they'll understand it. To help teachers bring Citizen Math lessons to life, each lesson includes an online module with interactive graphs, tables, videos, and other elements. To access this module, a teacher can navigate to the main page for the lesson, then click the button labeled "Enter Teach Mode." If a teacher has an LCD projector, they can project the interactive onto a screen at the front of the classroom. If they have an interactive white board such as a SMART Board, even better.

For every question in the student handout, there's a corresponding screen in the online module. (Some questions will have multiple screens, for instance a question that involves both a video and an interactive graph.)

The online modules are designed to be used by the teacher and only the teacher. They are NOT intended to be used by students on their own personal devices. Why? First, the modules often include answers to the questions; if students had access to the online module, they could skip ahead and miss out on valuable mathematical work. Second -- and as we mentioned earlier -- Citizen Math lessons are designed to feel like conversations...and teachers are the principal facilitators. In the land of Citizen Math, teachers control the flow of the experience. They decide what to show and when. The online module exists to help them do that.

Now that you're familiar with the three components that make up each lesson, how should you go about using them? We recommend preparing to teach a Citizen Math lesson in three steps.

So that's it. Those are the components that come with each lesson. Each component plays a critical role in supporting a high-quality classroom experience. We hope you enjoy them!