A few years back, I attended a presentation by Dan Meyer and he shared a lesson design principle that has influenced much of my work since. Thankfully, he also blogged about it, thanking Alyssa Boike for her keen insight. The post and design principle is, "You can always add. You can't subtract."

In my previous post, you might remember my goal is to bring as many students as possible into math conversations and this principle accomplishes it. To illustrate this point, I will reference the following visual.  

That's it.
I have not included any directions on purpose or stated any facts about the visual. I would display this image to students as is because I want to give students the chance to make sense of it in their own way (see MP1). Yes, I could have removed more from this image and have done that before because once you see it, you can't unsee it. However, I'm using this specific image for reasons that will be revealed in my next two posts.

The main reason I haven't included directions with this visual is because I'm inviting my math students through the next lesson design principle: "Tell me everything you know about this."

 Let me share with you a question that has been going round and round in my head all school year, 

How do we bring as many students as possible into math conversations?

The prerequisite to this post is that we value math conversations in classrooms. This blog post (and those that follow) will mean nothing if you don't value students having conversations about the math they are learning. For the record, let me clarify that math conversations do not include teachers talking at students for the entire class period (or math block). That's not a conversation. A conversation requires give and take, where all included parties have a chance to contribute.

I think of it like this: you're with a group of friends and it's time to go to lunch. If one person says, "we're going to Restaurant A." then there wasn't a conversation that took place about where to go to lunch. None of the friends shared their preference or had the opportunity to provide input or convince the rest of the group of a place to eat lunch. On the other hand, one friend might want Restaurant A, another wants Restaurant B, and a few other friends want Restaurant C. The group of friends begin to have a conversation around which restaurant might be best. Each party provides their reasoning or proposes questions. There's a give and take where everyone has voiced their opinion and/or choice. 
 
In the classroom, a math conversation requires a give and take. It could be student-to-student, student-to-teacher, students-to-students, and even a back and forth between the teacher and whole group. So how do we bring as many students as possible into the math conversation? Here are a few ideas I've been playing around with this year. Some might surprise you, and some might not: 

• When designing a lesson, value the thought, "It's easier to add than subtract."
• Using the prompts, "Tell me everything you know about this." and "Tell a neighbor everything you know about this."
• Use estimation with as many math questions as possible by focusing on a reasonable range.

And now I have three blog posts to type up and share. Stay tuned!