Pair Drawings: An Activity to Build Classroom Norms

Welcome back math nerds!

This is my favorite time of year. Clean slate, clean classrooms, fresh ideas, and refreshing optimism. I also love this time of year because I love building classroom norms and setting the tone for the classroom culture that is necessary for productive and rich mathematical thinking and discourse.

Starting on the first day of school, I want my students to know these norms:

Learning mathematics is a collaborative effort. It’s something we do together; it’s not something that I do to you. 

How you respond to the frustration of struggling reveals more about your talents and character than your ability to avoid struggling altogether.

But I don’t want to tell my students these norms; I want them to practice these norms and uncover them for themselves by reflecting on their experiences.

“Pair Drawings” is one of three activities I use in the classroom to build culture and outline norms at the beginning of the school year.

The First Six “Estimation Stations” Are Here!

Estimation Stations are 10-minute activities for teachers to use to build number sense, promote statistical literacy, and foster purposeful student discourse about estimations in the elementary, middle, and high school classroom. These activities can be an ongoing, weekly instructional routine that teachers can use to invite students to have meaningful and purposeful conversations about their reasoning and work together to refine their accuracy as estimators (individually and as a class).

“Elicit” and Our Role as Illusionists

Question:  If someone asks you what “elicit” means, could you nail the definition?  Try it. How’d you do?

Confession: I was an English Literature major in college. I tutored college-level math and fell in love with teaching because of math. But back then, words and expression and theater were my jam. And in many ways they still are.

I was co-writing an article the other month about instructional routines that elicit student discourse in the math classroom. And at one point, the word-nerd in me paused to ponder, “What the does ‘elicit’ really mean? Is it an invitation? Is it a pulling or a pushing? What other words have the same root as elicit? Illicit? Were they opposites? Did they have related etymologies?”

I figured it was worth exploring and down the rabbit-hole I went. Once again.

Clothesline Math and the Power of Discourse

I want to share with you a video that shows the raw power of using Clothesline Math in your classroom to promote student to student discourse.  I share this video because I want you to see how clothesline activities generate student to student discourse and promote student thinking and math development.  And I want you to feel empowered to use this tool in your classroom.  And I invite you to share what you learn in your elementary, middle, or high school classrooms.

“We’re Gonna Need a Different Denominator”

Check out this compeling video from Andrew Stadel. What do you notice? What do you wonder? How can this be used to teach students about adding fractions?

I conducted a lesson study about fractions with some 5th grade teachers.  We used Andrew’s elegantly simple lesson called Black Box 2 to get students talking about adding fractions with unlike denominators.  This task is ideal for introducing the intellectual need for finding a common denominator before adding fractions procedurally.  Student discourse is rich and meaningful and lively.  Give it a read.  You won’t be disappointed.

Making Data and Stats Matter More in K-6, Part 2

Welcome back math geeks!

I love teaching young students about data and statistics.  And I enjoy finding ways to make data and statistics matter more to young students.  But I’m troubled by two curriculum practices about how we teach students to think about data and statistics, especially at the K-6 level.  This post is Part 2.  In my first post, I wrote about how data is often represented to students in heavily scaffolded textbook pages that rob students of the opportunity to purposely engage in thinking, wondering, and discourse…and a solution to this practice.  (If you missed Part 1, click here.)

In this post, I’ll outline another troubling practice and my attempt to help to teachers work around this obstacle.

How Much Sugar in a Soda? A 3rd/4th Grade Division Problem

I conducted a lesson study with some elementary teachers.  We used Dan Meyer’s engaging lesson called Sugar Packets to get students talking about an interesting problem, sharing their thinking, showing what they know about division strategies.  Dan has the lesson listed as 6th grade ratio and proportional reasoning activity, but we found this problem to be suitable for both 3rd and 4th graders and possibly as a review for 5th graders.  There is a remainder in the solution.  And we found that this lesson works best if students haven’t had many opportunities to learn about remainders.  It’s a wonderful introduction to thinking about the contextual and mathematic meaning for the remainder.  (If you teach 3rd grade, I think you’ll find that your students will dig it!  Don’t let the remainder spook you off!)

This lesson addresses many of the Operation and Algebraic Thinking standards for 3rd and 4th grade.  It is also a rich opportunity for students to reason abstractly and quantitatively and to communicate their reasoning with each other.

So, give it a read and give it a go!  Let us know what you learn.  Let’s get better together.

Making Desmos Elementary

For the past few weeks, I’ve had the fun opportunity to write for the Global Math Department newsletter.  Haven’t heard of the Global Math Department?  It’s great tool to find out what’s going on in the online math world about math teaching and watch professional development webinars.  Check the site out here and read about some of the fine folks that coordinate the work here.

In the last newsletter, Bridget Dunbar (@BridgetDunbar), Anna Bornstein (@Borschtwithanna), and I (@mathgeek76) wrote separately about the importance of grade level teachers sharing and learning from teachers at other grade levels.  Teachers of all levels have a lot to learn from each other.  You can find the complete newsletter here.  (If you sign up, you’ll get weekly newsletters straight to your inbox!)

Here’s what I wrote about using Desmos as an instructional tool in the elementary classroom.  While historically used by secondary teachers, several elementary teachers are creating a lot of useful stuff.  Give it a read.  Share your thinking.  And I invited you to a call to action.

Punch-A-Bunch: A 3-Act Math Lesson on Probability

Welcome back math geeks!  I need your help making a lesson better.
I love Price is Right because many of the games require contestants to make predictions.  This often involves estimating prices of products.  But sometimes contestants have to make choices of a different nature, and these choices are ripe opportunities to think about probability and expected value.  And I love when a fruitful 3-Act Math opportunity presents itself.  (I’ve written about one before here.)

The example I want to share now doesn’t seem to fit a 3-Act format.  Maybe that’s because it’s not truly a 3-Act Math lesson.  But I don’t know what else to call it.  I’m curious about your thoughts on how to make it better. 

Some questions I’m asking: 

Is it too clunky? 
What grade levels will find this lesson useful? 
What concepts/standards does it best target? 
What opportunities did I miss? 
What extensions can be made?

I’m inviting your feedback in the comment section.  Thanks for helping me get better!