So, I’ve begun my adventures in subbing. I spent most of the summer panicking that I didn’t have a job yet, and when one finally came along, it wasn’t quite what I expected. I’m grateful for a job in any form, but it’s been a process sort of mentally giving up plans I’d made in my mind over the last few months of what my classroom would look like, how we would start the year and the mathematical learning trajectory I was excited to be on with my students. Trying to make the best of an unexpected situation, I found myself asking:

## what can I do as a substitute?

And specifically, what can I do in terms of engaging with and eliciting students’ mathematical thinking? To be honest, sometimes not much. There have been days I go in knowing my job is to do whatever is written in the sub plans, which is often to open the curriculum book and attempt to “teach” something I’ve never seen before. Once, we had a little extra time so I decided to do a choral count to reinforce ideas about place value, but for the most part, students have just independently done worksheets.

I was excited when I found out I got to sub in a friend and former classmate’s 4th grade classroom, and even more excited when she told me I was welcome to add or change anything about the schedule, if there was something I particularly wanted to do. They had extra time in math, and I thought for awhile what we could do in the 30-45 minutes we would have after doing the planned quick image activity.

I decided to bring in a variety of games, books, puzzles and manipulatives that would provoke mathematical thought and allow students to freely play around with them and see what happened. I thought of what we could call this time and settled on ‘Math Recess’, the title of a book by Sunil Singh and Christopher Brownell encouraging math play. I was also inspired by hearing Tracy Zager advocate for “D.R.E.A.M” – “Drop Everything And Math” time in schools, where students have time to playfully explore mathematics. (I am sure there are many people who have been proponents of math play in school – these are just two sources I was thinking about as I was planning what this time would look like).

I tried to have a good mix of activities students could explore – I brought 21st Century Pattern Blocks and found dominoes in the classroom, we had games from Math for Love and books such as Which One Doesn’t Belong? and How Many? and a collection of Open Middle problems students could work on independently or with partners.

Students were immediately drawn to dominoes and Prime Climb (pictured above), and many eventually became intrigued with the pattern blocks – some made characters, such as a “person in the snow”; others made new shapes (stars!) or worked to figure different ways to fit the blocks into the hexagon cutout.

(As an aside – a student and I had an interesting and rather philosophical conversation regarding his creation of “person wearing a coat in the snow”. I couldn’t guess that was what he was making, but once he told me what it was, I remarked how it was interesting that I couldn’t see it until he told me what he had made, and then I could see it, and I wondered why that is. He said because when you know what you’re looking for, it’s easier to find.)

## Part of play is embracing the unexpected

Despite the success of the above activities – the ones that were more independent or required more think time to really get into (the books and the challenging math problems) sat mostly untouched. Realizing that students were not likely to sit and think about the mathematical ideas presented in these choices while their friends were building and playing with each other, I decided to follow the students regarding other things they were interested in pulling out and playing with. For example, one student wanted to build with unifix cubes and was meticulously making sure each stack had the same number of cubes in order to build a “house”.

Other students asked to draw or read. At the time, since this wasn’t my class, it was the end of the day and no good seemed like it would come from requiring that kids only engage with the math activities (especially since this was likely a one-time experience for them), I said okay. About eight kids spent the time drawing with each other or reading independently. I wasn’t sure if this was the right choice to make – I really wanted kids to be engaging with math – but then at the end, one of the kids who I thought had been drawing came to me with the following question:

Student(hiding the above paper): If you guess the number on this paper, you’re the master of the universe.

Me: Infinity? (Student turns around paper). What number is that?

Student: I don’t know!(Students continued discussing this idea as they packed up.)

Another student: That can’t be a real number, because there are no commas.

Turns out that giving students room to be creative beyond what I had planned allowed for them to come up with really interesting mathematical ideas on their own!

## What is the goal of math play?

- Moving forward, I’m thinking a lot about the goal of this kind of math play.
- Should it just be a total free time for students to do whatever they like (relating to math)?
- Should teachers use this as a time to assess specific ideas students have about mathematical concepts?
- Should the options change based on the unit being studied?

- What does it look like to have a routine of math play in the classroom?
- How often does it happen?
- How long do kids get each time?

- What separates “math play” from other kinds of inquiry-based math?
- And in what ways does it or does it not matter to understand this difference?