Intro to Math: Circles and Squares

School is back in session! One of the students I tutor apparently has no homework tonight, otherwise I don’t know when I would have had time to put this into writing – things got busy in a hurry.

I’m doing the whole #teach180 thing so if you’re desperate to see more frequent updates from the classroom you can follow me on Instagram, @multiplefactorsi. I’ll be posting every day, held accountable by a reminder on my phone. I hate tiny little red numbers on that screen, so you know I’ll be following the rules.

Anyway! The first week of math class I always do “intro to math.” We started with some talk about what topics in math we were going to do over the year, and then we spent some time on an arts integration project inspired by these tasks for small children. This would have been awesome if we had more time, or maybe they would have gotten old – who can say? A couple students finished them beautifully at home, and others have kept their unfinished projects in case of momentary boredom. I’ll attach that whole assignment.



PDF of the assignment: day-1-arts

The second day was all about seeing things from multiple perspectives and integrating multiple viewpoints into collaborative work. We started with a number talk, something I loved when I first saw it but just never used. I took the one from YouCubed’s “Week of Inspirational Math,” week 2 day 1. I had been very nervous that our conversation would be nothing like the thought-provoking and joyful example video, but this went amazingly. Here’s our board:


Inspired by Sarah at Math = Love, who was in turn inspired by other bloggers, we then launched Broken Circles. That was great! I love hearing students talk about math, but I also loved the no talking rule. It’s also an inspired touch that one circle completes itself. In one group, the person with the “A” pieces sat there, self-satisfied while the rest of the group struggled, and it was kind of glorious. It’s almost like the point of this task was to show that working together and paying attention is crucial.

Between that and our next collaborative task, we went over our group norms. I translated them into Spanish for an extra touch, and perhaps that will inspire me to do more group work in Spanish class? Time will tell.


The end of Wednesday we started the Pentomino task – I blogged about Pentominoes last time I did it, SO long ago! This year I didn’t leave as much time and consequently they didn’t come up with quite as many combinations, but I do still think it was a useful exercise in visualization and pattern recognition. I’m kind of in love with my independent reflection for that task, attached. Why indeed can you not build a 6×6 square?

Independent Reflection PDF: pentomino-ir

Things are shaping up, but I already know I won’t have nearly enough time to blog as I’d like : 0

Group Norms

Working collaboratively is an incredibly important skill, and increasingly so. So in addition to teaching math, I’ve been working on strategies for teaching communication and collaboration skills.

I got a jump on this during bonding week this year. Every year we divide the school into small groups of maybe 5 or 6 and task them with creating boats. We have this rotation – year 1 these boats are strictly cardboard and duct tape, year 2 strictly trash bags and duct tape, and year 3 cardboard, trash bags, and duct tape. It’s year 3 but this picture is from last year:

boats for blog

Chaos, right? But super fun chaos, and we get more buy-in than you’d expect. Even still, we had noticed this tendency for boat group communication to be subpar. The groups would usually defer to the ideas of whoever was loudest, kids sometimes got mad that their idea didn’t feel listened to, and without a teacher consistently in the room (which would ruin it in other ways), it was totally OK to not participate for kids who didn’t feel like it.

So this year we had them do limited-resource challenges in small groups, and then reflect on these group dynamics upon entering their boat groups. We orchestrated the groups so that nobody was in a group with someone they just worked with, so they could talk openly about their experience. I wrote up a set of reflection questions:

Communication Discussion Questions:
1. What was the most challenging part of communicating with your previous group?
2. Did you feel that your ideas were listened to?
3. Did you always feel comfortable sharing your ideas?
4. Did you feel that you listened to other ideas? Why/ why not?
5. What qualities in someone else make them easy to communicate/collaborate with?
6. What qualities in someone else make them difficult to communicate/collaborate with?
7. Do you find it helpful when someone steps up to be the leader, or does that make you more reluctant to share?
8. What can you do as a group member to make sure nobody is dominating the discussion?
9. What can you do as a group member to make sure quieter people are joining in?
10. What can you do as a group member to make the decision-making process easier?

So now in my math 2 class we’ve started our first group task, the rectangle pattern task I discovered last year. Before breaking into groups we went over the group norms, based on concepts we talked about in my college classes and the book Designing Groupwork by Elizabeth Cohen. Group norms:

For a productive group…
1) Stay in your group
2) Ask the other group members first
3) Everyone is accountable for what the group is doing
4) You are responsible to ask for and offer help

I like the last one best although the first one is a close second.

Best question ever: “wait – are we doing this to practice working in groups or to learn the math?” Answer – both!!! I think I exclaimed that with three exclamation points in class as well.

Tomorrow we finish the task in math 2 and launch the vector fields task in math 4.

Intro to Math Week Year 3: Arts Integration Edition

Just finished my last academic day of the first academic week of the school year. As it has been for the last couple of years, this week is “intro to math week,” and this year I focused specifically on arts integration, keeping the mathematical standards of practice front and center.

On day 1 we spent some time on the syllabus, focusing on class procedures and previewing the upcoming units. Thanks to keeping this blog I have plenty of pictures of previous classes doing the work they’ll be doing, so it’s not just a line about functions or data or whatnot on a sheet of paper. Then I had them each take a Math Attitude Survey. Somewhat unsurprisingly, most of the new ones had some pretty negative associations with math. Kids also weirdly LOVE sharing bad experiences in math classrooms, so it’s a nice first day icebreaker. I took everyone’s three words and put them into a word cloud:

math word cloud 2015

I’ve always been too scared to re-administer the survey at the end of the year, but I think I should do it, or at least have them give me three words again.

The next day was all about arts integration. I had them re-examine the mathematical practices and compare them to the National Core Arts Standards, since I had personally noticed so many great links. Some of them were a little unsure at first, or had trouble understanding what individual standards meant, but they didn’t shy away from asking each other or me for clarification, and the resulting conversations were pretty cool.

art and math

Then we watched this TED talk by Daina Taimina, or at least most of it – it’s super long [for my kids’ attention spans & non-university math levels] and the important parts are at the beginning and end. I love this talk so much though. It inspires me to see her construct her own understanding, especially given her initial troubles with the subject, I enjoy seeing stereotypes smashed, and is the perfect example of arts integration. The art form makes the mathematics more concrete and comprehensible, and the mathematics provides structure and context for some interesting-looking pieces.

Typically I have some major emphasis on group norms, but I didn’t want to insert something else random into this week, so instead today we just had an extended journal reflection and then dove right into our first topics. I’ll teach them the group norms as we start doing our first group tasks. I realized earlier that I’ve never actually blogged the group norms, so I’m working on a separate post about that.

So far things are going well BUT hey it’s only the first week.

Intro to Math Week

The first week of regular classes was an “Intro to Math” for all 4 groups.

Day 1: Syllabus (boring) & growth mindset (inspiring!)

Day 2: Establish group norms & introduction to Pentominoes

Day 3: Pentominoes Task

For their first collaborative challenge, each group had to come up with as many different ways to form a 5×5 square using Pentominoes.


Between the 4 classes, the students came up with 193 distinct ways to form the squares! I’m very impressed with their teamwork and problem-solving skills so far.

To wrap up their work in groups & introduce an element of individual accountability, I gave them an independent reflection that is a little bit more abstract. We didn’t finish that in class last week so we’ll go back to it on Monday.

As classes get into full swing I’m very quickly realizing that:

1. I do NOT have enough time to cover everything! At our school, every Tuesday is a field studies day, plus students all either do service learning or an internship on Fridays. Classes are already only 50 minutes long, but on Thursdays they’re 30 minutes because of the school meeting & P.E. (I’m teaching yoga!). The schedule is awesome and the students get lots of valuable experiences they wouldn’t ordinarily be able to have, but it’s a huge challenge for an integrated curriculum.
2. Teaching 4 totally new classes is going to be really difficult. Most of the material I have taught before, but in a different order, or a different way, and certainly to different groups of students. I alternate between being REALLY EXCITED about trying new stuff and REALLY OVERWHELMED at how much work I have to do on a constant basis.

I hope everyone else has started off the school year well!