OoO: Four 4’s

Back in late July, the call went out to the mathtwitterblogosphere to share first day/week activities. Since late July isn’t even the halfway point of my summer vacation, I resisted the urge to blog at that time. Instead, I lurked and reflected. A month later I received an email from a colleague asking for some first day ideas. In this post I’ll share one of those ideas.

It’s common for middle/high school teachers to begin the year by reviewing order of operations. The thought here is that a mastery of OoO within arithmetic is necessary for student success in algebra. I’m not convinced (see Timon’s post).

On Day 1, I’d often overhear a student say “What a geek! He’s got a math clock.”

Taking advantage of this, I’d ask students to find expressions for the numbers 1 to 12 using four 4’s and mathematical symbols (+, −, ×, ÷, brackets, decimal point). If I were to start the year with OoO, the the four 4’s puzzle would be an improvement on the BEDMAS worksheet. Each student can contribute something and gain confidence by solving the problem. This is important on Day 1 (and Day 93). Multiple solutions are shared and appreciated.

By giving students a target number, rather than an expression, the need for a rule to clarify ambiguity arises. It becomes more than a mnemonic to memorize. For example, students may present the first expression below as a solution to target numbers of 3 or 9:

(I’m not sure if these add anything to this activity, but if you want these cards, here they are: Four 4’s)

Last year, I wrote

I’m just not able to lecture students for 75 minutes about consequences of unexcused absences, procedures for handing in homework, and lists of food & drink items that are acceptable to have in the classroom. Imagine sitting through this four times on Day 1. Welcome back!

On a personal note, I hope that Gwyneth is as excited about the first day of Grade 12 as she was about the first day of Grade 2 (and Kindergarten). I hope that she’s doing math on Day 1 (and Day 93).

Gwyneth Day 1 of Grade 2
Gwyneth Day 1 of Kindergarten

Never let them see you smile.

At least ’til November.

Anyone else remember being given this advice by veteran educators at the start of your teaching career? The thinking here was that it would prove too difficult to get students back on track once you loosened the reins. If you must, loosen up at the end of the semester. I could never pull this off. My true self, or at least my true teaching self, would make a special guest appearance by the end of the first class.

I often struggled with planning for the first day of classes. I’m just not able to lecture students for 75 minutes about consequences of unexcused absences, procedures for handing in homework, and lists of food & drink items that are acceptable to have in the classroom. Imagine sitting through this four times on Day 1. Welcome back!

“And one more thing… here’s a review worksheet that covers everything you should know from Math 9. See me or a counsellor if you’re having difficulties with it.”

I was also uncomfortable with the let’s-get-to-know-all-about-each-other approach. No “Find someone who…” searches for me.

When students left my classroom for the first time, I wanted them to believe that

  1. We were going to get to know each other as people, and
  2. We were going to do this while learning mathematics.

Here’s a PMa 10 1st Day Jigsaw activity that, although not perfect, attempts to convey this message.

I cut the squares and placed them in envelopes. In small groups, students pieced the puzzle back together so that questions and answers shared a common edge. An answer key is not provided, but the jigsaw puzzle part of the activity does provide students with some feedback.

These are not rich problems – they are review questions of important concepts & procedures from Math 9. However, I did listen to some interesting conversations. For example, in many groups, there were debates about which power (3^-2, -3^2, or (-3)^2) was equal to -9. One student said he remembered that a negative means flip (his words, not mine) and matched 3^-2 with 1/9. His group members asked him to explain why this works.

Please let me know what you think of this activity. Also, do you have a Day 1 lesson to share?

As a new school year begins, are you looking for posters to decorate your classroom? Learn how to create a gigantic math poster of your own.