So, I'm taking this opportunity to have my students reflect on the school year. I'm taking this opportunity to pose problems that stretch their brains. I'm taking this opportunity to engage them in the sorts of activities that are meaningful but don't tie directly into the tested curriculum.
My kids keep coming to my class expecting to watch a movie. Eventually, they're going to realize that's not how Ms. Hagan rolls :)
One of my favorite activities from the past week was called Four Fours. I learned about this puzzle from the #MTBoS, but I'd never tried it out with my students.
The Task: Form the numbers 1-100 using exactly four fours. Feel free to use addition, subtraction, multiplication, division, exponents, roots, factorials, decimals, and concatenation.
We played around using four fours and some math operations to figure out what they made.
My students had never been exposed to the idea of factorials before, so that was a fun mini-math lesson to give. I've never used factorials with my students because they aren't included in my state's tested standards. But, you know what, that shouldn't matter. I need to stop worrying so much about what's on the test. I'm selling my students short. I have a chance to expose them to a side of mathematics they have never seen, and I need to take that.
Several of my students asked some really good questions about where factorial would fit in with the order of operations. I wish I had asked them where they thought it fit in instead of just giving them an answer. Actually, I think this is something I need to work on for next year. I go back and forth with whether I should review the order of operations at the beginning of the school year. Some years I do because I find that my students bring over so many misunderstandings from middle school. But, I never feel like this reviewing does much good because students are convinced that this is review material and they understand the order of operations perfectly fine.
But, what if I took it further next year? What if we talked about the order of operations, and then we discussed where to put all of the stuff that studying Algebra 1 and Algebra 2 and higher level math subjects brings with it? We need to talk about factorials. We need to talk about roots. We need to talk about the vinculum. (I love exposing my students to new math-y words!) We need to talk about the difference between parentheses that signify grouping and parentheses that signify multiplication.
In other words, I need to step up my game.
To structure this activity and my students' responses, I printed off the "Mind Your 4s" sheet from 17GoldenFish.
I wish I could say I passed out the pages for students to write their answers on and the room was instantly filled with rainbows, butterflies, and smiling students.
That's NOT what happened
In fact, for the first 30 minutes of first period, I thought I had made the biggest mistake in the world by assigning this task to my students. There was complaining. There was grumbling. Yes, I realize those are kinda the same thing. I guess I just want you to realize that the vibe in my classroom was not a good thing. Students were asking, "Ms. Hagan, why do you hate us?" To this, I answered, "I don't hate you. I love you. That's why I'm trying to stretch your brain today."
The Growth Mindset Bulletin Board was working overtime.
Student: This is too hard!
Me: This will take some time and effort!
Student: I give up.
Another Student: I will use some of the strategies I've learned.
Seriously, it wasn't pretty. I have only about 9 students in my first period Algebra 1 class. 4 of the students were working semi-diligently. The other 5 students were sitting and complaining. They tried to just sit and play on their cellphones, but I stopped that by threatening to take them away for the rest of the day. No one wants to lose their phone for the entire day during first period! I didn't think my students were getting anything out of this activity.
But, thirty minutes into class, something changed. One kid excitedly announced that he had figured out how to find a certain number. Another student asked how he had found it. Instead of telling what he did, he gave a hint about using factorials. This led to a couple of other students figuring it out and exclaiming happily as a result. Pretty soon, the kids were going crazy with excitement each time they found a new number. They were helping each other, coaching each other, encouraging each other.
Students who sat idle for the first half of class were talking about how they didn't find as many solutions as their classmates because the rest of the class had gotten a head start. Teenagers...
The same cycle continued for much of the day. The class would start off grumbling. But, the excitement of a student or two would somehow turn the class around. The sheet I gave students to fill out had 5/100 answers already filled in. To get their participation grade for the class period, students had to fill in 25 additional answers. Of course, they were encouraged to do more than that.
It was fun to see students make observations during this activity. For example, in almost every class period, one student would exclaim that the majority of the answers they had found were in the far right hand column. To this, I said, "Well, it makes sense since that column is multiples of four." I'm kicking myself now, though. What I should have said: "How interesting! Why do you think that is?" #stilllearning
I did have a problem with a student looking up answers on their phone. I'm just skeptical when the completed assignment looks like this. I know that as I worked on the activity that my answers were much more sporadic and spread out.
I had several students remark that this activity would have been so much easier if we were using the number 5 instead of the number 4. I joked that they had just found the next day's activity for me: Five Fives. In fact, when I gave the students a logic puzzle the next day, they complained that they would rather be solving Five Fives.
It was a great brain stretching activity. It was a good review of the order of operations. It let my students experience factorials. And, they learned what the word concatenate meant. It kept them busy for an entire fifty minute period. And, I think it was a lot of fun. Definitely doing this again!