Simplifying radicals? Who needs it?

There was a time I thought radicals should be simplified. A factor of a radicand should never be a perfect square. To do otherwise was just sloppy math—so I thought. Now, I think differently. You should consider it too.

pic fromthemathlab.com

Making the square root of 40 look like 2 on the square root of 10 serves no real purpose in the mathematics of real life. You can readily estimate the square root of 45, but trying to do that with three square root 5 is a much more complicated task, and for what? If I am going to the fabric store and I am asked how much ribbon I want, I better not say, “4 root 2” and expect to get the correct amount. At the hardware store, I am far better reasoning that the square root of 32 feet would be a bit less than 6 feet, and a bit more than 5 and one-half feet and just say 2 yards. The lumber department does not want to hear this nonsense about radicals and square roots.  They want to cut my lumber and send me to the register to check out so they can help the next person also get a reasonable amount of lumber.

Photograph by question_ev3rything on reddit

Now, I know, one needs to simplify radicals to combine radicals via addition, such as the square root of 27 plus the square root of 12, but seriously. This is not reality. This is a contrived problem that I have never seen come up in real life. Ever. And I sew and measure and do real life things with math—at home. It does not come up.  It’s clever, like a party trick, but not terribly useful.

I do make certain my Math 2 students can “simplify radials,” but just for the “man.” Not for real life. I used to “ding” my students (take off 1 point just to be mildly irritating to get them to conform to convention) for not simplifying radicals. I am totally rethinking that.

Reality says leave radicals as they are so they are easy to estimate to be useful and to check for reasonableness. Done.

Last spring’s project…square roots…get it?

 

year two–take two

Happy Saturday all! I’m supposed to be getting ready for a couple PD sessions that I am presenting over the next two weekends, but I can’t get a comment from @SAMSDrSapsara at @mrsstipemath’s Thursday night 7th grade zoom (time stamp 00:27:14) collaboration out of my mind. Dr. Jessica Sapsara said, “I feel like when I’m making my anchor charts for the things, it’s really coming…way…after the unit has passed and I’m like, alright, let’s get something up so when we’re referencing it later as units come through…let’s look at that one again…so we have better working language…visuals…” And I thought to myself, “self, that’s where you were last year, if you made them at all!” That got me thinking about even more exciting differences between years 1 and 2 of implementing Open Up Resources 6-8 Math Curriculum. I know I reflected on this earlier,  but there’s more. Here’s my summary so far:

• Anchor charts—Like I said, year 1 I was lucky to make them at all. In fact, I did not understand their usefulness until it was too late. Year two, I am deliberate in their creation as well as in pointing to them during lessons and even as students present, intentionally connecting student ideas to the charts.
• Lesson preparation—I was so tired last year that I would fall asleep as I was reading the lessons. I’d get up in the morning and get about half-way through the teacher guide and then my room was filled with kids that needed support for the other course I teach, so there went my preparation time for Math 8. Year two, I am seeing so much exciting mathematics and even more brilliance in the authoring of this curriculum. I am excited about reading it and doing it and energized by it, so much so, that I read it before I even go home the day or even two days before the lesson. I am copying and cutting my cool downs and black line masters for an entire unit at one time rather than daily. I am importing my slides for an entire unit into one Google slides presentation. I just edit daily to remove what was covered that day in preparation for the next. (Note to self…hide the slides rather than deleting them, thereby making the file useful for next year! Yep, here I am, learning through reflection!)
• Student copies/student workbooks—Year 1 saw me rushing around daily or all day Sunday editing and copying student pages for the week ahead. Year 2, my district purchased student workbooks. That in and of itself has given me back part of my life. I am so fortunate that my district cared enough about its teachers and time and copying costs to purchase student workbooks.
• Attention on student learning—this was a luxury rarely afforded in year 1 because I was so intent on my own learning. In year 2, student learning is what fuels me. Seeing the lesson by lesson progress and retention is reassuring that I am actually helping students become mathematicians.
• Student engagement—what an improvement!. In year one, I had three students per class I felt were really with the program. In year two, I have all but three students demonstrating understanding and actively owning their learning. I need to remember that when I am beating myself up about those three students, but still, that’s 3 students too many.
• Student results—What a difference! They are truly remarkable. When I review cool-downs I can see student thinking and reasoning and catch misconceptions so they can be addressed timely. Year one, I was lucky to get a cool-down in the same day as the lesson. Now when I pass out the cool-downs, I hear students say, “we’re done already?” Students self-assess daily as they turn their cool-down into the basket based on their level of understanding, thanks to @mrsstipemath.
• Supplemental activities—Year 1 had virtually zero supplemental activities for students. Year 2, they are actually part of the game plan. They include Desmos activities to further student learning and assess student understanding; Quizziz games so students can self-assess and develop fluency with concepts; Desmos graphing calculator sessions to quickly and easily make math visible; practice problems from the curriculum; review sessions using practice problems for unit assessment preparation. I am still trying to get to Khan Academy  exercises, but haven’t managed to get them worked in—yet.
• Pacing—This is a non-issue in year 2. I attribute this to not over-teaching as well as to keeping moving even without 100% buy-in from students. I know the material and concepts are coming around again and both the students and I will get another crack at nailing down the standards. I also understand the learning goals more clearly and know that keeping them bite-sized is essential to student success. That my students were successful at all last year was truly a miracle.
• Community support—In year 1, I felt like my blog was my only companion as I learned this new curriculum and relearned how to teach—or perhaps, finally learned how to teach. This year, there is so much community support. There are the organized supports such as the face book groups and Monday night twitter chats (#OpenUpMath) as well as monthly zoom sessions by the Gurus of Open Up Resources 6-8 Math. My district is also providing monthly professional development specifically for users of the Open Up Resources 6-8 Math curriculum. I also have a network of users across the country as my personal Professional Learning Community. I find it hard to believe I made it through last year without these committed educators.
• School-life balance—This did not exist in year one. I worked very hard, but not very smart and it took a physical toll on me. This year, I am more rested even though I am doing more each day. I manage to eat healthier, sleep more, exercise regularly, read for pleasure, find time to support my learning community and even spend time with my husband. These activities have all improved my mood and attitude and help me recover from slumps and meltdowns more quickly.

Year two just keeps getting better too. I actually feel valued and appreciated by my colleagues across the country. I feel confident in my classroom and I am excited about the future. My community members experiencing year one now who are taking advantage of the support of the Open Up Resources 6-8 Math community are doing so many wonderful things for their students. I am grateful for them and want to support them as we move forward together, as a community of learners.