As I was preparing a unit on expressions (translating, evaluating, and simplifying), I decided to branch out and include a real-world “problem” to entice students to see the benefit of writing equations and expressions. I ended up creating a video detailing a pretty involved scenario in which students would need to sift through possible constants and variables. At the end of the video, I asked the question – How can you model a possible solution to this problem? Because my 5th grade son’s teacher is such a great sport, she offered to test the lesson in her classroom and we certainly found some interesting results. Upon being asked to generate a model for the problem, all the students started drawing these elaborate schematics and asked if they could create them in 3-D. It became very evident that students aren’t quite comprehending the numerous meanings of math models. Looking over Henry Pollak’s discussions on math modeling for the common core, I decided to make a follow-up video helping students see that mathematical modeling can take many different forms. Here is the link to the original video: https://www.youtube.com/watch?v=nXBL79tlBg4. I would love for teachers to try showing this video to their students and see if their misconceptions for math modeling are the same. The youtube link for the math modeling video is https://www.youtube.com/watch?v=Iew9nppByKs&feature=youtu.be.

# Category Archives: Math lessons

# Using objectives purposefully in the math classroom

When I was first asked to write my objective on the board in my classroom, I flat out refused. I dug my heels in the sand and complained, “What for?” It seems that administrators were convinced that statements such as, “Students will be able to ….” was the latest and greatest idea for making students achieve unrealistic goals. Personally, I didn’t see the point! Did the students care? Why was I writing something for the benefit of my administrators that only walked through my classroom about once a year. One more thing to do in an already crowded day!

Many years into my career, I had the incredible opportunity to participate in a professional development course led by Corbett Harrison and Kindra Fox, that focused instruction on the research of Wiggins and McTighe and their book, *Understanding by Design*. It was as if a perpetual light-bulb had been turned on over my head! Students need to know what they are learning and why they are learning it. Also, we have to set our learning targets before writing our lessons, then we create the acceptable evidence of mastering that target, and only then should we plan lessons to achieve those goals! I was doing everything completely wrong!

After one year in this professional development course, I was hired to be a trainer and teach other teachers how to bring Wiggins and McTighe’s research to life in all math classrooms. I am completely passionate about creating essential questions that engage students and involve them in their own learning. I love to get students enthusiastic about what they are learning. In that vein, I created a video that is meant to “hook” students into learning about surface area and volume. Not only does the video raise interesting and exploratory questions, but it also provides a driving essential question that can be used throughout an entire unit on 3-D Geometry. Here is the link to the essential question video, http://www.youtube.com/watch?v=SJGpKnI-784, which is on you-tube. I hope your students enjoy!

# How can you combine linguini and trigonometry?

The other night, my son was discussing what he was learning in trig class and it made me reminisce about the days that I taught trig. When I first started teaching that class, it scared me. If you made the tiniest mistake, the students turned on you like wolves. After a while, I got my groove and turned the class into a great inquiry-based course that I adored teaching. One of my favorite lessons from the beginning of the year is an activity called linguini trig. I adapted it from an article I found called “Spaghetti and the Sine Curve” that appeared in The Mathematics Teacher in the 90’s. The whole lesson is an amazing way to show students how the trigonometric functions are graphed and it gives them a solid foundation in periodic graphs. I decided to replicate the lesson on video (about 15 minutes long) for teachers to see how the lesson looks from start to finish or students could view it to solidify understanding of the concepts of graphing. The link to the video on youtube is http://www.youtube.com/watch?v=9umDGwytyos. I hope you enjoy! Here are some documents you need for the lesson: graph template001 graph template002