Nervous system

When it came time to tackle the nervous system, I decided we needed to be as hands-on as possible, working with models to help students understand what was going on in this complex system.  I chose three activities for us to do.  We did Pom-Pom Potential from http://teach.genetics.utah.edu/, then we did the Nerve Cell Communication activity from the Life Science Learning Center of the University of Rochester. (It's easy to request the link to be able to access their library of activities.) We finished up with a fun reflexes and reactions lab.

Doing the activities in this order brought us from micro to macro, but I think next year I'll reverse it and go macro to micro so students can go from what they can identify with (reflexes and nerve cell endings) to the more abstract of action potentials.

We had some good discussions about the membrane potential graph of a nerve impulse that was in the question sheet I made to go with Pom-Pom Potential. I would have liked to spend more time talking about the "macro" part of the nervous system of the nerve impulses traveling through the body and the benefits of reflex arcs. Hopefully each year I will tweak this to be better than the year before.

PS-One of my students was "babysitting" for a Junior health student during this activity--thus the doll in the corner of the pom-pom picture.

Combining Constructions and Radians

We ran out of time in our last topic of circles to go over circle constructions and radians. I felt it was best use of time to give a test on a day I had to be out, so I cut those two topics from the test. I have some more freedom with our next unit, so I had put together student notes for each of those cut concepts, treating them as separate ideas with radians coming first and then constructions. A couple of days before the lesson, I was struck with an idea. Part of the constructions that students were doing was to find the center of a circle. Then for two of the constructions they also had to work with the radius. Why not combine practice finding the center of a circle and the radius with explaining the concept of radians?

I ripped apart their notes and just gave them the construction instructions first. Several students asked why there were staple holes in the one sheet of paper I gave them. I explained that I had changed my mind about how we were learning our last two topics. Once we had gone over how to find the center of a circle, and constructing inscribed squares, equilateral triangles, and regular hexagons, I gave them a cardboard circle from the top of a pie tin. I asked them to use constructions to find the center of this circle. Then I explained that a radian is another way to measure an angle and that one radian is the size a central angle has to open to intercept an arc the length of the radius.

I had them use a measuring tape to measure the length of the radius and then curve the measuring tape around the outside of their circle, repeatedly marking the length of the radius around circle until they ran out of room. I asked each group how many radii they could fit around the circle. Fortunately, they all said 6 with a little bit of room left over.

We talked about the circumference of a unit circle and that it would be 2𝜋. Then we estimated what 2𝜋 was--about 6.28.  Light bulbs started for some, that the little bit of left over on their circle represented the .28 of 6.28.  Then I handed out their radian notes and we talked about how this idea related to the formula for arc length with radians.

I threw a lot at them today, but I am hoping that it was the start of a solid understanding of radians as they prepare to go into Algebra 2 next year.

Here are the notes that I gave them to go along with this lesson.  I gave them the constructions page first though, and then the radians and arc length pages.  The questions included are from old Geometry Regents exams.

And Then There Were Circles

A few weeks ago I shared with a couple of my colleagues my excitement over finishing putting together the details for the rest of our year in AP Biology. Within that week, administration came to me to ask if I would be willing to take on a math class for the last 6 weeks (+ Regents exams) of school since one of our math teachers was leaving after Spring Break. His Geometry class met for 3 periods that I was already at school for (and was not actually teaching), and only one other day for a double period.  I agreed to take it on. Fortunately, the class only has two more topics to learn before we start studying for the Common Core Regents Exam in June, and they are both fun, hands-on topics.

I met with this class for the first time this week and we jumped into circles and circle theorems. I had read a couple of math blogs about circle theorems from Mathsville and Mr Reddy Maths Blog. I also had about 15 hula hoops from when I had taught a Sunday School class and we did a weaving project. I pulled out the twine and yarn and we got to work demonstrating several of the circle theorems. Can you guess what theorem each hula hoop represents? There are several other hula hoops of theorems, but it's very hard to see the yarn in the pictures with students holding them.

I also put together some graphic organizers for my students to keep track of it all. We started with definitions and then moved onto theorems.  For theorems, they worked on adding the diagrams, I gave them the words. This made for a fun first class with this group.