Day 129: Skills Review & Practice

This time I picked Area of Quadrilaterals for the skills review, and each section raised the class average 0.5 on my 4 point scale. I made a point to emphasize how pleased I was with the results, even though the overall grades themselves were still very low. For example, my 5th hour went from 1.1 to 1.6. 1.6 is still a failing grade (passing line = 2), but it's progress, and that's what I'm looking for. If students can make another gain of similar size before June, they'll pass the class. 

The whole argument for SBG is to encourage student effort in the hopes that they'll begin to make the connection between effort and success. I've been so bogged down with creating this whole curriculum, as well as implementing SBG in my other classes (in addition to my regularly scheduled teaching), that I've lost sight of the real focus behind what I set out to do. I need to make more of an effort to highlight student growth and hard work. It's not even that I've instead been publicizing high achievement, it's that I don't do either. I make grades available, both in class and online, but I never talk about them and ensure that students understand where we're at as a class and how far we've come. 

After the skills review quiz, I gave the students the class period to work on the worksheet handed out yesterday. More thoughts on that tomorrow. 

Day 128: Formalization of Conclusions

We went through the major ideas to come out of the computer lab investigation from Friday. Having the pre-made applet on hand was very helpful - students who hadn't completed the work could still participate in the discussion just by looking up at the screen. 

Conclusions

1. Radii are congruent (not what I was expecting, but important nonetheless)
2. Distance from point of tangency to point of intersection for two tangents is equal
3. Line connecting center of circle to point of intersection is an angle bisector
4. The angle formed between radius and tangent is a right angle
5. The angle formed by intersecting chords is equal to half the sum of the intercepted arcs

Students then began work on U9 WS2. 

Day 127: Investigation with GeoGebra

I created a set of instructions for a student led investigation of the conclusions for tangents to circles and the angles and arcs formed by chords. Most students were able to follow the instructions for the construction, but struggle with the conclusions. At least with the tangent half of the exercise, some students did make some relevant conclusions, but the chord angle/arc equation eluded everyone. 

Additionally, I made applets in GeoGebra for students to play around with and get around making the construction themselves (and also to help guide them toward the conclusions). 

Tangents to Circles
Arcs and Angles formed by Chords

Day 126: Discussion and Assessment

As usual, even after 1.5 class periods to work, most students weren't finished with their work. I did still check the worksheet for completion at the start of class (to confirm my suspicion), then went through as many problems on the worksheet as we could to still allow 15 mins at the end of class for a quiz. 

I don't normally give quizzes on the day we go over something, because it's not a measure of retention. Possibly just a confirmation bias, but results on the quiz were much higher than usual. My main reason for doing this was that I have tomorrow planned in the computer lab, and I hate trying to proctor a quiz in a foreign environment. 

Day 125: Skills Review Quiz & Practice

I'd almost forgotten about giving Skills Review quizzes, but I found some over spring break while I was cleaning, and start of the 4th Marking Period seems like a great time to get back in the habit. So, I picked the lowest standard from the oldest unit of the semester which dealt with angles formed by parallel lines intersected by a transversal. Surprisingly, most students didn't complain too much and better yet - the results actually raised the class average on the standard from 1.9 (2 is passing) to a 2.4 (about a C-). 

After a few examples, students spent the rest of the hour working on U9 WS1. 

Day 124: Special Segments & Angles in Circles

Simple lecture discussing chords, secants, and tangents. Then a simple discovery (led by myself) regarding central angles and inscribed angles). I generally hate lecturing, but the students are so conditioned to it, their behavior is MUCH better when I lecture. I don't think they're necessarily learning more, but they're giving me less grief, and that's really more important, isn't it? (I'm totally kidding - just exhausted from staying up to watch my Wolverines lose the NCAA title game last night). 

I used the document camera, because that tends to go over better than the tablet & projector combo does (no idea why - they students just don't like that). I used to rely on the tablet so I could make PDFs of the notes, but now I can use an app called CamScanner on my phone to snap pics of the notes and upload them to the cloud as PDFs. Cool beans. 

Also getting better at making interacting applets in GeoGebra to show basic ideas (quadrilateral inscribed in a circle was today's attempt). All of this stuff is available at my class website: www.mrfuller.net.

Day 123: Unit 9 - Circles

Whoo - a new unit! Circles might be one of my favorite topics (how many times have I already said that this year?) There's just SO MUCH you can you do with circles and I guess I'm as mystified by the perfection of the shape as the ancients were. 

In any event, to ease students back into school after spring break, today was a very simple intro discovery lesson. 

• Draw point A
• Have students agree on a common distance (pick a number between 1 and 10), and draw a new point X cm away from point A
• Repeat Y times (pick another number between 10 and 20). 
• (Amazingly, this is the step that killed everyone. You should have seen the misinterpretations)

1. What is the longest possible segment you can make connection 2 of the points you drew?
2. What is the relationship between your answer to #1 and the distance we used to start?
3. Find the perimeter of the shape by measuring the point-to-point distance at every gap and adding them up (you should have heard the groans)
4. What is the relationship between the perimeter and the longest segment?

And then I gushed about how awesome Pi is. They didn't care.