Geometry

Upload lesson files here. Along with your file, give a brief description for your choosing it to be the lesson of the week.

=Lessons due by 1/30=

Matthew Laroche Lesson of the Week 9/23/11 Segment and Angle Bisectors Comments: Matt, Glad to see you are using PowerPoint to help with your notes to help students with the material. There are lots of notes for them to take and this a way to help. Dr. C.

Matthew Laroche Lesson of the Week 9/30/11 Geometric Sequences

Comments: Matt, From your reflection, although the lesson did not go as planned, at least you prepared what your cooperating teacher requested. I would have liked to have seen all examples you planned to use with your class in the plan itself. Looking for patterns is a rich topic, and indeed many believe the study of mathematics is that of seeking patterns. Dr. C. Isosceles Triangle Lesson //This lesson was co-taught by Sean Caffrey and Lori Head// This was a good experience not only in co-teaching, but also in differentiating instruction for a low ability/high needs class. Sean's LOW due Jan 30

__Comments__ Nice way to get in informal proof, Sean. Paper folding is really terrific. Can you support students to write their understanding of ideas of the lesson as an additional component, either in or out of class? Dr. S.

I like you're reflection on the importance of differentiating goals in this type of class. I think it is important for each student to have a fair chance to experience some form of success in the class. -Ben

Sean, this was a great way to use an informal proof and get the students involved in the lesson. I also liked how the lesson allowed the students to develop their own understanding of the relationships in the triangle before giving them the formal definitions. -Kevin

Triangle Inequality Lesson = = This lesson was taught by Benjamin Robertson

This lesson had students use dry spagehetti to form triangles and "nontriangles" and then observe their results to make a conjecture about the relationship between the three side lengths in a triangle. I used a packet which I found on the "Illuminations" web site in this lesson.

__Comments__

Ben, I really liked how you checked the first half of the students' packets before giving them the second half. I think that's a great way of doing assessment in the classroom, I may have to steal that idea! Also, it's good to know that you found an activity from another source and it worked well for your lesson.

-Sara

Ben, your reflection says a lot about your sense of the strengths of your lesson and where it can be made better. And Sara, I like the fact that you may use Ben's idea. Sharing with each other is one purpose for the wiki. Dr. S.

Ben, I'm finding that having activities such as this are very enriching for the students, but they are so dependent on clear instructions and classroom management. I like how you present the directions both orally and written; it's little things like these that seem to help us maximize our instruction time. -Sean = =

Special Right Triangles = = //by Jon Yarumian//

This lesson was an introduction to some of the properties of special right triangles. We start out with a 45-45-90 triangles and them move onto the 30-60-90 triangles. The students learn how to find the missing lengths of these triangles when provided with one of side by using proportion formulas.



__Comments__  Jon, are students familiar with the origins of these 'special' right triangles? Experience has taught me that when students know that the 45-45-90 right triangle can be made from a square by cutting it along the diagonal, they tend to remember that the hypotenuse has to be larger than the side. Dr. S.

Intro to Polygons by Sara Almquist My school is still doing midterms this week, so this is my first draft for my first lesson next week. I'm really trying to come up with a good activity to do in the middle of the lesson after we go over the basic concepts, but I can't think of anything. As for the worksheet that's mentioned, my teacher has a lot of good worksheets to choose from, I just have to decide which one I want to use in case I can't come up with an activity. It seems that the classes to a lot of bookwork and worksheets, and I want to get away from that, but I'm finding it hard to come up with alternatives. Any suggestions would be great!! __Comments__ It is not the first time that students have seen polygons...they began working with them in elementary/middle school. What is different is the precision of the definitions. It might be a good idea to check with students to see if they can restate the formal definitions in their own language - helps the remembering process! Was interested in your assessment, but did not see a reflection. - Dr. S.

=Lessons due by 2/6=

 Test Review Lesson Groups Working in Stations Sean Caffrey Worksheets  __Comments__ Sean, I really like your use of manipulatives with the worksheets. It seems like a small detail, but is extremely beneficial to many students. Additionally, I like how you used a specific time frame to give the students a feel for what pace they should be working at on the test. Test taking strategies are important for students to learn and this never seems to be directly addressed, so anytime you can embed them within a lesson is a good thing. In your reflection, I couldn't agree more with the benefit of allowing a student to work through their own struggles. -Ben

Sean, I think it was a great idea for you to represent one section of the book for each station. I'm curious to know how well the students did on the test after that type of review. I'm sure it must have helped the more kinetic learners and visual learners. I also like how you really thought about how you were going to give out directions, it definately makes the whole class go smoother. -Sara

Sean, I found myself wishing I could see the boards and pieces. Did you construct them for this review? You covered all the topics and the questions required higher levels of thinking. Your reflection was very telling when you said that you put a lot of time into devising the instructions. By doing so, you were able to manage the time quite effectively. Don't be too hard on yourself that one or two questions were left undone....I understand that it would have been better had all been reviewed, but there was a lot to review! Setting a time limit was very supportive of getting a sense of timing for the test. Nice job! By the way, how did the students do? Dr. S.

Similar Polygons Lesson Plan Ben Robertson

This is a lesson which I taught on Wednesday 2/5/09 on Similar Polygons. The emphasis of the lesson was for students to understand the concept of scale factor and the definition of scale factor. I selected this lesson as my LOW because it had elements that went poorly as well as elements that went well. I had to change my plan midlesson, but feel that I made wise decisions and am pleased with the results.



__Comments__ Ben, I liked how you focused on what the students were interested in, I'm sure they enjoyed it as well. I also like how you made sure to talk about real world examples in class, I bet that students don't get to talk about real world applications many other times. The graphing activity was a really good idea, too bad you didn't get to it; I would have liked to know how it went! -Sara

Ben, it sounds as if you made one of the "in the moment teacher decisions" when you chose the extension activity over the graphing one. Like Sara, I think the graphing activity was a good one - perhaps you will find a way to use it before you finish this section. I am pleased that you recognize the power of rehearsal! If you like the analogy that teachers are actors whose classroom is their stage, then the need for rehearsal makes sense. What actor would ever go on stage without practicing his/her lines? I suggest that you write out the questions that you want to ask and then say them out loud once or twice before you get to the classroom. They will sound OK to you or not...if not, you have time to rework them before you are 'on stage.' Dr. S.

Ben, Great job adapting your lesson to what the students were more interested in. Sometimes I find that the hardest part of planning an effective lesson; finding examples that can get the students motivated. I agree with your comment in your reflection about practicing what you are going to say before actually teaching the lesson. Sometimes, I go over what I'm going to say in my mind so many times that I feel I have already taught the lesson numerous times. -Kevin

**Intro to Polygons and Parallelograms** Sara Almquist

This was the first lesson I taught (and as of now the only one, my second is on Friday). I think that with this particular class, I'm going to have a lot of trouble getting them to participate, not many students did. What I liked about this lesson was that the closing activing I had, all the students had a specific thing to do, so they all had to participate at least once.

__Comments:__ Students have seen polygons before and they know many characteristics. At this point, they begin to classify them in meaningful ways and perhaps prove conjectures. It would be worthwhile to see what their middle school texts said about polygons so that you have a frame of reference for future planning. The worksheet is a nice one; how did students do with matching the characterisitics with the fugures? I trust that there was a "by eye" caveat as I did not see any marks on the figures to indicate congruence, parallel, perpendicular, angle measurement, etc. Dr. S.

 Circumference and Arc Length by Jon Yarumian This lesson is on circumference and area. I am going to give them a graphic organizer that has space for all of the definitions and examples on it. I am going to have them use the first several minutes or so to get all of those definitions from the book while I go out and check homework. I want to see if this will speed up the time needed for direct instruction and make it more interactive. __Comments__

Jon, I was anxious to read your reflection on this lesson. Dr. S.

Lessons Due By 2/13/09

Exploring Proportions (in Group Stations) Activity in the Spirit of Austin Powers ** Sean Caffrey **



__Comments__ Sean- I love how you bring pop culture into your lesson. Im sure that students really enjoyed playing the role of an investigator. I really like how you thought about ways to get students engaged and active .- <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">Amanda

Sean, This seems like a great and interesting lesson. I'm sure the students felt like they were not even doing any math. You seem to have a knack for creating lessons that can get the students involved and working together - something that I am working hard to incorporate into my own lessons. I agree with you that it's important to look for those teachable moments and to ensure that the students are not "fudging" their way through the work. -Kevin

Sean- This is a fantastic lesson. You've taken a very important concept and presented it in a way that will be interesting and memorable for the students. The use of characters and culture that they are interested in will peak their interest much more than some cliche word problems from a text book and teach the same concept. I really like how you put a lot of thought into how you are going to group students and are always very thorough in your preparation. I find more and more that although it is hard to find the extra planning time, it pays huge dividends in the classroom and is well worth the extra time. -Ben

Quiz Review for Similar Polygons/Triangles Benjamin Robertson

I chose this lesson because it was a lesson that did not go particularly well. I anticipated going through a quick review of the material and having the students be ready for the quiz the next day. However, the students had many questions and were having particular difficulties dealing with similar polygons when one polygon was embedded in the other. I feel that I could have anticipated this difficulty better and addressed it better during the preceeding lessons.

__Comments__ <span style="font-family: 'Comic Sans MS',cursive;">This is one of those areas where experience helps. Embedded figures are more difficult...you will know this the next tme you teach it, for sure! Dr. S.

Determining if a Parallelogram is a Rectangle, Rhombus, or Square Sara Almquist This was actually my lesson from last Friday, but I thought it went pretty well. The students seemed to really enjoy getting to get up and work in partners for the first worksheet, and they got really into the game we did at the end.

== == == ==

= = __Comments__ <span style="color: #000000; display: block; font-family: 'comic sans ms',cursive; text-align: left;">Sara, the game at the end sounded very interesting. I can see why students enjoyed it. I'm curious....were there any errors by an intermediate player that were carried through the rest of the problem by other players? If so, how did you handle that? Dr. S.


 * Lessons due by March 13, 2009 **

**Ratios, Proportions, and The Da Vinci Code** I did this lesson with three different classes this week. I found the same results from pretty much all the classes. The students overall enjoyed the activity, but I the directions for the 4th and 5th questions on the worksheet needed to be phrased better because I had a lot of questions about them. We also didn't have enough time, and I needed to allow time in the following class for them to finish. I haven't really debriefed it yet either, I collected them to grade and I'm going to do it once I hand them back. The good part was that a lot of the students actually had answers that were pretty close to 1.618, one student even got it exactly!
 * Sara Almquist**
 * March 13, 2009**

Comments: <span style="font-family: 'Comic Sans MS',cursive;">It will be interesting to see how the students did on the worksheet. Yes, I agree that some editing of the questions will clarify the expectations for the next time you use this activity. Dr. S.

<span style="font-family: 'Comic Sans MS',cursive;">Sara- Just like Sean above, I really like that you've taken a piece of pop culture and made it a key part of your lesson. I think the idea of this lesson is great and with some minor tweaks to the questions you will be able to use this activity for years to come. While the idea of this lesson is just to use ratios and proportions, it really opens the door for some higher level mathematics that some of the higher level students may want to investigate. It's great that most of the students got close to 1.618!!! - Ben

Due March 20

**Geometry Review** Comments: <span style="color: #000000; display: block; font-family: 'Comic Sans MS',cursive; text-align: left;">Nice way to conduct a review,Sean. Dr. S.
 * Sean Caffrey**

**<span style="color: #1a141a; font-family: Verdana,Geneva,sans-serif;">Angle Measures of Triangles ** **<span style="color: #1a141a; font-family: Verdana,Geneva,sans-serif;">Kevin Simpson ** This lesson went well and the students enjoyed having an activity to begin the class. I'm trying to build up their skills to prepare them to write a formal proof, so I thought starting with a proof without words would guide them in the right direction.

Comments: <span style="font-family: 'Comic Sans MS',cursive;">A nice extension to this lesson (for now) might be to ask students to write a few sentences to describe their process for determining the sum of the interior angles in a triangle. Dr. S.

=**Lessons due by March 27, 2009**=

<span style="color: #bb3030; display: block; font-family: 'arial black',gadget,sans-serif; text-align: center;">Medians & Centroid of a Triangle <span style="color: #bb3030; display: block; font-family: 'arial black',gadget,sans-serif; text-align: center;">Kevin Simpson This lesson involved the students cutting out a triangle and finding that the center of gravity. Then by drawing the medians of the triangle they discover that the intersection of the medians is the same location as the center of gravity. I really liked the way this lesson went and with a few modifications with be a fantastic lesson for the next time I need to teach this subject. Comments <span style="font-family: 'Comic Sans MS',cursive;">The lesson was well thought out; definitely one to tweak and use again! Dr. S.

Kevin, this lesson sounds really interesting. I know how hard it can be to give/write directions clearly for an activity that takes an extended amount of time, but you put a lot of thought into how to word everything to it was understandable to students. I'm sure activity also really helped the kinestitic and visual learners. I also think it is important to provide students with appropriate tables or graphs like you said, I've found that they get very concerned with how nice their own charts turn out when they have to draw them, which takes way too much time away from the activity or instruction. -Sara

Kevin- This sounds like a great lesson. My cooperating teacher actually taught a very similar lesson the first week of student teaching. We found that we had some of the students make their triangles too small which made the rest of the activity difficult. It sounds like the students enjoyed this hands-on activity. This is a great way for you especially since you have block scheduling to get kids moving around and engaged in the subject matter. This is really a great example of a really simple activity that can go a long way in engaging students. Great job! -Ben

**Special Right Triangles** I started this lesson with an investigation worksheet. I wasn't really sure how well it would work, but it turned out to be one of my most effective and interesting lessons so far. The worksheet created a lot of discourse among students, which is something I've been working on. It also really aided in their understanding of the concepts. They did get pretty confused about halfway through of the second part, so I stopped them before they finished so we could go over it. <span style="color: #b04545; display: block; font-family: 'arial black',gadget,sans-serif; text-align: center;">
 * Sara Almquist**

Comments <span style="font-family: 'Comic Sans MS',cursive;">Nice lesson, Sara. I am glad that you achieved the goal of having students talk with each other - it helps them and you! Dr. S.

** Special Right Triangles **
 * Benjamin Robertson **



This was my lesson from last week that I apparently forgot to upload, sorry about that. Ironically, this lesson is similar to Sara's lesson above. It took a little bit to get students past asking "are we going to have to do this on a quiz" and to get them to just focus on the logic behind each of the steps, but once they got a few steps into the process they became engaged and enjoyed the activity.

=Lessons due by 4/3=

<span style="display: block; font-family: 'arial black',gadget,sans-serif; font-size: 130%; text-align: center;">Triangle Inequality Kevin Simpson

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">This lesson included an activity that helped to get the students moving on a Monday morning. I used a lesson from the Illuminations website and helped to improve the lesson by using some of the techniques that Ben had used when he taught this same lesson. Some of the students struggled a little when trying to understand what was meant by not being able to form a triangle out of three lengths of pasta. I'll need to clarify this point more the next time I teach this lesson.



<span style="display: block; font-family: 'Comic Sans MS',cursive; text-align: left;">Comments Searching the NCTM site was fruitful for this lesson, wasn't it? Dr. S.

Exploring the Trigonometric Ratios Benjamin Robertson = = = = = = This lesson was used to introduce the students to the trigonometric ratios sine, cosine, and tangent. There is an activity included in which students had to construct several similar triangles and find the trigonometric ratios of each acute angle in the triangles, record their findings in a table, and make a conjecture about what their findings. All things considered, this lesson went well and the students seemed to have a great understanding of how to calculate each of these ratios.

<span style="font-family: 'Comic Sans MS',cursive;">Comments
==You can add to this lesson by having students go backwards...take a value of the sin (or cos or tan) for an angle and come up with plausible right triangle side measurements. Doint such establishes firm connections between sides and angles. Dr. S.==


 * Lessons due by 4/17 **

Trig Ratios and Solving Right Triangles Sara Almquist

This lesson went okay with the students. Minus the story at the beginning, it wasn't that interesting though. I was actually behind in my plans for the week, so this ended up being more of a catch-up day for all the rest of the concepts we had to cover before vacation. The students did seem to learn the intended concepts for the lesson and we did get to do many example problems.

Comments: Sarah, would it have made a difference if you had thought about critical questions to pose and put them into the lesson? Could you have asked students to conjecture trig ratios for 45-45-90 right triangles with different lengths for the sides before you did the calculations? With those results confirmed, if you asked for a conjecture for the 30-60-90 right triangles as a follow-up, students could defend their thoughts and you could facilitate a brief discussion that would lead into the last part of the lesson. Dr. S.

<span style="display: block; font-family: 'arial black',gadget,sans-serif; font-size: 140%; text-align: center;">Midterm Review - Jeopardy Kevin Simpson

<span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 90%; text-align: left;">This week was midterms so my lesson of the week is the Jeopardy midterm review that we did. The class really enjoyed the review game and I was impressed that they were able to answer all but two of the questions, without much difficulty. Even some of the normally quiet students were actively involved.



Comments: Interactive nature of this one was a nice decision. Dr. S.

** Angles of Elevation and Depression ** This lesson went well. It required students to find the distance between my feet and an object on top of the book shelf using only a string and a protractor. Students enjoyed this challenge and really liked being able to check their solutions using a tape measure to give some real life validity to the problem.
 * Benjamin Robertson **



Comments:


 * Due April 27 **

** Volumes of Pyramids and Cylinders, Introduction to Spheres **
 * Sara Almquist **

This lesson went well. Although the students had a little bit of a tough time seeing the whole "estimation" part of using the candy and how it wasn't exactly. I was actually talking to one of the teachers in my department after the fact and she said she used to do the same thing with rice, which is probably easier to come by and less expensive.

Comments: Sounds like you have a lesson you will use again. If you have a set of clear plastic 'solids' you can also use water. I find that asking students to conjecture the number of times the square pyramid can be filled and emptied into the cube heightens interest. Dr. S.


 * Quadrilateral Family Tree/Parallelogram Investigation **
 * Benjamin Robertson **

This lesson had students utilize a graphic organizer to explore the hereditary relationship of the properties of certain quadrilaterals. Students found this visual aid to be helpful in clarifying the relationships which exist between certain quadrilaterals. Students then did an investigation of the properties of parallelograms by constructing their own parallelograms, making measurements, then conjecturing about the properties of parallelograms.

Comments: Nice lesson Ben. I really liked your parallelogram worksheet. Dr. S.

=Lessons due May 4=