http://www.screencast.com/t/wwA5PqNuIKln

The second screencast is for IXL Math, a website focused on providing online practice questions.

http://www.screencast.com/t/Eip3fjIKr

As a pre-assessment to gauge students knowledge entering the unit I took the selected response questions from form B of their block test. (Pre-Test) To provide students a more accurate response option I included a choice “e” which is “have not seen this type of question before.”

As summative assessment I have assigned practice questions from the book or provided a practice activity for the skills covered each day. This will act as a measure of the day to day progress of students, and help regulate my pacing through the concepts. I also plan to have student do exit/entrance writes throughout the unit to help gauge students’ affect toward the lessons and their perceived ability with the skills.

The first page introduces the topic and provides a warmup for students. We will already have spent a day pre-learning vocab so this should be a review from their definition worksheet. After providing time for students to complete the warmup on their own, we will go recreate the images on the Smart Board to verify understanding.

This page is Sol Lewitt’s work. I will demonstrate naming and measuring of angles by using the Notebook tools to highlight chosen angles from the image. I will then copy them onto page 3, name them and use the protractor tool to measure them. As guided practice student volunteers can perform the same task.

This is largely an introductory unit for the students, much of the content is laden with tough vocabulary that becomes easily muddled due to all of the minute differences between key terms. Ironically some of these terms came up in my math methods course last week, and 6 graduate students preparing to be math teachers had trouble recalling definitions of specific terms. From my personal experience I think this is largely due to a vocabulary list approach to this content. These lists were mostly disconnected with their physical meanings for me and so they didn’t stick past whatever test I had to take. As an educator I view the real purpose of learning these terms as a way of identifying like angles in order to answer geometric questions without needing to measure angles, which is often unavailable anyway. The vocab meanings are much more important than their sometimes confusing words. My lessons will be packed with images to and examples to show the relationship with much less stress on the terms. If a student can explain why two angles are equal in measure, but can’t remember that we call them corresponding angles I feel that the goal has still been accomplished.                                Another major struggle is the “fun” factor or motivating students to engage with the content. One of my plans to address this is to rely on product assessment much more than the usual textbook assignments. For example the first chapter is on naming and measuring angles. Instead of numbing students’ minds with an assignment like 2-40 even on page 178 I am asking them to draw the layout of their dream (8 room) house in which they must name and measure 15 angles, only 2 of which can be right angles. The following day is classification so they could simply label which angles are right, acute and obtuse.  My hope is that the creativity and relation to something that people actually do outside of school will help students enjoy the content more. I also think it is actually a more valuable use of their time than seeing angles only as lines in a textbook.

The UDL concepts I am specifically using in this curriculum are 1.3, 2.1, 2.5, 3.2, 4.2 and 7.2.

Goal: Use properties of parallel lines, transversals, and angles to find missing sides and angles

8.3.1 Use properties of parallel lines, transversals, and angles to find missing sides and angles, and to solve problems including determining similarity or congruence of triangles.

8.3.2 Use models to show that the sum of the angles of any triangle is 180 degrees and apply this fact to find unknown angles.

8.3.3 Use models and logical arguments to show that the sum of the angles of any quadrilateral is 360 degrees, and apply this fact to find unknown angles.

8.3.4 Use models to explore the validity of the Pythagorean Theorem, and use it to find missing lengths.

8.3.5 Apply the Pythagorean Theorem to find distances in a variety of 2- and 3-dimensional contexts, including distances on coordinate graphs.

8.3.6 Use models and referents to explore and estimate square roots.

This is a graphic that Sandy introduced in class that I really liked and so I made an activity out of it I could use in a math class. Retrieved from: http://www.economist.com/node/21543174

1)   If the average iPad costs $600, how much money does apple get for each iPad sold? How much money goes toward Chinese labor?

2)   What does the highlighted sentence “A 20% rise in the yuan would add less than 1% to the import price of an iPad” mean in terms of dollars for a $600 iPad?

3)   According to this article http://www.worldsalaries.org/china.shtml, average Chinese labor wages are approximately $600 per month. If we assume this average is based on a 40-hour work-week, how much more would American laborers making $8.50 per hour cost per month?

4)   How much would the price of an iPad that currently costs $600 increase if it was made with American labor?

This graphic was retrieved from: http://informationlandscapearchitect.blogspot.com/

It is a great example of an uncommon style of graphic display, but it incorporates concepts like the coordinate plane that students are used to seeing. I would have students explore the similarities and differences between this display and ones they are familiar with to build the skills necessary for approaching new styles of displaying data. I would also ask specific questions to see if students could find information from this graphic. It would also be interesting to see whether or not students could summarize the important relationships shown in the graphic (e.g. population size, health and wealth) using words.

I retrieved this image from http://infostatistics.tumblr.com/post/557258403

It is a good example of a cross-content area activity. Graphics like these are used all the time in health class and in health magazines/ websites. In my experience health teachers didn’t necessarily take time to discuss how to read these graphics and I actually relied upon my strong abilities in math. Students without this confidence or understanding likely need more guidance to comfortably read information in this type of format.

I retrieved this image from http://www.wellsfargoadvantagefunds.com/wfweb/wf/ev/planning/growing.jsp

I would use this image as an activity encouraging students to think critically about the images they see in the media. I would prompt students to take into account the source (and their potential motives) as well as the meaning/ probable accuracy of the data. I would also use this image to relate to their background knowledge in lines of best fit and exponential equations.

I retrieved this image from: http://www.economist.com/node/21537909

I would have students rewrite this image as a normal histogram to show how displays they are used to seeing in math can be rearranged to make something more visually interesting. We would also discuss the added benefit of placing this information on a map to help correlate numbers to geographic regions.

I am teaching the last section of math 3, which is the name for 8^th grade pre-algebra at Thurston Middle School. This is largely an introductory unit for the students so much of the content is laden with tough vocabulary that becomes easily muddled due to all of the minute differences between key terms. Ironically some of these terms came up in my math methods course last week, and 6 graduate students preparing to be math teachers had trouble recalling definitions of specific terms. From my personal experience I think this is largely due to a vocabulary list approach to this content. These lists were mostly disconnected with their physical meanings for me and so they didn’t stick past whatever test I had to take. As an educator I view the real purpose of learning these terms as a way of identifying like angles in order to answer geometric questions without needing to measure angles, which is often unavailable anyway. The vocab meanings are much more important than their sometimes confusing words. My lessons will be packed with images to and examples to show the relationship with much less stress on the terms. If a student can explain why two angles are equal in measure, but can’t remember that we call them corresponding angles I feel that the goal has still been accomplished.

The two competing ideas on how to teach this content that I know of are the vocabulary list memorization approach and then the more conceptually focused approach. I find the conceptual focus much more valuable as I explained above. It is also my opinion that if students begin to really understand these relationships now, then the names of such relationships are more likely to stick when they see them again later. By asking students to simply drill and recite the vocabulary meanings now doesn’t allow for them to actually attach the words to anything meaningful. My approach will hopefully give students a stronger foundation of knowledge to attach names to in the future. I also feel that math, especially units like this, are extremely valuable in developing strong reasoning skills. Math can be used to help students view the world in a more analytical and logical way, much like critical thinking is often stressed in history classes. Memorization largely takes away this component in a math curriculum, so it is my goal to help students further develop this way of viewing their surroundings.

One of the most important applications of this content is in design or drafting. I really like the idea of having students design a new school or community center. This connects well to technology if design software is available for students to use. It would also make an ideal final project based assessment for this unit. Students could be responsible for different sections of the building and be required to identify important angle relationships used in the design process. I would try and bring in a guest speaker who works in a related field to give students a chance to see someone using these skills in their career. On top of the technology connection inherent in creating the project students could give a presentation on their work, which brings in oral and written communication. I think tasks where students are asked to explain their thinking is important to enriching their understanding of the content, especially since later on in math being able to explain your thought process is the most important skill.

Another potential project or activity I could do in relation to their history class. Depending on their current unit it would be easy to take architecture or art from the civilization they are studying and analyzing its angle relationships. Egypt, for instance would be extremely interesting because I know enough about their geometric tools to make an interesting history/math lesson about how Egyptians formed angles in their architecture. I designed a project for Tech 2 in which students had to take images from the internet and analyze the angles as well as present their findings to the class. To connect it to history I could have students find pictures relating to their current unit. A project like this would be extremely useful in showing students how important mathematical concepts have been throughout history, as well as giving them further insight into the amazing accomplishments of the people they are studying.

Because this is largely an introductory unit for the students, much of the content is laden with tough vocabulary that becomes easily muddled due to all of the minute differences between key terms. Ironically some of these terms came up in my math methods course last week, and 6 graduate students preparing to be math teachers had trouble recalling definitions of specific terms. From my personal experience I think this is largely due to a vocabulary list approach to this content. These lists were mostly disconnected with their physical meanings for me and so they didn’t stick past whatever test I had to take. As an educator I view the real purpose of learning these terms as a way of identifying like angles in order to answer geometric questions without needing to measure angles, which is often unavailable anyway. The vocab meanings are much more important than their sometimes confusing words. My lessons will be packed with images to and examples to show the relationship with much less stress on the terms. If a student can explain why two angles are equal in measure, but can’t remember that we call them corresponding angles I feel that the goal has still been accomplished.

Another major struggle is the “fun” factor or motivating students to engage with the content. One of my plans to address this is to rely on product assessment much more than the usual textbook assignments. For example the first chapter is on naming and measuring angles. Instead of numbing students’ minds with an assignment like 2-40 even on page 178 I am asking them to draw the layout of their dream (8 room) house in which they must name and measure 15 angles, only 2 of which can be right angles. The following day is classification so they could simply label which angles are right, acute and obtuse.  My hope is that the creativity and relation to something that people actually do outside of school will help students enjoy the content more. I also think it is actually a more valuable use of their time than seeing angles only as lines in a textbook.

In talking with Thurston’s 8^th grade special education teacher I found two major areas to focus on with this content, and really math in general. The number one issue she identified was difficulties in reading. Even if a student’s comprehension is good, if they are a slow reader they can quickly fall behind the pace of a normal classroom. One of the tools I would use to help a student struggling in this area is to provide printed and probably tiered notes. This way they wouldn’t have to worry about reading and writing everything and could hopefully focus on the key concepts. Relating new terms back to background knowledge is often effective too. One of the wonderful things about math is that it builds upon itself so much that often students have seen terms before in a different context. If I can help them see these connections then less time is spent trying to relearn a concept. With Sped students it is important to try and work with them in this area on an individual basis though. Often connections like this don’t come as easily as they do to general students and faulty background knowledge can be even more debilitating.

Many Sped students need extra help conceptualizing abstract ideas. Heavy use of images, as already planned, will help with this but often having a way for them to physically interact with the concepts make a huge difference. One of my thoughts here is to use parallel lines with an intersecting line drawn on paper in which they can cut out an angle and match it to other angles of the same measure. This should make it easier to see how certain angles in that relationship correspond. Furthering that to complimentary and supplementary angles they could cut out two angles and put them together to make a line or a right angle. This physical manipulation allows students to not only see what is really going on with these angles but also explore their complex relationships.

I am fairly confident that my attempts to relate the content to both the class as a whole and students with specific difficulties will be at least somewhat beneficial because I have made a concerted effort to allow for multiple entry points. The curriculum provided by the publishers is largely text based and relies almost entirely on written descriptions to explain the content. My students will of course have access to this, but along with discussing this orally I am choosing to focus on visual understandings. Then to add further understanding and reach struggling students I am providing a more kinesthetic way of interacting with the material to provide another way for students to understand the concepts.

The UDL concepts I am specifically using in this curriculum are 1.3, 2.1, 2.5, 3.2, 4.2 and 7.2.

This project was very beneficial for me in becoming more comfortable in the use of Smart Tech’s Notebook software. I chose this software because it is what is used in my placement, and I found it easier for creating the 3D images I used. I think what I found most insightful though, was how beneficial the creation process is. There are many ways I could have organized this image, but I chose what made sense to me in order to highlight the connections I wanted students to notice. This is important for me to keep in mind when creating other tools like this in the future, because it wouldn’t be nearly as useful if the organization didn’t match my purpose. Even further I think I would ideally have students create their own organization of the information. I could provide pre-made images for them to work with, and their task would be to make a graphic organizer that made sense to them. They could then explain their thought process and the connections they found to be important.

My high school pre-calculus class, and specifically teacher, is what finally shifted my perceptions of math. Mr. Schmidt stuck very rigidly to direct instruction, which can often be a dull environment, but he made a concerted effort to fully explain the concepts and apply them to situations outside of the classroom. Unlike many of my preceding teachers, he did not simply regurgitate examples from the book. He was able to facilitate a higher level of thinking regarding the concepts, and his enthusiasm for the subject wore off on me. I remember him getting very excited anytime someone questioned a concept in class reminding us that “math is pure” as he jumped into a thorough examination. This environment is one I strive to replicate in my own classroom. I don’t want to rely solely on direct instruction, but I recognize how valuable it can be in math when used like Mr. Schmidt did. I want to help students think more deeply and critically about math, rather than simply accepting the statements of a textbook. Equally important to me is the connection of math to “real world” applications. He got me thinking about this for the first time simply through a focus in his lectures and examples. My goal is to take this a step further.

The final learning environment with a profound impact on my curriculum design actually took place outside of the classroom.  My father, a chemical engineer, called me up asking for help with a rate of flow issue between tanks at his site. I was able to answer his questions using math that I had learned earlier in the year in my calculus class. This experience solidified my desire to pursue a career involving math because it greatly improved my self-efficacy and showed me just how valuable math can be. It was like solving a puzzle, but the incentive had more than just intrinsic value because it was solving a real problem.  This is the kind of experience I hope to replicate in the project based learning portion of the curriculum. If at all possible I want students to be able to take a concept from the classroom and use it out in their community. This would ideally involve professionals who could help provide students with insight into jobs that use math and encourage the creativity of such a project.

The Fallout series takes place in a post-apocalyptic world in which there was a nuclear holocaust that took place in the fifties. Now society is weak and fragmented and there are a number of creatures that have been formed from decades of radiation exposure. This particular game takes place in what used to be Las Vegas.

There are many small communities in the area, but a few major groups are fighting for control of the area’s resources. New Vegas is the recovered remains of some of the old Las Vegas strip, and is controlled by a rich entrepreneur. He gets the electrical power for New Vegas from the Hoover Dam, which is run by the NCR. The NCR is a national, mostly military, group that is attempting to bring back the old system of American government. The two factions work together for their individual gain, but both would prefer to have full control of the region. The third major group is Caesar’s Legion, a ‘barbaric’ tribe-like group that is in many ways modeled off of ancient Roman society. The names and system of this society are a great way to interest players in the actual Roman society. While it teaches only a little, it definitely encourages gamers to look for more information. Their agenda is to take over the Hoover dam for its valuable electricity. The goal for you in all of this is to choose either to side with one of these groups, or attempt to take over the region for yourself.

In the beginning you get to choose what your character looks like and his or her strengths. This is important because it really determines the approach you take when completing tasks in the game. There are fighting aspects to the game in which you collect weapons from bats to guns which you use often throughout the game against wild creatures or opponents in the game. The more important part of completing the game, though, is in conversation. To gather information, get help or complete most tasks you must talk to the people living throughout the region. Conversation happens by choosing your response or questions from a list in the game. The character you are talking to responds according to what you have chosen to say. For this reason it is beneficial for your character to have more points in speech and charisma. This also requires you, as the gamer, to analyze the situation and decide on the best course of action. This decisional aspect could be beneficial in developing similar skills in the real world. People are constantly analyzing situations and assessing costs and gains.

The game is free-roam with a large map encompassing the Vegas area all the way to the Hoover Dam. It is not exactly accurate to the real world, but it is similar and could help gamers improve their geographic knowledge of the region. Beyond that gamers are required to use their map-reading and navigational skills.

I think in all areas the educational value of the game could be improved by making the information more accurate. By this I mean making the map more like the real layout of the region, or by making Caesar’s Legion even more like the cultural and political make-up of ancient Rome. I also think that online play in this environment would add a much more complex and realistic component to the decisional process. If gamers had to work and converse with other gamers within the game to complete tasks they would be forced to further develop their critical thinking skills. In the game there are also companions who you can have travel with you and help you with your tasks. If these people were real, then gamers would have to work as a team and specialization would become a key component to becoming proficient in the game.