Brian, Lesson Plan

Target Audience: Geometry Class grades 8-12 mainly 9-10

Big Idea: Using sketchpad to show relationship between geometric drawing and construction

Goal: Using sketchpad, have the students go up to it and draw a geometric figure without the use of a ruler or compass and have each of them compare the drawing. Teach the students the different between drawing a geometric figure and constructing a geometric figure. This will help them learn that precise geometric construction is important when calculating parts of geometric figures like circumference.

Standards addressed:
G.1.2 Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass, explaining and justifying the process used.
G.4.3 Construct triangles congruent to given triangles,
G.6.4 Construct tangents to circles and circumscribe and inscribe circles
G.8.9 Perform basic constructions, describing and justifying the procedures used. Distinguish between constructing and drawing geometric figures.

Resources
www.indianastandards.org/

Target Audience: Algebra 2 Class Grades 10-12

Big Idea: Using Microsoft excel to construct graph of cost/profit margins involving CDs

Goals: This is a lesson to get students to build graphs using Microsoft excel using cost and profit to determine the optimal price to sell a CD at for the highest profit. The students will hopefully get a better grasp on several concepts including Modeling, Function Graphing, Quadratic and Linear Relations, Data Collect and Analysis, Best-fit Lines, Analysis and Interpretation of Graphs, and Optimization


Standards:
A2.2.4 Find a linear equation that models a data set using the median fit method and use the model to make predictions

Resources
http://www.eduref.org/cgi-bin/printlessons.cgi/Virtual/Lessons/Mathematics/Functions/FUN0001.html
www.indianastandards.org/

Target Audience: Pre-Calculus class Grades 11-12

Big Idea: Having students learn about probability and chance by constructing graphs on Microsoft excel to show the outcome of various experiments

Goals: Have students learn more about factorials and other mathematical processes to determine a correlation to chance and the increase of variables involved in a situation

Standards: PC.9.1 Use a variety of problem-solving strategies, such as drawing a diagram, guess-and-check, solving a simpler problem, examining simpler problems, and working backwards

Resources:
http://illuminations.nctm.org/LessonDetail.aspx?ID=L290
www.indianastandards.org/

Karen, Lesson Plans

Lesson One:

Target Audience: Geometry class grades 8-12. (In my case, 8^th grade)

Big Idea: The students will investigate the Pythagorean Theorem using Geometer’s Sketchpad

Goal: The students will use Geometer’s Sketchpad to manipulate shapes in order to make sense of the Pythagorean Theorem. The ultimate goal will be for them to make their own conjectures and judge the validity of their conjectures. Also, once they have sufficiently covered the Pythagorean Theorem, they will investigate the converse.

Standards:

G.4.1 Identify and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.
G.5.1 Prove and use the Pythagorean Theorem.
G.8.2 Decide whether a solution is reasonable in the context of the original situation.
G.8.5 State, use, and examine the validity of the converse, inverse, and contrapositive of “if – then” statements.
G.8.7 Construct logical arguments, judge their validity, and give counterexamples to disprove statements.

Resources:
www.indianastandards.org
http://www.wpunj.edu/icip/itm/Lessonpl/sketch/pythag.html

Lesson Two:

Target Audience: 7^th Grade Algebra I class

Big Idea: the students will use graphing calculators to investigate special types of linear systems

Goal: The students will break up into groups and choose one of the linear systems and discover the differences between the systems. Also, what it looks like when the systems have a solution, do not have a solution, have multiple solutions and make the visual connections with the slopes of the equations.

Standards:

A1.4.1 Graph a linear equation.
A1.4.3 Write the equation of a line in slope-intercept form. Understand how the slope and y-intercept of the graph are related to the equation.
A1.9.5 Use the properties of the real number system and the order of operations to justify the steps of simplifying functions and solving equations.

Resource:
Larson, Boswell, Kanold, and Stiff. Algebra 1.Evanston, IL. McDougal Littell, 2004.

Lesson Three:

Target Audience: Algebra I students (7^th -8^th grades)

Big Idea: Students will put in various values in a scatter plot and find the best fit line.

Goal: The students will learn the skills it takes to make the best fit line using a graphing calculator. They will also take this knowledge to help further their investigation and understanding of what a “best fit line” is. They will also investigate what happens to the best fit line when the plot information is altered.

Standards:

A1.3.1 Sketch a reasonable graph for a given relationship.
A1.4.5 Write the equation of a line that models a data set and use the equation (or the graph of the equation) to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.

Resource:
Larson, Boswell, Kanold, and Stiff. Algebra 1.Evanston, IL. McDougal Littell, 2004.

Angela, Lesson Plans

Lesson 1:

Target audience: high school geometry students (grades 10-12)

Big Idea: teaching triangle properties by use of Geometer’s Sketchpad

Goal: Explain the difference between different triangle properties through the use of geometer’s sketchpad, and have the students explore by creating the triangles and exploring the shapes and their properties themselves.

Standards:
G.4.1 Identify and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral,
and equiangular.
· G.4.2 Define, identify, and construct altitudes, medians, angle bisectors, and perpendicular bisectors.
· G.4.7 Find and use measures of sides, perimeters, and areas of triangles. Relate these measures
to each other using formulas.

Resources:
www.indianastandards.org
http://www.dynamicgeometry.com/general_resources/classroom_activities/index.php





Lesson 2:

Target audience: High school Algebra I students (grades 9-11)

Big idea: Graphing algebraic equations

Goal: Teaching the students, through use of graphing calculators, what equations look like, what their parts mean (zeros, coordinates, x and y intercepts, etc.).

Standards:
A1.6.8 Understand and describe the relationships among the solutions of an equation, the zeros of a function,
the x-intercepts of a graph, and the factors of a polynomial expression.
A1.8.9 Use graphing technology to find approximate solutions of quadratic and cubic equations.

Resources:
www.indianastandards.org
http://www.coolmath.com/graphit/index.html



Lesson 3:

Target audience: High school Probability and Statistics students (9-12)

Big Idea: Gathering information and using it to make charts and make connections

Goal: Students will use information they gather on their own from classmates to create charts of their own through the use of graphing calculators or a spreadsheet computer program.

Standards:
PS.1.1 Create, compare, and evaluate different graphic displays of the same data, using histograms, frequency
polygons, cumulative frequency distribution functions, pie charts, scatterplots, stem-and-leaf plots, and
box-and-whisker plots. Draw these by hand or use a computer spreadsheet program.
PS.1.2 Compute and use mean, median, mode, weighted mean, geometric mean, harmonic mean, range,
quartiles, variance, and standard deviation.
PS.3.3 Use the principle of least squares to find the curve of best fit for a set of data.
PS.3.4 Calculate and interpret the correlation coefficient of a set of data.

Resources:
www.indianastandards.com

Angela, Resources

http://en.wikipedia.org/wiki/Blogging
This website gives a description of what a blog is and what it can be used for. The history of the blog is also described. There are multiple types of blogs, and each one is explained at this site, along with the legal issues that surround them. This site is useful, because it gives a great amount of information about a variety of issues dealing with blogs. This site can be used to teach about blogs before utilizing them in your class. Therefore students will be more informed about them before they become involved in using them.

http://www.lib.berkeley.edu/TeachingLib/Guides/Internet/SearchEngines.html
This website is useful becuase it offers a table that compares three different popular search engines. The features offered by Google, Yahoo, and Ask.com are listed in a convenient table form so that the advantages of each can be easily viewed. This helps people to decide which search engine is best for them to use in a specific situation, based on certain criteria.

http://www.searchengineshowdown.com/
This site is like the one mentioned above, but it offers more resources. It compares more than just 3 search engines, and includes more information about search engines in general. It has a section for news and reviews as well. This page is helpful because it also helps users decide which search engine is best for their web searching needs. This site and the above site can be used in an educational setting becuase when students are asked to use search engines to find something specific, they can refer to this site in order to decide which one will work best for what they need to find. This will make the search process easier for them, because they will be able to find the information they need faster.

Karen, Resources

http://en.wikipedia.org/wiki/Search_engine
This wikipedia site describes what a search engine is and how search engines work. It also gives examples of popular search engines including: Google, Yahoo!search, Microsoft, and Charity search engines. It also outlines the history of search engines and the difficulties that search engines have faced throughout the years. This website does a good job of not being biased towards one search engine over the next and it provides the reader with knowledge on the advantages and disadvantages of using a search engine. This website also includes links to other informative websites on search engines.
Technology Standards: Technology Research Tools, Basic Operations and Concepts, Technology Productivity Tools

http://what-is-what.com/what_is/wikipedia.html
This website describes what wikipedia is. It starts off by showing where the word "wikipedia" originated. What-is-what.com also goes into what the purpose of wikipedia is and how it exists. It discusses the pros and cons of wikipedia. I think that this website provides the reader with a good perspective of what goes on "behind the scenes" with wikipedia. I also think that it does a good job of posing both the good and bad of using wikipedia for a source of information.
Technology Standards: Social, Ethical, And Human Issues

http://searchenginewatch.com/
This website does various things involving search engines. On this website, you can find out the best way to use specific search engines, for example, how to correctly type things in for a math search engine. Also it discusses search engine marketing. It also has current articles posted on search engines. The link bar on the left has a lot of resources including: web searching tips, search engine listings, and search ratings and stats (to name a few). I would describe this website as a search engine for search engines.
Technology Standards: Basic Operations and Concepts, Technology Research Tools

Brian, Reflection

http://www.edutopia.org/php/article.php?id=Art_415
This online video talks about an elementary school called Sherman Oaks which is a charter school in San Jose, California. At this school the students have a large amount of access to computers and can use one whenever they need it. It said that the students do not need to go to a lab and that all of the technology resources were available in the class room. The classroom also has access to scanner that the students could put a photograph of him/her on the computer and edit it with paint or another program.
The class also uses e-mail a lot to stay informed on what are some of the goals and what are some of the other important things discussed in class. E-mail connects every staff member to the administration and each other. It said in the video that if someone did not check their e-mail that often that they could miss something important.
The last thing that the class has is the teacher’s computer which is linked up to the TV which has a touch screen option so students can work. This is good because the class can look upon what the teacher wants to have them look at with little time used in writing something down on the board. Students can also go to the teacher’s computer and show the rest of the class something from a project or something from their notes. This is a helpful technology that is a good thing for students of all levels.
The technology in this video seems student centered with them using it most of the time. The few technological things that teachers had include e-mail and the linked TV. The students have a lot more things that they can willingly use.
Preparations to lessons plans that would need to implement these technologies without creating distractions. With this much access to the computer many students could become easily distracted by the thought of being able to go on the computer and surf the web. As a teacher the best way to avoid this is by making your lesson plans involve the use of some of this technology with slight regularity. This can be helpful because the student not only becomes technologically literate, but he/she becomes more interested in the lesson. Ways to judge how well they are using the time on the computer is by having them take assessments to make sure that they are not wasting time that they are given on the computer. Ways to assess what students are learning is by taking assessments that involve judging typing speed and overall technology literacy.
The biggest challenge that a teacher would have when integrating new technology is teaching the students how to use it. If it is a new technology then many students would possibly be illiterate of these things. Another thing that would be a problem is getting the students to use them. If the students do not like the technology, or feel that it is not needed then they would ignore the new technology and it would be a waste of resources to bring it into the classroom.

Karen, Reflection

This is the technology video I watched:

http://www.edutopia.org/images/movies/toadb.wmv

A short summary of the video case.

This video case was about a fourth grade horny toad project at Waterville Elementary School in Waterville, Washington. The project involves cooperation between Mrs. Peter’s fourth grade class, scientist Karen Divornich, and local farmers. What happens is that the farmers record when and where the spot horny toads. The students combine the information and map out the data using computer programs. A lot of their progress and learning comes from using different technologies.

2. What technology was used in the video?

The farmers and the students used computers to compile all of the data that they collected. Also they used the computers to create maps and different charts. Some other technologies that the students were able to use include GPS comparison devices and a radio collar tracking device to help them track/find the horny toads.

3. The technology used in this lesson was teacher-centered (meaning the teacher, not the students, utilized the technology), or student-centered?

All of the technology was student based. Each student and farmer had the chance to work with a computer to organize their own data. The video did not show as many teacher-led activities. All of the students were provided with GPS units and the students took turns using the radio collar tracking system to track down a marked horny toad.

4. Do you agree that the technology makes the lesson more engaging? Why or why not?

I definitely think that the technology made the project more engaging. In fact Karen Divornich even commented on how there trip out to the farm was not just a field trip but it was an experiment that the students took seriously. They set out to find horny toads using the aid of technology instead of playing tag or putting minimal effort into the task.

5. Think about what kind of preparations that teacher might need to make to implement this lesson. What would the teacher need to think about, both from a technological standpoint and a pedagogical standpoint?

This lesson is quite different than most lessons for several reasons. First of all, it is an on-going project rather than a 50 minute lecture. In order to run this lesson a teacher would have to be in the right demographic area. They would need to have farms in the town. Although you could carry out this project with different animals, to replicate this project a teacher would have to find an area that has a large population of horny toads. From the technological standpoint, a teacher would have to be proficient with GPS systems, tracking device, and the respective computer programs in order to monitor the student’s use of the technology. Although the GPS and tracking machine aren’t really necessary, they do provide another level of learning to the project.

6. What strategies would you use to assess student performance in the video?

I would have to assess their performance by how well they were following my instructions on how to use the technology as well as their interest level and willingness to participate further in the activity.

7. What are the advantages of using the technology in the lesson?

The students get to actually see what a GPS device system does and how to use it. Like I stated before the GPS system was not 100% necessary but it does provide a different perspective to finding the horny toads.

8. What challenges would the teacher and students face when integrating the technology in learning and teaching?

I think it would be difficult to teach students, especially young students how to be proficient with these advanced technologies. I know that I often times find foreign technology difficult to follow and I think I would have to get very comfortable with it before I was able to explain how to use it to students.

Angela Reflection

This is the technology video that I watched:
http://www.edutopia.org/video/movie.php?reset=cookie&keyword=037&id=Art_980

In this video, a school in San Fernando was shown as they gave their students the opportunity to use technology to create thier own videos. The students had to go through a whole process of planning the video and recording it in order to get the final project. The technology used in this class were video cameras, laptops, and a lab known as the "computer inspiration studio" that contained multiple desktop computers that students were able to use for website design and video editing. These technologies were completely student centered because they students were the ones who were in charge of creating the videos. The teachers were able to help them if they had troubles, but the students were the main people utilizing the technology in order to complete the projects. The technology did make the lesson more engaging for the students because it gave them a chance to create a project that they completed on their own. The end result of their hard work, the completed video, is a project that reflects their personality and their work ethic, and they are able to take pride in working on it and the finished product.
The biggest thing a teacher would need to do to prepare for such a lesson would be to make sure that the technology is in working order and there is enough resources for everyone to use. Because the lesson and the projects are based solely on using computers and video cameras, if these resources are not available to the students, they cannot work on their projects. The teachers must also take adequate time to introduce their students to the process of making a video. The students cannot just pick up a video camera and know how to use it, they must recieve instruction on how to use the equipment, and how to complete the process that leads up to recording their video, like writing scripts and editing. In order to assess the students performance, in this case, the teacher decided to let the students write the rubric under which they would be graded. The teacher would be able to grade the studnets on the planning of the video, how they worked together, and the final product. This technology offers advantages because it gives students a great deal of responsibility. They are in charge of using different technological devices, as well completing a quality product. They are able to get the social experience of working in groups and must rely on helping others with their projects while having others help them. They are also able to integrate other topics into the production of their video, for example, the need to use mathematics in order to successfully utilize animation. One of the challenges the teacher wold face by integrating this technology into teaching and learning is censoring the videos. The teacher must make sure that the final project will be appropriate for showing in school. Another challenge they will meet is obtaining enough resources for the students. A class such as this one tends to become very popular, but not everyone can take it, because they have limited resources, and with the students handling the equipment on a regular basis, they take the risk of breaking it and ending up with even less resources.

Brian, resources

http://www.google.com/
Google is a great search engine to use because not only does it tie in to blogger.com, but it has several different searches that can be used for different subjects and for different things as well.

http://www.yahoo.com/
Yahoo provides many different things that can help a student who is searching for something. Not only does it have the search ability to through millions of resources, but also have the ability to use e-mail to contact other people who might be working with them.

http://www.ask.com/#subject:askpg:1
This is an interesting site because it gives students the ability to ask a question and receive several sites that can have the answer. It is highly accurate with the results and they can be really helpful.

E-portfolio and blogs

I believe that blogs are a good way to keep in touch with your class outside the class room. It is also a great way to address questions that other students might have. If a student has a question you can address it and it can help other students as well. If other students see the same question then they can look at the answer that is given and can also provide some insight of their own.
E-portfolios are good not only from a professional standpoint, but also a good thing for students use as well. If a teacher has a website then students can go there and get lessons that they may have missed, or get updates that may have been added after class. A website can also provide students with additional resources that can help them with their studies.