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Location to Our Buried Treasure

We could use this in a math class to teach: distance, area, proportions, scale, and for pirate students...treasure maps.

Lessons w/ Technology (Reflection 7)

Geometer’s Sketchpad Wallpaper

Target Audience: An entry geometry class, either honors 8th grade or early high school.

Goal/Idea: To have students understand rotations, reflections and translations. Students will design a geometric “wallpaper” and apply translations to the design.

Resources: Geometer’s Sketchpad software

Standards: G.2.4: Apply transformations to polygons in order to determine congruence, similarity, symmetry, and tessellations. Know images formed by slides, flips, and turns are congruent to original shape.

Linear Equations in slope-intercept form

Target Audience: An Algebra I class, early in the class or semester.

Goal/Idea: To have students understand slope intercept form and how the slope and y-intercept change the look of the line. Students will analyze sets of equations where slopes, or y-intercepts vary. This will allow students to see how graphs change, by holding variables constant.

Resources: Graphing calculators, overhead, and overhead calculator.

Standards: A1.4.1: Graph a Linear Equation
A1.4.2: Find the slope, x-intercept and y-intercept of a line given its graph, its equation, or two points on the line

Frequency of Music Notes

Target Audience: A high school precalculus class

Goal/Idea: Students will understand graphing sine and cosine curves, in relation to the frequency of the music notes from tuning forks. This includes the changing of the period of the graphs.

Resources: Graphing Calculator, Calculator-based Labs (CBL), and tuning forks

Standards: PC.4.5: Define and graph trigonometric coverage
PC.4.6: Find domain, range, intercepts, periods, amplitudes, and asymptotes of trig functions.
PC.4.7: Draw and analyze graphs of translations of trigonometric functions, including period, amplitude, and phase shift.

Reflection 7

Target Audience: Geometry students, grade 10-11.
Big Idea: Have students understand what is really needed to prove geometric concepts.
Goal: Have students examine properties of quadrilaterals and start to make informal conjectures and proofs related to those quadrilaterals.
Standards: G.3.1, G.8.3
Possible Resources: Geoboards, Geometers Sketchpad

Target Audience: Grades 7-8
Big Idea: Students further understanding of the coordinate plane.
Goal: To provide practice plotting and naming points on a coordinate grid using Battleship.
Standards: 7.4.1, 7.4.2, 8.3.5
Possible Resources: Battleship Game

Target Audience: Geometry Classroom
Big Idea: Helps students understand how parts of a funtion relate to the whole part.
Goal: To let students distinguish difference in shapes and see patterns in the shapes.
Standards: G.3.1, G.3.3, G.8.7
Possible Resources: Pattern Blocks http://nlvm.usu.edu/en/nav/frames_asid_171_g_4_t_4.html?open=activities

Reflection 7

Target Audience of the Lesson:
This lesson is targeted for Algebra I students. These students may be in grades 8 – 10.

Overall Goal of the Lesson:
The goal of this lesson is for students to learn how to factor the difference of two squares, perfect square trinomials, and the difference of two cubes.

Student Learning Objectives:
After the lesson students should be able to:
• identify and factor binomials that are the differences of squares
• identify and factor perfect square trinomials
• identify and factor difference of two cubes

Assessment: (Go back to your learning objectives. What will the students do to demonstrate they have met the learning objectives? Make sure each objective is paired to an assessment measure)
To demonstrate that the students have met the learning objectives, a worksheet can be given to each student. This worksheet will have multiple problems for them to complete including differences of squares, perfect square trinomials, and difference of two cubes. Students could also be given a short quiz over the lesson with each type of task described during the next class period.


Indiana Content Standards Addressed: (Copy and paste entire standard from http://www.indianastandards.org/)

A1.6.5 : Divide polynomials by monomials. Resource
A1.6.6 : Find a common monomial factor in a polynomial.
A1.6.7 : Factor the difference of two squares and other quadratics. Resource


Target Audience of the Lesson:
This lesson is designed for an Algebra I class. It is targeted towards students in grades 8 and 9.


Overall Goal of the Lesson:
The overall goal of this lesson is getting students to learn how to multiply polynomials using the FOIL method and Distributive Properties. Another goal is to have students learn how to multiply polynomials in real-life situations.

Student Learning Objectives:
After the lesson students will be able to:
• Classify a polynomial by degree and by number of terms
• Multiply polynomials by using the Distributive Property
• Multiply two polynomials using FOIL
• Apply polynomials to real-life situations

Assessment: (Go back to your learning objectives. What will the students do to demonstrate they have met the learning objectives? Make sure each objective is paired to an assessment measure)
In order to demonstrate that the students have met the learning objectives, you can write problems on the chalkboard or overhead projector. Students will have to either solve the problems themselves or give the instructor step by step instructions to solve the problems. Students can be given worksheets to work on in class and turn them in by the end of the period. Lastly, students can be given homework problems out of the book to work on at home and returned by next class period.

Indiana Content Standards Addressed: (Copy and paste entire standard from http://www.indianastandards.org/)

A1.6.1 : Add and subtract polynomials. Resource
A1.6.2 : Multiply and divide monomials. Resource
A1.6.3 : Find powers and roots of monomials (only when the answer has an integer exponent).
A1.6.4 : Multiply polynomials. Resource
A1.6.6 : Find a common monomial factor in a polynomial. Resource


Target Audience of the Lesson:
This lesson is designed for middle school math. It is targeted towards students in grades 6 and 7 learning about fractions.

Overall Goal of the Lesson:
The overall goal of this lesson is to introduce the concept of common denominators. Another goal is to get students involved in interactive activities by using felt board fraction shapes.

Student Learning Objectives:
After the lesson students will be able to:
• Show awareness of the concept of fraction equivalencies and common denominators
• Correctly write addition equations that represent various felt board equations

Assessment: (Go back to your learning objectives. What will the students do to demonstrate they have met the learning objectives? Make sure each objective is paired to an assessment measure)
To demonstrate that the students have met the learning objectives they should write addition equations on their paper that equal the given felt board fractions. Students could pose their own fractions to their peers. Afterwards, students should solve addition equations together in class. Finally, students could be given worksheets with colored fractions and addition equations. They would have to write addition problems or vice versa for their answers and turn them in during the next class period.

Indiana Content Standards Addressed: (Copy and paste entire standard from http://www.indianastandards.org/)

6.1.4 : Convert between any two representations of numbers (fractions, decimals, and percents) without the use of a calculator. Resource
6.1.6 : Use models to represent ratios. Resource
6.1.7 : Find the least common multiple and the greatest common factor of whole numbers. Use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction). Resource

Reflection 6

There are many connections that can be made between manipulation and the ISTE Technology Standards. Manipulation is used for the students. It is based around students and helps them to better understand different concepts. Not only does it do that, but it also helps students have a better relationship with technology. It allows them to get more acquainted with technology and the concepts their learning. Manipulatives can be used to follow several of the standards. Including communication, creativity, and solving real world problems while using technology. So, therefore, manipulation is used for both the technology sake and to build students' academic skills.

Manipulation Resources

http://www.webgraphing.com/graphing_advanced.jsp

This web site can be used for graphing, analyzing and comparing equations. This program also shows where graphs are increasing and decreasing. This application will allow students to visualize the equation they are working with and provide a geometric perspective to their algebra work. While the program requires membership for the full benefits, it is free to sign up and use for students and teachers.

http://www.emints.org/ethemes/resources/S00000592.shtml

This website has an entire collection of manipulation activities. The activities range for grades 6,7,8. Students will get work with fractions, decimals, graphs, tessalations, and many other things. While this may seem inappropriate for many secondary teachers, the activites can be modified to fit courses of appropriate level. For example, the problem of the spinner can relate directly to work with probability. Also, some of the links provide material on lessons for an entire class period and some lessons encouraged the use of technology like the Smartboard.

http://www.shodor.org/interactivate/activities/

Again, this is a massive list of interactive lessons that can be used by teachers. The subject matter varies and there are multiple activities per subject. In particular, students direct a robot through a mine field laid out the cartesian plane. Its a list of fun activities that allow students to visualize the math they are working with.

All of these are about engagement and keeping the student invloved and focused. These are all great activities that will be useful for all of us.

And for the standards, manipulation can apply to anything and everything. All of these activites are supplements to actual lesson and there is a lesson for everything. The manipulation activities are here for students to reinforce their learning. Their learning comes from the standards, so its hard to inculde working with manipulations in the standards.

Math Manipulatives

http://mason.gmu.edu/~mmankus/Handson/manipulatives.htm

This website has several different resources that can be printed off and hand made for different math classes. For example, it includes base ten blocks, base five blocks, a reference for making paper fractions, graph paper, and polar graph paper. This website is a good reference for teachers who want to use tangible objects in the classroom. Students can use these to help better their knowledge in certain areas.

http://mathforum.org/trscavo/geoboards/

This website uses geoboards as manipulatives in the classroom. It has several different useful lesson plans that teachers can use. It tells teachers how to use the geoboards in the classroom so that the students get the full effect from them. It talks about two-dimensional geometry objects such as parallelograms, triangles, and squares. Along with that, it has dot paper with different dimensions that teachers can download, print off, and use in the classroom. It talks about how using the geoboards helps students strengthen their understanding of finding area as well. It shows different shapes that can be used for the activity of finding area.


illuminations.nctm.org/ActivitySearch.aspx

This is probably the best website I found. It has great math resources for students of all ages. You can select the grade level you wish to view. You can also enter in the subject you wish to find. Once you do this, it takes you to a page with numerous games and activities that helps you learn certain math concepts. For example, I selected the grade level 9-12 and clicked on the first option you gave me which was a game about the spread of a fire. It is used to better understand probability. Teachers can use this in the classroom to help students strengthen their understanding in numerous areas. Students could enjoy these activities while having fun and learning at the same time.

Reflection 6

My team topic connects with almost all of the ISTE standards because the nature of our topic is so expansive. I do think that some have a more direct connection than others. Manipulatives can help students discover basic operations and concepts, but it can be easy for these concepts to get lost in the process of the manipulations. I feel that manipulation connects to standard 3 the most. They are using these technology tools to enhance their learning. By manipulating and seeing how math is actually working, manipulatives can further understanding and help students pose questions that they might not have previously considered. I also think that standard 6 relates to our topic. By taking a topic they know a little bit about, and applying that knowledge to do some manipulations definitely helps students with problem solving strategies and decision making.

Manipulation Resources

http://nlvm.usu.edu/en/nav/vlibrary.html

This is one of the best websites I've found. It is a forum of virtual manipulatives. They have it really well organized so that you can easily find exactly what you're looking for. The manipulatives are categorized by content standard and by grade level. You can search the content standard at all grade levels, the grade level using all the standards, or you can pick a specific standard and grade level. Each manipulative has a link that has parent/teacher information. This is extremely helpful because they list the objectives, lesson plan, extension activities, assessment, and the materials that go along with the manipulative. Another nice bonus is that each manipulative can be translated into spanish.

http://www.explorelearning.com/
This page is a collection of “gizmos” that help in teaching a lesson. It is very well organized, so finding a gizmo for a specific lesson is easy. From the home page there are two drag down menus, one is math, one is science. By using the math menu, you can pick grade levels and then choose a math type.
You may need to install shockwave player, but its worth it because these gizmos are a really good addition to any lesson.

http://www.ct4me.net/math_manipulatives.htm

This website is good because it has a short introduction section that defines what a manipulative is, the pros and cons of manipulatives, and what role manipulatives play in the classroom. After that there is a list of manipulatives that they find to be helpful. It isn't as organized as the first website I listed, but they do break them up into categories like basic computation, algebra, calculus, and statistics. This website also has links to a lot of other helpful things for teachers, some being math projects, software, news, and journals.

My Video Reflection

http://www.edutopia.org/video/movie.php?reset=cookie&keyword=137&id=Art_1145

My video was titled "An Incredible Journey." It was about a Charter School in Nevadan, California using project based learning curriculum. They talked about how usually students drag into school in the morning, and get more excited as the day goes on because its closer to the time they can leave, while teachers usually come into school with lots of energy and leave at the end of the day drained. This method of teaching should have the students leaving just as tired as the teachers because it requires the students to work for their learning. While this style of teaching is sometimes referred to as discovery learning, some of the teachers don't completely agree with that terminology. They feel this is more of a process of structured projects guided by the teacher rather than one "discovery" after a certain task which was specifically designed to evoke that discovery. This school used water probes to get data from a watershed nearby. They then took the data into their science labs, and math classes to analyze different aspects of it. They worked in groups which helped them with important social skills that aren't always addressed in regualr classrooms. This project lasted for 12 weeks which teaches important skills like time management and task management which are also sometimes ignored in regular lessons. The project culminated having them creating a video news report that discussed all of their results, and presenting their results at a showing in front of family, friends, and other professionals. Its a style of teaching that incorperates many different content areas as well various technologies.

There was a lot of technology used in the video. There was a lot more student centered technology. I think this is due to the fact that the idea of the teaching style promotes students using many different technologies to further their understanding in a broad scope of topics. Since there are so many different content areas that one lesson can cover, many different technologies can be easily incorporated. The students were using palm pilots with water probes to record data from their local stream. They were also in a digital media classroom which had computers, video recorders, green screens, and audio equipment. They later had to present all of their conclusions as a speech which involved the use of basic technologies like powerpoint.

I think technology made the lesson much more engaging simply because without the technology there would be nothing to be engaged in! This entire lesson was based on the fact that they were using technology. They not only used technology to collect their data and to analyze their data, but they also used it to creatively present their conclusions.

They recommended in the video that in order for a teacher to be well prepared for this type of lesson it is best to plan backwards. They feel that you should think about the expected outcome and go from there. Ask yourself questions like who are your students, what they need to know, what do you want them to know, and what should you teach them. Also, the teacher needs to become familiar with the technologies that are used. If a student is struggling with the technology and you as the teacher cant help them, the main idea of the lesson is lost in something that could have easily been prepared for.

I would assess the students by giving them periodic journal entries. This would allow them to tell me how they feel the project has been going, what they like and dislike about certain parts of the project, and any complications that have come up since the last journal entry. Since this style of learning is based over 12 weeks, and is a continuous effort it is difficult to quiz on their knowledge of the topic, since they every day they are working towards completing the cumulative final project. The movie said that the teachers in this case assessed the students by having classroom reflections where they debrief for self-evaluation, asking the students what worked and what didn’t. They said that reflection on learning is equivalent to retention.

The advantage to this is that the students must know what they are talking about in order to finish their project. They can’t learn something, be tested, and forget it since every part of the project is a continuation of earlier learning. Some of the challenges to this is that not every school has this advanced technologies, and even if they do, not all teachers will understand how to use some of them as well as others. Also, some of the teachers in the video said that as a teacher you have to keep track of all the groups of students’ because it is easy for them to fall behind and shut down. The students also voiced that sometimes it was hard for them to stay motivated on a project that was so long term and that they could get easily distracted.

Video Case Analysis

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


The video case that I viewed talked about virtual learning and displayed the attributes of Virtual High School. It discussed the ways students could learn online and take courses online that were not offered at their high school. It also showed how teachers could integrate online learning with their classes. Some teachers would use blended learning. This consisted of teaching in the classrooms as well as teaching part of the course on the internet.
Most of the technology that was used in the video consisted of computers and the internet. There were also calculators, interactive whiteboards, and live whiteboards used in the math classes. Compact discs were used for the music class. Microphones, voice recorders, and speakers were used also. In one instance, telephones were used when students called their teacher.
The technologies used in the lessons were both student-centered and teacher-centered. The students were able to go online to take the virtual courses. They used the technology to better enhance their knowledge on the subjects. The students also used the live boards to do some of their work online. Some of the teachers used the virtual learning in their classrooms. They would create their own courses online through Virtual High School. The teachers also used the microphones, recorders, and speakers to communicate to the students. In most cases, the teachers would create or design courses or lessons through virtual learning and the students would use what the teachers created to further their knowledge.
I do agree that the technologies used in this video make the lessons more engaging. It is something new and different for the students to be involved in. It is not the same old routine of sitting in class taking notes and listening to the teacher lecture all the time. The students are able to get a more hands on approach to their learning. Also, the virtual learning allows students to be able to do their work at any time of the day. The students will have time to do other things in their busy schedule. For instance, one student was able to practice ice skating at a more opportune time since she could do the work at night. Also, I think using any technology gets students more interested in what they are doing. I think it helps them feel like they are doing something important and fun.
Teachers wanting to create a course through the virtual learning site would have to go through about the same amount of preparation as though they were actually teaching it in a classroom. They would have to think through what they would want to get across to the students. The teachers would have to provide more explanation for the students who may not know how to use the technology. They would also have to try to use wording online that their students would understand. The teachers might also want to think about common mistakes their students might make. They might also have to provide more examples for the students since they are not interacting with the students in person.
Teachers who want to assess student performance who use the virtual learning could test them in the same way they would in the classroom. They could use online documents with questions they have to answer. Teachers could have examples of different things that the students have to answer. Students could also be assigned final projects that they would have to post online. Then the teacher could evaluate their performance on the projects.
Some advantages of using the virtual learning are the flexibility of taking classes and doing homework when you want. Students might be more interested in learning what they are doing when technology is involved. Teachers and students get to know each other better when they interact online and phone each other. Teachers can detect student weaknesses faster. Students can have hands-on experience and can learn through the use of visuals. Students and teachers can communicate to each other through a microphone. Also, teachers can tell students what they are doing wrong while working on a problem online. Both the teachers and students can be at home while doing this.
Some challenges the teacher would have is not getting all of the students involved in what they are doing in class while using the virtual learning. Some students may get lost and not know what they are doing. Teachers would have to go more in detail about what exactly they want the students to be doing if the class is taught online only. Students have to be more self-motivating. If they do not have the teachers with them telling them to get their work done they may not do it. Another challenge with virtual learning is that students may not understand what is going on in the class. If no communication is involved, the students may have trouble with the work and the teachers will not be able to tell the students what they are doing wrong. Finally, teachers and students are not able to form good relationships with each other through virtual learning.

Video Analysis

http://www.edutopia.org/video/movie.php?reset=cookie&keyword=137&id=Art_1127


The video “Laptops on Expedition” documents a seventh grade class’ journey to success. This school in Maine is the most ethnically and economically diverse school in the district. The students were struggling and test scores were in the bottom third of the state. Then, students and teachers began to work with technology on a regular basis. All classes are connected to work on one central project. In the video, the students analyzed and discussed the endangered animals of Maine. The information which included, a paper or report, a video documentary, artwork, and data all came together on a CD that was given to each of the students at the project’s end. The goal of this interconnected project was to allow students to contribute to the project in an area they excel in. Every student is a part of the final product; everyone is a team.

This unity and project were helped in a major due to the school’s use of integrated technology. Students had access to laptops with wireless Internet. This allowed them to research individual parts of a project while at the same time working on a common task. Students had access to digital media technology. The students were responsible for filming, directing, and editing their documentary. The students used cameras and editing software again on the provided laptop computers. Another use of technology was used in the soundtrack of the documentary. Students in the band and orchestra recorded and edited their own musical talent and placed it on the documentary. Students ran this project themselves, and it always turns out well.

The students are engaged in the technology and the project. The teachers in this film simply led the students to an ending goal. The students did the research, the students made the film, and the students organized the CD. The technology was for them. The only time a teacher assists is when students have questions about guidelines or using the technology. The teacher becomes a guide or mentor and the students and their technology drive the project.

The technology is what makes this project so special. Any student can write a report on an endangered animal. Any teacher can take the class to the library for research. Instead, the teachers left it up to the students. The technology helps them engage in their task. It makes it exciting, fun, and different. I personally feel it may be easier for current students to research on the Internet than in the library. The openness of the project let the students venture to any desired goal. They had access to pretty much anything and that opportunity to work with such fun, new, exciting technology inspired the students.

The teacher may not be “teaching” in the old fashioned sense, but that does not mean they are not busy. The teacher needs to ensure that all students are working and on task. This technology may inspire students, but it can also distract them. Teachers also need to do a good job introducing the lesson or project and the technology. If either part is unclear, students will be in over their heads. Lastly, as a team of teachers, a project like this takes a tremendous amount of planning, creativity and dedication. Every area has to be involved, while still teaching the material of a school/state’s curriculum.
In the end, the project and technology provide students with a new way of thinking and learning. School is no longer centered at the front of the classroom, but at the front of their own ability to explore.

Reflection 4

I dont have too much experience with blogging. A couple of my friends had blogs which I would look at while I was bored and online. I never made one for myself because I didnt really have much to tell people and I didnt think too many people would be that interested in what I would be writing about anyways. Now that I realize blogging doesnt have to be a "diary" and can be used in the classroom like an online discussion forum my opinon of blogging has changed.

Reflection 3

In my first reflection I talked about some of the technology I was familiar with. Most of it was something I used on my own for school like Microsoft Word, Powerpoint, or Excel. I also talked some technologies I was familiar with, but not completely comfortable using on my own, becasue I had only seen them used in my classrooms at school by teachers. My second reflection was about the newer technologies and what I thought about them. I think these new technologies are going to be helpful to new generations of students, but it also scares me to think how all of this will change the school dynamic that I've become so used to.

Reflection 4

Working with blogs is way easier than I thought it would be. This is the first time for me to be a blogger. I never started befreo because I felt as if I never had anything worthwhile to publish. This has shown me that it is easy and can be applicable to both work and one's personal lifestyle. The blog provides a great way for students to stay in contact and up to date with class material, since it can be accessed outside of the classroom.

Reflection 3

Reflections 1 and 2 were basic ways I have used technology in my classes. It has all been basic stuff for paper, projects, and presentations. It is exciting to use and talk about the new technology that I have not used or heard about. When we listed our technologies in Reflection 2, the technology on the top of my list, was stuff I have never used before. New material and technology can make class fun and exciting for both students and teachers.

Reflection 4

I have never used blogging before. I knew what it was, but I have never had the interest to use it. Now that we have started using it for class, I think it is a fun and creative way to communicate to people and share you ideas with them. I am excited to create my e-portfolio. I have a special interest in creating things like this. However, I do not have too much experience in using FrontPage. The only time I used it was in W201. I would like to learn ways to make my website really stand out and look great. Is there anywhere that I can go on the internet to help me with this?

Reflection 3

In Reflection 1, I discussed the different experiences I have had with technology. These include Microsoft Word, PowerPoint, and Excel. I have experience with the internet and other various basic computer technologies. A good technology integration experience I have had was in Euclidean Geometry with Allan Edmonds. We used Geometer's Sketchpad integrated with what we were learning in class. Sketchpad helped me to better understand what I was doing and how certain concepts were true.
In Reflection 2, I listed my top five technology innovations. My top two were manipulation and podcasts. I also mentioned that I thought the interactive whiteboards and tablets were a great idea to use in the classroom, especially a math class. I think it would get more students involved in their work as well.

i love manipulation...almost as much as koalas love climbing trees

Manipulation, Of Course!!

Blogging about manipulation is my hobby!!!

Get Excited, Its Time to Blog!

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