Hi Everyone,
Number Puzzles Virtual Manipulative
I love the Number Puzzles Virtual Manipulative for several reasons.
First, it challenges students to solve relatively difficult math puzzles. For each puzzle, students need to come up with a strategy. For example, they must consider whether it is better to put a high or a low number in the vertex of a triangle? Keep in mind that this changes depending whether the sum for each side of the triangle is large or small.
Second, this virtual manipulative forces students to do computation. I feel that most students will find it annoying to have to keep typing numbers into a calculator. Thus, they will challenge themselves to do the computation in their heads. Obviously, the ability to do computation in one's head is a very important skill, and thus, this virtual manipulative helps students build this skill.
Third, these puzzles are fun! I allowed my middle school students to play these puzzles during lunch, and they loved them. I do not think they even realized that they were doing math. Thus, if you want to trick students into doing computation in their heads then this is certainly one of the best ways to do it.
I suggest that you try this virtual manipulative at home. You will find that it is actually very entertaining.
Sincerely,
Marc
Thursday, February 25, 2010
Yola Website
Hi Everyone,
Up to this point, I have been using a Google website. I like Google because I am familiar with it. However, I just created a Yola website, and I realized that Yola websites are much better than Google websites. You will be surprised just how user friendly Yola websites are.
Check out my new Yola website:
Marc Vogel's Math Manipulatives 1 Yola Website
I have already posted the two Pattern Blocks lesson plans that I created on my Yola Site. I also posted the supporting documents. Thus, you can find everything that you need on my Yola site to conduct two lessons with Pattern Blocks in your respective classrooms.
I will post the lesson plans that I create in the future on this site, so I suggest that you check it regularly.
Sincerely,
Marc
Up to this point, I have been using a Google website. I like Google because I am familiar with it. However, I just created a Yola website, and I realized that Yola websites are much better than Google websites. You will be surprised just how user friendly Yola websites are.
Check out my new Yola website:
Marc Vogel's Math Manipulatives 1 Yola Website
I have already posted the two Pattern Blocks lesson plans that I created on my Yola Site. I also posted the supporting documents. Thus, you can find everything that you need on my Yola site to conduct two lessons with Pattern Blocks in your respective classrooms.
I will post the lesson plans that I create in the future on this site, so I suggest that you check it regularly.
Sincerely,
Marc
Updated Blog
Hi Everyone,
Throughout my blog, I converted the web addresses that I posted to links. I hope this makes it easier for you to find everything.
Sincerely,
Marc
Throughout my blog, I converted the web addresses that I posted to links. I hope this makes it easier for you to find everything.
Sincerely,
Marc
Wednesday, February 10, 2010
Week Three - Backyard Improvements Lesson Plan
This lesson plan, like the lesson plan from week two, uses Pattern Blocks.
Marc Vogel's Week 3 Lesson Plan
Marc Vogel's Yola Website (Contains Lesson Plans and Supporting Documents)
If the link above does not work then copy and paste the following link into the address bar:
http://sites.google.com/site/mathmanipulativeslessonplans/home/lesson-plan-for-week-three
I based this lesson plan on the Backyard Improvements Lesson Plan, which you can find under the Patterns and Functions link for Grades 7 - 8 on the Super Source CD-ROM.
Marc Vogel's Week 3 Lesson Plan
Marc Vogel's Yola Website (Contains Lesson Plans and Supporting Documents)
If the link above does not work then copy and paste the following link into the address bar:
http://sites.google.com/site/mathmanipulativeslessonplans/home/lesson-plan-for-week-three
I based this lesson plan on the Backyard Improvements Lesson Plan, which you can find under the Patterns and Functions link for Grades 7 - 8 on the Super Source CD-ROM.
Reflection on Perimeter Search Lesson for Week Two
As you know, I demonstrated the Pattern Search lesson in class this past Monday. When I tried it with two of my high school students that stopped by after school it was very successful. I feel that I was able to meet all of the objectives of the lesson. The interesting thing is that the students never seemed to realize that they were doing mathematics. To them, the activity was like a game. One would think that high school students would not want to play with blocks, but the reality is that they enjoy working with manipulatives as much as elementary school students.
For anyone who wants to become a mathematics teacher, this lesson is a good way to reinforce the concept of perimeter. Students generally enjoy a challenge, and they enjoy a challenge that involves manipulatives even more. To students, the activities in this lesson are more like "fun time" than they are work. Thus, it is easy to get students engaged by using this lesson.
For anyone who wants to become a mathematics teacher, this lesson is a good way to reinforce the concept of perimeter. Students generally enjoy a challenge, and they enjoy a challenge that involves manipulatives even more. To students, the activities in this lesson are more like "fun time" than they are work. Thus, it is easy to get students engaged by using this lesson.
Tuesday, February 9, 2010
Week Three - Reaction to the Private Universe Project Video - Workshop 3: Inventing Notations
One thing that I thought was very interesting in the video was the high level of support that the Englewood teachers’ received. It is not uncommon in the field of education for teachers to be required to attend a workshop that is labeled as professional development and then not receive any further professional development on the topic discussed in the workshop. While teachers are obviously expected to implement new ideas that they learn in a workshop, they are often not given any support from facilitators coming to their classrooms or meeting with them after school. Thus, the end result is often that when a teacher gets frustrated he or she often gives up because there is nobody with whom to discuss the situation that he or she has encountered. As a result, continuous professional development is the most effective way to get teachers to learn and implement new things. Fortunately, for the Englewood Public School System, the teachers did, in fact, receive continuous professional development. As a result, the ideas seemed to be implemented in classrooms effectively.
On a different note, I particularly liked that the students in the video were given the opportunities to share their ideas. This is the best way for students to learn from one another. I found it interesting that students came up with vastly different strategies for solving problems. For example, some students made lists, other students created diagrams, and some students made tables. Allowing students to create their own representations of their solutions provides a teacher with the ability to see how students “see” problems. In essence, by allowing students to share their solutions, a teacher can learn how students think about a problem and how they go about solving it. This is very valuable information that is not always easy to acquire.
One must remember that a student’s level of interest generally correlates with his or her level of engagement. Thus, I particularly liked the decision that the teacher from Redshaw Elementary School in New Brunswick, New Jersey made, which was to allow students to work on problems that interested them. The video informs the viewers that the students were not interested in solving for the number of possible combinations of two different colored blocks to form five-block towers and six-block towers. However, the students were interested in the number of combinations of four-block towers that could be made from three and four different colors. Thus, choosing to use the pizza problem was a great decision because it is similar to the type of problem that the students wanted to solve. This demonstrates a teaching strategy that is flexible and adaptable to student interests. Students are more likely to learn when they enjoy what they are doing. Thus, this method of teaching is admirable because it is more likely to be effective. As a teacher of science, I try to choose topics that interest my students to teach them the major themes of biology. For example, we are currently learning about cell division, and several students have asked questions about cancer. While cancer is only a subtopic of the unit on cell division, I will now spend additional time discussing cancer its relationship to cell division because the students are interested in it. In essence, I can use the students’ interest in cancer to get them to learn the information about cell division that is required by the New Jersey Core Curriculum Content Standards. Thus, when I become a mathematics teacher I hope to incorporate this strategy of teaching into my teaching of the new subject matter.
I was really surprised by one Conover Roads Elementary School fourth grade student’s method of solving the pizza problem. The student was able to use a system of binary numbers to come up with the solution. I felt that it was a better strategy than the ones that I used to solve this problem on the first day of class. The student’s method was very efficient, and I think I could have solved the problem faster had I used his strategy. In addition, his chart made it much easier to determine if there were any duplicate solutions. My own realization that I learned from this elementary student provides me with additional motivation to include the sharing of ideas in as many mathematics lessons that I teach as possible. This way the students can learn from one another.
Also, the discussion between Amy Martino and this same student from Conover Roads Elementary School demonstrated that students will not necessarily notice isomorphisms unless one actually encourages them to think critically and creatively about two problems that are basically the same. This type of activity where students are forced to think critically and creatively is so important at a young age. All too often, students struggle with being able to come up with original ideas. They want to be told what to do and how to do it. By encouraging students to think critically and creatively in elementary school, students will be more capable of dealing with high level thinking questions in high school and in college.
On a sad note, I agree with the narrator that the world is full of “Brandons”. What she meant by this is that there are many very intelligent students who “slip through the cracks”. In my opinion, these students are capable of thinking critically and creatively; however, they do not fit the mold of a typical “smart” child. In other words, they may not do well on standardized tests or some performance-based assessments. However, when these students are given free reign to solve a problem in their own way they can be impressive. I have seen this time and time again in my biology classes. For example, some students who rarely do well on tests, quizzes, and labs shine when I assign my Cell Parts Project. Basically, I require the students to teach the class about a cell part in any way that they see fit. Many students use PowerPoint Presentations. Other students create songs, games, or movies. However, my point is that some students who fail assessment after assessment are capable of demonstrating a high level of understanding in an assignment like this. Thus, we must give students the opportunity to think about problems in their own way. This will allow students the opportunity to make the material make sense to them. I plan on incorporating these ideas into my teaching when I become a math teacher.
In conclusion, I felt that the video made several important points. Students should be given the opportunity to think critically and creatively in mathematics class. Also, at least at first, they should be given free reign to determine what notation to use and how to use it. In addition, students should be able to convince someone that their answer is correct. Lastly, students should share their ideas with their classmates, so that they can learn from one another. In my opinion, anyone who incorporates these ideas into their teaching of mathematics is likely to be more effective.
On a different note, I particularly liked that the students in the video were given the opportunities to share their ideas. This is the best way for students to learn from one another. I found it interesting that students came up with vastly different strategies for solving problems. For example, some students made lists, other students created diagrams, and some students made tables. Allowing students to create their own representations of their solutions provides a teacher with the ability to see how students “see” problems. In essence, by allowing students to share their solutions, a teacher can learn how students think about a problem and how they go about solving it. This is very valuable information that is not always easy to acquire.
One must remember that a student’s level of interest generally correlates with his or her level of engagement. Thus, I particularly liked the decision that the teacher from Redshaw Elementary School in New Brunswick, New Jersey made, which was to allow students to work on problems that interested them. The video informs the viewers that the students were not interested in solving for the number of possible combinations of two different colored blocks to form five-block towers and six-block towers. However, the students were interested in the number of combinations of four-block towers that could be made from three and four different colors. Thus, choosing to use the pizza problem was a great decision because it is similar to the type of problem that the students wanted to solve. This demonstrates a teaching strategy that is flexible and adaptable to student interests. Students are more likely to learn when they enjoy what they are doing. Thus, this method of teaching is admirable because it is more likely to be effective. As a teacher of science, I try to choose topics that interest my students to teach them the major themes of biology. For example, we are currently learning about cell division, and several students have asked questions about cancer. While cancer is only a subtopic of the unit on cell division, I will now spend additional time discussing cancer its relationship to cell division because the students are interested in it. In essence, I can use the students’ interest in cancer to get them to learn the information about cell division that is required by the New Jersey Core Curriculum Content Standards. Thus, when I become a mathematics teacher I hope to incorporate this strategy of teaching into my teaching of the new subject matter.
I was really surprised by one Conover Roads Elementary School fourth grade student’s method of solving the pizza problem. The student was able to use a system of binary numbers to come up with the solution. I felt that it was a better strategy than the ones that I used to solve this problem on the first day of class. The student’s method was very efficient, and I think I could have solved the problem faster had I used his strategy. In addition, his chart made it much easier to determine if there were any duplicate solutions. My own realization that I learned from this elementary student provides me with additional motivation to include the sharing of ideas in as many mathematics lessons that I teach as possible. This way the students can learn from one another.
Also, the discussion between Amy Martino and this same student from Conover Roads Elementary School demonstrated that students will not necessarily notice isomorphisms unless one actually encourages them to think critically and creatively about two problems that are basically the same. This type of activity where students are forced to think critically and creatively is so important at a young age. All too often, students struggle with being able to come up with original ideas. They want to be told what to do and how to do it. By encouraging students to think critically and creatively in elementary school, students will be more capable of dealing with high level thinking questions in high school and in college.
On a sad note, I agree with the narrator that the world is full of “Brandons”. What she meant by this is that there are many very intelligent students who “slip through the cracks”. In my opinion, these students are capable of thinking critically and creatively; however, they do not fit the mold of a typical “smart” child. In other words, they may not do well on standardized tests or some performance-based assessments. However, when these students are given free reign to solve a problem in their own way they can be impressive. I have seen this time and time again in my biology classes. For example, some students who rarely do well on tests, quizzes, and labs shine when I assign my Cell Parts Project. Basically, I require the students to teach the class about a cell part in any way that they see fit. Many students use PowerPoint Presentations. Other students create songs, games, or movies. However, my point is that some students who fail assessment after assessment are capable of demonstrating a high level of understanding in an assignment like this. Thus, we must give students the opportunity to think about problems in their own way. This will allow students the opportunity to make the material make sense to them. I plan on incorporating these ideas into my teaching when I become a math teacher.
In conclusion, I felt that the video made several important points. Students should be given the opportunity to think critically and creatively in mathematics class. Also, at least at first, they should be given free reign to determine what notation to use and how to use it. In addition, students should be able to convince someone that their answer is correct. Lastly, students should share their ideas with their classmates, so that they can learn from one another. In my opinion, anyone who incorporates these ideas into their teaching of mathematics is likely to be more effective.
Week Three - National Library of Virtual Manipulatives Pattern Blocks Program
On Tuesday at lunch, I asked six students to find the largest perimeter and the smallest perimeter of a shape created by any six pattern blocks. Basically, I asked the students to do the activity that I demonstrated on Monday night in class. I divided the students up into three groups of two. I allowed one group to work on the problem using the National Library of Virtual Manipulatives program titled Pattern Blocks under the measurement section of the grades 6 - 8 tab. For this, the students were allowed to use the Smart Board that I have in my room. I asked the other two groups to solve the problem using the "real" pattern blocks. Interestingly, the two groups that used the "real" pattern blocks solved the problem faster.
However, the students who used the virtual manipulatives program seemed to enjoy the activity just as much as the students who worked with the "real" pattern blocks. In addition, the students who worked with the virtual manipulatives seemed to have fun changing the colors of the blocks. This is something that you obviously cannot do with the "real" pattern blocks.
In conclusion, I would recommend using the "real" pattern blocks over the virtual pattern blocks program if you are limited by the amount of time that you have to complete a lesson. However, since students naturally gravitate toward technology, if you have the time to devote a few extra minutes to an activity then it might be well worth your while to use the virtual pattern blocks program. In addition, keep in mind, if your district has the technology available then it is cheaper to use the virtual pattern blocks program. I looked up the cost of "real" wooden pattern blocks on the Discount School Supply website, and the cost is $10.99 per case. Thus, if cost is an issue then consider using the pattern blocks program on the National Library of Virtual Manipulatives website.
However, the students who used the virtual manipulatives program seemed to enjoy the activity just as much as the students who worked with the "real" pattern blocks. In addition, the students who worked with the virtual manipulatives seemed to have fun changing the colors of the blocks. This is something that you obviously cannot do with the "real" pattern blocks.
In conclusion, I would recommend using the "real" pattern blocks over the virtual pattern blocks program if you are limited by the amount of time that you have to complete a lesson. However, since students naturally gravitate toward technology, if you have the time to devote a few extra minutes to an activity then it might be well worth your while to use the virtual pattern blocks program. In addition, keep in mind, if your district has the technology available then it is cheaper to use the virtual pattern blocks program. I looked up the cost of "real" wooden pattern blocks on the Discount School Supply website, and the cost is $10.99 per case. Thus, if cost is an issue then consider using the pattern blocks program on the National Library of Virtual Manipulatives website.
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