Click Here to Access the Program
Grades: 6 - 8
Category: Number and Operations
This is a very simple virtual manipulative. However, it is very effective for giving students an opportunity to practice depicting the union and intersection of sets on venn diagrams. If a teacher were to give students several problems of this nature, it would be challenging for that teacher to give each student individual feedback. However, this program makes this possible. Students can click on the "check" button to see if their answer is correct. They can also click on the "show solution" button to get the answer to a problem that they cannot solve. These two options make it possible for students to get immediate feedback, which is something that a teacher likely cannot provide without the help of technology.
Another nice feature of this program is that the problems it creates get progressively more difficult. Thus, more advanced students can work quickly and get to the harder questions, and students who are struggling with either the concept of venn diagrams or unions/intersections of sets can take their time and work on the easier problems.
However, there is one thing that could improve this program. This would be the addition of a "hint" button. While I like that students can check their answers and also get solutions to the problems that they cannot solve, I would like there to be an option that helps students without giving them the answer. I suppose this option could be provided by the teacher; however, I think students might jump to click on the "show solution" button too quickly. In essence, the desire for immediate feedback could get in the way of true learning by struggling to solve difficult problems.
Saturday, April 10, 2010
Sunday, April 4, 2010
Extension of Geoboard Activity from Class
Area of Quadrilaterals
Posts Trees Area
4 0 1
4 1 2
4 2 3
4 3 4
5 0 1.5
6 0 2
6 1 3
6 2 4
6 3 5
7 1 3.5
7 2 4.5
7 3 5.5
The formula A(P,T) = 0.5P + 1T - 1, where A stands for area, P stands for the number of posts, and T stands for the number of trees, still works for all of these examples.
Posts Trees Area
4 0 1
4 1 2
4 2 3
4 3 4
5 0 1.5
6 0 2
6 1 3
6 2 4
6 3 5
7 1 3.5
7 2 4.5
7 3 5.5
The formula A(P,T) = 0.5P + 1T - 1, where A stands for area, P stands for the number of posts, and T stands for the number of trees, still works for all of these examples.
Lesson Plan - Week Eight - Shelf Brackets Geoboard Lesson
Click Here for the Lesson Plan and Supporting Documents
This lesson is great if you are trying to get students to develop a deeper understanding of the properties of right triangles or trying to get students to use more than one method for finding the area of right triangles. It is also very good for getting students to think deeply about proving that they have found all of the solutions. It is not an easy task to develop and present a convincing argument that one has found all possible solutions to a particular task. This lesson requires that students do this.
Once again, I tested this lesson out on my girlfriend. It worked very well. However, in my opinion, her argument that she had found all possible solutions was weak. Thus, I think the discussion on proving that one has found all possible solutions could take a considerable amount of class time. Also, if students have not been trained on how to develop such an argument throughout the course of a school year then this might be challenging. Thus, in the future, I will try to train my students on how to prove that they have all possible solutions starting in September. Lastly, I feel that requiring students to prove that they have found all possible solutions is very important because it forces students to think like mathematicians.
This lesson is great if you are trying to get students to develop a deeper understanding of the properties of right triangles or trying to get students to use more than one method for finding the area of right triangles. It is also very good for getting students to think deeply about proving that they have found all of the solutions. It is not an easy task to develop and present a convincing argument that one has found all possible solutions to a particular task. This lesson requires that students do this.
Once again, I tested this lesson out on my girlfriend. It worked very well. However, in my opinion, her argument that she had found all possible solutions was weak. Thus, I think the discussion on proving that one has found all possible solutions could take a considerable amount of class time. Also, if students have not been trained on how to develop such an argument throughout the course of a school year then this might be challenging. Thus, in the future, I will try to train my students on how to prove that they have all possible solutions starting in September. Lastly, I feel that requiring students to prove that they have found all possible solutions is very important because it forces students to think like mathematicians.
Virtual Manipulative - Week Eight - Point Plotter
Click Here to Access this Virtual Manipulative
This is a great virtual manipulative to use if you are going to teach students to graph on a coordinate plane. Even though this virtual manipulative is very simple, it is an excellent learning aid because it gives students immediate feedback as to whether they are correct or not. In order to get this feedback, all students have to do is plot the points and click on the check answer button. The program will tell a student whether he or she got all the points correct, some of them correct, or none of them correct. It will even indicate which specific points are correct and which ones are not. The ones that are not correct will show up red, and the ones that are correct will show up green.
Another nice thing about this program is that it makes it easy to provide differentiated instruction. For the students who are good at graphing, they can do the program without the grid values. However, the teacher can set the program to show grid values for the students who are not as strong at graphing. Also, the program contains many different problems, so students who are good at graphing can do additional programs while the students who are not as good at graphing can complete fewer problems.
Sunday, March 28, 2010
Week Seven - Geoboard Challenge Lesson Plan
Geoboard Challenge Lesson Plan and Supporting Materials
This lesson plan requires the use of Geoboards. I tried out this lesson with a family member, and it certainly is an effective lesson. The reason that I feel that it is effective is because it requires students to play a game in order to meet the objectives of the lesson. In other words, the lesson is fun, and when students do something that they consider to be fun they are more likely to be engaged in the learning experience.
This lesson plan requires the use of Geoboards. I tried out this lesson with a family member, and it certainly is an effective lesson. The reason that I feel that it is effective is because it requires students to play a game in order to meet the objectives of the lesson. In other words, the lesson is fun, and when students do something that they consider to be fun they are more likely to be engaged in the learning experience.
Week Seven - Spinners Virtual Manipulative
Click here: Spinners
This virtual manipulative is simple, but it has excellent applications. The number of spins can be changed, and the spinner can be altered in a number of ways. The number of colors, the colors themselves, and the size of the colored regions can all be changed. The particularly nice thing is that you can record the results of the spins. These results are presented in a graphical form, which students can copy and transfer onto a sheet of graph paper. Thus, this virtual manipulative can be used to teach graphing skills. In addition, the virtual spinner has applications with regard to probability and percentage calculation. Students can calculate the theoretical probability and then compare it to the experimental probability. In addition, the bar graph results can be converted to percentages.
Obviously, "real-life" spinners could be used in a classroom. However, it is not likely that the color choices and the size of the colored areas on the spinner could be altered. In addition, it would take a long time to spin a spinner hundreds of times and record the results. Thus, for many reasons this virtual manipulative is better than a "real-life" manipulative.
This virtual manipulative is simple, but it has excellent applications. The number of spins can be changed, and the spinner can be altered in a number of ways. The number of colors, the colors themselves, and the size of the colored regions can all be changed. The particularly nice thing is that you can record the results of the spins. These results are presented in a graphical form, which students can copy and transfer onto a sheet of graph paper. Thus, this virtual manipulative can be used to teach graphing skills. In addition, the virtual spinner has applications with regard to probability and percentage calculation. Students can calculate the theoretical probability and then compare it to the experimental probability. In addition, the bar graph results can be converted to percentages.
Obviously, "real-life" spinners could be used in a classroom. However, it is not likely that the color choices and the size of the colored areas on the spinner could be altered. In addition, it would take a long time to spin a spinner hundreds of times and record the results. Thus, for many reasons this virtual manipulative is better than a "real-life" manipulative.
Sunday, March 21, 2010
Week Six - Napkins and Place Mats Color Tiles Lesson Plan
CLICK HERE for the lesson plan and the supporting documents.
The objectives of this lesson are to identify and extend patterns, explore the sequence of perfect squares, make predictions based on patterns, and express relationships algebraically.
I had four eighth grade students do the activities in this lesson at lunch on Thursday. They enjoyed the lesson, but they found the part where they had to come up with algebraic expressions to be very challenging. This is likely because the students that volunteered to do the activities are in the lowest eighth grade math level. If they were in algebra then these activities would have been a lot easier for them because they would have been used to expressing problems algebraically. However, with a lot of assistance, the students were able to come up with algebraic expressions to represent the patterns they saw.
On another note, when the students were working on the activities from this lesson I could see that they were very good at identifying patterns and relationships. Thus, they found all aspects other than the part that specifically relates to algebra to be relatively easy.
Also, after the students completed the activities, I felt a sense of accomplishment because I was able to reinforce concepts related to patterns and relationships and help students with the difficult task of learning algebra. In essence, I was able to help students discover math patterns and express them algebraically.
The objectives of this lesson are to identify and extend patterns, explore the sequence of perfect squares, make predictions based on patterns, and express relationships algebraically.
I had four eighth grade students do the activities in this lesson at lunch on Thursday. They enjoyed the lesson, but they found the part where they had to come up with algebraic expressions to be very challenging. This is likely because the students that volunteered to do the activities are in the lowest eighth grade math level. If they were in algebra then these activities would have been a lot easier for them because they would have been used to expressing problems algebraically. However, with a lot of assistance, the students were able to come up with algebraic expressions to represent the patterns they saw.
On another note, when the students were working on the activities from this lesson I could see that they were very good at identifying patterns and relationships. Thus, they found all aspects other than the part that specifically relates to algebra to be relatively easy.
Also, after the students completed the activities, I felt a sense of accomplishment because I was able to reinforce concepts related to patterns and relationships and help students with the difficult task of learning algebra. In essence, I was able to help students discover math patterns and express them algebraically.
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