GeoBoards Lesson 2

This week I chose to do the lesson on geoboards titled Making Fourths. This activity is designed for grades 3-4. The main purpose of it is to get students to understand and learn how to create fourths using their boards. In addition, it gives students the opportunity to see How many ways they can show fourths on their Geoboard?
• Use as many rubber bands as you need to divide your Geoboard into 4 equal parts.
• Do this in as many different ways as you can.
• Record each of your solutions on geodot paper.
• Compare your results with the rest of your group’s.
• Be ready to explain why each of your solutions shows fourths.

Virtual Manipulatives- Geobaords-Geometry gr 3-5

The virtual manipulative I was exploring with is the Geobaords for grades 3-5. I really enjoyed playing around with this because you are not actually working with rubber bands. I also liked that it gives you different problems to solve like create the letter W or symmetry problems such as completing the other side of a tree. However, what i did not like is that it does not assess your work. Students will not know if they completed it correctly.

Geoboards Lesson Plan

The geoboards lesson plan I chose it titled 3,4,5 and More. This lesson is designed for grades 3-4. The purpose of this lesson is to have students be able to classify polygons according to the number of sides and discuss attributes of geometric shapes.

Virtual Manipulative- Fractions-Parts of A Whole gr. k-2

The virtual manipulative I experimented with this week is Fractions. This virtual manipulative is very good in introducing parts of a whole. You can divide the whole into however many pieces you would like and all you need to do is click on a piece of it and it identifies what part of a fraction it is. In addition, you can change the shape of the whole. (ex. circle, rectangle) The only thing I would do differently with this manipulative is have an option to give you examples of fractions and the student demonstrates it. Other than that I think it is a good visual manipulative on fractions.

Private Universe Workshop 6. Possibilities of Real-Life Problems

In this video students were given a problem called the Cat walk. It was very interested to see how the student’s techniques for solving this problem changed as they tried to indentify the answer. The students really worked towards a solution. What I really liked about this video is the student collaborated with each other and how they truly learned from each other. After working on this problem they were than asked to determine whether or not the CEO should bet or not. During this video you can see how the students’ thinking has developed. I think that giving students real like situations grasps the students interest. As the other videos have shown it is very important to give the students freedom and time to solve problems and instill in them the importance of knowing why an answer is correct and how they went about solving it.

Color Tiles Lesson Plan

The color tiles lesson I chose was called Fraction Bars. In this lesson,children use Color Tiles to build a fraction bar that represents a whole. They then write a set of clues to enable others to build the fraction bar. Students will be able to develop a model for fractions, use fraction notation, and work with equivalent fractions. I really like this lesson because writing and solving about fractional parts of a whole fraction bar helps children gain a concrete understanding of the meaning of fractions, fractional equivalence, and how fractional parts relate to the
whole. I believe this lesson is grade and age appropriate for grades 3-4.

Virtual Manipulatives- Point Plotter (Algebra gr.6-8)

I found point plotter to be very useful. This virtual manipulative game starts off with giving you 3 points that it wants you to plot. For instance, (6, 2),(9, -8),(5, 6) by clicking on the coordinating grid. After you plot all three you check the answer. If it is correct you can solve another problem. This helps students identify the x and y axis. It also helps understand where the negative numbers are and the positive numbers. I would use this as a follow up activity to a lesson.

Private Universe Project-Workshop 5 Building on Useful Ideas

This video really focused on two important factors Ownership and building on knowledge. These teachers’ main goals are to have these students really understand the worth of what true learning is. The students were able to think deeper and really work on solving problems using thinking rather than practice. The video also demonstrated the importance of manipulative. A teacher’s role in the classroom really is the key to getting students to thinking mathematically. The teachers in this video were asking their students why they think that is the answer and how they got it. These simple questions will open up door ways to expand how students try to solve problems. Many students were than able to build on prior knowledge and use what they learned before to help solve more complex questions.

Private Universe Project-Workshop 4:Workshop 4. Thinking Like a Mathematician

This video was really interesting to me for many reasons. It started off with a teacher introducing the Towers of Hanoi. It proved that you can teach children to learn to problem solve on their own by just giving them the opportunity to explore. I really enjoyed watching them figure out the patterns and how many years it would take to move a hundred disks. This allowed the students to gradually work up to the skill the teacher wants them to succeed at. Part II of the video was a high school math teacher. This teacher’s goal was to teach the students how to think independently. It reminded me of when I was in elementary school and my math teacher would just sit and do problems over and over. After reviewing the concept she would make us go up to the board and each student was required to do a problem on. If we get this problem wrong she would yell and embarrass us in front of our peers. Students would be afraid to be called up to the board. Instead of encouraging us to think on our own her focus was to teach to the books. If this student gave us the opportunity to think on our own like the teacher in the video we would have felt confident to go to the board. I really appreciated the fact that this teacher had an environment conducive to learning from one another.

Virtual Manipulatives-Color Chips gr, k-2

I used this manipulative game on one of the second grade students that I am with for an after school activity. She seemed to understand it and really enjoyed playing it. She was able to complete the computer questions and come up with her own. She really enjoyed coming up with her own because she can add as many big numbers as she can. I really liked this manipulative because students can visually see the pieces and can add them off the screen. Students will really benefit from this activity.

Private Universe Project-Workshop 3:Inventing Notations

After watching video 3, I began to reflect on myself as a teacher. I thought about how many times I expected a student to solve a problem using what I consider the “traditional” way. This video represented what students can do and different learning styles. It was focused on how children themselves can teach other classmates. They were asked to solve the 4 Topping Pizza problem. Students have so much to offer when they are given the freedom and opportunity to solve problems. The most important part was that the students had to identify and vocalize their individual techniques. I also liked that students were asked to prove how they knew they got the right answer. Lastly, I believe that when teachers teach to meet the interest of their students they are more likely to be effective.

Virtual Manipulatives-Complete the Pattern (gr.k-5)

This week I decided to use the virtual manipulative, complete the pattern. I really liked this one because of the color choices it used and because it varied the patterns. In addition, if the student got the pattern wrong it would tell them Oops! This isn't the pattern we had in mind. Change some your colors and try again. I like that it uses positive words so that the student does not get discouraged. Also, if you solve it correctly is says Good Job! The point of this manipulative is that so teachers can see whether or not students know what patterns are and whether or not a student can determine if something is a pattern or not.

Math lesson-Pattern Blocks

The math lesson I chose was the Pattern Blocks, Hexiamonds. This lesson is designed to teach students about what Hexiamonds means, how many different Hexiamonds they can make, and reinforce congruence using flips and rotations. The students will be using green triangle pattern blocks and a pattern block triangle paper.

Private Universe Project-Workshop 2: Are you Convinced?

I am a perfect example of someone not being able to justify how they solved a problem. Many times I can solve the problem but I cannot put into words the mathematical reasoning behind it. This video made me realize the importance of giving an explanation for the answer and knowing if I am sure that I have the final correct answer. As a teacher I often expect my students to do so but never realizing that it is something I struggle with myself. I really enjoyed the way each teacher went about solving the towers. I was able to compare it to how we did it in class on Monday and how each of us had a different way of trying to solve it. It is also interesting to see that students were able to figure out the patterns and were more likely to respond to how they got their answers. They were even able to continue using more and disks for their towers. I learned that it is important to challenge children and ask them after solving anything if they are sure they are correct? I think that will make them double check their work and will allow them to think with reasoning.

Virtual Manipulatives- Peg Puzzle (gr. 6-8) & Towers of Hanoi (gr.3-5)

Algebra gr. 6-8 Peg Puzzle
I used this virtual manipulative on my husband. I first started my giving him the directions and the goal of this assignment. The goal is to switch the pegs on the left with the pegs on the right by moving one at a time. I explained that you can not move backwards and you can not jump over more than one. He first started with 4 pegs. He completed this puzzle with no problem. He than tried the 6 peg puzzle. After the third move he got stuck. The best thing about the activity is that unlike the hands on one from class the virtual notifies you when you are stuck. It states," You're Stuck-none of the pegs are allowed to move." I feel that this is beneficial because instead of wasting time trying to figure out if you can move you can start over right away. After a few tries he was able to solve the 6 peg puzzle. So I challenged him to the 8 peg puzzle. He than realized that there was a pattern to the 4 and 6 peg puzzle he tried several more times to figure out the pattern so that when he begins the 8 peg he can move through it easily. He began to write down each move in order to see if it can be replicated if more pegs are added. When he started the 8 peg puzzle you can see that he was a little frustrated, he solved it once and than couldn't figure out how he did it. He tried over and over until he was comfortable to solve it and explain what the pattern was he used to solve it.

Algebra gr. 3-5 Towers of Hanoi
For the towers of Hanoi I decided to test it on a third grade student from my building. I chose this student because he was in my class during lunch. In the virtual manipulatives game its default is 3 disks. However, for practice I told the student to start off with 2 disks. I explained to the student the directions and the goal. The goal of the towers of Hanoi is to move a stack of disks from one peg to another in as few a moves as possible. I also explained the rules which are you can only move one disk at a time and that you can not stack the larger disk on the smaller one. The student than began to solve the 2 disks. He was able to do it on the first try. He was then notified that Congratulations! You moved the towers in as few moves as possible-3. The student was very happy to see that. He than tried 3 disks. He completed it but unfortunately he did not complete it using the least amount of moves. So he tried a few more times until he did. I was very proud of him. I than asked him if he thought there was a pattern? He said that he wanted to try a few more times so that he can see if there was one. After trying several more times he stated that the smallest peg moves the most out of all of them,and that it moved from the first spot to the last and than from the last spot to the middle and then from the middle to the first again and finally back to the last spot, also that the largest peg only moved once which was from the original spot to the last spot. Unfortunately, we did not have enough time to try 4 pegs.

Private Universe Project-Workshop 1: Following Children's Ideas in Mathematics

This video was very interesting. I liked the fact that as a grad student I was given the opportunity to do the same project in class and then watch a video of younger students doing the same thing. I was able to reflect and see how they thought or what approaches they took compared to mine. I also enjoyed the level of effort the students put into these projects. As an adult I often can have the easy way out, which is giving up but these students even tried when school was over. I can also relate to the students who forgot certain math lessons in certain grades and how the effective teachers and lessons they presented always stand with me. It also really made you see how kids are capable of thinking in complex ways and how they have to be given the opportunity to do so. When you give your students the chance to show you what they can do you will be shocked as to what they come up with. Whenever I plan a lesson, I will always try to give my students the opportunity to strengthen their mathematics problem solving skills. I believe that students learn best from hands on activities which will allow them to begin to think mathematically.

Virtual Manipulatives-Count the Money gr.3-5

Count the money for grades 3-5 is a very good to help kids learn how to count money. This manupulative is very clear and the best thing that I like about it is the fact that it is not timed. Being a special education teacher I know that my students would feel pressured to be timed to solve a problem. In addition, this game corrects you by telling you if you solved the problem correctly. It also gives you three options to count money such as, how much money, pay exact amount, and make a dollar. These three different strategies are very beneficial for every day life. In the section pay exact amount if the student placed too much or too little money they will be notified as to what mistake they made. I believe this manipulative is very useful.

4 Towers Assignment

I tested the 4 tower lesson on a 5th general education grade student. The studetn was given a total 100 blocks (50 in black and 50 in purple). He was then given the instructions to create different combinations of 4 tower blocks, mixing the colors but not repeating the patterns. He began by creating all different types and then moved on to creating the opposites of each of the original one he created. He created 8 pairs with a total of 16. He still continued to look and was not sure if he had created the total amount that he could. He finally asked me if he was required to use all the block he was given. I really enjoyed watching the way he created these towers. I felt as though he was very comfortable until he reached 16 and then began to double guess himself. He had all the pairs together and then started to see if he can create a grid. He realized he couldn't so he paired them up and said he was finished.