Lesson Plan : Yack in the Box

This lesson involves the students working with fractions. The students begin by creating a bigger rod by combining two or three rods. The combination of rods represent one whole unit. Students form addition and subtraction sentences involving fractional lengths of the other rods. The students also will also be able to represent fractions with equivalent expressions. They can begin with combining yellow and black rod, calling it yack rod. Then students will use the white rods to see how many they will need to represent an equivalent rod. The process will continue until the orange rod is use to represent the length of the combination of two rods.

NLVM : percentages

This week I was playing with the Percentages found in Number and Operations in Pre K-2. I like this manipulative because I know that students still have a problem with percentages even at the high school level. The good thing about this is that it lets you input the values yourself. For example, you can put in the whole, the part and it will compute the percentage for you. You can also work backwards, where you can input the percentage, the part and it will compute the whole. The equation that is use is a ratio and proportion equation. Part over the whole equals the percentage over a 100%. If you try to input a part that is greater than the whole, it will tell you that the part needs to be less than the whole. That way the students will understand that while working with numbers where the maximum is a 100 percent, the part can not be bigger than the whole. It would be a good intro to the possibility of having numbers over a 100 percent.

Lesson Plan : Concrete Foundations

Number 7th-8th : Concrete Foundations
Objective: Writing and Solving Equations


Students will use the cuisenaire rods to write equations containing variables. Practice combining like terms, and visualize concepts of the properties of addition. Students will begin by determining how many other combinations can be made to form a wall of a certain length. Then students will be giving a list of equations representing walls made of stone. Each equation will have a missing "stone" and students will use the rods to find out the missing "stone". Example would be: red+green+purple = blank+green+purple. After they are done students will share their results. Students will use the concept of combining like terms and replace the blanks using variables.

Online Manipulative: Online game templates

http://www.murray.k12.ga.us/teacher/kara%20leonard/Mini%20T%27s/Games/Games.htm

This website has a lot of powerpoint templates. Most of them are blank and are ready to use. For some you can fill in the questions and answers. Some are just templates to keep score where you ask the questions yourself. The website is useful and you can change the templates to your liking.

Geo Board Lesson Plan(2)

I found this lesson on the cd. It is called Pythagoras Delivers the Mail. The objectice of this lesson is to devise methods for finding areas, learn about Pythogorean Theorem. The lesson starts with the students creating a triangle, any size, using the geoboard and drawing it on the center of a dot paper. Using a ruler draw a square congruent to the side of the triangle. Then they would need to find the area of each of the squares. Repeat the process with an obtuse triangle and an acute triangle. Students will then share their results with each other. Students will be told that there is a relationship to the squares and the right triangles. Students should notice a relatioship known as Pythogogearn Theorem. Students will be presented with a real life problem to relate their understanding to the lesson.

Virtual Manipulative : Base Blocks Decimals

The virtual manipulative that I found was under the number and operations grade 6-8. It is called Base Block Decimals. I like this manipulative because it breaks down the process of the subtracting and adding decimals. If there is something that students hate just as much as fractions or more it would be decimals. The program goes from one decimal place to 3 decimal places. It uses blocks to represent the given problem and lets you choose the base of the blocks, from 2,3,4,5 and 10. What I also like the fact that it uses fractions to break up the columns. When adding decimals all you have to do is group the blocks. When subtracting you have to match the blue blocks and the red blocks to cancel each other out. The only problem with this is that when dealing with 3 decimal places the answers are wrong. It is a a good manipulative to start dealing with decimals.

Lesson Plan ; The Square Challenge

OBJ: Determine the area and perimeter using different techniques/strategies (such as Pythagorean Theorem, logical reasoning or square roots).

Materials: One Geoboard per student and about 5-8 rubber bands.

Students are to create different squares and determine the area. Students will be told that the distance from each peg is one unit. Students will be encouraged to show of the different types of squares that they found, and to explain how they found the area. After the show and tell, they will be asked how you can determine the perimeter of the squares. Students may show combinations of different techniques and completely different strategies to come up with area and perimeter.

Virtual Manipulatives : Factor Tree

This game was under the Algebra 6-8. The idea of the game is to find the prime factorization of the numbers given by the computer. You could even enter your own number in order to find the prime factorization of it. Lets say you enter the number 500. It will ask you to input at least one of the factors, any factors. Once you put in 4, it will fill in the other factor, 125. It will then ask you to factor both numbers by inputing one of their factors until only prime numbers are left. Once this is accomplished at the bottom it will tell you the prime factorization of the number. If you enter the wrong factor for the number then it will tell you that 7 does not evenly divide 500. It would be a good reinforment for my class espcially since just recently they learned about radicals. I would be a great way to learn about GCF(Greatest Common Factor), since you can factor two numbers at the same time using the factor tree program.

Private Universe: possibilities of real life problems

I like the last video because it made me think the different ways that we can come up with to try and relate real life problems to the classrooms.Even though I would be putting aside the curriculum that I follow, it might be in the best interest of the students to once in a while introduce a problem and observe how they can come up with a solution with the knowledge they already obtain. I like that none of the researchers gave any answers or told them that they are close to the answer. They have to understand that someone long ago started with the same problems and detemination to find answers. How can someone be sure that their answer is correct when no one else has the answer. All that is left is the knowledge that you have and use it to prove it or use it to develop other ideas. Most of the groups in the video were certain that they had the correct answer, but after talking they began to realize that they were wrong. That type of environment is how math got started. Using their ability to analyze problems and come up with conclusions will benefit them with whatever they encounter in life.

Virtual Manipulatives : Spinner

This spinner turns out to be very useful when talking about probability. The class can conduct an experiment and compare to their own results. The fact that you can change the colors to numbers and a combination of both or even anything that you would like to have in a spinner. What I also like about this manipulative is that it can record your results as you use the spinner. Even though you can only use it for maybe a day when teaching a lesson on probability, the use of technology will be very helpful.

Building on Useful Ideas

This video was very helpful in reinforcing the students coming up with their type of techniques and solutions to problems they have not seen before. I believe that if a student develops a technique or sees a pattern for him/herself it will stick and have a chance to develop into something more. What I try to do in classes is give them information but see if anyone can develop any kind of pattern or see something that is not so obvious. When a student or group of students develop the idea, it would be much easier to attach the vocabulary that goes with it after it becomes comfortable. The development of an idea using previous knowledge will work better than a teacher telling students what to do and how to think.

Private Universe : Thinking Like a Mathematician

This video was very enlightning. I like to play puzzles and logic games as well. I also believe that it trains my mind without any other distractions. The towers of hanoi would be a great example of a puzzle that has lot of math concepts without any notice. Not many people know about the use of math in the real world. In the beginning of the video Fern Hunt talks about figuring out equations for how different materials reflect light. She then explains how this equations and theories will be helpful to business and other companies. The use of these equations would benefit a lot of people. When they reintroduce the problem to the students, they were able to start figuring out the problem using what they learned in school. As one student solved the problem he was able to show and explain how he came up to the answer. Using binary code he was able reinforce his answer. As the other students were learning how to use the binary code, they started to use it for other problems.

Virtual Manipulatives : Algebra Balance Scales

The reason I enjoyed using the balance scales because I was able to see what I say in class. One of the main points of one variable equations is to see that the equations must be balanced. As long as the equation stay balanced the problem is solved correctly. The manipulative start with a given equation and using blocks to balance the scale. After you put the correct blocks on each side, you are able to solve the problem. This can not be used to start solving one variable equations, so it can be used to reinforce the idea of balance. What you do to one side of the equation must be done to the other side.

Lesson Plan : Color Tiles

Color Tiles (Area and Perimeter of My Pool)

NJCCS
4.3 Color Tiles
3. Identify that rectangles with same perimeter may have different areas.
Entry Skills:
Students should be familiar with calculating area and perimeter of a rectangle.

Strategies Utilized for Achieving Objectives
• Direct Instruction
• Modeling
• Guided Practice
• Independent Practice
• Cooperative Learning

Materials: paper, pen/pencil, color tiles, calculator


Introduction:
Students use color tiles to investigate ways to create a shape that has a perimeter with the greatest possible area. Students should recognize that rectangles with the same perimeter may have different areas. Find ways to compare the area of different shapes.
Procedure:
• Ask the students “How many different rectangles can you make using 30 tiles?”
• Have the students come up with a conclusion about how many different rectangles can be made using 30 tiles. Have students come up with which combination has the greatest area and/or perimeter.
• Have the students show and explain their conclusions.
• Come up with a relation between area and perimeter
• Come to a conclusion of which combination if a rectangle would be show the greatest area? What about another shape?

Follow Up Discussion:
A group discussion will occur following the 5 minute exercise. Students will be asked to verbalize their solutions and show their chart on the board or on the overhead.

Assessment:
Assessment and understanding will be based on participation in the activity and class discussion. Students will be worksheet on various polygons and determine the degree of measurement.

Lesson Plan : Pattern Block

Sum of the Interior Angles

NJCCS
4.3 A Patterns and Algebra Algebra 1
3. Identify and determine the sum of interior angles
Entry Skills:
Students should be familiar with the definitions of a regular polygon and sum of the interior angles of a triangle.

Strategies Utilized for Achieving Objectives
• Direct Instruction
• Modeling
• Guided Practice
• Independent Practice
• Cooperative Learning

Materials: paper, pen/pencil, protractor pattern blocks (triangle, hexagon, square and protractor), a worksheet of various polygons.


Introduction:
Students will be giving various polygons(triangle, square, hexagon) . Using the protractor students will determine the number of degrees for each angle of each pattern block. Give the students the regular polygons and have them draw triangles extending from one vertex (defined as a point of intersection between two edges of a polygon).

Procedure:
• Ask the students “How many degrees are in any triangle?”
• Have the students come up with a conclusion about how many degrees are in each regular polygon based on the number of triangles they were able to draw
• Have the students come up with a relationship between the number of sides of the polygon and how many triangles they were able to draw from one vertex
• Come up with a generalization/formula (n-2)
• Build on the formula based on how many degrees are in each triangle 180(n-2)
• Ask how many angles are in each regular polygon and complete the formula



Follow Up Discussion:
A group discussion will occur following the 5 minute exercise. Students will be asked to verbalize their solutions and show their chart on the board or on the overhead.

Assessment:
Assessment and understanding will be based on participation in the activity and class discussion. Students will be worksheet on various polygons and determine the degree of measurement.

Virtual Manipulatives : Right Triangle Solver

I was looking through the Virtual Manipulatives and came upon the Right Angle Solver. I started to play around with it and found it very helpful. While it starts out like a normal problem, it lets me choose or identify the term in the picture. After that it let me choose, it gave me a few methods to solve the problem. As I was highlighting the methods it showed me examples of each method. If I chose the wrong method to use, it would give me a reason why I could not choose it. I was able to see the method used and correctly fill in the blanks. This is a very helpful tool to further the understanding of properties of right triangles.

Private Universe : Inventing Notations

This video deals with the students presented with another problem that would challenge them just as much as the other problems. Since this was not the first problem, they were able to jump right in start to organize their thoughts on paper. While one group seemed to get a bit flustered in a short amount of time because of the degree of difficulty, the other group argued about which would be the best way to solve the problem. The level of interest seemed to be a lot higher for every single student in the groups. From the beginning of the problem they had the idea of getting the correct answer but knew that they would have to have conclusions about how they came up with the answer in order to convince others. They also knew that just because they had an answer and everybody agreed, it did not mean that it was the correct one. One student said that everyone needed to be convinced because it was possible that maybe the one student who wasn't convinced could have the correct answer. I was very impressed with the intensity the students work on the problem. The fact that they were willing to eat lunch and then come back to work on the problem meant that they were into it.
The focus was brought to a student because of his unique way of the solving the problem. The fact that he was using binary code to solve the problem was very impressive. He was asked were he came up with the idea, but it just popped in his head. As they worked more with the problem he started to realize a few more things. It shows that children at a young age are able to come up with ideas and think like mathematician without the use of variables or any other algebraic symbol.

Video : Private Universe Are You Convinced?

Watching video 2 reminded me of the process we went through in order to come up with strategies and answers to the problem. What I noticed is that the teachers had pretty much the same thinking process that the students had when they were working on the problem. Both used different strategies such as drawing the towers, patterns, but usually trial and error. Both were asked to give reasons in order to convince others why there knew that there was not anymore combinations. The 4 story problem forces anyone use inductive and deductive thinking. Towards the end I like that the students where able to see a pattern within their own patterns. All four students shared how they solve the problem and were willing to share their strategies. They also had to realize that coming up with a pattern would be the best strategie to solving a problem with 4 cubes or 10 cubes.

Peg Puzzle : Virtual Manipulatives

I've seen this type of problem before, for example, using frogs jumping over each other. I have always enjoyed this problem especially because I can never seem to remember how to solve it. So every time I see the peg puzzle, it is like starting all over. The idea seems to be simple enough that is until someone gets to about 6 pegs. The pattern seems to be obvious but after solving the puzzle for the first time, repeating the process is not easy. After repeating the process you can start figuring out other patterns that are not so obvious. Using this would help a student look beyond just a simple pattern. Also using the virtual manipulative is more convenient than having actual peg puzzles in class.

Towers of Hanoi : Manipulative

I explained the directions and goal of the Towers of Hanoi to my girlfriend. We started from the beginning using two disks. She completed it with ease, so we moved on to 3 disks. She got it in one try, and told her to count the number of steps. We moved on to 4 disks and she started getting frustrated. After a few tries, I told her to focus on her moves and think about when there was only 2 and 3 disks. She said that she felt that there was a pattern but couldn't exactly see it. She ended up getting the 4 disks within 43 steps. She felt it was too long and I decided to tell her that it's only supposed to take 31 steps. We wrote down how many steps it took from 1 to 4 disks. She started to see the pattern and we figured out how many steps it would take all the way to 7 disks. This game is very helpful when analyzing patterns. While it can be frustating, it forces the person think in an enjoyable manner.

Video : Private Universe Children's Ideas in Mathematics

Watching the video made me realize that the development of a child's mind is very important. In the video I was able to see that at a young age they are able to come up with strategies to problems. The video shows that giving a student a chance to come up with a strategy or possible solution would create more of a thought process than telling the student how to solve the problem. This concept deals with stimulating their minds. This would be a great way to start lessons, though not every lesson, to see what new ideas students can conjure up. The students would benefit more than if they were simply taught the solutions. The important thing is to challenge their minds at a young age. Starting the process at an early stage in their lives will eventually lead to higher order thinking not just in math, but in any subject that challenges them. I strongly believe that students who come up with their own ideas and strategies will have a better understanding of the concept than memorizing steps.

4 Story Tower Cubes

I decided to give it to my girlfriend to see how many combinations she could come up with the cubes. She first began with making a tower of orange, then started replacing one orange with one black. After she was done with all the combinations by replacing one cube, she began replacing two orange cubes and then 3 orange cubes. The last piece she formed contained all black cubes. At the end she formed 15 different combinations. I asked her how she knew she was done and she responded that she did not know. My question made her second guess herself and she looked at all the combinations she had made. Within a few minutes, she figured out that she missed one.

Virtual Manipulatives :Algebra Balance Scales

I chose to play around with Algebra Balance Scales. It is a very helpful tool when dealing with simple linear equations. I thought it would be a great way to reinforce the idea of solving linear equations. The algebra scales can help with the idea of balancing out equations instead of just solving the variable in the equation. It would be easier to visualize the problem instead of just having the student look at numbers and variables on a piece of paper. I am not considering stretching out the exercise for more than a day, but it would put the idea in a student's head. The question I would like my students to ask themselves would be , "What do I need to do to balance the equation?", instead of , " What do I need to do first?". This could set a strong base to deal with longer and more difficult linear equations.