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.