Geoboards and Tessallations

Lesson Plan: Tessellating the Geoboard
In this lesson student will practice finding shapes that will tessallate their geoboards. This will allow students to identify tessallations, identify shapes that will be tessallations and how some shapes will tessallate their geoboard in more than one way.

Virtual Manipulative

The manipulative I experimented with this week was called Diffy. It was under Numbers and Operations for grades 6-8. The object of the manipulative is to complete a puzzle by finding the difference of given numbers. After a couple of rounds I Thought of the puzzle as somewhat boring and simple. Then I noticed you could choose what you wanted to subtract. The choices were whole numbers, decimals, money, fractions and integers. This allowed the puzzle to be more challenging and would allow students to work at their level. This manipulative also allows for students or teachers to make their own problems. If the number entered was wrong it disappeared and allowed for another number to be entered. If the answer provided was correct the number changed to the appropriate color of the puzzle. After completing the puzzle the screen began flashing and changing colors.

Lesson: Making Flags

The lesson Making Flags was taken from our manipulative cd. This lesson asks students to desing their own flags using color tiles. They can make a flag however they like and must use more than on color. After making their flag they then must determine the fractions and percents of each color in the flag. For example, a flag with 32 color tiles and 8 blues would be one fouth blue or 25%. This allows students to identify fractions, reduce fractions and identify the percent of a fraction.

Library of Virtual Manipulatives

Turtle Geometry
Turtle Geometry allows students to program the movements of a turtle to get to a certain point, through a particular obstacle or to match a certain shape. It also provides a blank work space so a teacher can set up a specific challenge or so students can challenge each other. The student must plan ahead and think about what they want to tell the turtle to do. For example, they can tell the turtle to turn left or right and how many degrees they want it to turn and they can also provide inputs for movement form 1 to 5 spaces. This was an interesting manipulative and I can see benefits in this however, I don't see this as one of the better mathematical manipulatives.

Private Universe Project Video 6: Problems and Possiblities

The final video demonstrated a 2 week summer institute for 18 students who all participated in the Rutgers study in one way or another. They were provided a problem called the Cat Walk. This consisted of a cat moving in a series of 24 pictures. The pictures had a background so the distance of the cat could be measured and the students were provided a time. They were then tasked with trying to identify the speed of the cat in the 10Th frame and the 20Th frame. Their methods for solving this problem as in previous videos slowly developed and improved as they went. They were able to present their ideas to their peers and the researchers allowing for student discovery and collaboration. The video demonstrated how students need opportunity to build personal representations in order to understand the standard scientific representations and that mathematical knowledge grows from personal and real life experiences. The students were all able to graph their time and velocity of the movement of the cat and they did this in several ways. They were also able to take these graphs and representations and put them into a real life experience. They expanded the distances first to 10 times and then to 50 times the original distance. This allowed them to visualize, feel and live the actual accelerations of the cat. They were then able to identify the motions of the cat and where it was at certain points and relate it to their graphs. They were then given a scenario that a CEO of a company had the opportunity to bet on the speed of the cat in the 10Th frame. The students were to tell the CEO if he should place the bet. The three groups presented and decided that the CEO should not place a bet on this because their were to many variables. This final video really demonstrated how their mathematical problem solving abilities had grown and as a student stated in the video "The Rutgers way the students present ideas and get to show the others what they discovered and a regular class would never do that."

Week 5 Virtual Manipulative

This week I chose the Function Machine found in Number and Operations grades 6-8. This was pretty cool because it showed the input and output of a machine. I was given four numbers and I had to feed them into the machine and the machine would then spit out a new number. On the right side there was a function table and it would automatically begin filling in the table with my input and outputs. I would then have to figure out the pattern and solve three blank outputs. This did tell me if I had made an error and allowed me to fix it. I believe this would be great as extra practice for students who have difficulty with input an outputs and it also provides a pretty good visualiztion of input and output however, it did become rather boring pretty quickly.

Private Universe Project Video 5

Building on Useful Ideas
The video started by demonstrating how several teachers were using manipulatives in the classroom and the different strategies they used to use manipulative to work with the students. A couple of teachers were using trains. They had a block of a specific length and had to use several smaller blocks to make the same length block. This was similar to the unifix cubes because the students were attempting to find as many combinations as possible. I thought it was very interesting how the video demonstrated the use of these manipulative across grade levels. The teachers wanted to allow the students to answer questions with "clarity" and would not accept "vague answers". They listened to their students and wanted to see how their students solved the problems. They wanted the students to have skills to figure things out with out giving up and allow them to be curious about problems. As Arthur Powell stated "we are getting students to take ownership of a problem, think deeply about it and exchange ideas with each other."
They also showed a teacher who began her day using different math related problems. She began the day with this to get her students thinking and all of the teachers were working on getting their students to think mathematically.
The video then went on to the previous core of student and how they were building upon strategies they learned in previous years. They were using Pascal's triangle to solve more complex mathematical problems. It is interesting to see the students go back to previous problems and use the same methods they used years ago to help them solve more complex problems. It's as if they use it as a reference then expand from there.