My PBL Project

Introduction:

In my project I am going to demonstrate how changing the volume of a shape does not mean that we have to have a completely new shape. By making a few cuts into a chocolate bar I can show you how to make a perfect rectangle by getting rid of one square. By manipulating the slope of a diagonal line, I am going to trick your eyes, so that instead of seeing and believing your will believe and then see . Understanding that everything I do, involves geometry. When the diagonal cut is made from the second bar on the left side up to the third bar on the right, it allows to move the chocolate, thus making the third from bottom row smaller. This missing layer is equivalent to the square taken and put into the cup, but is hardly noticeable because the viewer counts each square - and doesn't actually measure the chocolate bar. The missing chocolate square is taken off the length of the bar, instead of a gap in the top left corner. Every thing from baking a cake to equally dividing a candy bar. I am here to show you how easy it is to apply math to something as simple as splitting up a candy bar. I will split it so carefully that you will hardly notice the difference from the original shape.

Driving Question

How does changing the dimensions of an object affect it's shape?

Materials:

1 Infinite Chocolate Wooden Bar

Procedure :

First off, we will measure a diagonal line across the chocolate bar . Then, we will cut the chocolate bar across the line that we measured and break the chocolate bar. Then, we will slide the bottom piece of chocolate to the live where we cut earlier . Then, we will place the other two pieces of chocolate to fit together to form the perfect rectangle . Finally, we get to eat the chocolate!

Scientific Principal:

Area

Volume

Geometry

Explanation:

This is a simple math puzzle that has been around for several years. When a diagonal cut is made from the second bar on the left side up to the third bar on the right, it allows the person moving the chocolate to take out an extra layer along the width of the bar, making the third from row smaller. This missing layer is equivalent to the square taken and put into the cup, but is hardly noticeable because the viewer counts each square - and doesn't actually measure the chocolate bar. This project needs the person to know their basic geometric shapes along with the area of the chocolate bar.

Reflection Questions

1. What geometric principles are applied to the chocolate in this demonstration?

Change in shape and volume are principles that were applied to the chocolate that made it infinite. When you geometrically change the slope of a chocolate bar from one side of chocolate to the other, you can create an infinite change of shapes in the volume of chocolate.

2. How can this transformation be represented by one equation?

There are two formulas for area that are used in this experiment. The first equation is the area of a rectangle which is base multiplied by height. Lastly the remaining equation is the area of a triangle which is base multiplied by height divided by two.

3. Is the chocolate really infinite?

Yes, When all the pieces are broken off from the bar, while rearranging, the bar is ever so slightly increased in size, along the slant line while the other parts rearrange. If you don't increase the chocolate bar as stated above, the cubes don't really match up, and would leave a bit of space in between them. That's where the infinite chocolate comes from!

4. What makes the demonstration successful?

When a diagonal cut is made from the second bar on the left side up to the third bar on the right, it allows the person moving the chocolate to take out an extra layer along the width of the bar, making the third from row smaller. This missing layer is equivalent to the square taken, but it isn't noticeable since the viewer doesn't count each piece.

5. How can I use this in real life?

Chocolate bars are made by machines who calculate the slope of every inch of the chocolate bar . The machines do this so that the company won't lose money on wasted chocolate that would be discarded if it was ruined ,this saves the company millions. If it were not for the machines being precise millions of pounds of chocolate would be wasted every year. So the next time you open a chocolate bar, just know it is not the initial size on how it was created. This trick can help manage limited resources and make more profit.