BY: HARRISON MIZRAJI

My Object:

My Dresser

Constructed on Paper

The constructions you see here are constructions of the front and side of the dresser. All the measures have been dilated by a scale factor of .25. I have graphed this so each square unit is equal to one inch.

Transformations Made:

To make a replica of my object, I dilated the figure by a scale factor of .25, so I was able to graph it to scale.

Measures:

Original Dilated by scale factor of .25:

60 in 15 in

30 in 7.5 in

8 in 2 in

8 in 2 in

8 in 2 in

8 in 2 in

10 in 2.5 in

10 in 2.5 in

16 in 4 in

Ratio:

The ratio of the figures is 4:1. That means that every original measure was divided by 4, or multiplied by .25. This can be determined by looking at the measures. For example, since the length of the dresser is really 60 inches, 60 divided by 4 is 15 and 60 multiplied by .25 is 15. If all of these numbers were reduced to simplest form, the original measurements would be 4 and the dilated figures would become 1.

Materials:

Sharpie Marker

Cocoa Pebbles Box (Cardboard)

Scissors

Measuring Tape

Straightedge

Tape

Construction

I measured the sides correctly, set the points, and cut the box. I then drew the shelves (points) with a straightedge. I then folded and taped the box together.

Final Model!!!

Proof Demonstrating How my Model is Similar to the Object I Chose:

To find out if the figures are similar, each pair of corresponding sides has to have the same ratio. This means that they have to be proportionate. As I have shown in previous slides, when taking two corresponding measures and dividing them by one another, the answer will always be 4 for these specific measures. Thus, the ratio is 4:1 for the object and the dilated object.

1.What object did you choose to make a model of and why?

I chose to make a model of my dresser, because I felt that it would be interesting to model something that I use everyday, and it has more than one shape within it.

2.How did you determine the appropriate dimensions between the object and its model?

I determined the appropriate dimensions between the object and its model by thinking how big a model should be compared to the actual object. I decided that if the model were 1/4 of the actual object, it would be a good size because the object is pretty large itself.

3. What steps did you take to create your model? Be sure to include all mathematical calculations.

In order to create my model, I had to measure the actual dresser. It came out to 60inx30in. This meant that I had to make it smaller. I decided to dilate it by a scale factor of .25 which is either dividing by 4 or multiplying by .25. I got the new points, and I constructed them on paper. Then I measured a cereal box to the corrected dilated points, and I made the physical model with materials such as tape, scissors, a cereal box, a sharpie, and measuring tape.

4.What challenges, if any, did you experience during this process?

The challenges I experienced while doing this project were measuring the dresser, and actually making the physical model.

5. What geometric principles, properties, postulates, or theorems did you use to make your model?

I looked at similar polygons properties. I also used dilation as a principle.

6.What did you think of this activity?

I thought that this activity was interesting. It took a large amount of time, but it helped and was actually kind of fun!

**QUESTIONS!**