## Tuesday, February 23, 2016

### Science reflection blog

I think that this project really helped me learn more about my personal interests. I was able to connect our food,nutrition and fitness unit to surviving in the wild. I think that by doing a project like this, will help students dig deeper into a topic, thus learning deeper contexts and to also learn more about what they are interested in. I also find that this types of projects will motivate students to learn more about a scientific topic and gain more interest in science. I really think that if we did another project like this for our next unit, I will be able to understand the deeper side of our unit.

## Tuesday, February 16, 2016

### Math blogpost 2

In the second lesson of our preparation for the final jump, our group has decided that we should make different graphs for different heights, as the momentum of the object falling down will increase if it is thrown from a greater height. There are a number of graphs that I could have made to represent the amount of elastics needed for each jump. Our group chose to make a quadratic equation for each meter. The reason why we did this is because the shape of a quadratic graph reflects the shape of the jump. In other words, if the barbie jumps from a higher height, she will gain more momentum therefore will use the full potential of the elastics, making it use less elastics per units in the jump in general.

Another option that we thought about was a Gauss graph to show the maximum stretch of an elastic. But we thought that it was unrealistic because it is not guaranteed that the each elastic is going to be used to it's maximum stretch because from some heights, the barbie will not be able to carry out the momentum.

Here is our graph for under 2 meters

y=x^2-4

The explanation for this graph is in my first post

And for 4 meters it is:

Another option that we thought about was a Gauss graph to show the maximum stretch of an elastic. But we thought that it was unrealistic because it is not guaranteed that the each elastic is going to be used to it's maximum stretch because from some heights, the barbie will not be able to carry out the momentum.

Here is our graph for under 2 meters

y=x^2-4

The explanation for this graph is in my first post

And for 4 meters it is:

y=6/7(x-9)^2

Our group came up with this graph by testing the amount of elastics needed for a jump in the height of 4.15 meters, 4.52 metes and also 4.92 meters. The results were that we needed 31 elastics for 4.15 meters, 32 for 4.52 metes and 33 for 4.92 meters. We tried to plug in these numbers in a matrix calculator to figure out the pattern but as we really don't know how to use one, a few minor errors occurred. So that there were some irrational numbers in the equation that we got. We converted the irrational numbers into numbers which we can understand and came up with this equation.

For 5 meters it is:

y=(x-14)^2

For us to get the equation of this graph, we followed the same steps as the one for 4 meters. The only problem was that we could only get differing heights for 5 meters. Which were 38 elastics for 5.75 meters, 37 elastics for 5.29 meters. We could only get these trials for 5 meters because if we added more, the barbie would hit the floor and if we added less the jump would enter the 4 meter range. Therefore, we predicted that as the barbie is falling under the same controlled variables, we predicted that we should assume that the graph would look somewhat similar.

## Thursday, February 4, 2016

### Is democracy better suited for some countries?

Montesquieu once said that a democracy might not always be the best form of government for some regions of the world. I strongly agree with his statement because a democracy can be rather hard to run if the general population is uneducated and are easily manipulable. Uneducated and unprivileged people are rather easy to manipulate and if this is the case in a country, a democracy wouldn't really be effective because a political figure might abuse his power and still make the population believe in his lies. Therefore, a democracy in a country like this will not last long and will be soon replaced with a government in which only seeks out for the benefits of themselves. Moreover, in some cultures people do not value the opinion of every individual but the opinion of a leader, and if their belief systems are built up this way, the people are not going to be aware of the fundamentals of voting. Resulting into an ineffective government. The best case scenario for a situation like this is to hope for a good leader who would look into the well-being of the population rather than his own self interest.

## Wednesday, February 3, 2016

### Math barbie project #1

Our wonderful math teacher, Mr. Ockness came up with the idea to improve our familiarity with quadratic equations by making us investigate bungee jumping. This project is about bungee jumping a Barbie doll from a given height and making the jump as thrilling as possible by getting the doll close to the ground. The approach that our group is going to take on this project is to find a pattern such as how much the length of the jump increases. In other words, we are currently trying to find the slope of the graph. Here are some statistics that might help us run realistic trials and determine the pattern of the quadratic equation.

The first graph that I came up with is a curve that goes down and back up exactly where it came from and therefore is identical to the y axis. I have marked the x intercept which is (0,2) and the maximum value of y (0,192). I don't think this graph is entirely correct as this graph was purely made by looking into only one trial and as we haven't really found a pattern yet, we don't have any guesses of the slope of the graph and that is why there is no visible curve to it.

2.

The second graph is also just an estimation/hypothesis judging by the statistics of the first trial. The equation of the graph is y=x^2 the reason why I estimate that the graph would look something like this is because I figured out the 14^2 is 196 and as 196 is extremely close to 192 cm I figured out that the real quadratic equation could look like something like this. What y stands for in this equation is the height of the jump, and what x stands for is the amount of elastics. Another thing that proves that this graph might be something like the real one is that if u input 192 into the value of y, 192=x^2 the value of x will turn out to be 13.88 which is pretty close to 14. And I think that for the graph to be exactly target, I think that I can adjust the 0.12 difference in value by adding a y intercept of -4

And if I do that the graph would look like this;

by looking at it in such a big scale, the y intercept of -4 does not make such a big difference, but if we plug the x and y values in to the equation of y=x^2-4, the values match out perfectly. And as we now have some sort of hypothesis that is on the right track, we are able to test this equation in different heights and make certain adjustments for our final project.

Plans for next class:

1. do two more trials in different heights

2. test out how gravity works in different heights

3. make adjustments to our current equation

Here is a video of our first trial:

Barbie weight: 89.1 g

Barbie height: 30 cm

Length of rubber band (not stretched): 7.5 cm

In our first trial, we jumped the barbie from a height of 1.92 meters found out that it will take 14 rubber bands for the barbie to jump and almost hit the ground by 2 cm. By only judging by this trial, the x intercept of the quadratic equation is only 0 as it is a multiple root equation also the maximum value for the graph is 192, a quadratic equation with a positive slope is usually not able to have a maximum value. But in this case, as the maximum height of the jump is 192 cm, the Barbie doll will not be able to bounce up and go in to heights beyond that. Cause if it did, it would either be that Mr. Ocksness bought some extremely high quality rubber bands, or that our project has just defied the laws of physics.

The graph that I could come up with by only taking this trial into consideration is this:

( up to this point, we really don't know what x and y really stands for but this graph is just a reflection of what happened)

1.

The first graph that I came up with is a curve that goes down and back up exactly where it came from and therefore is identical to the y axis. I have marked the x intercept which is (0,2) and the maximum value of y (0,192). I don't think this graph is entirely correct as this graph was purely made by looking into only one trial and as we haven't really found a pattern yet, we don't have any guesses of the slope of the graph and that is why there is no visible curve to it.

2.

The second graph is also just an estimation/hypothesis judging by the statistics of the first trial. The equation of the graph is y=x^2 the reason why I estimate that the graph would look something like this is because I figured out the 14^2 is 196 and as 196 is extremely close to 192 cm I figured out that the real quadratic equation could look like something like this. What y stands for in this equation is the height of the jump, and what x stands for is the amount of elastics. Another thing that proves that this graph might be something like the real one is that if u input 192 into the value of y, 192=x^2 the value of x will turn out to be 13.88 which is pretty close to 14. And I think that for the graph to be exactly target, I think that I can adjust the 0.12 difference in value by adding a y intercept of -4

And if I do that the graph would look like this;

by looking at it in such a big scale, the y intercept of -4 does not make such a big difference, but if we plug the x and y values in to the equation of y=x^2-4, the values match out perfectly. And as we now have some sort of hypothesis that is on the right track, we are able to test this equation in different heights and make certain adjustments for our final project.

Plans for next class:

1. do two more trials in different heights

2. test out how gravity works in different heights

3. make adjustments to our current equation

Here is a video of our first trial:

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