1) Represent repeated multiplication with exponents
3x3x3x3 = 81 = 81
2) Describe how powers represent repeated multiplication
The power above is . Powers have a base and an exponent. The base (3) would represent the number multiplied by the exponent (4) as shown in number one. The exponent is how many times 3 would be multiplied. This power would be the equivalent to 3x3x3x3.
3) Demonstrate the difference between the exponent and the base by building models of a given power, such as and
4) Demonstrate the difference between two given powers in which the exponent and the base are interchanged by using repeated mulitplication, such as and
= 2x2x2 = 8
= 3×3 = 9
5) Evaluate powers with integral bases (excluding base 0) and whole number exponents.
= (-2)(-2)(-2)(-2) = 16
= 5x5x5 = 125
= 6x6x6x6x6 = 7,776
= (-4)(-4)(-4)(-4)(-4) = -1024
6) Expain the role of parentheses in powers by evaluating a given set of powers such as , ,
With , the repeated multiplication would be (-2)(-2)(-2)(-2) which would equal 16.
With , You are applying the exponent of 4 to the base of 2, then you will apply the negative symbol in the form of -1.
-1x2x2x2x2 = -16
With , You are essentially doing the same thing as .
-1x2x2x2x2 = -16
7) Explain the exponent laws for multiplying and dividing powers with the same base.
When multiplying powers with the same base, keep the base, then add the exponents. For example, x = = 19,683
When diving powers with the same base, you keep the base, then subtract the exponents. For example,
÷ = = 243
8) Explain the exponent laws for raising a product and quotient to an exponent.
When raising a power to an exponent you keep the base, multiply the exponent(s), and if there is a coefficient, apply the exponent to the coefficient.
2 * = * = 4*15,625 = 62,500
9) Explain the law for powers with an exponent of zero.
Any base (except 0) with an exponent of zero will equal 1.
10) Use patterns to show that a power with an exponent of zero is equal to one.
The base (4) with exponent (0) will essentially have 4 divide into itself, so 4 ÷ 4 = 1
11) Explain the law for powers with negative exponents.
When dealing with negative exponents, any base (except zero) raised to a negative exponent will equal the reciprocal of the base raised to a positive exponent, for example:
12) Use patterns to explain the negative exponent law.
13) I can apply the exponent laws to powers with both integral and variable bases.
Yes, I can.
÷ = = 125
= = 64
14) I can identify the error in a simplification of an expression involving powers.
When simplifying a power using the power rule, you have to remember to apply the coefficient to the exponent not mulitply them together. With the first example above, the coefficient was multiplied by 3 rather than applied the exponent of 3. This made it equal 6 rather than 8, which is incorrect.
15) Use the order of operations on expressions with powers.
x = x = 25*16 = 400
I first did the power law which states that the exponents are applied to the coefficients, and the powers are raised by the exponent. Then, I did the product law which multiples the coefficients and adds the exponents of the powers of the same base.
16) Determine the sum and difference of two powers.
+ = 81 + 216 = 297
– = 6,561 – 256 = 6,305
17) Identify the error in applying the order of operations in an incorrect solution
In equations like this, you would do the power law first. However, the negative exponent law was done first, here is the result.
This is going to take much longer to find the answer. However, you can do the power law first. So,
18) Use powers to solve problems (measurement problems)
The side length of a cube is 5 cm, what is the volume of the cube?
Well, in order to find the volume of the cube, you have to find the length, the width, and the height, since this is a cube, they are all going to be equal so you can find the volume of the cube by doing this:
19) Use powers to solve problems (growth problems)
A bacterium quadruples itself in 1 hour, How many will there be in 5 hours?
The base represents how many bacteria are produced, and the exponent represents time (5 hours).
20) Applying the order of operations on expressions with powers involving negative exponents and variable bases.
- ÷ = ÷ = =
Bernoulli’s principle states that: Low Velocity = High Pressure and High Veolocity = Low pressure. If you imagine an airplane wing, It is designed for the air on the top of the wing to be faster than that of the bottom of the wing. Since the air is slower on the bottom it creates a high pressure zone which will create lift.
1. Draw a path of trajectory of your rocket.
2. Which force is acting on the rocket at the moment of launch? (use arrows to indicate direction)
3. As the rocket was half-way up, which force(s) is/are acting on the rocket? (use arrows)
4. As the rocket begins to veer into another direction, which force is acting on the rocket? Explain why this is happening.
Lift, Bernoulli’s principle states that: Low Velocity = High Pressure and High Velocity = Low Pressure. The air going over the rocket is travelling at a faster rate than the air under the rocket. The high pressure on the bottom will create lift and keep the rocket up.
5. Did some rockets work better than others? How does the shape of the nose and fin effect the trajectory of the rocket? Explain in terms of the four forces that act on a rocket ship.
Yes, some did. I found that if the nose better fits the fuselage, the farther it went. Without proper fins, the rocket just sat in the air and spun on the way down. The main goal of making your rocket go far is that you decrease drag while increasing lift. If the nose is flat on top of your rocket it will increase the amount of drag on your rocket making it not go so high. If it is shaped in a way where it cuts through the air, the rocket will be more aerodynamic and fly much farther. Same for the fins, the fins are also supposed to make your rocket more aerodyamic and decrease drag, If they are positioned in a way that makes it cut through the air, the fins will also contribute to less drag.
Acceleration: The rate that an object increases in speed.
Center of Drag: The center of which drag will act upon an object the most.
Center of Mass: The center of which mass of an object will balance.
Drag: An accumulative amount of a resistant force on an object.
Inertia: An object will be in rest unless acted upon by an outside force.
Mass: A unit of measurement relative to an objects property.
Momentum: The amount of movement an object has.
Pressure: A force that exerts force upon another object. (Gas,Liquid, Solid).
Velocity: A measurment of how fast something will move in a certain direction.
1. How did the height you estimated your rocket would reach compare with the actual estimated height?
To be honest, I thought it would’ve gone a little bit higher than it did.
2. What do you think might have caused any differences in the height you achieved?
Shape of the cone, shape and positions of the fins.
3. Did your rocket launch straight up? If not, why do you think it veered off course?
No, it initally veered off course. I think it was because of the top of my rocket. The top of the rocket was slightly crooked and did not point up straight. The cone was also more slightly loose, but it helped with the deployment of both of my parachutes.
4. Do you think that this activity was more rewarding to do as a team, or would you have
preferred to work alone on it? Why?
I would preferred everyone did their own rocket. I think it is a more satisfying experience if the rocket was sucessful because it was your work and not between two people. Work would be split between two people which can make it harder to agree on a design and bring two seperate aspects of the rocket together.
5. Did you adjust your model rocket at all? How? Do you think this helped or hindered
At first, the size of the fins on my rocket were going to be much bigger than they were. But, if they were the size I intended them to be, they wouldn’t fit very well on the rocket and be much more blocky. I think making the fins smaller and more sleek along the rocket actually helped my rocket.
6. How do you think the rocket would have behaved differently if it were launched in a weightless atmosphere?
If it was in a weightless atmosphere, I think the rocket would go farther, but the speed it would go be much more slowed down.
7. What safety measures do you think engineers consider when launching a real rocket?
Consider the location of most launch sites as part of your answer.
Making sure the area around the lauch pad is clear of debris. Building the launch pad on relatively flat terrain which is clear of any trees and such. Making sure that the rocket is clear for takeoff if there was any air traffic up in the sky.
8. When engineers are designing a rocket which will carry people in addition to cargo, how do you think the rocket will change in terms of structural design, functionality, and features?
Rocket design would accommodate living quarters for those on the rocket. To increase ability to communicate with those who are on land. Depending on the length of travel or if they are orbiting around Earth, the rocket would not only need space for food, water, and toiletries, but something would have to send it to those in the rocket.
9. Do you think rocket designs will change a great deal over the next ten years? How? I think designs for rockets will have little change over the next ten years. Maybe a few moderate changes. The design of a rocket could be made to accommodate more people, be slightly more aerodynamic, or become more fuel efficient.
10. What tradeoffs do engineers have to make when considering the space/weight of fuel vs. the weight of cargo?
The more fuel there is, the more the rocket will weigh and there would be less space for the cargo. If there is a lot of cargo, the rocket will weigh more and there wouldn’t be sufficient space for fuel in order to get to a set destination especially if it is a good distance away from Earth.
Your Digital Footprint says a lot about you, and it’s important that you keep it the way that you want employers and college admissioners to see it. When you apply for a job, one of the first things that employers will do is look up is your name. It only takes seconds to do and can really harm you if they find anything possibly unsuitible for the job you applied for. Your application can be negatively affected by your digital footprint and any social media that is under your name can be easily searched only by typing in your full name. Having a bad digital footprint can not only affect the outcome of a job application, but can also negatively alter the views of not only yourself but people who are related to you like your family. This is why managing your digital footprint is essential to you and others.
One strategy to positively manage your digital footprint is to keep your identity as safe as possible when online. Openly sharing account information, your address, information about family members who do not actively use social media or browse online can all affect your digital footprint. Making sure you keep this under wraps is a good start to a healthy digital footprint.
Another strategy is to have a mindset where you must understand that when you post something on the internet, it is there to stay, that is why you must make the necessary precautions before you may post something you may regret in the future. Always check if your post is negative, controversial or even grammatically incorrect. Some platforms are more forgiving, allowing you to edit your post, others are not. Taking some of these precautions will make you more uniform and fit for a future job or college application and have people view you in a positive manner.
Also a good strategy is to keep account information that you even keep privately, hidden. Malicious social media users intend to do harm to your account by stealing account details, releasing information that you thought was private to the public, and identity theft. One way to prevent this from happening, is to have more complex passwords along with somewhere to keep them safe. This will make it harder for people to access your account. Another way is to keep information off social media as a whole, the more information you put
out there, the more risk that will come with it. It’s always reasonable to keep private information, well, private.
To follow up with the first two strategies is to be in the mind of the employer. If you were hiring someone for a job and you saw your social media profile, would you think that applicant (a.k.a you) would be eligible for that job opportunity? Search yourself up on the internet and see for yourself. If your social media profile doesn’t show up in the search results, you have already done a good job about keeping yourself hidden away on the internet. If your profile does pop up, see what shows up. If you find something that doesn’t seem appropriate or suitable for the job that you want, you may want to fix that.
My last piece of advice is to be cautious around controverisal arguments on the internet. People will obviously have opposite views of eachother and will express their opinion if need be. If you have an opinion that would like to share on a certain topic that people may deem as “controversial”, always be careful about what you post as it may spark a negative, back and forth argument. It’s important to be resilient and it is ok to disagree with arguments. Try to refrain from using vulgar language and bringing up even more controversial topics to the table as this will show on your social media profile.
What I learned about the internet, is that it is NOT a toy and should not be treated like one. Social media can affect whether you can get a job or not, the way people view you as a user of the platform or even can put your sensitive information at risk. Your digital footprint will reflect on all of these topics. It is YOUR sole responsibility that you can maintain a healthy digital footprint on the internet as it can greatly impact your life. Helpful ‘Digital Footprint’ videos and projects like these can spread a message to others about this topic. It is easy to share and easy to pass it on especially on various social media platforms.
Wow, I can’t believe Summer has already ended, it went by so quickly. I’m happy to see familiar faces and people I’ve never seen before, I can already tell that Riverside is going to be different. What I’m excited about is going to classes that I chose to go to, there were so many choices. I’m excited about new opportunities to make new friends so I can get to know more people, and I’m also excited about more technology oriented classes. I’m going to make the most out of my years here at Riverside, and I’m safe knowing that people will support me on the way, whether it be the simplest task, or the most difficult.