What I Have Learned About Grade 9 Exponents

~What Is An Exponent?

An exponent is how much times a number is being multiplied by itself. In other words how many copies of itself it’s making. For example if a have a number like 2 to the power of 3, in this case the 2 is being copied 3 times. This is equal to 8. Another example of an exponent is a power. A power is basically what an exponent is but using a fancier word. I will get into more of what you can do with an exponent and just how important they are in math.

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~What Is The Difference Between Evaluating and Simplifying?

The difference of evaluating and simplifying is quite simple. Evaluating means actually doing the equation and figuring out what for example 5 to the power of 2. Simplifying is subtracting exponents using three laws. The first one is the multiplication law, then the division law and lastly the power law. For example if I have 5 to the power of 6 multiplied by 5 to the power of 3 in this case we add the exponents so the answer would be 5 to the power of 9. Another example is using the division law which is subtraction. If we have 4 to the power of 7 subtracted by 4 to the power of 5 since we only subtract the exponents the answer becomes 4 to the power of 2. I will explain each of these laws more thoroughly and how they work.

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~Multiplication Law and How It Works

What is the multiplication law? The multiplication law is where if you have two numbers that have the same base and is a multiplication question, you can leave the bases the way they are and add the exponents. For example, if I have 6 to the power of 2 multiplied by 6 to the power of 8, since the bases are the same we are able to add the exponents  so therefore the answer is 6 to the power of 10. Well what if we have a negative base multiplied by a negative base? That’s a good question what happens is for example if we have (-6) to the power of 3 multiplied by (-6) to the power of 2 as I said before the bases aren’t the things that are changing its the exponents. Since we know that we add the exponents the answer becomes (-6) to the power of 5. That’s how the multiplication law works with both positive and negative numbers.

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~Division Law and How It Works

What is the division law? The division law is the same concept as the multiplication law but instead of adding the exponents, you subtract them. For example if we have 4 to the power of 6 divided by 4 to the power or 3 we subtract the exponents and up with 4 to the power of 3. What is it’s a negative? Just like the multiplication law the bases aren’t the things that are changing but its the exponents that are. So if we have (-5) to the power of 7 divided by (-5) to the power of 5 we subtract 7 from 5 and you get (-5) to the power of 2. Oh wait we forgot something, since the exponent is even the base becomes positive therefore our new and final answer is 5 to the power of 2. The picture on the very left is an example of the first example I mentioned and since 4 divided by 4 is one we are doing it 3 times and we are left with three four’s left over.  Therefore our answer is 4 to the power of 3. Just like the picture on the left, the picture on the right is using the same example but only negatives and it also shows that when you have a even exponent with a negative base it becomes a positive base. That’s how the division law works.

 

~The Power Law and How It Works

Out of the three laws this law uses 2 exponents and brackets in an equation. For example if we have (2 to the power of 3) and outside of the bracket we a have a 2 that’s an example of a power multiplied by a power or the power law. So in this case we leave the base and multiply the exponents. Therefore the answer is 2 to the power of 6. What if the base is negative? The thing about these three laws is that they are connected in at least one or two ways and this is where it connects. YOU NEVER CHANGE THE BASE ONLY THE EXPONENTS. So if we have (-2 to the power of 3) and a 2 outside the answer is (-2) to the power of 6. Again it has an even exponent so our final answer is 2 to the power of 6.

 

~Applications of Exponents

An application of exponents is Pythagoras. Pythagoras is a squared multiplied by b squared equals c squared. For example if we have a question with a right triangle like the one below that says 5 one side and 7 on the bottom side and c on the longest side, we know that this is a pythagoras question. We can immediately identify the hypotenuse is the because it’s the longest side of the triangle. Our first step is to square the 5 and 7 so we end up getting 25 and 49. Now the second step is to add the two so we get 74. Now we have our C. There is one more step. We have to find the square root of 74. In this case it’s 8.6 and that’s our final answer. That’s an application of exponents.

 

~One More Thing I Learned About Exponents

One more thing I learned about exponents is that there is a thing called a coefficient. A coefficient is basically an invisible 1 when a whole number is by itself because it doesn’t matter so you leave a whole number as is but there always is one. When working with exponents it’s very important because when you are simplifying equations and there is just a whole number, there is actually an invisible 1 that you have to add as well so it’s really important to keep coefficients in mind. This also applies when an exponent is a 0. For example if we have 2 to the power of 0 since anything multiplied by 0 becomes 0, in this case there is a coefficient so it becomes 1. This is very important so I am happy that I was able to learn what a coefficient was.

 

~Scources

http://www.solving-math-problems.com/math-exponents.html

https://www.proprofs.com/discuss/q/340683/the-multiplication-law-exponents-says-that-for-any-numbers-a

https://virtualnerd.com/middle-math/number-algebraic-sense/powers-exponents/evaluate-exponents-examples

 

 

 

Hovercraft Project/Reflection

1) What went well?

Our choice in material was very nice because it turned out to be very light weight. Our hovercraft ended up going farther than we expected. We worked well as a team. We adjusted our plan went something didn’t work out.

2) What didn’t go well?

The hovercraft didn’t go straight. The skirt was un-even. The hovercraft kept spinning. The hovercraft would bounce up and down at some points as well. The weight wasn’t balanced causing one side to lift up while the other side was causing friction by rubbing on the ground.

3) What would we do better?

We would take more time to make the skirt because that was one of the main problems. We would be more time efficient because we spent more time on the easy tasks not leaving as much time for the hard tasks. We could’ve got a better understanding about how to make a hovercraft. For example, what will work, and what won’t work.

Here is our Hovercraft Video

By: Josh G and David G

What I Have Learned About Grade 9 Fractions

~ Fractions On Number Lines:

Fractions on number lines for me was something that actually took awhile for me to catch up on because of my understanding of how it works. Eventually, I got help and I understood how it works and that it was easier than I thought. For example:

If we have a fraction like 4\frac {2}{3} we know that it’s a positive fraction so it goes to the right. If its a negative it means it goes to the left as shown on the number line to the left. Since this fraction is positive its going to the right so any number that’s right of zero is positive. Our fraction is a mixed number so we automatically go to the 4. Since our denominator is three, that’s how many spaces between numbers there are. Since our numerator is two, that means that we are counting two spaces. Therefore 4 \frac {2}{3} is located there on the number line.

~ Comparing Fractions

Comparing fractions is something that wasn’t challenging for me because luckily fractions one of my favorite things in math and I also have some experience with it. Here is what I learned. Say we have a fraction like \frac {5}{7} and \frac {6}{9} the first thing we need to find is the LCM, also known as the lowest common denominator. In this case its sixty-three because nine and seven don’t have any other common numbers that they both go into. Now, since we know the LCM we now have to change the fraction. So this means that since seven multiplied by nine is sixty-three we need to multiply the top by nine as well. Same thing with the nine we multiply the top by seven. Now our fractions are \frac {45}{63} and \frac {54}{63} and now its a lot more easier to compare the numbers because we can look at the numerator and tell which one is greater.

~Adding and Subtracting Fractions

adding and subtracting fractions is something that I’ve already gotten practice with before so this specific subject so adding and subtracting fractions was quite easy for me. I did learn to use negatives in fractions so that was basically all I learned in this unit. An example of this \frac {-2}{-6} + \frac {-4}{7} I’m happy that I was able to improve my understanding of adding and subtracting fractions. Negatives are a big role in fractions and without knowing it, I would’ve been stuck for a long time on it. I’m happy that Mrs. Burton expanded on adding and subtracting fractions because if I didn’t expand on the negatives and where they are placed then for my future math years I would’ve made so many mistakes when I shouldn’t have and the more I know the better.

~Multiplying and Dividing Fractions

Multiplying and dividing fractions is something that I also picked up along the way but I also learned some multiplying equations with negatives and same thing with dividing equations. I also learned the term reciprocal which means the numerator and the denominator get flipped around.  Multiplying and Dividing fractions otherwise was pretty easy for me. Another thing I want to add is that out of all of these fractions and processes, multiplying and dividing fractions was the easiest one for me out of all the fraction methods I have learned. The reason why it was easy is because I like multiplying and dividing numbers and I like how straight forward the process is. That is the reason why multiplying and dividing fractions was my favorite method and the easiest one for me.

~One Other Thing I learned About Rational Numbers

One other thing I learned about rational numbers and fractions is just how useful they are. For example take this fraction as an example, \frac {3}{4} means two things, first off it means that there are three pieces out of four in that fraction. And lastly it can also mean a division question. Not only does it mean multiple things but it also can be converted into two things. A decimal and a percent. In my opinion fractions are awesome because not only can they be converted and mean multiple things but, percents, decimals and fractions are all connected! This is not only something that I learned about fractions and rational numbers but something that I find fascinating. I am glad a did this unit and i’m happy of my understanding on fractions and rational numbers.

Picture Sources: The picture sources are both videos there is no cite for them.

 

 

Element Research: Fermium

Who discovered the element?

Fermium was discovered by a group of scientists who was led by Albert Ghiorso in 1953. They discovered the element while studying the radioactive debris off of the first hydrogen bomb.

What is the element?

Fermium is a element with a boiling point of 1527 degrees calculus but the element is still not fully explored by people today because we don’t know the boiling point yet. It is a very toxic and radioactive element.

Where was fermium discovered?

Fermium was discovered in 1953 in the debris of the first thermonuclear explosion which took place on a Pacific atoll on November 1st, 1953.

How did they discover fermium?

When they were checking the debris of the thermonuclear explosion, they found other elements combined and that’s how they got fermium. There are also 21 known isotopes of fermium.

Why did they discover fermium?

The scientists weren’t looking for a specific element, they were trying to see what they could find. Fermium was something that they just stumbled upon on. Since this was the very first thermonuclear explosion, they wanted to see what they could find so lucky for them, they found a whole new element.

When did they discover fermium?

They discovered fermium in 1953 in Stockholm where a group of brave scientists decided to make a thermonuclear explosion to see what they could find.

Whoa! What are some cool facts about fermium?

1.) It’s very radioactive                                                                                                           

2.) It is created by bombarding plutonium with neutrons.

3.) There is only a little bit of fermium produced so many of its chemical properties and characteristics aren’t really know yet. They have very little information on fermium.

4.) They kept its discovery a secret until the cold war that happened in 1955.

Part 2:

1.) What questions did you need to research your topic?

All of the questions that were asked for me to do, is the ones that I researched. So all of them.

2.) What new or familiar tools did you try to use as you worked through this project?

Honestly, I didn’t use any new tools I used google because its a really easy tool to use and its the one that i’m most comfortable using. I also Used citation machine which is a tool I’ve used in the past and its a very helpful and reliable tool to use.

3.) What was the process you used to investigate the topic?

I thought in my brain which questions made the most sense. For example on the whiteboard, Mr. Horton put questions and all he put was who, what, where, how, why, when and whoa!? I had to think of questions using those words. Then using my questions, I began my research from there.

4.) How did you verify and cite the information you found?

To verify the information, I checked multiple sites to see if the information matched and if it did I knew it was accurate. Then I used citation machine to cite the websites that I used.

5.) How did the process of completing the challenge go? What could you have done better?

The process of the challenge was very confusing at the beginning but once I found out what I needed to do, the process became a lot smoother and easier as I went through. I think I could’ve put more information and I could’ve made my questions a little more different because I found that a lot of my answers to the questions I made were very similar.

 

Sources:

Gagnon, Steve. “It’s Elemental.” It’s Elemental – The Element Fermium, https://education.jlab.org/itselemental/ele100.html.

of Chemistry, Royal Society. “Fermium – Element Information, Properties and Uses: Periodic Table.” Royal Society of Chemistry – Advancing Excellence in the Chemical Sciences, http://www.rsc.org/periodic-table/element/100/fermium.

Staff, Live Science. “Facts About Fermium.” LiveScience, Purch, 10 Oct. 2013, https://www.livescience.com/40348-facts-about-fermium.html.

Tech, Lenn. “Fermium.” #100 – Fermium – Fm, https://hobart.k12.in.us/ksms/PeriodicTable/fermium.htm.

Picture Sources:

https://pixabay.com/illustrations/radioactive-graphic-2056863/

https://ca.wikipedia.org/wiki/Fitxer:Electron_shell_100_Fermium.svg

https://en.wikipedia.org/wiki/Fermium

By: David Gilaev

 

 

 

 

Digital Footprint

How might your digital footprint affect your future opportunities?

That’s a good question. My digital footprint could affect me when i’m interviewing for a job. They take things very seriously and if they find one thing that affects other people in a negative way or something that you did that’s either stupid or wrong, they could decline your interview and your career could be thrown down the drain. This can also apply to college applications which is really important for your future because that’s how you get a job! Your twelve years of school gone to waste because you can’t even go to college!

Describe at least three strategies that you can use to keep your digital footprint appropriate and safe?

1.) If you think that your post isn’t that appropriate for example when posting on Instagram, you can archive your post which means you are the only one who can see the post and no one else. Remember THINK BEFORE YOU POST! 

2.) Before you post anything you can check with peers or your parents to make sure the post is appropriate and safe so you can know weather the post is safe or not.

3.) You can post more positive things rather than having more negative inappropriate posts. Since a lot of things that you post is still online without you knowing, the best way to cover those things up is by posting more positive things so that if you ever get interviewed for a job, your feed is filled with positive things and not negative or inappropriate things.

What information did you learn that would pass on to other students? How would you go about telling them?

I would tell them everything I said in my paragraphs and i’d tell them in shorter words like, always think before you post and remember how it can affect your future and is it actually worth posting or important? Always be careful of what you do. This doesn’t only apply to your digital footprint but to the internet in general because it’s more dangerous than you think.

-By: David Gilaev

Sources:

Kyle Loftus: https://www.pexels.com/photo/man-standing-in-front-of-couple-2429413/

Omkar Patyane: https://www.pexels.com/photo/access-blur-close-up-colorful-238480/

Timea Kadar: https://www.pexels.com/photo/black-light-post-near-tree-2214035/