Grade 9 – Page 2 – Jessica's Blog

Everything I know about exponents

jessicam2018 on November 5, 2018November 13, 2018

Prescribed Learning Outcomes for Exponents:

1) Represent repeated multiplication with exponents

This wants you to show repeated multiplication, but using exponents. For example, 5x5x5x5, is the same thing as $5^4$ . 5 being the base, and 4 is the exponent. Another example is 2x2x2, which is the same thing as $2^3$ . The number 2, is the base, and then how many 2’s there are, is the exponent.

2) Describe how powers represent repeated multiplication

Powers can represent repeated multiplication. If you had, for example $7^5$ , it can be also written as repeated multiplication 7x7x7x7x7. Because you have five sevens.

3) Demonstrate the difference between the exponent and the base by building models of a given power, such as $3^2$ and $2^3$ .

$3^2$ , is 3 to the power of 2, or 3 squared. And if written as repeated multiplication it would be 3×3. $2^3$ would be 2 cubed, or 2x2x2.

$2^3$ is a cube with a width, length, and height of 2. If it was cut into cubes and you count it up, it would be 8, or you can do length times width times height. $3^2$ is a square with a length and height of 3. And if you count that up, it would be 9.

$2^3$ = 8

$3^2$ = 9

4) Demonstrate the difference between two given powers in which the exponent and the base are interchanged by using repeated multiplication, such as $3^2$ and $2^3$ .

$3^2$ and $2^3$ are not the same. Just because you change where the exponent and base is, the value will be different, in most cases. $3^2$ is 3×3=9, and $2^3$ is 2x2x2=8.

5) Evaluate powers with integral bases (excluding base 0) and whole number exponents.

Here is a bunch of examples on bases and powers. This question is basically asking you to solve the powers with number bases and exponents. The bases could be even or negative, and this is what happens.

$0^2$ = 0x0 = 0

$1^3$ = 1x1x1 = 1

$2^4$ = 2x2x2x2 = 16

$3^5$ = 3x3x3x3x3 = 243

Even bases and even exponents make even answers.

$(-3)^3$ = (-3x-3x-3)= -27

If the base is negative, and the exponent is odd, then its a negative answer.

6) Explain the role of parentheses in powers by evaluating a given set of powers such as $(-2)^4, (-2^4), -2^4$ .

Brackets can make the powers different. Here is what it really means of where the brackets are.

$(-2)^4$ = (-2)x(-2)x(-2)x(-2) = 16

$(-2^4)$ = (-1x2x2x2x2) = -16

$-2^4$ = -1x2x2x2x2= -16

If the exponent is outside the brackets, like $(-2)^4$ then that means its (-2)x(-2)x(-2)x(-2) and it equals positive 16 because an even number of negatives equals a positive. For $(-2^4)$ and $-2^4$ , the – sign is the coefficient, which makes it -1 then 2x2x2x2 which equals -16.

7) Explain the exponent laws for multiplying and dividing powers with the same base.

Whenever you have powers with the same base, then you can use either multiplying or dividing exponent laws.

For example, $y^3y^2$ , is y to the power of 3, times y to the power of 2. Instead of figuring that out then multiplying them, or if you don’t know what y is, you can also add the exponents. $y^3^+^2$ which would then equal $y^5$ .

The dividing one is almost the same. Except you would subtract the exponents instead. So $\frac{y^3}{y^2}$ would be the same as $y^3^-^2$ which is $y^1$

8) Explain the exponent laws for raising a product and quotient to an exponent.

This might sound confusing, but once you learn it it won’t be. Raising a product to an exponent is like $(ab)^2$ . Which then you can use the power rule. You can write $(ab)^2$ like $(a^1b^1)^2$ , so you just want to multiply the 2 to the ones. So it then becomes ( $a^2b^2$ ). Another example can be $(2a)^3$ . The coefficient, 2, you just bring it to the power of 3 so its 8, and then the a is $a^3$ . And when you write it together it’s ( $8a^3$ ), because you don’t know what ‘a’ is.

The quotient rule, is also like that, in a way. So if you havethe exponent 3 of the fraction is saying that it is $\frac{2}{3} . \frac{2}{3}.\frac{2}{3}$ so it can be written as 2 cubed divided by 3 cubed which equals 8 over 27.

9) Explain the law for powers with an exponent of zero.

If the exponent of a power is zero (0), then the number is just one. What I mean is, if you ever get a power the exponent is 0, for example $y^0$ , then its just 1.

10) Use patterns to show that a power with an exponent of zero is equal to one.

So you know that $y^0$ equals 1, or anything with an exponent of 0 also equals 1.

But why? Well, so you know that $\frac{y^4}{y^3}$ is $y^4^-^3 = y^1$ . So when its $\frac{y^3}{y^3}$ , $y^3^-^3 = y^0$ . And $y^0$ equals 1, because 1 times $y^3$ equals $y^3$ .

11) Explain the law for powers with negative exponents.

When you have a negative exponents, its a little different. You just flip the whole thing around. For example, $x^-^2$ then equals $\frac{1}{x^2}$ . Another example is $2^-^3$ ,= $\frac{1}{2^3} = \frac{1}{8}$ .

12) Use patterns to explain the negative exponent law.
Divide by 2

2³ = 82²= 42¹= 2 2⁰= 1
2⁻¹= 1/22⁻²= 1/4
2⁻³= 1/8

If the base is something else, then divide it by that. Like if the base is 3 then divide it by 3 each time when your going down.

13) I can apply the exponent laws to powers with both integral and variable bases.

Integral, is like 1, 2, 3, 4, etc. and variable is like $y, x, etc.$ Variable is when you don’t know what the number is or the number can change. The laws for both of them are the same except the integral you can solve it.

$(2^3)(2^2)$ is, you know, $2^3^+^2$ which equals $2^5$ = 2x2x2x2x2 = 32

$(x^2)(x^3)$ is $(x^2^+^3)$ = $x^5$ = ( $x$ )( $x$ )( $x$ )( $x$ )( $x$ ) but since $x$ is a variable you can’t solve it. So the answer would just be left as $x^5$ .

The same for the other exponent laws as well.

14) I can identify the error in a simplification of an expression involving powers.

If you get something like $5^2$ x $5^3$ = $25^1^5$ , then you know its wrong. Because your not suppose to do it like that. You can use exponent laws $5^2^+^3 = 5^5 = 3 125$ .

Or I know that $\frac{7^6}{7}$ does not equal $7^6$ because the 7 under the $7^6$ is actually a $7^1$ and $7^6^-^1 = 7^5$ .

15) Use the order of operations on expressions with powers.

Using order of operations on expressions, with powers is to use the right operation first. If you get one for example, $(-7a^-^2b^3c^0)^-2$ . Instead of turning over the whole thing because of the -2 exponent outside of the brackets, you can use the power law. Then it becomes. $(-7^-^2a^4b^-^6c^0)$ After that you can use the negative exponent rule. $\frac{a^4}{-7^2b^6}$ . And when you solve it, it becomes $\frac{a^4}{49b^6}$ . You might ask, wait what happened to the c? Well, since its $c^0$ the 0 times anything will still be 0, and then when an exponent is 0 the whole thing becomes 1. And 1 times anything is the same thing. So you don’t have to write it.

16) Determine the sum and difference of two powers.

You can’t use the exponent laws when there is + or -. So you will just have to do the exponent, then add the sum/difference. For example, $3^2 + 2^3$ , it’s 9+8=17.

And $3^2 - 2^3$ is 9 – 8 = 1.

17) Identify the error in applying the order of operations in an incorrect solution.

If someone does $3^2+3^3=3^5$ then I know its wrong because you cannot use exponent laws for addition. You must do 9+27 which the correct answer is 36. Because exponents first, then addition.

18) Use powers to solve problems (measurement problems)

How can you use powers to solve word problems? (Measurement problems) Well this is how!

There is a blue square with a side length of 5cm. there is a red square overlapping the blue square, and the red square has a side length of 4cm. What is the area of the blue square is visible? If drawn out, it would look like this.

You can use exponents to represent and solve this. To find area, its side length times side length, which in this case is 5cm, so its $5^2$ = 25. And $4^2$ is 16. So then you do 25-16 because the 16 is covering the 25.

25-16=9. So the answer is $9cm^2$ .

19) Use powers to solve problems (growth problems)

An example question – There once was a blob. The blob doubles every hour. How many blobs will there be by the 9th hour?

You would solve it like $2^0$ to start with. And then every hour is the exponent. 1st hour, = $2^1$ = 2. Second hour = $2^2$ = 4. And the 9th hour would be $2^9$ which is 512. There will be 512 blobs the 9th hour.

20) Applying the order of operations on expressions with powers involving negative exponents and variable bases.

Here is an example question.

First you would make the -3 exponent, not negative. So you would flip the whole fraction around, here. After you have done that, you would then use the power law. and the final answer would be… $\frac{-64b^9d^6}{c^3a^1^2}$

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Climate Change Blog

jessicam2018 on October 22, 2018

How long will it take to stop climate change, and what can we do anything to speed it up, what can any person do to stop climate change?

Research Questions:

Why does climate change happen? How do humans affect it?

Is climate change dangerous?

What are we currently doing to stop climate change?

Is there anything else that we can do to reduce climate change?

Where is climate change mostly happening?

Why does climate change happen?

There are many causes to climate change. One of them is, a ‘greenhouse effect’. All life on Earth needs the sun’s energy to survive. When sunlight passes through the atmosphere, some of it is reflected into space, and most of it onto Earth. In the atmosphere, there are some gases which traps the heat. Some of those gases, don’t respond to any changes in the temperature. So, they sort of force a part of the climate change to happen. Examples are water vapor (H2O), nitrous oxide (N2O), carbon dioxide (CO2), and methane (CH4). Unlike Earth, Mars has a very thin atmosphere, so there are no gases to make the greenhouse effect. So, there is no life. Because humans, over the past years have been burning fossil fuels, it makes more carbon dioxide in the atmosphere. Things that will happen are that the Earth will become warmer, when it’s warm it will evaporate more and then more precipitation, when it gets to hot it will melt ice and glaciers, so sea levels will begin to rise, and then some crops will need more water to survive.

Another reason that climate change is happening, is that it could be the sun’s energy is changing. Since most of the energy we get is from the sun. But there are things that prove that it isn’t happening. For example, since 1750, the energy from the sun remained very close to the same.

Is climate change dangerous?

Climate change is happening all around the world. Glaciers are melting, ice which was on rivers, and lakes are breaking sooner, trees are flowering sooner, and many more. Near the future, we predict that there will be more wildfires, more drought in some places, and more tropical storms. Scientists say that climate change will continue because of greenhouse gasses caused by humans. Many things are likely to happen. For example, sea levels will increase 1-4 feet by 2100. Hurricanes will be become stronger, there will be more droughts, our precipitation patterns will change, changes will continue and temperatures will rise.

What are we currently doing to stop climate change?

I can’t find anything online. People are writing how we can stop climate change, but nothing about what we’re doing. I’m sure some people are trying to stop it, but I can’t find anything.

Is there anything else that we can do to reduce climate change?

There are many ways you can help stop climate change. One is using energy more wisely. You can use better light bulbs. Unplug electronics when you’re not using them. Buy renewable stuff, don’t waste food. And lots more.

Where is climate change mostly happening?

The entire Earth is heating up.

Solution 1

What if we stop producing greenhouse gasses right now? Is it possible that it would stop climate change? Because, since the greenhouse gasses are mainly why the Earth is heating up, is it possible that if we stop using them, the Earth will stop climate change? Well, it sounded like a cool idea so I searched it up, and this is what I found. Ok, so we all know that the Earth’s temperature is changing quick, mostly because of all the carbon dioxide in the atmosphere, which is caused by humans burning coal, oil, and some other natural gases. Even if we managed to stop using the gases, how much carbon dioxide is already stuck in the atmosphere? If you didn’t know, when carbon dioxide is in the atmosphere, it’s like a blanket around the earth. Sea levels will rise and weather will change. Well, it sounded like a good idea, but the answer is no. Even if we stop using greenhouse gases, the carbon dioxide which is already in the atmosphere, will stay there, for thousands and thousands of years, until it goes through the formation of ‘calcium carbonate’ (limestone). So, because since humans don’t live that long (or at least yet), the only way to make it disappear is if we take it out ourselves.

If we wanted to do that, we would have to not only take away the carbon dioxide, but along with the greenhouse gases, like methane and nitrous oxide. Also, reverse deforestation and other things that affect the Earth’s ‘energy balance. There are a lot of good paragraphs of information I found, but basically what it was saying is that, “there will be no new normal, only more change.” I do not own that quote. All rights go to its original person. Anyways, I don’t think we can even stop using carbon dioxide just like that. The use for them are just increasing. Finally, my point here is that even if it’s not possible to stop climate change, we can try to slow it down. If we manage to slow it down, maybe humans, mammals, aquatic life, and plants can adapt more easily to the Earth. Even if somehow, we stop climate change now, it won’t be like the past anymore. The Earth is still warm. The only thing we can do is slow the change. If we can just eliminate the gases being used in a few years, then we can slow down the warming, and make it somehow controllable, then that could work. It would steady the changes, and let nature and all to adapt. If we can adapt to the earth more easily, then we will have less problems about climate. Final quote, “Rather than trying to recover the past, we need to be thinking about best possible futures.”

Solution 2

What most sites are saying is that we should reduce the amount of carbon dioxide and greenhouse gases used, and adapt to what is going to happen in the future. But how can we do that? Well, one of the ways is that we can reduce the ‘sources of the gases’. Like you know how we burn fossil fuels and stuff for heat, electricity, transport, gas, etc. So, if we, humans can find a way to reduce the usage of those things, it will be better for the atmosphere.

Solution 3

Another way, is that we can ‘enhance the sinks’ which gather and store these gases, also known as ‘storage tanks’. For example, oceans, forests, soil, etc. And hopefully we can find a way to just make the carbon dioxide somehow disappear. People around the world are focusing on the climate problems. They are working now to build flood defenses, heatwaves and higher temperatures, stuff to deal with floods and storms better, and improve their water storage and use. Even if we are focusing to find ways to reduce climate, we need to find ways to survive what we are living in now. Anyways, back to the other idea. We need a bigger storage space to put the carbon dioxide. Is it possible to shrink carbon dioxide, so more can fit into an ocean? I know it’s a weird idea but if we can keep the number of atoms together and just put them closer would that work? Another weird idea I just thought of is what if we can use a giant mirror like thing so the sunlight will not go to Earth, and all of it will go back into space. But we need the sun to survive so is it possible to make an artificial sun? Ok, that wasn’t the best idea. Because there will be lots of assumptions. What if we can invent something new to store carbon dioxide, and it’s very efficient?

Change won’t happen quick. It will take time. So here are a few ways that we can take to reduce climate change now. Walking, biking, using the bus, is all better than using your car. Don’t overbuy stuff. Basically, don’t waste. Reduce, reuse, recycle :D. Use less energy at home, limit your air travel. If you have to drive, try an electric car. Renewable energy is great. Also, if the world can eat less meat, that would be great too. Because to make meat, takes up a lot of land, and adds to the greenhouse gases. Try to eat more plants. Support climate change, and try encouraging others.

Reflection

What questions did you need to research to research your topic?

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

What was the process you used to investigate the topic?

How did you verify and cite the information you found?

How did the process of completing this challenge go? What could you have done better?

The questions I did to research my topic are “Why does climate change happen? How do humans affect it? Is climate change dangerous? What are we currently doing to stop climate change? Is there anything else that we can do to reduce climate change? Where is climate change mostly happening?” I used Google. I went on official sites, websites, blogs, all kinds of sites to try and find useful information. I prefer going on websites rather than YouTube videos, because its quicker to get information, in some cases. If it’s a page of text I can read through it quickly, but if it’s a video I can’t skip and have to watch the full thing. And I think it’s easier to create a YouTube video then a website. I first thought of a main question, other questions to help solve the main one, answered the other questions, find solutions, and then reflect on all of this. When I found information, to make sure it was reliable, I looked to see if there’s an author, when it has been last updated, if there’s any spelling/grammar errors. Then if everything looks alright and it was pretty useful information I used easybib to cite it. This challenge was really fun and enjoyable to me. I learned a lot more about what’s happening to the Earth, and what ways we can do to reduce climate change. The only thing that I would change is that I wish that we had more time to do it.

Sources

Jackson, Randal. “Climate Change Causes: A Blanket around the Earth.” Edited by Holly Shaftel and Susan Callery, NASA, NASA, 8 Aug. 2018, climate.nasa.gov/causes/.

Jackson, Randal. “Global Climate Change: Effects.” Edited by Holly Shaftel and Susan Callery, NASA, NASA, 16 July 2018, climate.nasa.gov/effects/.

Suzuki, David. “Top 10 Things You Can Do about Climate Change.” David Suzuki Foundation, BriteWeb, 3 July 2018, davidsuzuki.org/what-you-can-do/top-10-ways-can-stop-climate-change/.

Rood, Richard B. “If We Stopped Emitting Greenhouse Gases Right Now, Would We Stop Climate Change?” The Conversation, 19 Sept. 2018, theconversation.com/if-we-stopped-emitting-greenhouse-gases-right-now-would-we-stop-climate-change-78882.

Jackson , Randal. “Global Climate Change: Effects.” Edited by Holly Shaftel and Susan Callery , NASA, NASA, 16 July 2018, climate.nasa.gov/effects/.

Couldn’t cite this one but here is the link.

https://environmentaldefence.ca/2018/03/29/11-actions-fight-climate-change/?gclid=EAIaIQobChMInOGjvZeZ3gIVjFuGCh15-g5KEAAYAiAAEgJQRfD_BwE

Aquatic Field Studies

jessicam2018 on October 15, 2018

Our class went outside on some days and measured the temperature of the pond. We got a lot of numbers and then calculated our water quality. We learned stuff about water quality parameters and then tested a local water way. We also learned about invertebrates which live in waters and then searched for them in 2 waterways. The Coquitlam River, and the Oxbow pond. Ours said that the water could be better, but it was good already. That means the health of the pond was ok. We found 3 damselfly nymphs. Water quality is related to the things that live in it, because some of them could live in like very clean water, and then some can live in both clean and not so clean water. So then after that, we went to the Coquitlam river. One person from each group would put on lifejackets and other stuff and get a net, and scrap rocks to see if they could get something. Our group found 3 stonefly nymphs. It was creepy, it looked like it was running in water and then the legs were so fast. What I learned from this activity was that the water quality can affect what lives there. There are category one, two, and three types. Where one, means the water quality is good, and three means it can be good or bad. The Coquitlam River water quality, was index 87.2.

Digital Footprint

jessicam2018 on October 2, 2018

Computer Digital Citizenship - Digital Footprint Image result for digital footprint

Image result for digital footprint

How might your digital footprint affect your future opportunities? Give at least two examples.

It might affect your career. Like when you apply for job, the person who hires you might try to google you.
It might affect your education. Your teacher might find something about you online.
It might affect your life

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

Don’t put your real name for everything
Think before you post something
Use strong passwords
Post positive stuff

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

Everyone can see what you post.
Whatever you post might affect your future.
Including Instagram, Facebook, Youtube, Snapchat, etc.

Image result for stay safe

Pictures are not mine – Credit to

https://www.teacherspayteachers.com/Product/Computer-Digital-Citizenship-Digital-Footprint-2188504

https://www.videoblocks.com/video/digital-footprint-animated-word-cloud-text-design-animation-sgfnviwahej0zjow2m

https://www.virtuallibrary.info/digital-footprint.html

Digital Footprint

https://slideplayer.com/slide/10865801/

https://www.georgetownisd.org/Page/18759

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