Category Archives: Grade 9

Everything I Know About Exponents

Posted on by under Math 9

1) Represent repeated multiplication with exponents:

2 x 2 x 2 x 2 x 2 = 2^5

2) Describe how powers represent repeated multiplication

In the previous example, the base is 2 because that’s the number that your multiplying and the exponent is 5 because that’s the number of times the base multiplies by itself.

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

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

2 x 2 x 2 = 2^3

3 x 3 = 3^2

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

The exponent tells you how many times to multiply the bases together some examples…

7^2 = 49

3^4 = 81

5^5 = 3125

2^9 = 512

1^{363} = 1

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

The parentheses are placed in powers to differentiate coefficients from integer bases.

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

(-2^4) = -1 x 2 x 2 x 2 x 2 = -16

-2^4 = -1 x 2 x 2 x 2 x 2 = -16

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

When your multiply powers with the same base, you can keep the base and add the exponents (Product Law). For example…

2^2 \times 2^3 = 2^{2+3} = 2^5

When your dividing powers with the same base, you can keep the base and subtract the exponents (Quotient Law). For example…

2^5 \div 2^2 = 2^{5-2} = 2^3

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

The power rule is that you keep the base, multiply the exponents together and you raise the coefficient to the exponent. For example…

[(2)(4^3)]^2 = [(2) (4^{3 \cdot 2})] = (4)(4^6) = (4)(4,096) = 16,384

9) Explain the law for powers with the exponent 0.

Anything to the power of zero will equal 1 because…

2^5 = 32

2^4 = 16

2^3 = 8

2^2 = 4

2^1 = 2

2^0 = 1

Every time the exponent decreases the answer divides by it’s base.

10) Use patterns to show that a power with the exponent 0 is equal to 1.

2^5 = 32

2^4 = 16

2^3 = 8

2^2 = 4

2^1 = 2

2^0 = 1

Every time the exponent decreases the answer divides by it’s base so the answer for any power with the exponent zero has to equal 1 unless 0 is the base because 0 \div 0 = 0.

11) Explain the law for powers with negative exponents

When there is a negative exponent in a power you must reciprocal the base and make the exponent positive.

Here are a couple examples:

2^{-3} = \frac {1}{2^3} = \frac {1}{8}

\frac {3}{y}^{-2} = \frac {y}{3^2} = \frac {y}{9}

12) Use patterns to explain the negative exponent law.

Like said in 10) every time the exponent decreases the answers divides by it’s base. So once the pattern gets to 0 and starts to go down to the negatives the pattern continues. In this case every time the exponent decreases the answers divides by 2. (See image below)

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

Example 1: Product Law

2^3 x 2^2 = 2^5 = 32

b \cdot b^2 = b^3

Example 2: Quotient Law

9^3 \div 9 = 9^2 = 81

y^8 \div y^7 = y^1 = y

Example 3: Powers Law

(5^2)^2 = 5^4 = 625

(x^2)^3 = x^6

Example 4: Zero Exponent Law

134^0 = 1

k^0 = 1 or possibly 0 if k = 0

Example 5: Negative Exponents Rule

3^{-2} = \frac {1}{3^2} = {1}{9}

x^{-6} = \frac {1}{x^6}

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

Here are some examples of simplifications of expressions and their errors;

Example 1: 4^3 x 4^4 = 16^7 = 268,435,456

The error in this example is the very first step. When using the product rule you add the exponents and keep the base. You do not multiply the bases.

Example 2: 2^4 x 4^3 = 8^7 = 2,097,152

In this example the bases of the powers are not the same so you cannot do the product rule. You must do BEDMAS.

Example 3: y^8 \div y^4 = y^2

In this example you can do the quotient rule because the bases are the same but in the quotient rule you subtract the exponents. Do not divide.

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

4^2 \div 2^2 + [(2)3^2 + 3^2]

= 16 \div 4 + [(2)9 + 9]

= 4 + (18 + 9)

= 4 + 27

= 31

In the example above I used BEDMAS

16) Determine the sum and difference of two powers.

There are no shortcuts for subtracting and adding powers. You have to use BEDMAS.

Sum: 3^2 + 4^2 = 9 + 16 = 25

Difference 4^3 - 2^5 = 64 - 32 = 32

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

Incorrect example

9^2 + 4^2 \div 2^2 - 3^2

= 81 + 64 \div 4 - 9

= 145 \div 4 - 9

= 36.25 - 9

= 27.25

In this example the exponents are evaluated first which is correct but in the second step 81 and 64 are added and the rest of the equation was solved left to right which is incorrect. After exponents is division so you must divide 64 by 4 first and then add and subtract left to right.

Corrected Example:

9^2 + 4^3 \div 2^2 - 3^2

= 81 + 64 \div 4 - 9

= 81 + 16 - 9

= 97 - 9

= 88

18) Use powers to solve problems (measurement problems)

Find the area of the coloured area in the picture below.

img_3542

6^2 - (2^2 + 1^2)

= 36 - (4 + 1)

= 36 - 5

= 36cm^2

19) Use powers to solve problems (growth problems)

Example, In Science class the students made expanding goo and every 10 minutes the size of the goo doubled. They started out with 5ml of goo, how much goo was there after…

A) 10 minutes: 5 \cdot 2 = 10ml

B) 30 minutes: 5 \cdot 2^3 = 40ml

C) 1 hour: 5 \cdot 2^6 = 320ml

D) y hours: 5 \cdot 2^y = yml

20) Applying the order of operations on expressions with powers involving negative exponents and variable bases.img_3559

 

 

 

Song Analysis

Posted on by under English 9

 

Here is my analysis of my song of choice…

“Let Her Go” by Passenger

Well you only need the light when it’s burning low
Only miss the sun when it starts to snow
Only know you love her when you let her go

Only know you’ve been high when you’re feeling low
Only hate the road when you’re missing home
Only know you love her when you let her go
And you let her go

Staring at the bottom of your glass
Hoping one day you’ll make a dream last
But dreams come slow and they go so fast

You see her when you close your eyes
Maybe one day you’ll understand why
Everything you touch surely dies

But you only need the light when it’s burning low
Only miss the sun when it starts to snow
Only know you love her when you let her go

Only know you’ve been high when you’re feeling low
Only hate the road when you’re missing home
Only know you love her when you let her go

Staring at the ceiling in the dark
Same old empty feeling in your heart
Cause love comes slow and it goes so fast

Well you see her when you fall asleep
But never to touch and never to keep
Cause you loved her too much and you dived too deep

Well you only need the light when it’s burning low
Only miss the sun when it starts to snow
Only know you love her when you let her go

Only know you’ve been high when you’re feeling low
Only hate the road when you’re missing home
Only know you love her when you let her go
And you let her go
And you let her go
Well you let her go

Cause you only need the light when it’s burning low
Only miss the sun when it starts to snow
Only know you love her when you let her go

Only know you’ve been high when you’re feeling low
Only hate the road when you’re missing home
Only know you love her when you let her go

Cause you only need the light when it’s burning low
Only miss the sun when it starts to snow
Only know you love her when you let her go

Only know you’ve been high when you’re feeling low
Only hate the road when you’re missing home
Only know you love her when you let her go
And you let her go

Imagery and Figurative Language:

Hyperbole – “Everything you touch surely dies” This is a hyperbole because everything you touch doesn’t actually die. You can’t kill anything by just touching it, it’s just an exaggeration.

Alliteration – “Only miss the sun when it starts to snow” There is a repeating “s” sound in sun, starts, snow.

“Staring at the ceiling in the dark” is an example of imagery because it creates an image in your head and you can visualize what the lyrics are telling you.

Repetition – In the song there are lot of lines are repeated like “And you let her go”.

Tone, Attitude:

  • The tone is sad and heartbroken
  • meaningful phrases/ words like, “loved her too much”, “dived too deep”, “hate the road” , “missing home” , “hoping” and “empty feeling in your heart.”
  • The words and the tone in his voice gives the songs tone/ attitude.

Style:

  • 14 stanzas/verses
  • Chorus rhyme scheme: AAA ABAA
  • Verse rhyme scheme: AAA, BBB, CCC and so on until the chorus again

Interpretation:

  • You don’t realize what you have until it’s gone
  • ex. “only need the light when it’s burning low
  • Main idea in the song “only know you love her when you let her go”

 

Song Analysis Paragraph

The song “Let Her Go” by Passenger has a lot of meaning and he uses lots of comparisons to help show the deep meaning. He expands on the statement that you don’t realize what you have until it’s gone with all of these comparisons to the main idea; “Only know you love her when you let her go.” The song also contains lots of figurative language and imagery. “Everything you touch surely dies” is a hyperbole because you can’t kill everything by just touching it. He is trying to say that whenever you get involved in something you accidently mess it all up. In the song he expresses how much he regrets letting her go with his heartbroken and sad tone as well as repeating “let her go” many times, an example of repetition. Another piece of figurative language he uses is alliteration with a repeating ‘s’ sound; “only miss the sun when it starts to snow.” The alliteration in this song seems to help with the flow of the lyrics. An example of the descriptive imagery he uses is, “staring at the ceiling in the dark, same old empty feeling in your heart.” In that example he creates an image using your sight and feeling. Passenger’s song has 14 stanza’s or verses and the majority of them has a rhyme scheme that goes aaa (low, home, go) bbb (glass, last, fast) ccc (eyes, why, dies) and so on. To sum everything up, the song “Let Her Go” by Passenger is a very poetic and meaningful song with a main point; you don’t always realize what you have until it’s gone.
 

 

 

Science App Review

Posted on by under Science 9

Define/Discover: The problem is that I want to know the anatomy of the human body. Does this app cost money to download? How will this app help me learn the anatomy of the human body? Is this app actually going to help me with my learning?

Dream: If I could get an app that’s free and helps me learn the anatomy of the human body I won’t have to deal with searching everything up on the internet and struggling to find what I was looking for. I could easily find everything I need in a single app and I won’t have to worry about connecting to Wi-Fi either. With an app that can help me I could have a much better understanding of the anatomy of the human body.

Design: My plan is to search the web and the app store to find a free app that could possibly help me or anyone learn the anatomy of the human body. I will download any possible apps and see if they have what I need and if they are easy enough to use. I will then decide which app would be most helpful and useful for my learning.

Deliver:

The app that I am using is called BioDigital Human and it is free to install. It provides 3D anatomy and health condition models like the lungs, the heart, the musculoskeletal system and much more. It has many useful features; you can focus on certain small parts. For example, if you wanted to know what a specific part was called then you can simply select the part and the app will give you the name as well as a thorough description of the part.

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There are also different ways you can view the 3D models. Standard, X-ray and Isolate.

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If you really wanted to, the app lets you dissect/remove parts of the model so you can look inside.

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There is so much more you can do with this app like draw so you can circle parts that you might want focus on or maybe a write a quick note. The app will even make a quiz for you with the option of easy or hard and you can even select the how long you want the quiz to be as well. So have fun and play around with the app.

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Debrief: Overall, I think that this app can be very useful for all grade’s. I find that it is simple to navigate, it has all the features needed plus extra features that could provide extra help as well. I have also realized that this app is great for people who learn by looking at pictures (models) because it provides amazing 3D models that you can view. When I found this app I thought it went beyond my expectations because all of the extra features although it would benefit if were available on Android and other systems other than just iOS. This app is a great find and I’m sure it will help me now and in the future.

 

 

 

 

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