Archive of ‘Math 9’ category
What is a Linear Relation?
A Linear Relation is an equation that when graphed makes a straight line. It makes it simple to check if your answer is correct if your line is not straight or you cant put a line through your plots you’ve done it wrong.
How to Find the Rule for a Pattern
When you’re trying to find the rule for a pattern you should start by seeing how much it is going up or down. In this case, it is going up 2 so that becomes the first number you use ( in front of the x ). Next you need to see what you do to x times the number to get your y. In this case 2 times 1 is 2 and plus 1 is 3. so your final equation would be 2x + 1 =y.
How to Plot a Point
When you are plotting points it’s important to keep double-checking. With the graphs it’s easy to miscount and put something in the wrong place. The x value is where you should look first the x-axis is the Horizontal line, You just look across it for the number you have. Then you take your y value and look on the vertical line for that number and plot it down at the hight of y and length of x.
How to Graph a Linear Relation
A linear relation is when your equation makes a straight line. As long as you have plotted correctly you w
ill get your straight line
How to Graph Vertical and horizontal lines
When you are given a rule that is just a number = x or a number = y it means it is going to be a straight line. When given a question like this you just find that one spot on the graph for example 2 on the x-axis and put your line there.
Vocabulary:
- X and Y axes: The different lines on a graph, x is horizontal y is vertical.
- T-chart: The chart you put your coordinates into to help organize and come up with an equation.
- Coordinate: The location your plot is on the graph. An example of a coordinate is (2,4)
- Origin: The middle of the graph or (0,0). It is a fixed place on the graph.
- Plotting: Plotting is to put your coordinates on a graph.
- Linear pattern: When your coordinates have a pattern going up or down and it results in a slanted straight line.
- Increasing pattern: When your pattern goes up.
- Decreasing pattern: When your pattern goes down.
- Horizontal line: the X-axis and the line that is flat.
- Vertical line: the Y-axis and the line that is going straight up.
Something I learned that wasn’t mentioned
I learned that when plotting you can skip numbers on the x-axis. Before I thought that you had to have one on each number of the x-axis but it turns out you don’t.
What is an Inequality?
A inequality is an equation where instead of the = sign you have <,>,≤,≥
What do the symbols mean?
< This is the greater than symbol, if you see this it means that what is on the right side is larger then what is on the left
> This is the Less than symbol, if you see this it means that what is on the left side is larger then what is on the right.
≤ This is the Greater or equals to symbol, if you see this it means that whatever is on the right side of the symbol is larger or the same as what is on the left side.
≥ This is the Less then or equals to symbol, if you see this it means that whatever is on the left side of the symbol is larger or the same as what’s on the right side.
How to solve Inequalities
You solve inequalities the same way you would solve an equation. Using legal moves to get your final answer. For my example, I have 6p+2 < -112 . First, I took away 2 from each side making the question 6p < -114. Next I divided both sides by 6 to get p< – 19.
How to check your Answer
Checking your answer is also the same way you would check your answer with an equation. On the question above I got -19 as my answer. To check if I got the right answer you put -19 in the place of p making the question 6 (-20) + 2 < -112. First I multiplied the 6 and -20 on the left to make the question -120 + 2 < -112. I added up the -120 and 2 on the left to make the question -118 < – 112. From this you just have to see if this is a true statement. In this case -118 is smaller then -112 so the statement is correct making the answer correct.
How to graph inequalities
There are two important parts to remember when putting inequalities on a number line. Firstly is to pay attention to which way the signs are facing. If you are plotting something with a < your lines go to the left. If you are plotting something with a > your line goes to the right. Secondly you have to pay attention to whether your inequality has a line underneath it. If your inequality has ≤ or ≥ then you need to leave your mark for example on a 9 empty in the middle or uncolored in.
What is an equation?
An equation is a mathematical expression that has an equals sign.
What are equivalent equations
Equivalent equations are two equations that have the same answer or roots when solved.
How to solve equations (find what x = ?)
~Visually with algebra tiles
Solving equations with algebra tiles is to me the most confusing way of solving equations. The x piece represents any X’s in the equation and the one piece represents the hole numbers in the equations. Solving equations have a few key rules, if you stick to these rules you should never get a wrong answer. Firstly if you add something to one side you have to add the same thing to the other side.
~Algebraically
Algebraically is almost the same as using algebra tiles, the only difference is instead of tiles or shapes you are using numbers.
~BFSD (brackets, fractions, sort, divide)
BFSD is like the BEDMAS of equations. BFSD is the order in witch you should solve equations to get them correct. First you look at the brackets and solve anything in brackets ( if there are no brackets you can just skip this ) next you look to see if the question has any fractions, if so you solve those next. After you sort your question so it is easy to answer. Lastly you dive to get your final answer.
How to verify (Check) a solution (answer) is correct
Once you have solved your question you take the answer to how much a X is valued at and fill it into all the X spots in the original question. Sole once side at a time and if you get the same answer on each side you did your question correctly.
Vocabulary
Equation: A math question where both sides of the = sign are equal. For example 6 + 10 = 16 or x2 + 4 = -7 + 2x
Equivalent: Two numbers or equations that are equal in value, function or meaning
Solution: The answer to a equation
Coefficient: The number before a variable ( X, Y, Z etc )
zero pairs: Adding or subtracting a number or variable by itself to get 0, canceling it out.
Variable: An unknown number represented by a letter.
Constant: A whole number with no variable attached.
common denominator: When adding or subtracting compare multiples of the denominator to find a common denominator, this makes it easier to solve.
Distribute: spreading something out. Mostly seen in multiplying a number by all the contents inside a set of brackets.
What is a polynomial?
A Polynomial is a question including multiple terms. A term could be a single number or variable.
Polynomial Vocabulary
- Degree:The largest exponent of all the terms ( Each term is added together ) .
- Constant: A term in the question that does not change.
- Coefficient: The number in front of a variable used to multiply with the variable.
- Leading coefficient: The first coefficient in a question.
- Binomial: A polynomial with two terms.
- Trinomial: A polynomial with three terms.
- Monomial: A polynomial with one term.
How To Use Algebra Tiles
Adding Polynomials
Adding polynomials is more like sorting then anything. To add polynomials you find same variables and add them together. Since you don’t know the value of the variable this works, if i where to say that x = 4 then this no longer works and you have to fill in all the x’s with 4’s.
Subtracting Polynomials
To subtract polynomials you have to remove brackets first. the rule’s with subtraction are easy to remember anything in the bracket after the subtraction line becomes reversed, if it was a positive number it would turn into a negative number and if it where negative it would turn positive. after you re write the question you can simplify by adding.
Multiplying Polynomials
Multiplying polynomials was also a lot simpler then i thought it would be. in the photo we have the question 4 (3x² + 2x) for this question you would multiply 4 and 3 and get 12. then you add the x² onto the end to get 12x² and for the 4 x 2x the answer would be 8x. It is pretty much the same if the number outside the bracket has a variable for 3x²y (2xy – 3xz) each variable has a invisible ¹ , and since we are multiplying we can use the multiplication law and add the two exponents. For the 3x²y x 2xy you can add the invisible ¹ to make the answer 6x³y and continue like that for the rest of the questions.
Dividing Polynomials
Dividing polynomials is pretty similar to multiplying polynomials in the scene that your multiplying and dividing . when you divide a polynomial you divide the bottom number with the top number. and then add the variable to the end. for example you would divide the 4 and the 2 to get 2 then add the 4x². If there is a variable on the bottom you do the same thing as multiplication but subtract the exponents.
Connections between polynomials and past units
There is definitely a large connection between the current unit and the past units. This unit connects the most to exponents, since some variables have exponents i think if this unit was before exponents it would have been a lot more confusing.
What is a Exponent?
A exponent is a small number that would be above a number for example a³ it is a short way of saying a x a x a. You can re-write a exponent as a whole number by multiplying the bottom number as many times as the number on the top in this case a x a x a. Using that question again lets say a is 5. you would do 5 x 5 witch is 25 then multiplying 25 by 5 to get 125.
What is the Difference Between Evaluating and Simplifying?
Evaluating is a term that is used in math books instead of the word solve. simplifying means to fix the question make the question your working with simpler so it is easier to solve, some places you might simplify are; multiplying fractions or making your final fraction smaller. The difference between evaluating and simplifying is large because they really are super different things. Solving a question and making it smaller are two different things, but i guess if i were to try to find a common ground between the two i would have to say with both your trying to solve the question.
Multiplication Law and why it works
The multiplication law is used for multiplying numbers with exponents, first you look to see if the bottom numbers are the same if they are you can continue. the law only works if the bottom numbers are the same. next look at the top numbers and add them together to get your final answer. the bottom stays the same. this law only works if the bottom two numbers are the same.
Division law and why it works
The division law is almost the same as the multiplication law. the bottom says the same, the only difference is you subtract the two exponents instead of the top. and again this only works if the bottom two numbers are the same.
Power of a power law and why it works
The power-law is a law that is used when you get a question like (4³)³ . in this case you need to multiply the 3 and the 3, the bottom number stays the same.
applications of exponents
Exponents are like fast/simpler ways of writing a number times itself __ times. instead of writing 3 x 3 x 3 you can write 3³. Exponents are used
one more thing i learned about exponents
I learned that there is no shortcut when adding and subtracting exponents ,you have to solve the exponent then work with that. Its annoying but its the only way to do it.
Home phone line wires
Driving around to fix telephone cables.
Name of your host: ______Paul Bernat______ Relationship to you: _____Father_____
The Interview: (ask your host these questions)
- What is your job title? _____TELUS Network Technician working in the Frames(copper jumper work)____
- What is your job description?__Complete TELUS inside orders that provide Telephone, Internet, TV to customers so that our Installation & Repair Technicians (I&R) can do the work at Customer premises.
- What are the duties and/or tasks you perform at your job? Complete jumpers orders at TELUS Central Offices, Drive to Remote Offices to complete jumper orders, Jumper orders at the TELUS SAC boxes that are closer to the customer, receive phone calls from I&R Techs to troubleshoot not working customer circuits or run in a missed order for I&R, at TELUS Stores do Firmware upgrades on TELUS Security panels to save customer facing Technicians time during setup at customer premises.
- What qualifications do you have for this job in the following areas:
- a) training? ___On the job training, training new employees, classroom training, online courses
- b) education?__1988 Graduated from College of New Caledonia with Diploma of Electronics Engineering Technology, education courses at the TELUS Education Center, Online courses.
- c) experience? _31 years combined employment at TELUS(including time at BCTel) with
9 years as an Inside Equipment Installer, 7 years as a Central Office Switchperson, and
15 years as a Network Technician in the Central Office Frames
- d) skills and attributes (personal qualities)?_Self starter, self motivated, quality workmanship,
skilled with hand tools, do the job correctly the 1st time, can learn any new skills. __________
- What are some of the things you like about the job? Can work independent of others, set my own pace, do the job well and you are left alone limited supervision, can listen to music/podcasts on headphones while working, new TELUS services creates new types of work to add variety, occasional overtime to earn extra income, good benefits and vacation time, employee discounts.
- What are some of the things you dislike about this job? _Can be repetitive in the work done day to day, some days there is too much work or sites to complete in a workday, most Managers are great but the odd one can make your work life unbearable.
- How do you anticipate this job changing in the next 5 years or so? _As TELUS migrates from Copper Wiring to Fibre Optics at the customer premise the type of work will change to Fibre patch cords for the connections.
Other question (s): ______________________________________________________________________________
Student Reflections:
- Give three reasons why you would like this job (be specific):
- a) You can listen to music while you work, which would be nice for long days since it can help the time pass faster.
- b) You don’t really have to talk to anyone, other than a good morning or can you help me with ___?
- c) The job was easy to understand after awhile and was not too confusing.
- Give three reasons why you would not like this job (be specific):
- I don’t have much interest in phone wires so i feel it wouldn’t be a fulfilling job for me. I would always zone out or get distracted because I don’t have a real interest in what im doing.
- My dad’s work had this machine that makes a clicking noise all day and I was getting really annoyed at it, i feel if i worked there I would go crazy over the constant clicking.
- c) In ways yes, having to not talk to anyone is good. whoever I like to socialize so i think having little to no people would be bad for me because even if i just say something every little but hours upon hours of no contact seems agonizing.
- Is this job for you? Why or why not?
I don’t think the job is for me, like I said before, I don’t have much interest in the type of work my dad is doing so going to school just to do a job i have no interest in would leave me bored every day.However driving around all day was nice because you never had to sit still for long.
- Explain the value of the TOKTW experience in relation to your ideas about your post secondary (after high school) plans (education?, training?, travel?, work?).
I think this is a valuable experience and it did make me think about possible jobs i would want to do after high school, I had always been curious what exactly my dad did. I had a brief idea but I had always wanted to go with him for a day and just see what he did daily for 30 years. It also made me realize I want a job that i can stay at for years that will keep me preoccupied and interested in what im doing, my dad seemed so content with what he was doing so i can see how he did it for so long.
Final Reflection
All in all my day with my dad went better then a thought it would. In all honesty i though he would tell me to wait in the car well he did his jobs, but he exceeded my expectations and let me help sometimes. He talked to me a lot more then i though, he even tried to make jokes wich was not something he does much at home.His work was different then what i though it was. i was under the impression he fixed those big boxes on the side of the street ,he actually puts in or takes out jumper cables (?) in buildings. I had fun on the day with my dad and i wish i was feeling better that day, i felt nauseous and had a bad stumic ache all so i spaced out for most of the day witch i’m regretful about. If i ever get the opportunity again to go with my dad again i would %100 say yes because i wanted to enjoy it more then i was able to.
What I Learned About Grade 9 Fractions
What have i learned about grade 9 fractions? Well a lot! fractions are not exactly a strong suit of mine so i found this unit rather hard, but it taught me a lot to.
adding and subtracting fractions
In the past i had never quite figured out adding and subtracting fractions. For adding subtractions you look at the denominators. Are they the same? if they are you can simply add the top numbers together and keep the bottom number the same. Beside this is a photo of how i would add fractions with the same denominator.
However if the denominator is different there are more steps to getting your final answer. When i go to find the bottom number, i write down the number and then multiples of that number ( like 4,8,16,32 extra). and find when they overlap like how 4 and 8 meet at 16 then 16 is the new denominator for the answer. then you have to multiply the top number by what you had to multiply the bottom by. then add the wto together and you have your answer.
When subtracting fractions you can follow the same rules. seeing fi the bottom is the same and if it is then it stays the same. the only difference is that you subtract the top. if the bottom is different its the same steps but subtracting the top.
Dividing and Multiplying Fractions
I learned that you can convert division questions into multiplication questions wich is really helpful for me since division is also something i’m not great at.
for division i normally just convert them into multiplication questions no matter what because i don’t really understand the division questions. to convert a division question to a multiplication question all you have to do is flip the second fraction.from there you can simplify if the opportunity is there.
Putting Fractions on the Number Line
I learned how to put fractions on the number line which to me was surprisingly not as confusing as i remembered it to be. You look at the first hole number first is it positive? is it negative? in this example it is positive so it would be to the right of the number line. you should look at the hole number first in this example it is a 1 so your answer will be between 1 and 2 on the number line. Now your left with 3/4 the four represents how many spaces are between the 1 and 2 and the 3 represents how many of those ‘spaces’ that fraction is on the number line.
Comparing Fractions With Unlike Denominators
i learned that when Comparing fractions with unlike denominators you should convert them into common denominators if the answer isn’t clear like 
and 
. for me i like to draw it out in circles, even though that is the way you do it in elementary school i find it helps me more.
One other thing i learned/converting mixed numbers into fractions
This unit i learned how to convert mixed numbers into fractions, first you multiply the hole number by the denominator, then add the hole number to the top.
To me my digital footprint is important because it stays worth me my hole life. Because it stays with you your hole life, nothing on the internet can really be deleted. When you go to get a job they look at that stuff, and mabye you thought you deleted that photo but your friends might have re posted it. Now an employer is looking at you fooling around acting silly, do you think they are going to chose you or someone with a clean footprint? I’d your applying for a scholarship they offen look at your social media,any inappropriate post or cyberbullying could stop you from getting the scholarship. 3 strategies for keeping your digital footprint safe: 1. Dont post anything inappropriate. This is a sorta simple step, if you wouldn’t show your parents then dont post it online. 2.Be nice. Dont comment negative things on others post, if your on Twitter I know it can be tempting to talk back to that person that insulted your fandom but by doing that your only starting negativity and Twitter fights wich is no fun. 3.Keep your private messages clean. They might have private in the name but that dosnt stop your friend from screenshotting your conversation.
If I could tell other students something I would tell them to be careful with the internet it is an amazing thing but it can also ruin people’s lives if they are not careful
ill get your straight line
