Math 9 – Caitlin’s Blog

What I Learned About Grade 9 Linear Relations

On June 6, 2020

What is a Linear Relation?

A linear Relation is a pattern that goes up or down by the same amount every time.

How to Find the Rule for a Pattern?

When trying to find the rule for a pattern you need to look for how much the y list is going up or down by. If it was going up by +4 then it would be multiplied by x, to become 4x=y. But that wouldn’t equal 5. So, to get it to 5 we will have to add +1 to the equation. It should look like this 4x+1=y. now you can use this equation to keep the pattern going.

How to Plot a Point?

When you have numbers on either side of the T-chart you could be able to plot them on a graph. The number under x will determine where the along the x-axes you dot will go. Same for the y, it will determine how high up the dot will be.

How to Graph a Linear Relation?

The coordinates on your t-chart should make a straight line when all placed on a graph.

How to Graph Vertical and horizontal lines?

To create a straight line all you need is a number=x or a number=y. If you want it to go up and down 3 to the right of zero, then you would put 3=x. Same thing would happen with y but it would go across.

Vocabulary:

X axes: The horizontal line on a graphing chart
Y axes: The vertical line on a graphing chart
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: It is a fixed place on the graph, aka the middle of the graph or (0,0).
Plotting: To put your coordinates on a graph
Linear pattern: When your coordinates have a pattern going up or down and it looks like a slanted straight line.
Increasing pattern: When your pattern goes up
Decreasing pattern: When your pattern goes down
Horizontal line: The X-axis/the line that goes across
Vertical line: The Y-axis/the line that goes up and down

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Math 9 Core Competencies Reflection

By Caitlin

On December 17, 2019

In Math 9

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What I learned about grade 9 Polynomials!

By Caitlin

On December 14, 2019

In Grade 9, Math 9

What is a polynomial

A polynomial is an expression, made from variables and coefficient. Variables can be showen as letters to separate them from the numbers.

Vocabulary

Degree-The degree is the biggest exponent in the expression.

Constant-The constant term is the term that does not change, if the variable changes.

Coefficient-The coefficient is a number quantity placed before and multiplying the variable in an algebraic expression, like (4 in 4x²)

Binomial-A binomial is an expression with two Coefficients. For example (5x+3)

Trinomial-A Trinomial is also an expression about, but except of two coefficients, there is three. So in stead of (5x+3) a Trinomial looks like (2x²+3x-8)

Monomial-For monomial it is only one like (6x)

How to use algebra tiles

Adding polynomials

When adding polynomials, you have to organize all the numbers that have like terms. When you have them grouped, then you just simply add the coefficients together.

8x+4+3x+2x+7

8x+3x+2x 4+7

=13x+11

Subtracting polynomials

When subtracting, do the same thing as with adding but after sorting just subtract instead. But if you have a bigger number subtracting from a smaller number you will have to go into the negatives. ( It becomes negative, you have to switch out the plus sign for a subtract sign)

8x-4-3x-2x-7

8x-3x-2x 4-7

=3x-3

Multiplying polynomials (distributive)

When multiplying, it will look something like this 5(3x+4) but when you multiply, you will writ it out as 5×3x and 5×4. Then will end up with 15x+20. But if you have something like 2x+5(3x+4) you will have to multiply the numbers with like terms, like in adding and subtracting. (2x)(3x) and (5)(4) = 6x+20

If you have an exponent on the multiplier and none on the bottom, it will change the exponents on the variable. I there is a exponent on both then you add the two exponents together. (Remember if there is just a variable and no exponent, then the exponent is 1)

Dividing polynomials

when dividing polynomials I like to write mine out as a fraction like $\frac{6x+4}{2}$ whereyou have to start off by spitting the top part in half $\frac{6x}{2}$ and $\frac{4}{2}$ then divide and after you will put the two results together. $\frac{6x}{2}$ and $\frac{4}{2}$ = 3x+2

If you have an exponent on the numerator and none on the bottom, it stays the same. If there is a exponent on both then you subtract the denominators exponent from the numerators.

Connections from Previous Units (Exponents and Rationals)

In this unit we used different concepts from the beginning of the year that we did during this. Like in our exponents unit we learned all about them so when it came to this unit we knew what we needed to do with them.

What I have learned about grade 9 exponents!

By Caitlin

On November 16, 2019

In Math 9

What is an exponent?

An exponent is a number that tells you how many times to multiply a number by itself. Like 5³=5×5×5=125.

What is the difference between evaluating and simplifying?

The difference between evaluating and simplifying is that when you are evaluating you are actually solving the question and solving what the power makes the base.

5³×5⁴=5³⁺⁴5⁷=5×5×5×5×5×5×5=78125

But if you are simplifying then all you do is add/subtract/multiply the exponents together.

5³x5⁴=5³⁺⁴=5⁷

But simplifying only works if the bases are the same.

Multiplication law and why it works?

The multiplication law is basically just if you have the same base you leave it and you add the exponents together

5³x5⁴=5³⁺⁴=5⁷

This is also the same as if we

(5x5x5)(5x5x5x5)=5⁷

It works because if you do the math it goes, 5³=125 and 5⁴=625 so then we go 125×625=78125. But if you punch 5⁷ into your calculator it will also come up with.

Division law and why it works?

When dividing it is basically the opposite of multiplying because instead of add the exponents you are subtracting. So if you have

$\frac{5^5}{5^2}$

you just subtract the exponents like

5^5-2=5³

This can also be written out as

(5×5×5×5×5)/(5×5) = (5×5×5×5×5)/(5×5) = 5³

Power of a power law and why it works?

when using the power law you can have a base number and an exponent together in a pair of brackets with an other exponent outside, like

(5³)⁴ = 5^3×4

If you wrote it out in expanded form it would look like this

(5x5x5)(5x5x5)(5x5x5)(5x5x5) = 5¹²

Applications of exponents?

In the future I might use exponents, at some kind of building job and I needed to take measurements of my materials. To make it square I would be able to write 5cm² instead of 5cm by 5cm².

One more thing you learned about exponents?

One thing that I learned from this unit was that when you are dividing any number by 0 it will equal 1.

TOKTW 2019

By Caitlin

On November 12, 2019

In Math 9, Uncategorized

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This contraption goes under the water and the 6 capsules on the sides open up and suck in water samples.

This is the lab that my Mom used to work at when I was younger.

During our tour the group was allowed to go onto the roof of the 29 floor building.

The tour also lead us to the sever room where all of the memory from the company gets stored.

What I learned about grade 9 Fractions

By Caitlin

On October 19, 2019

In Math 9

In our unit we learned how to put fractions on a time line:

We would have to make them all have a common denominator. Then organize them by size. On the time line the jumps in between each whole number would be the same as the denominators of the fractions.

$\frac{2}{3}$ = $\frac{4}{6}$ $\frac{-4}{2}$ = $\frac{-12}{6}$ $\frac{6}{2}$ = $\frac{18}{6}$

We would have two different fractions, then we would have to figure out which one is greater using the greater or lesser signs. Like

$\frac{-3}{4}$ > $\frac{-2}{3}$

I thought that I had a bit more of a difficulty when we put integers in the mix, because some times I would forget to add the sign in when I was doing my calculations.

We did add/subtracting of fractions, I was basically just creating a common denominator between the two fractions, then adding or subtracting the numerator.

$\frac{3}{8}$ + $\frac{2}{4}$

$\frac{6}{16}$ + $\frac{8}{16}$

$\frac{6+8}{16}$ = $\frac{14}{16}$

$\frac{14}{16}$ can also be reduced to make $\frac{7}{8}$

You can also do the same for subtracting

$\frac{3}{8}$ – $\frac{2}{4}$

$\frac{6}{16}$ – $\frac{8}{16}$

$\frac{6-8}{16}$ = $\frac{-2}{16}$

I felt pretty confident before we started, so I knew most of the strategy’s. But once we finished that we did multiplying and dividing fractions. Multiplying was pretty easy because all you had to do was multiply the numerators together and multiply the denominators.

$\frac{5}{6}$ × $\frac{2}{4}$

(5×2)=10 (6×4)=24

$\frac{10}{24}$

(10÷2)=5 (24÷2)=12 = $\frac{5}{12}$

But when you are dividing you can us the cheat where, you can rewrite it as a multiplication question. You flip the seconded fraction and you multiply.

$\frac{18}{24}$ ÷ $\frac{6}{9}$

$\frac{18}{24}$ ÷ $\frac{9}{6}$

(18÷9)=2 (24÷6)=4

$\frac{2}{4}$

(2÷2)=1 (4÷2)=2 = $\frac{1}{2}$

One thing that I learned that I am definitely going to use in the future that you can take a whole number, and make it $\frac{Whatever}{1}$ . I don’t know why I didn’t know this before, but I know it now and I am going to use it in the future.

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Tag: Math 9

What I Learned About Grade 9 Linear Relations

Math 9 Core Competencies Reflection

What I learned about grade 9 Polynomials!

What is a polynomial

Vocabulary

How to use algebra tiles

Adding polynomials

Subtracting polynomials

Multiplying polynomials (distributive)

Dividing polynomials

Connections from Previous Units (Exponents and Rationals)

What I have learned about grade 9 exponents!

What is an exponent?

What is the difference between evaluating and simplifying?

Multiplication law and why it works?

Division law and why it works?

Power of a power law and why it works?

Applications of exponents?

One more thing you learned about exponents?

TOKTW 2019

This contraption goes under the water and the 6 capsules on the sides open up and suck in water samples.

This is the lab that my Mom used to work at when I was younger.

During our tour the group was allowed to go onto the roof of the 29 floor building.

The tour also lead us to the sever room where all of the memory from the company gets stored.

What I learned about grade 9 Fractions

Riverside Links

My Tags