Alec's Algebra Post

How to Solve One Step Equations
Solving By Inspection
2+n=4
The first thing we're going to do is isolate the variable.
2+n-2=4-2
You may have noticed that I put a "-2" after the "4". This is because in algebra, what ever you do to one side, you must do to the other. This is called balancing the equation. Now all that is left is to solve.
n=2
One more thing, after you solve, you must verify your answer.
2+n=4 Since 4=4, we know that we got the correct answer.
2+(2)=4
4=4
Solving With Alge-Tiles
How to solve algebra equations using alge tiles

View more presentations from Alec Mojica.
How to Solve Two Step Algebra Equations
Solving by Inspection
2x+1=5
First, cancel the constant using opposites
2x+1-1=5-1
Instead of writing "2x+1-1" you could transpose.
2x=5-1
Now, you must simplify the variable. in our case, we must divide to simplify "2x"
2x/2=4/2
Similar to one-step equations, what ever you do one side, you must do to the other side. After doing all this, you get your answer.
x=2
Now we must verify our answer.
2x+1=5
2(2)+1=5
(4)+1=5
5=5
Now we'll try it using division.
x/2+2=5
x/2=5-2
(2)x/2=3(2)
x=6
Verify
x/2+2=5
(6)/2+2=5
3+2=5
5=5
Solving Using Alge-tiles
How to solve two step algebra equations using alge-tiles

View more presentations from Alec Mojica.

Alec's Great Big Book of Integers

Chapter One - Grade 7 Integer Review

-3-(-7)= 4

I used seven zero pairs because I did not have negative 7. I then took away the -7 and I found 3 more zero pairs. It left me with positive 4

-3-7= -10

I drew 3 negative chips then I drew 7 more.

3-7= -4

I drew -7 then drew +3. I found 3 zero pairs to find that I was left with -4.

3+7= 10

I drew 3 then i drew seven. My final answer was 10.

-3+7= 4

I drew seven then -3. I found 3 zero pairs which led me to an answer of 4.

Chapter 2 - Multiplying Integers

(+2)x(+3)= 6

+++ +++

2 groups of (+3)

(+2)x(-3)= -6

- - - - - -

2 groups of (-3)

(-2)x(+3)= -6

++ ++ ++ ----->

- - - - - -

Remove 2 groups of (+3)

(-2)x(-3)= 6

+++ +++

- - - - - - ------->

Remove 2 groups of (-3)

The Sign Rule for Multiplication (Negative Signs)

Whenever you there is an even number of negative factors, the product will be positive.

Whenever you there is an odd number of negative factors, the product will also be negative.

Chapter 3 - Dividing Integers

Partitive Division - When you use a number line to divide integers.

Example :

6÷2=3

-6÷ (-2)=3

Quotative Division - "Share" a number between a specific amount of groups

Example:

(-6)÷2= (-3)

Multiplicative Inverse - Rewriting a division question to a multiplication question. It helps you when you cant find a way to use quotative division or partitive division to solve an answer

Example :

6÷(-2)=(-3) Since I can not share 6 with (-2) groups, I use the Multiplicative Inverse

(-2)x(-3)=6

(-3)x(-2)=6

The Sign Rule for Division (Negative Signs)

The sign rule for division is pretty much the same as the one for multiplication, if there is an even amount of negative signs (-), your quotient will be positive. If there is an odd number amount of negative signs(-), your quotient will be negative.

Step-by-Step Examples:

6÷2= 3

1) I looked at both numbers and divided them (got 3)

2) No negative signs (0 = even number), this meant that it would be a positive number

3) My final answer was 3

-6÷ (-2)= +3

1) I looked at both numbers (not looking at signs) and divided them (got 3)

2) Two negative signs (2 = even number), this meant that it would be a positive number

3) My final answer was +3

(-6)÷2=(-3)

1) I looked at both numbers (not looking at signs) and divided them (got 3)

2) One negative sign (1 = odd number), this meant that it would be a negative number

3) My final answer was -3

6÷(-2)=(-3)

1) I looked at both numbers (not looking at signs) and divided them (got 3)

2) One negative sign (1 = odd number), this meant that it would be a negative number

3) My final answer was -3

Chapter 4 - Order of Operations With Integers

As we come to the end of this book, we talk about the Order of Operations with Integers. It's pretty simple to do, all you have to remember is one word:

B - Brackets

E - Exponents

D - Division

M - Multiplication

A - Addition

S - Subtraction

Division and multiplication, and addition and subtraction can be interchangeable since they are closely related.

Here is a step-by-step example:

(+5) x (-3) + (-6) ÷ (+3)=

1)We look if there are any brackets containing math statements.There are none.

2)We look for any exponents. There are none.

(-15) + (-6) ÷ (+3)=

3) We look for any multiplication/division statements. As you may see, there are two. We solve the first one we see because we read left to right.

(-15) + (-2) =

4) Solve the other division statement.

(-17)

5) We are left with adding. Add the two digits and voila! You get your answer.

Term 2 Reflection

Read along too!

Term 2 Reflection

In term 2, overall, I did pretty good on everything. This included things like surface area, volume, and percents. I think I did well is mainly because I listen when the teacher is talking.One thing I didn’t do well in was checking my work. There was this one question for volume that I thought it said you were supposed to put the clothes in the drawer. I will improve in the next term by reading the question more than once. In percent, I learned that to find tax, you have to multiply a number by 1.12. In surface area, I learned how to find the surface area of a rectangular prism (draw all the sides of the shape,multiply the measurements then add up all the products), triangular prism (draw all the sides of the shape, multiply all the measurements, divide the products by two, and then add), and cylinder (use formula, (2πr²)+(2rπh)). Now in volume, I learned the formulas to find the volume of a rectangular prism(v=lxwxh), triangular prism (v=bxh1xh2/2) and cylinder (v=πr²xh)

Now, what exactly is the difference between volume and surface area. Well, surface area is finding how many units are outside of something. An example of a question with surface area is, “How many gift wrap is needed to cover the product?”. Now, for volume, your finding how many units are inside. A question using volume is something like “ How many water is in the pipe?” .

Surface Area and Volume

Here is a question from 7.3 in the text book :










r=d/2 v=πr² x h
r=8/2 v=(3.14x4x4) x 10m
r=4m v=50.24m² x 10m
v= 502.4m³
Now, since it is only half of a cylinder, I have to divide by 2
502.4m³/ 2= 251.2m³

The area of the semi-circular trough is 251.2cm³

Here is a question from 7.4 in the textbook :


____
³ )8000 = 20 d/2=r v= πr² x h
20/2=r v= (3.14x10x10) x 20
10cm=r v= 314cm²x 20cm
v= 6280cm³
The volume of the vase is 6280cm³

Final Percent Post

1. Percent means out of one hundred. It is also known as hundreths. Percents can also be represented as fractions and decimals
For example, 89% = 0.89, 89/100

Representing Percents
You can represent percents by showing it on a hundred grid.
For example,
100%











Fractions, Decimals, Percents
Percents can also be shown as decimals, and fractions.
For example,
2/4= 50% 12%=0.12

Percent of a Number
You can use mental math strategies like halving, doubling, and dividing by 10 to find a percent of a number. You can also write the percent as a decimal then multiply it by the number.
For example,
12 1/2 % of 50 = 0.125 x 50 12 1/2% = 12.5%
= 6.25 = 0.125

Combining Percents
You can combine percents to find the answer to a problem.
For example,
Find the total tax.
5% PST + 7% GST = 12% total tax

You can find the increase of a number by adding the combined percent to the original number.
For example,
10% of 100 = 0.1 x 100 = 10
100+10=110

To find the increase of a number, multiply the original number by a percent greater than 100.
For example,
110% 0f 100 = 1.1 x 100
=110

You can use percents of percents to find amounts that result from consecutive percent increase or decrease.

2.


Click here to go to another scribe that I made on percents.

Click here to go to a site that explains more about percentage.

Alec's Scribe Post (Percents)

My assignment was to do 3 questions from pages 142 to 143.
3. This Question is asking to find the percent by using mental math.
a)












b)












c)












4. This question is the same thing as 3.
a), b), c)











8. The original price of a jacket was $84.00. A store manager marked the price down by 25 1/2%. By how much was the price reduced?




The price was reduced by $25.50.

Alec's Pay it Forward

Part One

Pay it Forward is helping people without expecting anything back. It's kind of like a chain reaction. If you help one person, then there is a chance they get inspired and they start helping other people. The big idea of Pay it Forward is to help make the world a better place. The whole idea came from a movie named "Pay it Forward" where a boy named Trevor is given an assignment to make the world a better place. He came up with an idea where if you help three people, then they'll help another and the number gets getting bigger, and bigger.

Part Two

For my act of kindness, I chose to send a letter to a Canadian soldier in Kandahar, Afghanistan. I chose this activity to let a soldier know that I believe in him. To let him know that I honor his patriotism and courage to this country. It must be really hard to watch other people die and at the same time know that your life is at risk.

"Courage is the magic that turns dreams into reality"

-Richard Abend

(Quote was used in my letter)

Part Three

On Thursday, December 16, I made a rough copy of a letter that I would later on send to a Canadian soldier. When I first planned to send a letter, I thought it would be a great idea. I've heard many stories of how soldiers love to receive letters, and I thought that I could make them feel good even if they are miles away from their loved ones. On Friday, December 17, I typed a good copy of my letter. Then, on December 19, I went with my dad to send the letter. It felt really good. I hope when the soldier receives it, they have a positive reaction because I put a lot of heart into that. I did not say pay it forward because defending the country is already a huge responsibility.

Part Four

The idea of Pay it Forward is important because it helps make the world a better place to live. If everyone tried to Pay it Forward, then maybe there will be no poverty, no racism, and no war. I really hope my act of kindness makes a encourages the soldier to continue to be a true patriot. I hope it helps them to be brave even if they are far from their family.

Don't for get to Pay it Forward!!!

Scribe 6 - 2 Questions From Page 87

In this scribe, I had to pick two questions on page 87 and answer them. These are the two questions I decided to answer:

24. a) What are the next three triangular numbers

10, 15, 21

b) Add together any two consecutive triangular numbers. What do you notice about the sums?

The sums equal perfect squares.

Example, 1+3=4 3+6=9 6+10=16

25. A square digital photo on the computer has an area of 144 cm2.

a) What is the side length of the photo?

The side length of the photo is 12 cm.

b) The photo is enlarged so that the side length is now 36 cm. What is the area of the enlarged photo?

The area of the enlarged photo is now 1296 cm2

c) How many times as large as the original area is the enlarged area?

1296/144=9 The original photos area was enlarged by 9x

d) How many times as large as the original side length is the enlarged side length?

36/12=3 The original photos side length was enlarged by 3x

e) Use what you know about the square root of a perfect square to identify the relationship between the numbers in parts c) and d).

Alec's Sesame Street Video Post

Group Members - Alec M., John C., Brandon A., Mark C.

Part One two-term/three-term ratios -compares two/three quantities measured in the same units.

example: two-term ratios, oranges to apples 5:8

three-term ratios, oranges to apples to all 5:8:13

rates - compares two quantities measured in different units

example: $/100g = $1.69/100g

unit rate - a rate in which one is in the second term.

Proportional Reasoning - a relationship that says two ratios or rates are equal

Part Two

Description: A salesman tries to sell Ernie an "8"

Part Three

Wanna Buy a Rate?

Alec's Math Profile

Hello, I'm Alec, a student in grade 8. If someone asked me if I like math I would say yes because we use it every day in our lives. For example, when we go shopping, we use money which is part of math. Although there is many things to choose from, i would have to say the best thing i did in class that involved math was blogging. I love blogging because you have the chance to be very creative, and you also have the chance to show other people what you know in math.

Last year in grade seven, I loved doing algebra. I loved it because I thought it was fun and when I do fun things in class it makes me want to work harder on it, and sometimes it makes me get a higher mark. A unit i struggled the most in was fractions. It was pretty easy at the start, but once it got in to converting improper fractions to mixed numbers, it started getting a bit harder. I could improve that by studying more and maybe even by doing a little bit of extra work.

Grade 8 looks to be a fun year in math. I plan to be a more successful student this year and i could achieve that by studying more than last year. Actually, I have to admit, the only time I studied last year was when it was exams. I would like to learn more algebra this year since it's my favorite thing in math and I know it gets more complicated.

Last year, we also did blogging. One post (made by me) that I really liked was about subtracting mixed numbers. I liked it because to me, it felt like I did a really good job of explaining how to subtract mixed numbers. Blogging helped me become a better student by learning from other peoples blogs if I'm away that day. Without blogging, I may have failed some test. This year, I want to use the internet more in math and do more creative projects on the computer. I think this will help me learn math better because if I like doing something, it helps me get more focused.