Diorella's Algebra Post

Variable: The unknown, using a letter to represent the number.

eg. 15 + b = 23

Constant: The integer in an algebraic expression or equation.

eg. n + 16 = 9

You have to make a zero pair for the constant to cancel it out

Algebra: Writing mathematical phrases using letters to represent numbers

eg. n - 8 = -10

Solving Addition/Subtraction One Step Equations:
1. Isolate the variable
2. Cancel using the opposite
- Create a zero pair for the constant
3. Balance on the other side of the equal sign
4. Verify your answer

Solving Addition/Subtraction One Step Equations Using Algebraic Tiles:
1. Isolate the variable
2. Cancel the constant using a zero pair
3. Balance
4. Verify

Addition:

Subtraction:

Solving Two Step Equations:
1. Isolate the variable
2. Cancel the constant
3. Balance
4. Simplify the variable
5. Balance
6. Verify

Examples:

Here is a video that might help:

Diorella's Great Big Book of Integers

Chapter 1: Grade 7 Integer Review

(+4) + (-4) = 0

^ have four ^ owe four

(+2) + (-2) = 0

^ have two ^ owe two

Brackets are training wheels.

+4 + -4+4 - 4

4 - 4 = 0 (pure standard form)

zero pair: is a pair of the same negative number, and positive number. Together, they equal 0.
Making Zero Pairs:
a) -16=+16 b) -6=+6 c) -10=+10 d) +19=-19 e) -11=+11 f) -14=+14 g) -63=+63

1. -3 - (-7) = +4

use zero pairs and remove 3 groups of (-7) leaving you with 4 positives

2. -3 -7 = -10

Two negatives equal a positive so you just combine the two without zero pairs leaving you with -10

3. 3 -7 = -4

Use zero pairs and remove 3 groups of 7 (-21) which leaves you with 4 negatives

4. 3 +7 = +10

Since they're both positives, just add them together normally

Chapter 2: Multiplying Integers

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

When multiplying two positives, the answer will be positive so just multiply them like usual.

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

2 groups of (-3)

(-2)

(+3)=

Remove 2 groups of (+3)

(-2) x (-3)=

Remove 2 groups of (-3)

Sign Rule ( Negative Signs )

Even= when you have an even number of negative factors the product is positive.

Negative = When you have an odd number of negative factors the product is negative.

Chapter 3: Dividing Integers

2 types of division

6÷3=2

How many groups of (+3) are in 6?

*Partitive division or making parts

6

÷3=2

Share 6 with 3 groups

6

÷2=3

-6

÷(-2)= -3

(-6)

÷2= -3

6

÷(-2)= -3

When you have an odd number of (-) signs in a division question, the quotient (answer ) is gonna be negative

Chapter 4: Order of Operations with Integers

I'm going to show you how to solve this question:

[(+5) x (-3)] + [(-6) ÷ (+3)]=

= 5 x -3 + -2

= -15 + -2

= -17

If you follow the rule of BEDMAS

B= Brackets

E= Exponents

D= Division

M= Multiplication

A= Addition

S= Subtraction

You should get the right answer

Here are 2 videos to help you out

Term 2 Reflection

Sorry if it sounds like I'm rushing, I usually talk fast and I was nervous.
Listen! :)

Volume Post

Hi! These were the answers to questions #1 and #3 on our math test today!

If the pictures above still leave you confused with surface area, check out these sites :

1. http://www.basic-mathematics.com/surface-area-of-a-rectangular-prism.html
2. http://www.aaaknow.com/geo79_x9.htm
3. http://www.shodor.org/interactivate/discussions/SurfaceAreaTriangular/

Also, here are some videos :

Feel free to make any changes or comments on my post. Okay bye :)

Cylinder Volume and Volume Problems

Answers:

Answers:

Volume Scribe Post

Hi! These were the answers to questions #1 and #3 on our math test today!

If the pictures above still leave you confused with surface area, check out these sites :

1. http://www.basic-mathematics.com/surface-area-of-a-rectangular-prism.html
2. http://www.aaaknow.com/geo79_x9.htm
3. http://www.shodor.org/interactivate/discussions/SurfaceAreaTriangular/

Also, here are some videos :

Feel free to make any changes or comments on my post. Okay bye :)

Cylinder Volume and Volume Problems

Answers:

Answers:

Diorella's Final Percent Post

*A percent means out of 100. It's also another name for hundredths and can also be expressed as fractions and/or decimals.

4.1 Representing Percents Key Ideas :

Shade squares on a grid of 100 squares called a hundred grid to represent a percent. A completely shaded grid represents 100%. If you shade more than one grid, that represents a percent greater than 100%. To represent a fractional percent between 0% and 1%, you have to shade part of one square. Also, to represent a fractional percent greater than 1% you have to shade squares from the hundred grid to show the whole number, then shade part of a square from the grid to show the fraction.

4.2 Fractions, Decimals and Percents Key Ideas :

Percents can also be represented as a decimal or a fraction.

Ex. 3/4 = 0.75 = 75%

4.3 Percent of a Number Key Ideas :

You can use mental math strategies such as doubling, halving, and dividing by 10 to find the percents of some numbers. Write the percent as a decimal and then multiply by the number to calculate the percent of a number.

Ex. 20 1/2 % of 40 = 0.250 x 40 =10

4.4 Combining Percents Key Ideas :

Adding percents can be used to solve problems.

Ex. Add combined percent with original number:

25% of 100 = 25. 25 + 100 = 125

Ex. Multiply the number by a single percent greater than 100:

125% of 100

1.25 x 100 = 125

Percents of percents can be used to determine amounts that result from
consecutive percent increases or decreases.

Percent Review Video:

For this unit I did this percent scribe!

Here is a link that will help you understand this unit better :

http://www.mathsisfun.com/decimal-fraction-percentage.html

Also, here is a video link :

http://www.youtube.com/watch?v=VlqhVldVces

Diorella's Pay it Forward

Part 1

The idea of Pay it Forward was inspired by a boy named Trevor who was assigned an assignment from his SS teacher to think of a way to change the world. He thought of the idea of helping 3 people and those 3 people help 3 people, kind of like a chain reaction. It never stops as long as you pay the act of kindness forward. The more people you pay it forward to, the more people they pay it forward to and so on.

Part 2

Marie, Julibella, Angel, Marilen and I decided to pay it forward by buying a bunch of toys and donating them to the Children's Hostpital in downtown. We also made cards that said " You've been hit by an act of kindness. Please do your part and pay it forward! " We decided to do this activity because I know how it feels to stay in a hospital 24/7 and also because we wanted to know that those kids have people out there who care for them and to make them happy. We helped out the kids in the hospital on December 18, 2010.

Part 3

When we arrived at the hospital to donate the toys for our Pay it Forward we handed it to the nurse and took a picture with her. She seemed shocked but happy that we decided to donate toys there. I felt a sense of accomplishment and happiness because of what we did, I felt like I really helped those kids put a smile on their face and make their holidays better even though I didn't get to see them. We did not ask her to Pay it Forward though we left a card that says it in the bag for them to read and hopefully pass on when they play with the toys.

We also did another Pay it Forward project at Polo Park although it didn't go as planned. Marie and I dressed up as an elf and Santa Clause and just as we were handing out the candy canes and cards the security guards told us we couldn't hand them out but they were okay with the outfits. Although it was disappointing for us, we thought of another way to Pay it Forward by putting the cards on people's windshields at the Polo Park parking lot. It was cold but definitely worth knowing that we made a positive difference!

Part 4

The idea of " Pay it Forward " is important because although it starts off as just 1 person it will eventually help out many others. It's basically doing something nice to people without expecting anything in return. It's easy to do since all you have to do is help people and those people will pass it on to other people. Helping people out and knowing that they'll do acts of kindness too, warms my heart. Just a small gesture of kindness will do like holding the door open for someone, shoveling driveways, saying " thank you ", volunteering and so much more will make such a positive difference in this world. Now, could you just imagine when the whole world starts doing it? Amazing things could happen.

I really hope it made a difference in people's lives. If a group of junior high students could do this then other people should too. It doesn't take fancy things to change someone's life and I'm glad I could be apart of this.

PAY IT FORWARD :)

Percent Word Problems

Question 1

You just hired a new baker to work in your bakeshop. In one hour the baker burned 250 chocolate chip cookies. If this represented 21% of the day’s production, how many cookies had you planned on producing that day?

They planned to produce 1190 cookies.

Question 2
A serving of ice cream contains 240 calories. One hundred forty-four calories come from fat. What percent of the total calories come from fat?

The percent of that total calories that come from fat is 60 %

Question 3
A store that sells snowboards buys them from a manufacturer at a wholesale price of $57. The store markup is 150%. What is the retail price?

The retail price is $85.50

Sorry everybody that I couldn't put the grid pictures up, my computer would freeze and I tried it several times.

Here is a link to help you with percent problem solving. This one and this

Also, here's a video :

I hope my blog post helped you out! Sorry again if the colors or grid do not show :(

Feel free to correct my mistakes.

Triangles

1) Explain a² + b² = c²

a² + b² = c²

(4x4) + (3x3) = c²

16 + 9 = c²

25 = c²

So, a² in this case is 4 cm².

B = 3 cm² and C = 5 cm²

So, when you want to figure out what the hypothenuse is, you use this formula. So once you figure out that c² = 25, you find the square root of 25 which is 5 and that's what the hypothenuse on this triangle is.

* Notice that 3², 4² and 5² are all perfect squares.

( 3x3=9 ) ( 4x4=16 ) ( 5x5=25)

2) Use a second grid to create a² + b² = c²

Make the triangle

Look at picture.

3) C² to C ... How ?

To find out how to get C² to C you have to multiply the number by itself.

Ex. 5² you have to multiply 5 by itself.

5x5 = 25.

Then if you want to get from C to C² you have to do the opposite. This time, you have to figure out the square root of your number.

Ex. The square root of 25 is 5.

Triangle formulas and and formula calculators

This site should help you figure out the length of the hypothenuse and plus it has many formulas.

THANKS FOR READING MY SCRIBE POST ! And extra thanks to Mr. Harbeck for helping me make this scribe better :) Please feel free to leave any comments and suggestions you have.