Daniel's Algebra Post

One-step Equations
In order for you to understand the steps, there are a couple of words you need to know.

Variable - the unknown
-use a letter to represent a number

Constant - the integer in an algebraic expression or equation


Rules for Addition/Subtraction :
1.Isolate the variable
2.Cancel using the opposite operation (create a zero pair)
3.Balance on the other side of the equal sign
4.Verify your answer

Example:

Multiplication/Division
1.Isolate the variable
2.Cancel using the opposite operation
3.Balance
4.Verify

Example:

Two Step Equations

1.Isolate the variable
2.Cancel the constant
3.Balance
4.Simplify variable
5.Balance
6.Verify

Example:

Daniel's Great Big Book of Integers

Chapter 1 Grade 7 Integer Review

(+4) + (-2) = +2
Positive (4) and Negative (2) = positive 2
have 4 and owe 2 = have 2
Standard Form: 4 - 2 = -2
Make zero pairs:

-16 = +16, -5 = + 5, +6 = -6, -2 = +2,

-10 = +10, +3 = -3, +11 = -11, -9 = +9


CHAPTER 2 Multiplying Integers

(+2)x(+3) = +6
(2)x(3) = 6
(2)(3) = 6 *Standard form*
2(3) = 6


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

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

(-2)x(-3) = +6
remove 2 groups of (-3)=+6

(-2)x(+3) = -6
remove 2 groups of (+3)=-6

Sign Rule (negative signs):
Even = When you have an even number of negative factors, the product is positive.
Odd = When you have an odd number of negative factors, the product is negative.

Chapter 3 Dividing Integers

Sign Rule: If you have no negative or an even number of negative signs in a division question, the quotient is positive.

There are 2 types of division
Partitive Division or making parts
6÷3=2 ,
how many groups of 3 are in 6?

Quotative Division or sharing your total with groups
6÷3=2 , share 6 with 3 groups

6÷2 and -6÷ (-2) will give you the answer of 3 because the questions has no, or an even amount of negative signs.
(-6)÷2 and 6÷(-2) will give you the answer of -3 because the questions have an odd amount of negative signs


Chapter 4 Order of Operations with Integers

The order of Operations is called BEDMAS : Brackets, Exponents, Division, Multiplication, Addition, Subtraction

(+5) x (-3) + (-6) ÷ (+3)
(+5) x (-3) + (-2) [solved division first]
(-15) + (-2) [solved multiplication after]
= (-17) [solved addition]

Cylinder Homework

. represent multiplied(x)

2.π.r.r + 2.π.r.h ( is the formula for solving this equation )

cylinder 1. 2.π.r.r + 2.π.r.h ( FORMULA )
2. 3.14 .3 .3 + 2 3.14 .3 .5 =
56.52 + 94.2 =
150.72cm²

cylinder 2. 2.π.r.r + 2.π.r.h ( FORMULA )

2. 3.14 .4 .4 + 2.3.14 . 4. 15 =
100.48 + 380=
477.28²


http://www.mathsteacher.com.au/year9/ch14_measurement/15_total/cylinder.htmu/year9/ch14_measurement/15_total/cylinder.htm

Term 2 Reflection

Daniel's Final Percent Post

Percent means out of 100. It is 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 written as decimalsor a fractions.

Ex. 1/2 = 0.50 = 50%


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.

eg. 12 ½ % of 50 = 0.125x50 = 6.25


4.4 Combining Percents Key Ideas :
Adding percents can be used to solve problems.

Eg. Add combined percent with original number:
25% of 100 = 25. 25 + 100 = 125

Eg. 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.

RATIO:

Two Term Ratio-it compares 2 quantities measured in the same unit


EXAMPLE: boys: girls
:1:2

Three Term Ratio- compares 3 quantities measured in the same unit.

EXAMPLE: boys: girls: men
2:1:2

Part to Whole Ratio- compares different parts of a group to each other. It can

be written as fraction, decimal, and percent.


EXAMPLE: boys: everyone ( boys, girls, men )1:5

Part to Part Ratio- compares different parts of the group to the whole group.

EXAMPLE: boys : girls
1 : 2

RATE:

Unit Rate- a rate in which the second term is one.

EXAMPLE: $1/ per 3 cookies


Unit Price- a unit used when shopping.

EXAMPLE: $ per/ gram, $ per/ kilogram, $ per/ hour, kg per/ hour, etc.


PROPORTIONAL REASONING:


PROPORTION:a relationship that say 2 ratios or 2 rates are equal. Can be written as fraction.


EXAMPLE : ( $ 5 / 10 cookies) = ( $ 15 / 30 cookies)

Daniel's Pay It Forward

Part 1:

Trever an 11 year old boy thought of " Pay It Forward" . It was a project for school , it is where you help 3 people and except nothing in return. You just do it for because you want to. The 3 people that you helped , help 3 people each , it is like a chain . The people you help don't have to be people you know , they can be anyone needing help .

Part 2:

For my act of kindness my group ( Ryan , Michael , Cameron , Kaecee , and I ) donated used , and unused toys. We decided to do this , because these toys are just sitting around are homes . While other kids could be playing with them . We donated these toys to the foundation " The Helping Hand " which gives the toys to families that have immigrated to Canada. We did our act of kindness on December 17 at 12:00 pm.

Part 3:

Our act of kindness went really good because we donated toys that we would have never played with again . We donated the toys , and then asked the clerk if she knew what " pay it forward was and if she was going to " pay it forward" . When we donated the toys i felt very joyful , and giving , because i know the children are going to make good use of the toys , and i know they are gonna know that someone out there was nice enough , to give them these toys . When we asked her if she would pay it forward , she responded by saying " I have payed it forward , I donate toys , and clothes , and when I have spare time , i volunteer at various foundations"

Part 4:

The statement " Pay It Forward" means a lot to me because even one person can make a difference , just like we did for these immigrated families. I also think our act of kindness made a difference because it is almost Christmas , and now immigrated families in Canada can feel loved , and have new toys for this holiday season ..

and remember .... PAY IT FORWARD (:

Daniel's Pythagoras Scribe Post

Hope you all did your homework ! The pages were 91 - 94 . If you were stuck on any of of the following numbers ( 2, 7, 14, & 18. ) i hope this helped you .



2) A triangle has side lengths of 7cm, 11cm, & 15cm. Explain how you can determine whether or not it is a right triangle.

In order for a right triangle to be a right triangle , a2 + b2 = c2 . In this question a2 + b2 does not equal c2 . Therefore this triangle is not a right triangle.

7) The sides of a right triangle measure 9cm, 12cm, & 15cm.

a) What is the area of each square attached to the three sides of the right triangle?

a2=144cm

b2=81cm

c2=225cm

b) Write an addition statement showing the relationship between the areas of the three squares.
c) Describe, using words and symbols, the relationship between the side lengths of each square.


- The area of square a2 + square b2 is equvilent to square c2.

14) Show whether each triangle in the table is a right triangle.

18)The diagram is made of two triangles and five squares.

The area of square x is 28cm²

b) What is the area of square Y?

The area of square Y is 16cm2 because the hypotenuse for the 2 triangles is 28cm², and side B is 12cm2, therefore 16cm2+12cm2 = 28cm2. I think the question is asking ___ + 12cm2 = 28cm2





Links : Pythagorean Theorem ( this is the video )

Thank you Marilen for helping me finish this . Hope you all liked it (:

Daniel's Sesame Street Video

Daniel's Math Profile

Hello , my name is Daniel Sousa . I am a math student in grade 8 . If someone asked me if i liked math , i would say yes . I like math because it is one of my favorite subjects and i am pretty strong in it . The best thing i have ever done in math class was when we did a project on sandwiches , and then at the end we got to eat them .

Last year in grade 7 , my best subject was fractions. I was good at this because i was good , at adding and subtracting them . The subject in grade 7 that i struggled in was difficult algebra . I could get better at this by studying more , and doing the homework booklet .

This year i will try my best to , be better at math . I would also like to learn , advanced algebra . To be ready for grade 9 .

One post that i did last year that i am proud of was a study sheet for the exam . I really liked this post because i added pictures and it was very colorful. Blogging helped me become a better student , because when i would forget what the homework was . It would be on the blog . This year for math class i would like to continue doing the blog , and blog like last year.