Patrick's Math Questions Pg. 339, 10-12

Patrick's Algebra Post

One Step Equations:

To solve one step equations, you need to isolate the variable. To do that, you need to get rid of the constant, which is the integer in an algebraic equation or expression. To do that, you must cancel the number by using a zero pair. So now you need to balance. What ever you do to one side you must do to the other side. Then you must verify your answer to see if it is correct.

ex.

n +10 = 15

n +10 -10 = 15 -10

n = 5

Verify:
LS RS

n +10 = 15

5 +10 = 15
15 = 15

Alge-Tiles:

ex.

n-2=2

n-2+2=2+2

n=4

Verify:

n-2=2

4-2=2

2=2

Alge-Tiles:

Two Step Equations:

To solve two step equations, you must do what you have to do in one step equations, get rid of the constant. Then once that is gone you must isolate the variable. The opposite of multiplying is dividing, the opposite of dividing is multiplying, the opposite of adding is subtracting and the opposite of subtracting is adding. So you must cancel out all the numbers. Then you have to verify your answer.

ex.

2n + 3 = 11

2n+3-3= 11-3
2n = 8

2n÷2=8÷2
n = 4

Verify:
2n+3=11
2(4)+3=11
8+3=11

11=11

Alge-Tiles:

ex.

x÷2-2=1

x÷2-2+2=1+2

x÷2=3

x÷2x2=3x2

x=6

Verify:

x÷2-2=1
6÷2-2=1

3-2=1

1=1

Alge-Tiles:

Patrick's Fraction Video

Patrick's term 2 reflection

In term 2, we learned about 3 things. They were total surface area, percents and volume. We learned how to find the surface area of a triangle, cube, rectangles and cylinders. We also learned how to draw the net of an object. A net is what the shape looks like when you unfold it. It is kind of like peeling an banana. Finding the TSA for the shapes that we did was pretty easy for me. The only thing i made mistakes on were putting the units that they were supposed to be.
For percents, I did well on them too. When we were learning percents, we were pretty much just reviewing what we learned before. Like, we looked at how to convert fractions into decimals and percents. Decimals into fractions and percents. And percents into decimals and fractions.
I’m pretty sure I did really good on this term. This term was pretty easy for me. The only hard part for me, was remembering all the formulas to try and solve some questions. Like how to find the area of a cylinder just by using one formula. I was used to using separate formulas, first finding the area of the circle, then multiplying by two. Then finding the area of the rectangle for the circle. That’s how i did it. Next time, I am going to try and remember the formulas so it can be easier and quicker to solve some of the problems.

Patrick's Great Big Book of Integers

Chapter 1 - Integers Review

Zero Pair:

A pair of integer chips with one chip representing +1 and one chip representing -1

Example: (+10) + (-10) = 0

Find the zero pairs for the following integers:

-6 +10 19 - 16 -11 +14 63

+6 -10 -19 +16 +11 -14 -63

If a number doesn't have a positive or negative sign on it, that means it is automatically a positive integer.

Integers in Grade 7

(+4) + (-4) = 0

(+4) is how much pencils you have

(-4) is how much pencils you owe Mrs. Wilson because you borrowed some and forgot to give

them back

Brackets for integers are kind of like the training wheels for a bike.

Grade 7 form : (+5) + (-5) = 0

Standard form :5 - 4 = 0

Positive = RED (+)

Negative = BLUE (-)

Questions:

-3 - (-7) = +4

-3 - 7 = -10

3 - 7 = -4

3 + 7 = 10

Chapter 2 - Multiplying integers

Multiplying integers - Repeated addition if you need to remove something that isn't there. We use zero pairs.

Examples:

1. (+2) x (+3) = +10 (2 groups of +3)

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

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

4. (-2) x (-3) = +6 (Remove 2 groups of -3)

Sign Rule (negative sign)

Even: When you have an even number of negative factors the product is positive.

Odd: When you have an odd number of a negative factors the product is negative.

Chapter 3 - Dividing Integers

Partitive Division means to make parts of.

6 ÷ 2 = +3

-6 ÷ (-2) = +3

Quotative Division means to share with groups.

(-6) ÷ 2 = -3

The multiplicative inverse can help solve 6 ÷ (-2) by doing the question . The quotient is -3 and it will be a part of the question when the answer is -2.

6 ÷ (-2) = -36 ÷ (-3) = -2

Sign Rule:

The quotient of two integers with the same signs is positive. The quotient of two integers with different signs is negative.

6 ÷ 2 = +3

-6 ÷ (-2) = +3

They both have the same sign so it is positive.

(-6) ÷ 2 = -3

6 ÷ (-2) = -3

They both have different signs so it is negative.

Chapter 4 - Order of Operations with Integers

(+5) x (-3) + (-6) ÷ (+3) =
To solve this question, we will be using BEDMAS

We need to add square brackets to this problem, to make it easier.
SQUARE BRACKETS = KING OF BRACKETS.

[(+5) x (-3)] + [(-6) ÷ (+3)] =
(-15) + [(-6) ÷ (+3)] =
(-15) + (-2) = -13

Patrick's Math Notes Post

VOLUME





BASE (of a prism of cylinder)
-Any face of a prism that shows the named shape of the prism.
-The base of a rectangular prism is any face.
-The base of a triangular prism a triangular face.
-The base of a cylinder is a circular face.

HEIGHT (of a prism or cylinder)
-The perpendicular distance between the two bases of a prism or cylinder.

VOLUME
-The amount of space an object occupies
-Measured in cubic units

ORIENTATION
-The different position of an object formed by translating, rotating or reflecting the object.

____________________________________________________________________


Volume of a Rectangular Prism.


area of base X height
l x w
6 x 5 = 30cm²

30cm² x 10 cm = 300 cm³

Volume of a Triangular Prism.



area of base X height

b x h /2
7 x 5 / 2 = 17.5 cm²

17.5cm² x 10 cm = 175cm³

Volume of a Cylinder



area of base X height
π X r X r
3.14 X 5 X 5 = 78.5 cm²

78.5cm² X 10 cm = 785 cm³
___________________________________________________________________

These three videos should help you how to find the volume of a shape.





____________________________________________________________

Cylinder Volume and Volume Problems



r = d/2
r = 0.26 m/2
r = 0.13 m^2

V = (π x r x r) x h
V = (3.14 x 0.13^2) x 2.4m
V = (0.05m^2) x 2.4 m
V = 0.12m^3

0.12m^3 x 35 = 4.2, (round up) = 5m^3

The volume of concrete required is 5m^3.


a)Volume with the missing piece = l x w x h
Volume with the missing piece = 10cm x 16cm x 10cm
Volume with the missing piece = 1600cm^3

Volume of missing piece = l x w x h
Volume of missing piece = 10cm x 6cm x 5cm
Volume of missing piece = 300cm^3

Volume = 1600cm^3 - 300cm^3
Volume = 1300cm^3

The volume is 1300cm^3

b) You can check your answer by dividing the shape into separate rectangular prisms.

Final Percent Post

Percent means out of 100. Which is another name for hundredths. There are also Fractional Percents. they are percents that include a portion of a percent.
Example: 0.42%.

Representing Percent:
You can represent percent by drawing a picture or using a hundred grid.
Example: To represent 180% you would need two one-hundred grids. You would shade in the first one-hundred grid and shad 80 squares on the other one.

Fractions, Decimals and Percents:
Fractions, decimals and percents can be used to represent numbers in a lot of different situations. Percents can be written as fractions and decimals.
Example: 0.5% = 1/2%.

Percent of a number:
You can use mental math strategies such as halving, dividing and doubling ten to find the percent of some numbers. You can also calculate the percent of a number by writing the percent as a decimal and then multiply it by the number.
Example: 12 1/2% of 50 = 0.125 x 50
||||||||||||||||||||||||||||| = 6.25

Combining Percents:
Percents can be combined by adding to solve problems. 5% + 7% = 12%
When you want to calculate an increase in a number, you can add the combined percent amount to the original number.
Example: 12% of 100 = 0.12 x 100 = 12.
|||||||||||100 + 12 = 112
You can multiply the original number by a single percent greater than 100.
Example: 112% of 100 = 1.12 x 100
|||||||||||||||||||||||||||= 112



Here is a good website to explain percents.

Patrick's Pay It Forward.

Part 1:
A young boy named Trevor was doing a project that he wanted to do called Pay It Froward. His teacher really liked that idea. Paying It Forward was when you help three people. Then each of those people will help three more, then it will continue to grow so we can make everybody's life better. First he tries helping a homeless man, but that doesn't really work out, until the end. Then he tries helping his teacher, by taking him on a date with his mom. That doesn't really go well, until the end, again. The third person he tries to help was his friend. He was getting bullied by three people. Trevor tries to help his friend and he jumps onto one of the bullies. Sadly, he gets stabbed and then he passes away.

Part 2:

What was your Pay It Forward act of kindness?

My Pay It Forward act of kindness was helping the janitors of our school, Sargent Park.

Why did you choose this activity?
I chose this activity because I found out that some parts of the school are really messy, and the janitors have to clean the whole school every single day. So my group and I decided to help them out by making there job easier.

Who did you help?
We helped the janitors of Sargent Park.

What did you do?
We cleaned up Sargent Park School.

When did you do you act of kindness?

We did this after school on December 17, 2010



My friends and I decided that the janitors have a lot to clean, because Sargent Park is a really big school and there are only a few janitors. We swept the halls and classrooms. We cleaned all the bathrooms and we took out the garbage.

Part 3:
How did your act of kindness go?
I think that my act of kindness went very well because we cleaned a lot of the school.

What Happened?
The school got cleaned by us.

How did you feel?
I felt really good when I was helping out the janitors.

How did the person or people react?
He was very thankful that we helped him clean the school.

Did you ask the person or people to "Pay It Forward"?

Yes, I did tell him to pay it forward.

How did they react to your request?
He said that he will pay it forward, because its good to help other people, so we can help everyone.

Part 4:

Why is the idea of "Pay it Forward" important?
It is very important because if we pay it forward, we can help a lot of people.

Has your act of kindness made a difference?

I hope that it did.

Patrick's Textbook Post Pages 103-105. Numbers 5,8,11,14

area of square = a²
area of square = 6x6
area of square = 36cm²

area of square = b²
area of square = 8x8
area of square = 64cm²

a² + b² = c²
6² + 8² = c²

36 + 64 = c²
100cm² = c²



√100cm² = √c²
10cm = c

a² + b² = c²

50² + 200² = c²
2500 + 40 000 = c²
42500 cm² = c²
√42500 cm² = √c²

206 cm = c

√914 = √c²
30.2 cm = c

c² - a² = b²
30.2² - 17² = b²
912 - 289 = b²
623 cm² = b²
√623 cm² = √b²

25 cm = b

perimeter = a + b + c
perimeter = 17 + 25 + 30.2
perimeter = 72.2

b²=c²-a²
b²=5²-3²
b²=25-9
b²=16m²
√b²=√16m²
b=4m

c²=a²+b²
c²=6²+4²
c²=36+16
c²=52m²
√c²=√52m²
c=7.2m
The length of c is 7.2m.

Scribe 3 Show You Know Page 84 Page 85 Questions 3,7,12,14

Show You Know, Page 84.
Determine the side length of a square with an area of 196cm².

||||||196cm²
||||||/||||||||||\
||||14|||X|||14
|||/|||\|||||||||/||||\
||7 x 2 |x| 7 x 2

196=7x2x7x2
196=14x14
√196=14
The side length is 14cm.

Page 85 Questions 3,7,12 and 14.

Question 3:
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Use words and/or diagrams to explain how you know which factor is the square root of 36.

|||||36
|||/|||||||\
||6||X|||||6
/||||\|||||||/||||\
3 x 2 X 3 x 2

36=3x2x3x2
36=6x6
√36=6
The square root of 36 is 6.

Question 7:
Write the prime factorization of each number. Identify the perfect squares.

A)||||||42
||||||/||||||||\
||||7 |||x||| 6
||||||||||||||/||||\
||||7|||x|3||x||2
This is not a perfect square.

B)||||||169
|||||||/|||||||\
||||||13 |x| 13
This is a perfect square.

C)|||||||256
|||||||/|||||||||||\
|||||16|||X||||||16
|||/|||||\|||||||||/|||||||||\
||4||x||4|x||||||4||x||||4
/|||\|||||/|||\|||||/|||\|||||/|||\
2x2 x 2x2 x 2x2 x 2x2
This is a perfect square.

Question 12:
Determine the square of each number.

A)SxS=Area
||10x10=100

B)SxS=Area
||16x16=256

Question 14:
Determine the side length of a square with an area of 900cm²

√900=30.

Question 17:
A fridge magnet has an area of 54mm². Is 54 a perfect square? Use prime factorization to find the answer.

||||||||54mm²
|||||||/|||||||||\
|||||27|||||x|||2
|||/||||\
||9||x||3|||x|||2
/||||||\||||||||||||||
3 x 3|x|3|||x|||2

It is not a perfect square.

Arun and Parick's Sesame Street video

Group:
Patrick - Cookie Monster
Arun - Math Monster

Rate
Compares two quantities measured in different units
Unit Rate
A rate in which the second term is one
Unit Price
A unit rate used when shopping

Example: I eat 2 cookies in 2 minutes, that means I eat 1 cookie per minute.
1 cookie/min

Ratio

Two Term Ratios
Compares two quantities measured in the same units
Example: I eat 2 cookies and there are 4 in the jar. That makes it 2:4

Proportional Reasoning
A relationship that says that two ratios or two rates are equal.
Example: If I eat 1 cookie in 1 minute, then that means I eat 8 cookies in 8 minutes.

I couldn't find the video on Youtube, so here's a link of "Cookie Eats The Letter N"

Cookie Monster is trying not to eat the letter of the day.

Remake: Cookie Eats The Letter R

Perfect Squares

1x1, 2x2 and 3x3 are Perfect Squares.
OR
1² , 2² and 3² are Perfect Squares



Any number can be a square.
Example: 20
You have to find out the square root of 20.
You can use your calculator and punch in √(square root) 20, or 20 √ if there is an error.
√20=4.472135955. OR 4.47.

HOMEWORK: Tell me what you know about squares.
Find out what you know about these squares: [1] [2] [3] [4] [5] [6] [7] [8] [9]

Patrick and Arun's Sesame Street Video

Group:
Patrick - Cookie Monster
Arun - Math Monster

Rate
Compares two quantities measured in different units
Unit Rate
A rate in which the second term is one
Unit Price
A unit rate used when shopping

Example: I eat 2 cookies in 2 minutes, that means I eat 1 cookie per minute.
1 cookie/min

Ratio

Two Term Ratios
Compares two quantities measured in the same units
Example: I eat 2 cookies and there are 4 in the jar. That makes it 2:4

Proportional Reasoning
A relationship that says that two ratios or two rates are equal.
Example: If I eat 1 cookie in 1 minute, then that means I eat 8 cookies in 8 minutes.

I couldn't find the video on Youtube, so here's a link of "Cookie Eats The Letter N"

Cookie Monster is trying not to eat the letter of the day.

Remake: Cookie Eats The Letter R