Ryan's Algebra Post

Terms
Variable - is a letter that represents an unknown number in algebra (ex. q, x, z, t)

Constant - is the integer in an expression or equation (ex. x +6)
Expression - is a pattern; has multiple or infinite answers (ex. 2x)
Equation - has an equal sign; only one possible answer (ex. 2x = 6)

One Step Equations

Steps for Completing Equations

1. Isolate variable - get rid of constant
2. Cancel using opposite; use a zero pair for constant
3. Balance - do the same on other side of the equation
4. Verify - solve to equality

Addition

Addition Using Alge-Tiles

Subtraction

Subtraction Using Alge - Tiles

Multiplication

Multiplication Using Alge - Tiles

Division

Division Using Alge - Tiles

Two Step Equations

Steps for Completing Equations

1. Isolate variable - get rid of constant
2. Cancel using opposite; use a zero pair for constant
3. Balance - do the same on other side of the equation
4. Verify - solve to equality

Division

Division Using Alge - Tiles

COMING SOON.. ;)

Multiplication

Multiplication Using Alge - Tiles

COMING SOON.. ;)

How to Convert a Mixed Number (fraction) into a Proper Number (fraction)

Ryan's Term 2 Reflection

I enjoyed the second term, because most of the units we did was very simple and easy for me. Although I didn’t do that well in quizzes/tests, volume and surface area was fun. It was easier for me to solve these kind of problems, because all I had to do was follow the formulas. These types of problems, were like an incomplete puzzle, where you knew what to do to complete them, and you would have to find each value of the formula, to subsitute them in. However, percents were a bit confusing for me. Other than the hundred grids, I did well. My only trouble with the hundred grids, were that if you needed to represent a number such as 0.06 percent, would you have to draw a “zoomed” version of a square, which was out of 100 squares? This confused me because there seemed like a much more simple way to represent that, without finding an equivalent fraction. Overall, I enjoyed the units we did this term, more than the units we did last term.

Ryan's Great Big Book Of Integers

Chapter 1: Grade 7 Integer Review

What we remembered:

- integers can be represented on a number line

- "when subtracting something that isn't there, use a zero pair"

USING A ZERO PAIR:

3 - (-6) = 9

- 6 + 4 = (-10)

Chapter 2: Multiplying Integers

Chapter 3: Diving Integers

Question A: 6 ÷ 2 = ?

PARTITIVE DIVISION = spreading into parts or groups

This question says "How many parts or groups of (+2) are in 6?"

Question B: (-6) ÷ (-2) =

How many groups of (-2) are in (-6)?

Question C: (-6) ÷ 2 = ?

QUOTATIVE DIVISION = sharing

This question says "How do you share (-6) with 2 groups?"

Question D: 6 ÷ (-2) = ?

Using Multiplicative Inverse

6 ÷ (-2) = (-3)

Chapter 4: Order of Operations with Integers

Picture removed by Harbeck

Ryan's Volume Scribe Post

The questions I answered were numbers 4, 6, 8 in the homework book (pg. 80-81).

4. Calculate the volume of each rectangular prism.

a) l = 15 cm, w = 12 cm, h = 3 cm

v = l x w x h

v = 15 x 12 x 3

v = 180 x 3

v = 540cm3

Jumbo
r = d/2
r = 20 / 2
r = 10cm

v = (πr²) x h
v = (3.14 x 10²) x 40
v = (3.14 x 100) x 40
v = 314 x 40
v = 12, 560cm<sup>3

Popcorn Lover's
r = d/2
r = 30/2
r = 15cm

v = (πr^2) x h
v = (3.14 x 15^2) x 20
v = (3.14 x 225) x 20
v = 706.5 x 20
v = 14, 130cm^3

Popcorn Lover's has more space.</sup>

Full Circle

r = d/2

r = 1/2

r = 0.5m

v = (πr^2) x h

v = (3.14 x 0.5^2) x 10

v = (3.14 x 0.25) x 10

v = 0.785 x 10

v = 7.9m^3

"Hole" Circle

r = d/2

r = 0.8/2

r = 0.4m

v = (πr^2) x h

v = (3.14 x 0.4^2) x 10

v = (3.14 x 0.16) x 10

v = 0.5024 x 10

v = 5.1m^3

7.9 - 5.1 = 2.8m^3

Concrete volume is 2.8m^3.

Final Percent Post

What is a percent?

A percent is a value out of 100, that can be expressed as a decimal, and a fraction. It is also another name for "hundredths".

- ex. 65% means 65 out of 100 or 65/100 or 0.65

Representing Percents (4.1)

To represent a percent, you can use hundred grids because they are out of 100.

- ex. 65%

Fractions, Decimals, and Percents (4.2)
Percents can be represented as fractions and decimals. To convert a percent to a decimal, you must divide the percent by 100. To convert a decimal into a fraction, you write the decimal as the numerator. However, the denominator depends on the place value of the decimal.

eg. decimal = 0.003 -> fraction = 0.003/1000 (because the 3 is in the thousandths place)
decimal = 5.98 -> fraction = 5.98/100 (because the 8 is in the hundredths place)

Now when the denominator is set, you must multiply the numerator until it becomes a whole number (or multiply it by the denominator).

eg. 0.003/1000 -> 0.003 x 1000 = 3/1000
5.98/100 -> 5.98 x 100 = 598/100

Lastly, you must simplify your fraction.

Percent of a Number (4.3)
To find a percent of a number, you can use mental techniques like halving, doubling, and dividing by ten.

When calculating the percent of a number, convert the percent to a decimal, and multiply it by the number.

ex. 12 1/2% of 50 -> 0.125 x 50 = 6.25
12 1/2% of 50 = 6.25

Combining Percents (4.4)
To solve certain problems, percents can be added together to form one percent.

ex. GST + PST = taxes
GST = 5% PST = 7%
taxes = 5% + 7%
taxes= 12%

There are two ways to calculate the increase of a number. They are:

a) Adding the combined percent value to the original number.

eg. 12% of 100 -> 0.12 x 100 = 12
12 + 100 = 112

b) Using a singel percent greater than 100, and multiplying that to the original number.

eg. 112% of 100 -> 1.12 x 100 = 112

Ryan's Scribe Post

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?

Math Info
* Original Price = $84. 00

* Price down by 25 1/2%
* 25 1/2% = 25. 5%

Math Info

* 25. 5% = $21. 42

The price was reduced by $21. 42.

10. When water freezes, its volume increases by approximately 10%.
a) By how much does the volume of 750mL of water increase when it freezes?

Math Info

* 10% increase

Math Info

* 10% = 75mL

The volume increases by 75mL when it has an original volume of 750mL.

b) What is the volume of ice created?

Math Info

* 750mL = 100%

* 10% = 75mL

750mL + 75mL = 825mL

The volume is 825mL.

16. Josephine scored 12 baskets out of 30 shots in her first basketball game this year. Her scoring average was then 40%. The next game, she made ten shots and raised her scoring average for both games to 50%. How many of the ten shots in the second game were baskets?

Math Info

First Game

* Scored 12 baskets

* Took 30 shots

Second Game

* Took 10 shots

* __ shots out of 10 = baskets

* Average = 40%

All Games

* Scoring Averge = 50%

* Took 40 shots [30 + 10]

* 50% of 40 shots = 20 shots

Math Info

* 8 shots out of 10 = baskets

8/10 shots were baskets.

Glenn's Pay it Forward

PART 1

Pay it Forward is when you help someone and you don't expect anything in return. When you give the cards to people they might do the same thing to other people and probably a chain reaction. In the movie I watched Pay it Forward, in the movie this little boy named Trevor tried helping three people. My act of kindness was giving out clothes and cards. (Part 2)

PART 2

I choose this first activity because my parents said that, giving out my small clothes to the salvation will help the kids/adults have some clothes. Ichoosed the second activity because my cousins that did this project gave me suggestions and they said they got a good mark. I helped the people without clothes. i did this on the Friday the 17th.

Part 3

My act of kindness went out really smoothly and great, when I gave out the cards and gave clothes it made me feel helpful. When Me (Glenn),Alec, Jayvee and Ryan gave out cards and clothes they all said," Oh why thank you. !" The next thing that happened was my group saying, "Pay it Forward !"... The peoples reaction was shocked and shy at the same time because they had a camera close to there faces. :)


PART 4

The idea of "Pay it Forward" is important because it can change the lives of people these days and it can make people be more nice. I think my act of interest did change some of the peoples interest because it can tell people that you are important in any way.

Alec's Pay It Forward Post

PART 1

Pay it Forward is when you help someone or something but you don't expect nothing in return. In the movie Pay It Forward Trevor has an assignment of what can you do to change the world. What Trevor planed is that he will help 3 people and those 3 people will help another 3 and on and on and on.

PART2

My Pay It Forward Act of Kindness is giving out clothes and merry Christmas cards.

I chose this activity because I figure it out that I have a lot of small clothes that I need to throw away and I think to myself that why not just donate this clothes for the children who doesn't have one. I also chose this activity because I think that we're the only group that give out Merry Christmas cards. We did this act of kindness last Friday December 17, 2010.

PART3

Our project went out well because we hand every single one of our cards and we also have collected many clothes to donate for children and adults who don't have one. It felt good when we hand out the cards because people from the Polo Park say Merry Christmas back and even greet us happy holidays too. Our group asked the people who we give cards from to pay it forward by giving it to someone that did something good to them or to a complete stranger.

PART4

I think the idea of paying it forward is important because it help's us to change other people's live and it make's us more nice. I think my act made a difference because it helps other people's live by having clothes to wear in a cold or hot day.

Ryan's Pythagoras Scribepost

5. A right triangle has side lengths of 40mm, 75mm, and 85mm.

a) Sketch the triangle. Draw a square on each side of the triangle.

b) What are the areas of the three squares?

The area for square a, is 1,600mm2 (squared).

The area for square b, is 5,625mm2 (squared).

The area for square c, is 7,225mm2 (squared).

c) Write an addition statement with the areas of the three squares.

a(squared)+b(squared)=c(squared)

40(squared)+75(squared)=85(squared)

1,600(squared)+5,625(squared)=7,225(squared)

7,225mm(squared)=7,225mm(squared)

10. A triangle has side lengths of 120mm, 160mm, and 200mm. Is the triangle a right triangle? Explain your reasoning.

Yes, this is a right triangle because the sum of the area of each leg, is equal to the area of the hypotenuse.

a(squared)+b(squared)=c(squared)

120(squared)+160(squared)=200(squared)

14,400(squared)+25,600(squared)=40,000(squared)

40,000(squared)=40,000(squared)

15. Construction workers have begun to dig a hole for a swimming pool. They want to check that the angle they have dug is 90 degrees. They measure the diagonal as shown to be 9.5m. Is the angle 90 degrees? Explain your reasoning.

No, the angle is not 90 degrees because the sum of the area of each leg, is not equal to the area of the hypotenuse.

19. A right triangle has a square attached to each side. Two of the squares have areas of 10cm(squared) and 15cm(squared). What are the possible areas for the third square? Draw a sketch for each solution.

There is only one possible area for the third square, and that is the sum of the area of each leg: 25cm(squared). There is only one possible area because it is a right triangle.

Ryan Sesame Street Video Post

Ratio:
Two Term Ratio

- Compares two quantities measured in the same units
ex.
- a:b
- a to b
- a/b
- ab (Ratio Table)

Three Term Ratio
- compares three quantities measured in the same units
ex.
- a:b:c
- a to b to c
- abc (Ratio Table)

Rate:
- compares 2 quantities measured in different units
ex. $100/10 books

Unit Rate
- a rate in which the second term is 1.
ex. 20km/hr

Unit Price
- a unit rate used when shopping
ex. $3/pizza pop

Proportional Reasoning:
- a relationship that says that 2 ratios or rates are equal
ex. 15 donuts/30 donuts are equal to 1 donut/2 donuts

Ryan's Math Profile

Hello, my name is Ryan and I am a grade 8 math student. If another person asked me if I like math, I would say that I like some parts of it. For example, I enjoy learning and solving problems with fractions, circles, equations, multiplication, and others. Although I dont't get 100% on all my tests, math is still a fun and interesting subject to learn about. In nursery, I remember we were doing subtraction with erasers. I liked this activity because the erasers had a soft feeling and they had smiley faces on them! I also knew what the difference was when my teacher would remove an amount of erasers from the pile. That is one reason why I enjoy math. It is simple and can relate to everyday situations.

Last year in grade 7, I really enjoyed solving bedmas problems, fractions, circle problems, equations, and converting values. The circle unit was pretty easy for me, because we just had to consider the formulas, and do the steps. However, I didn't like doing problems on the cartesian plane, because we had to draw too much and needed to much materials, and I kind of got lazy. I also didn't do well in solving patterns because I didn't understand how to write the formula for how "x" would equal "y", and it took me a long time to discover the pattern. I think that I struggled in some units last year because I gave up on it, got lazy, and didn't ask questions to see if my understanding was correct. So this year I will try to not get lazy.

To be a successful grade 8 math student, I will be sure to not get lazy, because I would do my work, and not ask people if I did it correctly. I would also contribute orally in class more often, to show that I am being cooperative in class discussions, and to help me understand more about each unit. I would want to learn more about square roots, and multi step equations. However, I would be willing to learn about anything that should be learned in later grades so that it would be easier for me when I get to that grade.

In grade 7, I contributed to creating scribeposts for my class. Here is part 1 of my post that I'm proud of, and this redirects you to the second part of my post. I talked about a part of the exam that we needed to review, and are proud of them, because it took me a long time and I thought I made it look organized and simple. I also thought that my pictures were neat, although some were pretty small. The light grey text at the bottom took me a long time also, because I had to think about all of the combonations of values you can convert. Grade 7 blogging, made me improve on explaining what I learned in that unit, and gave me and other students, opportunities to share our ideas, and questions that can get eachother thinking. I'll try to consider more links in my scribeposts, and visit websites that will help me with future units, and units that we are learning about now.