Linda's Journal Entry

(Click picture to enlarge)

Scribe Post for February 23, 2010

Click and enjoy :)

Blogging for Mr. B :)

Hey there. As you can probably see, practically the whole class blogged especially for you! Doesn't this show how special you are to all of us? Well, I for one think so! You helped us grow not only as a student but as a person as well, and in such a short period of time too. I know a lot of times I make a lot of silly mistakes, but I'm glad you're always there to tell me where I'm going wrong. I sincerely hope that you'll be back to teach us all again soon because math class just isn't the same without you! We know that you're going through some emotional issues at this time, but you don't have to go through it alone. SPS is your #1 support team. Especially THE CLASS :) So of course we miss you! You've helped us out so much and it's only fair that we help you out! We wish you a Merry Christmas and a Happy New Year!

PS: Your mission for the holly days is to smile at least TEN times a day even if you aren't happy. Your smile makes someone else smile, and if you see someone smile, you'll smile, too :)

Re-Made Rational Number Video

Well guys, since the video Joseph posted many weeks ago had a bit of problems, Karen, Linda and I decided to fix it up. However, being what society is today, we put it off quite some bit. So sorry if it's hard to understand, or if the voice is a bit off.



PLEASE comment. Constructive criticism is always welcome. I'm pretty sure we also had some mistakes in there, but hey, nothing is ever perfect.

Question #13

Hi 9-05! I'll be here to explain to you all how to do question 13 in our textbooks!

13. The diameter of Pluto is 6/17 of the diameter of Mars. Mars is 17/300 the diameter of Saturn.
a) What fraction of the diameter of Saturn is the diameter of Pluto?

Okay, so the first thing we do is organize our information.

What We Know:
Pluto = 6/17 diameter of Mars
Mars = 17/300 diameter of Saturn

Goal:
Find Pluto's diameter of Saturn

Keyword(s):
Of - indicates multiplying
Fraction - indicates the answer form

Okay, now we can begin with actually answering the question.

How To, and Why?:
Since the word "of" is present, we need to multiply. Our goal is to find Pluto's diameter or Saturn so we multiply Pluto's diameter or Mars by Mars' diameter of Saturn because Mars' diameter is in relation to Saturn, and Pluto's diameter is in relation to Mars.

Wow, that was really ugly and time consuming. Let's try that again!
That's much better. Go ahead, try it on your calculator! It should work.

b) The diameter of Saturn is 120 000 km. What is the diameter of Pluto?
Okay, so we know Pluto's diameter of Saturn now, which is 1/50. But, just because, let's organize our information again, shall we?

What We Know:
Pluto's diameter of Saturn: 1/50
Saturn's diameter: 120 000 km
Measurement: Kilometers

Goal:
To find Pluto's diameter in kilometers

Keyword(s):
Kilometer - indicates what unit of measurement the answer should be

Okay, so since we know what Pluto's diameter of Saturn, and we know what Saturn's diameter in kilometers, all we need to do is multiply.

So that's how you do it! Comment if you're confused, have any questions, or just because! :)

Scribe Post November 25 2009

Question #20

Hell0 9-05! Linda here to explain how to do Question 20 from our math textbooks. Hopefully I've done this question correctly and you'll all have learned a thing or two. If not, I strongly suggest you comment about it! Read on, faithful bloggers!

20) Research to find out the current price of gasoline in Calgary, Alberta. It is 300 km from Calgary to Edmonton. How much would it cost to drive this distance in a car with a fuel consumption of 5.9 L/100 km than in a car with a fuel consumption of 9.4 L/100 km? Give your answer in dollars, expressed to the nearest cent.

WHAT WE KNOW
Distance = 300 km
Car A gas average speed = 5.9 L /100 km
Car B average speed = 9.4 L /100 km
Gas Price: 88.9 (This was found online)

ULTIMATE GOAL
To find out how much gas money Car A and Car B needs
To find how much more money Car B needs than Car A.

We know how many litres are used for 100 km, but we need to know how many litres it takes to go 300 km since that is the distance from Calgary to Edmonton. So we need to multiply 100 km by 3, and 5.9 L by 3 in order to find the amount of litres used for 300 km. The process is shown simply below.

(Note: If you have difficulties with multiplying decimals, I strongly suggest reading past scribes or consulting Mr. B)

OK! So now we know the total amount of litres it takes to get from Calgary to Edmonton using Car A: 17.7 Litres. Now we need to know how much it will cost, so we multipy the litres by how much litres cost.

So we know how much money Car A needs for a 300 km trip to Edmonton from Calgary. But we still need to figure out how much Car B needs for a 300 km trip from Calgary to Edmonton. Remember! Our GOAL is to find out how much more money Car B needs more than Car A.

Now we need to find how much gas money Car B needs. We follow the same process.

Here is where we multiply the total amount of litres by how much gas costs per litre.
Alright then! Now we know how much gas money each car needs in order to complete the 300 km trip to Edmonton! Our final GOAL is to see how much more money Car B uses than Car A. All we need to do now is...
Yup! That's right, find the difference! Car B used $9.40 more than Car A.


Thank you for reading my post! I look forward to reading all of yours and posting comments, as I hope you will comment on my post, too!

Rational Numbers

The term "Rational Numbers" refers to the fact that a rational number represents a ratio of two integers. Rational Numbers are numbers that can be expressed exactly by a ratio of two integers. Or more simply put, a rational number is an integer that can be expressed as a simple fraction. An example of a rational number is 5 because 5 can also be expressed as 5/1, or 4 because 4 can be expressed as 16/4.

An irrational number is a number that cannot be written as a simple fraction and has a decimal that goes on forever without a pattern. An example of an irrational number is Pi - 3.14159265... etc.

Question 11

11. List places or situations in which surface area is important. Compare your list with those of your class mates.

1) If you're buying carpet/tiles for flooring.

- You would need to know surface area of the room to know how much carpet/tiles you need to buy.

2) If you're painting the walls of a room.

- You would need to know how much paint to buy to make sure you have enough paint.

3) If you're a carpenter.

- When you're a carpenter you deal with a lot of measuring and with surface area because they need to know those kinds of things.

4) When you're buying furniture.

- If you are, you would need to know how well the furniture would fit into the room.

5) When you're kitchen cabinets.

- You would have to calculate the surface area of the kitchen cabinets and kitchen to figure out how the kitchen cabinets would fit into the kitchen.

6) When you're buying a hat.

- When you're buying a hat you need to know the surface area of your head and hat to see if the hat with fit your head perfectly.

7) If you're a construction worker.
- If you're a construction worker you have to know if whatever you're building will fit in the designated site.

8) If you're a contractor

- Contractors deal with construction or furnishing homes, so you would need to know how to calculate surface area.

9) When you're planning a big event.

- You have to know the surface area of the site and how many objects and people could fit into the site.

10) When you're building a CD rack.

- When you're building a CD rack, or any other shelf-like object, you would have to know the surface area of the objects the shelf or rack would hold, and how well it would fit inside of a room.

11) When you're potting plants.

- If you are potting plants you have to know the surface area of the plant so you know how much you have to dig in the ground so the plant has enough room in there to fit.

12) If you are an archeologist.

- If you were an archeologist and found dinosaur bones you'd need to have the information about those bones written out. That information would probably entail having to find the surface area of the bones.

13) If you're designing a shoe.

- If you were to design a shoe you would need to know the surface area of the foot so you know how much bigger the shoe has to be in order for the foot to fit inside comfortably.

14) If you're designing house hold objects.

- You would have to know how to find the smallest surface area possible so that the objects could fit nicely in a cupboard.

15) When you're watering your lawn.

- You would have to know the surface area of your lawn to know how much water would be used.

16) When you're putting up wallpaper.

- You would have to know how much wallpaper would cover up how much wall space.

17) Building a bird house.

- You would have to be able to calculate the surface area of the bird house so you know the measurements when you're constructing it.

Elegant Algabraic Expressions

Hi 9-05! Mr. B has assigned us all some homework for the weekend. We're supposed to answer a few questions about surface area, so I'm going to answer mine in the most blunt way possible.

WHAT IS THE MOST ELEGANT ALGEBRAIC EXPRESSION FOR ...

... surface area of a cube?

Well, you see, a cube has 6 faces and each of those 6 faces are equal. Since each of those faces are equal, whatever length one side is would be squared.

i.e. 3 by 3 cube

The most elegant algebraic expression for a cube would be 6s²

Example:
SA= 6s²

SA= 6(3²)
SA= 6(9)
SA= 54u²

... surface area of a rectangular prism?
Being a prism, a rectangular prism has 6 faces. Although, unlike a cube, a rectangular prism does not have all equal sides. A particularly good way to see how to calculate surface area of a rectangular prism wold be to see how its net looks like.

Seeing the measurements is a good way of seeing what parts of the rectangular prism have plane symmetry. The net above, however, is not the only way to portray the net of a rectangular prism. It's actually kind of confusing, but the picture itself is quite clear.

The most elegant algebraic expression for a rectangular prism is SA= 2(lw) + 2(hw) + 2(hl)

Example:

h=5

l=4

w=2

SA= 2(lw) + 2(hw) + 2(hl)

SA= 2(4)(2) + 2(5)(2) + 2(5)(4)

SA= 2(8) + 2(10) 2(20)

SA= 16 + 20 + 40

SA= 76u²

*remember to always add in the u² after your answer because we're dealing with 3D shapes

... surface area of a cylinder?

I'm sure all of you are familiar with how we learned this formula last year, where we just found the area of the two circles and the rectangle of the cylinder and added them all together. As you all should know, we learned a different way to calculate surface area of a cylinder.

During one of our math classes we learned that the circumference of the circle of the cylinder is equal to the width of its rectangle. To test this out just roll up a rectangular peice of paper and look at the circle and see that its width goes all around the circle, or rather the circumference.

Since we're calculating surface area of a cylinder, we know we need to have the formula for area of two circles. The formula for a circle is πr², so the formula for two circles would simply be 2(πr²). Now we need to find the area of the rectangle of the cylinder. We know that the width is equal to the circumference of the circle, and area of a rectangle is (lw) so we multiply 2πr by height, which is like the length of a rectangle.

So the most elegant algebraic expression for a cylinder is SA= 2(πr²) + 2πrh

COMPOSITE SHAPES
I actually didn't know what a composite shape was at first, but I found that it's a figure that can be divided into two or more shapes. This was what Mr. B has been telling us about for the past couple of days, but I didn't know what the technical term was then.
I think the best way to calculate the surface area for composite shapes is to look at the figure from all angles and add it all up because this can apply to all composite shapes. Some composite shapes have holes and spaces in them and this can make calculating surface area for composite shapes confusing.

HOW DOES SYMMETRY HELP US SOLVE SOME OF THESE SURFACE AREA PROBLEMS?
A figure usually has 6 faces; 3 sets of 2 symmetrical faces. Plane of symmetry are imaginary lines drawn on polyhedrons to show that both sides are symmetrical. Imagine these lines as if they cut right through the polyhedron. Symmetry helps us solve for surface area because if we see one face we know that on the opposite side there should be another face just like it. This rule usually applies for regular shapes, however. Understanding symmetry allows us to see that if one side has a measurement of so-and-so, then the other side should have that same length as well.

WHAT HAPPENS IF A PART OF ANY OF THESE SHAPES IS MISSING? HOW DO I FIND SURFACE AREA THEN?

Most polyhedrons usually have plane of symmetry. We can use plane of symmetry to find the missing part of a shape by finding its symmetrical other.

Example of Plane of Symmetry:

I hope in one way or another this has helped! Please feel free to comment! :)

Why 360°?

Hello 9-05 and 9-06! So Mr. B assigned 9-05 (because we're going to be the class) to make a post explaining to 9-06 why we use 360 all the time. I hope this short and concise post will be helpful to you!

First of all, 360 is a very round and friendly number to use. It's divisible by a lot of numbers (24 to be exact). Secondly, the Babylonians were devoted to geometric figures, and they based their number system on the number 60 rather than 10 like we usually do. This number system is called the Sexogonal System. Their calendar even had 360 days and their complete cycle was divided up into 360 units. We have adapted from the Babylonians because our clocks have 60 minutes and each minute is 60 seconds.

Here is an example of the Babylonian's number system.

The Babylonians thought that there were approximately 360 days in a calendar, since the Earth rotated about 1 degree around the Sun per day. So, when the Earth makes a full rotation around the Sun that would be a full circle. That's why the Babylonians used 360 to represent a full circle. Our place value is ones (1) tens (10) hundreds (100) thousands (1000) etc. because our number system is based on 10. As mentioned previously, Babylonians used the Sexagismal system. In the chart above, you can see all the symbols for each number character. I think that the 59 symbol and the 1 symbol would be the representative for the number 60, or perhaps the 50 symbol and the 10 symbol would be the representative for 60. I am not sure, because of the sites I've encountered, they were unclear about this. I think that the next place value would be something like 120 and it could be a combination of two 50 symbols and two 10 symbols or a 20 symbol, which is actually two 10 symbols. I think that an easier way to write these numerals using our number system would be 50 and 10 for 60. 50 and 50 for 100, etc.
So that is basically why we use 360̊̊ to describe a full circle. If I've missed anything, feel free to comment!

OTHER SOURCES:

Link one

Link two

Link three

Scribe for Tuesday September 29 2009

Hi, 9-05! Today we had a bit of homework, which was to study for our test on Thursday, to accept the blog authorship and to write in your journal (which you should be doing daily).

In class we were using 3D shapes (i.e cube, rectangular prism, isosceles triangular prism, etc.) and counted the lines of symmetry. When you are counting the lines of symmetry of a 3D object you have to count the lines as if they're like saws cutting through the object. You can see the equality better that way. This is plane of symmetry. When you're looking for lines of symmetry, it's easier to look for two faces that are parallel to eachother.

Towards the end of class we discussed nets of rectangles and cubes. We were given graph paper and were instructed to make a 2x2 cube and a 3x2x1 rectangle. We found that 6s² is the most elegant algebraic expression for surface area of a cube. You multiply 6 by one side (currently represented as s), and you square that because cubes are equal all around. We didn't have enough time to confirm what the proper algebraic expression is for a rectangle, so hopefully we will by tomorrow! :P

Remember ...
Tessellation means tiling, having to do with patterns.
The corner of a shape or figure is called a vertex.
... to study for the test :)

Feel free to comment if I've missed anything. Good luck everyone!