Kat's Scribe

May 13, 2008

Today in class, we were given a worksheet for homework. On one side, there are eight geometry questions. Here are the first four of these questions:

1. The length of a rectangle is 3 times the width. The perimeter id 96cm. Find the width and length.

2. The length of a rectangle is 5m greater than the width. The perimeter is 150m. Find the width and length.

3. The width of a rectangle is 12 cm less than the length. The perimeter is 156cm. Find the width and length.

4. The length of a rectangle is 2cm less than 7 times the width. The perimeter is 60cm. Find the width and length.




BUT WAIT!!

Before you attempt to solve these questions, take a look at the slide show beneath. It tells you 7 Steps to Solving the questions. It should make solving easier for you.

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And now back to the questions.

1. The length of a rectangle is 3 times the width. The perimeter id 96cm. Find the width and length.

2. The length of a rectangle is 5m greater than the width. The perimeter is 150m. Find the width and length.

3. The width of a rectangle is 12 cm less than the length. The perimeter is 156cm. Find the width and length.

4. The length of a rectangle is 2cm less than 7 times the width. The perimeter is 60cm. Find the width and length.

Chaseley's Scribe

Car Repairs

when you draw a t-table you have to make sure x is on the right if you are doing it from top to bottom. When it is laying down make sure the x is on the bottom.

When I said add one to figure number i meant to add one to x ( 1 + 1) . Then add 2 to y (1 + 2 = 3)

The algebraic expression I found was 2x - 1 =y.

Then I drew a chart to explain my answers.
When you draw a chart make sure you have your labels or you'll lose marks. When you number your chart always check if you marked it right on the line, not in the center. For "y" make sure you don't go up by 1,3,5,7,9,11. go up by 2's 3's 4's 5's or which ever way fits best. In this chart going up by 2's are the best.

Dhonell's Scribe Post

Today we learned about Algebra Tiles. We were given tiles which related to Algebra. Algebra looked like this.

The colored tiles were negative intergers. The white tiles were positive intergers. The little square is a 1. The long tile is the variable. While the big square is a variable squared.

In grade 8, you would only need to know about the long tiles and the small squares. In grade 9, you would use all 3.

We then learned about the terms we would need to know for Algebra.

Terms
Variables- n/x/any letter- any number can be a variable
Constants- +1/-1 -the number that never changes
Intergers
When you have intergers, think money.
- = owe money
+ = have money

We were then given practice questions to do.
Somethings to know before doing these qustions.
1 .Simplify liked terms
2 .Always try to have one variable & one constant on the other side of the equal sign.
3 .Variable goes first.
Here is some of the questions:
Example 1:

This is how the question would look like first(4n)(-2)(+1)(-3n). If you dont get the way the question is, you can put bubbles to seperate the intergers.
Then you notice that i put a red X through the white and green variable. That shows that there was a zero pair.
Next you simplify the liked terms. Where you get one positive variable and one negative 1.

Death Blow of Intergers

In this section, we talked about how if theirs intergers in questions with brackets, its a different story.
6 -(-3) When you see there are (-) signs touching, it means you can add.
6 + 3 = 9

6-(-3+2) When you get something like this, you do the brackets first.
6-(-1) = 7 Notice how the -(- looks like a plus sign. Thats a key trick when remembering (-) touch mean adding.

Conclusion
In class, we learned about algebra and got a ton of homework. Which im almost done so go me ! And thats all of my scribe post.

Chaseley's BOB

Surface Area Of a Rectangular Prism

surface area is the total amount of area a whole 3D shape contains.

formula: area front + area back+area side+ area side2+area top+area top+area bottom.

area front + area back = L x W
area side + area side2 = W x H
area top+ area bottom = L x H

SA = area front + area back+area side+ area side2+area top+area top+area bottom. SA= 2 (L x W) + 2(W x H) + 2 (Hx L)
SA= 2 (4cm ² x2cm ²) + 2 (4 cm ² x 2 cm ²) + 2( 2cm ² x 2cm ²)
SA= 2 (8cm ²) + 2 (8 cm ²) + 2 (4 cm ²)
SA= 16cm ²+16cm ²+8cm ²
SA= 40 cm ²

looks complicated ? REALLY ITS NOT :)

___________________________________________________________

volume of a rectangular prism

V=(L X W) x H
V= (17cm ² x 11 cm ²) x 1 cm ²
V= 187 cm ² x 1cm ²
V=187cm³

Volume is the amount of space an object takes up.

FORMULA: LxWxH= volume³

Dhonell's Bob

Surface Area

Surface Area is the area of the outside of a shape. Im going to show you how to get the surface area of a rectangular prism.

First you need to make a net. The net shows the front, the back, the top, the bottom, and the sides. But the front and the back are the same area, the top and bottom are the same, and so are the sides.

Once you have your net. You use the simple formula for adding the measuerments. (LxW)(WxH)(HxL) Since the net is flat, you have to square the number.

Well after you use the formulas with the measurements, you can add it up and get the surface area. You can use the example I gave you to help better understand.

Volume:
Volume is how much the entire shape takes up. To get the volume of a rectangular prism, you multiply the length (L), width (W), and height (H). That will get you the volume of the entire shape. The answer, is always cubed or in 3. ex. 18 cubic(3) centimeters.

Jocelyne's B.O.B.

Jocelyne's B.O.B.

SURFACE AREA:

The surface area is the area of the outside part of a shape. For a rectangular prism it would be the 2 sides, the top and bottom, and the front and back. A net is an easy way to show the rectangular prism's area .

The formula for this would be :

surface area = area top + area bottom + area side + area side² + area front + area back
OR
surface area = 2(L x W) + 2(H x L) + 2(H x W)
= 2(4cm x 2cm) + 2(2cm x 4cm) + 2(2cm x 2cm)
= 2(8cm) + 2(8cm) + 2(4cm)
= 16cm² + 16cm² + 8cm²
= 40 cm²

You can use the formula examples i showed you here to help you answer your own surface area question.

VOLUME:

The volume is the measurement of how much space the shape takes up. The answer is always cubed or in an exponent ³.The volume of a rectangular prism would look like this.


The formula for this would be:

volume = L x W x H
= 3cm x 2cm x 2cm

= 12 cm³
OR
volume = area of base x height

= 6cm² x 2cm
= 12cm³

Dhonells Scribe Post

Today in class, Mr Jerema told us to find the surface area of various shapes. We were told to to measure the sides of 6 different shapes and make a "net" view of each shape. For the scribe, I was assigned 3 shapes to do .
My First Shape :

My Next Shape Was :

My Final Shape Was:

Those were the shapes I had to do for the scribe. Sorry I didn't post this earlier.

-Dhonell R G.

Liezl's Pythagoras Growing Post

Part 1.

What is a Pythagorean Triple ?

A pythagorean triple uses 3 perfect squared numbers to answer this question a²+b²=c²

a and b are the legs of the triangle and when their numbers are added together they equal c which is the hypotenuse of the triangle.

An example of a pythagorean triple :

Part 2.


Part 3.

LeFrog
Lefrog stands 1.5 meters from a wall where a fly is 2 meters up. if Lefrog's tongue comes out of his mouth 70 cm from the ground, how far does his tongue have to stretch to eat the fly ?

First you use the info they gave us:

→ lefrog is 1.5 meters from the wall
→ the fly is 2 meters up
→ his tongue can stretch 70 meters


Here is a picture of what it might look like:



















Part 4.
Bubbles, Blossom and Buttercup were playing tag outside and Bubbles was it. Blossom was 7m away from Buttercup. Buttercup was 6m away from Bubbles. How far was Bubbles away from Blossom so that she can tag Blossom?

Katarina's Pythagoras Growing Post

Part One

Task: Describe what a Pythagorean Triple is and use your perfect square chart from 1 squared to 10 squared to find another one other than 3,4,5.

What is a Pythagorean Triple?
A Pythagorean Triple is a theory that states that the two side lengths of a right angle triangle(a & b) added together equal the hypotenuse(c). A² + B² = C²

Perfect Square Chart

When you look at the chart, you have to find which two perfect squares added together will equal another perfect square.
You can find that 6² + 8² = 10².

Part Two

Task: Using embeddable web 2.0, describe how to find the missing side of a Right Triangle using the Pythagorean Theorem, show how to solve both for a missing leg and the hypotenuse (note: you may use numerical examples ie. a=4 b=6 c=?)

Part Three

Question: You're locked out of your house and the only open window is on the second floor, 25ft above the ground. You need to borrow a ladder from one of your neighbours. There's a bush along side the edge of the house, so you'll have to place the ladder 10ft from the house. What length of ladder do you need to reach the window?

What do you know?

>The Window is 25 ft above the ground

> There is a bus that goes out 10 ft on the ground

>You have to lean the ladder on an angle to get it to the house

>You're trying to figure out how long the ladder is

Picture:

Part Four

You are stuck in a hole with an unconscious cannibal. You have to find a way to escape before the cannibal wakes up. The hole is 8m deep, so there’s no way you can climb out by yourself, so you look around and notice that there is a ladder laying on the ground beside you. You can’t lean the ladder directly against the wall because there is a pit of acid that is 4m long around the whole pit, kind of like a mote. So you have no choice but to lean the ladder 4m back. The ladder is long enough for you to get to the top of the hole. How long is the ladder?

Cedric's Pythagoras Growing Post

Part 1:
Describe what a Pythagorean Triple is and use your perfect square chart from 1 squared to 10 squared to find another one other than 3,4,5. (Note: You need a picture, not simply text.)

A Pythagorean Triple is that 2 side lengths (also called legs- A and B) added together
equals the hypotenuse (C). Also they use perfect squares to figure the hypotenuse.
(Means no decimal answers, just a whole number) It satisfies the solution:
a squared(a2) + b squared (b2) = c squared (c2)

A Pythagorean Perfect Square Chart.



Part 2:
Using embeddable web 2.0, describe how to find the missing side of a Right Triangle using the Pythagorean Theorem, show how to solve both for a missing leg and the hypotenuse (note: you may use numerical examples ie. a=4 b=6 c=?)

First we take 2 numbers (a=6 and b=8) and solve it. Take both a and b and make it
a squared + b squared =c squared. In numbers: 6 squared + 8 squared = c squared
6 x = 36 and 8 x 8 = 64. Add them together because it has to satisfy a squared + b squared =c squared.
36 + 64 = 100. 100 goes into 10. So C = 10 and C squared equals 100.

Here is a picture on what it looks like.
I used a picture cuz my bubbleshare and any other embbed thingies wont work. Ill change it when they start working. >.>


Part 3:
Explain how to solve a Pythagoras word problem. Use one of the examples we covered in class
(Worksheet A, B, LeFrog or Bonus Problem).

You're locked out of your house and the only open window is on the second floor, 25ft above the ground. You need to borrow a ladder from one of your neighbours. There's a bush along side the edge of the house, so you'll have to place the ladder 10ft from the house. What length of ladder do you need to reach the window?

What you already know.

-House to the second floor window is 25 ft.

-Ladder is 10ft from house.

Pythagoras Growing Post

Part 4: Now that you have seen many Pythagorean problems, create your own word problem.

My word problemo

My mom told me to get some cups from Wal-Mart. Wal-Mart is 12 km east from my house. Suddenly i got a phone call and she told me to get milk and SafeWay which is 10 km south from Wal-Mart. Now I had to go home. When i got home, i asked myself how much i walked from SafeWay to my house i guessed 99 km. How much did i walk from SafeWay to my house? was my normal guess right or wrong?

Part 1:
Describe what a Pythagorean Triple is and use your perfect square chart from 1 squared to 10 squared to find another one other than 3,4,5. (Note: You need a picture, not simply text.)

This is a picture of a Pythagorem Triple. A pythagorem triple says that the legs ( a and b) and the hypotenuse (c) of a right triangle follows the equation, a2 + b2 = c2. so if you add the legs together, you'll get the hypotenuse. This also shows that if you add the small square with the medium sized square, you'll get the biggest square. It uses perfect squares to find out the hypotenuse.


Proof

Perfect Square Chart

Here is the next pythagoream triple. It was quite easy to find out after you look at the perfect sqaure chart.

Part 2
Using embeddable web 2.0, describe how to find the missing side of a Right Triangle using the Pythagorean Theorem, show how to solve both for a missing leg and the hypotenuse (note: you may use numerical examples ie. a=4 b=6 c=?)

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Part 3
Explain how to solve a Pythagoras word problem. Use one of the examples we covered in class (Worksheet A, B, LeFrog or Bonus Problem).

I am going to explain how we solved LeFrog. First we had the question. Lefrog stands 1.5 meters from a wall where a fly is 2 meters up. If Lefrog's tongue comes out of his mouth 70 cm from the ground, how far does his tongue have to stretch to eat the fly?
LeFrogs tongue had to stretch 1.98 m to eat the fly.


To figure out this problem, you first look at the question and find out the lengths of the triangle to find the hypotenuse. The lengths of our triangle was 1.5 and 1.3. It was 1.3 on one side because of the calculations i did on the top left corner. We then had to find out the length of LeFrogs tounge. We then used our formula ( a2 + b2 = c2 ). We used this formula, when we got to c, we used our calculators to find the sqaure root of the number. Finally, we found the answer to how far LeFrogs tounge had to stretch to eat the fly.

PART 4 ABOVVE !!

Pythagoras Growing Post

A Pythagoras triple is like a mathematical equation which consists of a² + b² = c². You will have 3 perfect squares and if you add them together you will get a perfect square number. In the middle of the Pythagorean triple in this example, is a right angle triangle (90 degree angle). Where one side or square has a², another b², then c². Here we used the perfect square chart where 6² + 8² = 10². You can also use 3² + 4² = 5².






How to Find The Missing Side of A Right Triangle
Using the Pythagorean Theorem



#1
Well first we have to find out what are our sides. Here the right angle always points to the hypotenuse or c which is 10. a= 4 and we have to find out what b is. So what we have to do is make sure we have a formula to start off with then we insert our numbers 4² +b² = 10². Now we have to square the numbers, 4² become 16 and 10² becomes 100. To find b we have to go 16+16 = 100-16. So b² = 84. The square root of 84 will equal b which is 9.16. b=9.16
----------------------------------------------------------------------------------------------
#2
First start off with a formula. a² + b²= c². Then we punch in our digits 4² + 7² = c².Now we have to square the numbers 16 + 49 = 65. To find c we have to find the square root of 65 which is 8.06.


















Lefrog

question: Lefrog stands 1.5 meters from a wall where a fly is 2 meters up. if Lefrog's tongue comes out of his mouth 70 cm from the ground, how far does his tongue have to stretch to eat the fly ?

One of the word problems we had to do in class was lefrog. We had to find out how far lefrog's tongue had to stretch to reach the fly. The question was just like a find the missing side question where you have to find out c. Although you have to convert cm to m. Which equals 0.7m then subtract that from 2m. Then we have to find a right triangle and draw it out with 1.3 as a and 1.5 as b and then we had to find c. After we squared the numbers we got 1.69 + 2.25 = 3.94 m . c² = 3.94 . The square root of 3.94 = c or 1.98.

Word Problem

Mr. Triangle is traveling to Mr . circles house on a car . He isn't a very smart fellow either. So far he drove 6m east then turned south 9m. After he has hit the end of 9m he has to go for a pit stop and finds out that he might not have enough gas to reach mr circles house. How far does he need to travel?











Mr. Triangle has to travel 10.81m to travel to Mr. circle's house.

Pythagoras Growing Post

Part 1.
Describe what a Pythagorean Triple is and use your perfect square chart from 1 squared to 10 squared to find another one other than 3,4,5. (Note: You need a picture, not simply text.)

What is a Pythagorean Triple ?

A pythagorean triple is a triangle that has two legs and one hypotenuse. The legs are labelled as a and b and the hypotenuse is c. The theory of the pythagorean triple is when you add the side lengths a and b it equlas c. The equation would be a² + b² = c² .

An example of a Pythagorean Triple using the perfect square chart:
























Part 2.
Using embeddable web 2.0, describe how to find the missing side of a Right Triangle using the Pythagorean Theorem, show how to solve both for a missing leg and the hypotenuse (note: you may use numerical examples ie. a=4 b=6 c=?)

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Part 3.

Explain how to solve a Pythagoras word problem. Use one of the examples we covered in class (Worksheet A, B, LeFrog or Bonus Problem).

Lefrog stands 1.5 meters from a wall where a fly is 2 meters up. if Lefrog's tongue comes out of his mouth 70 cm from the ground, how far does his tongue have to stretch to eat the fly ?

First gather your information that you have now :

- lefrog is 1.5 meters from the wall
- a fly is 2 meters up the wall
- his tongue comes out of his mouth 70 cm from the ground

It should look something like this :

Lets start with the formula, it would be a² + b² = c². once you got the formula you start to fill in your formula with the information that you have already. a² + b² = c² now turns into 1.3m² + 1.5m² = c². With 1.3m² + 1.5m² = c² you have to square off the squared numbers to add it and so it equals c². Multiply the base numbers by itself.1.3m x 1.3m = 1.69m, 1.5m x 1.5m = 2.25m. Now you add those numbers together to equal c². 1.69m + 2.25m = 3.94m . Now you know what c² equals you just have to find the square root of it. You have to use a calculator for this so you just punch in 3.94 and press the square root button and that gives us 1.98. So now our answer is LeFrog has to stretch his tongue 1.98 m to eat the fly.


PART 4.

Now that you have seen many Pythagorean problems, create your own word problem.

Jim was riding his bike one sunny day and he rode down the block 8 meters until he hit a bush where a dog chased him to a parking lot . If the parking lot was 5 meters away from his house how far did the dog chase Jim from the bush to the parking lot ?

Pythagoras Growing Post

Part 1

Describe what a Pythagorean Triple is and use your perfect square chart from 1 squared to 10 squared to find another one other than 3,4,5. (Note: You need a picture, not simply text.)

This is a pythagorean triple. It uses perfect square numbers to satisfy a2 + b2 = c.

Part 2

Using embeddable web 2.0, describe how to find the missing side of a Right Triangle using the Pythagorean Theorem, show how to solve both for a missing leg and the hypotenuse (note: you may use numerical examples ie. a=4 b=6 c=?)

BubbleShare: Share photos - Powered by BubbleShare

Part 3

Explain how to solve a Pythagoras word problem. Use one of the examples we covered in class (Worksheet A, B, LeFrog or Bonus Problem).

LeFrog

Lefrog stands 1.5 metres from a wall where a fly is 2 metres up. If Lefrog's tongue comes out of his mouth 70 cm from the ground, how far does his tongue have to stretch to eat the fly ?

We needed to find what c was so we first change 700 cm into 0.7m by dividing 100 into 700. We then needed to subtract 0.7 from 2m to get 1.3. With a formula a2 + b2 = c2 we plugged in the numbers so now it was 1.3 2 + 1.5 2 = c2. Then got their squared number 1.69 + 2.25 = c2. Then we added them together to get c2 which is 3.94. Since we had to find c not c2 we found the square root of 3.94 which is 1.98.

Part 4

Now that you have seen many Pythagorean problems, create your own word problem.

A man named Johny went to buy groceries from Wal-mart which was 9 miles north from his house and after he was done he went home. Later Johny had enough money to buy a new laptop so he drove to Best Buy to buy one which was 16 miles east from his house. If Johny drove straight to Best Buy after he shopped at Wal-mart, how far would he have drove?

Kate's Pythagoras Growing Post

KATIE'S PYTHAGORAS GROWING POST

"Part One"

Task: Describe what a Pythagorean Triple is and use your perfect square chart from 1 squared to 10 squared to find another one other than 3,4,5.

What is a Pythagorean Triple?

A Pythagorean Triple is a theory that says the two side lengths of a right angle triangle added together = the hypotenuse. The equation for that would be:

A² + B² = C²

To find the next Pythagorean Triple you look at your perfect Square chart to figure out which will work.

When you look at that you have to decide which two perfect squares added together will equal to another perfect square.

Right away you can tell that 6² + 8² = 10²

Then you can draw it out.
















You can also show it this way:

A² + B² = C²
6² + 8² = 10²
36 + 64 = 100

It all means the same thing.


"PART TWO"

Task: Using embeddable web 2.0, describe how to find the missing side of a Right Triangle using the Pythagorean Theorem, show how to solve both for a missing leg and the hypotenuse (note: you may use numerical examples ie. a=4 b=6 c=?)

My Bubble Share

BubbleShare: Share photos - Play some Online Games.

" Part Three "

Question: You're locked out of your house and the only open window is on the second floor, 25
ft above the ground. You need to borrow a ladder from one of you rneighbours. There's a bush along side the edge fo th ehouse, so you'll have to place the ladder 10ft from teh house. What length fo the ladder do you need to reach the window?

So first you should lay out the information you know.
>The Window is 25 ft above the ground
> There is a bus that goes out 10 ft on the ground
>You have to lean the ladder on an angle to get it to the house
>You're trying to figure out how long the ladder is


Then Try to Draw it out... Like this...















You probably noticed its is a right triangle. After noticing that you can use the Pythagorean theorem to solve what C is. ( C is always the side the right angle is pointing to with its corner.) Since you know that A² + B ² = C ² you plug in the info you know already

The Theorem
A² + B² = C²

Then you put the numbers in you know. A² & B² can be swapped it doesn't matter what number is where. I always put the smaller number in A.
10² + 25² = C²

Then you have to square the numbers as the theorem states. All you have to do is take the base number and multiply itself by itself.
10 x 10 = 100
25 x 25 = 625

Then you put those numbers into your equation.
100 + 625 = C²

Now all you got to do to find out what C² is is add the two numbers together.
100 + 625 = 725

That means that C² is 725
C² = 725

Now you have to find the square root of that number to find out how long the ladder is.
The square root of 725 is :

Fraction :
















" Part Four "

Task: Now that you have seen many Pythagorean problems, create your own word problem.

My Word Problem

>>Giggle the snake was slithering through the park one day to meet up with his friend Shout. They started to argue about who was longer. Giggle said he was so long that he could reach all the way from the edge of the tree stump to the sticker half way up the side of the outhouse. If the outhouse was 8 feet tall and the stump was 6 feet away from the outhouse how long would Giggle have to be to be able to reach from the bottom edge of the tree stump to the sticker on the side of the outhouse?

ANSWER:

(Highlight to see text. It's in white so you don't see it until you want to)

This is all in words becuase I didn't know how to hide pictures.

If the outhouse is 8 feet tall & the sticker was half way up that means the sticker is 4 Feet high. Now you know that one of the legs is 4. The right angle is where the ground meets the outhouse.

To the edge of the tree stump is 6 Feet. To find the hypotenuse or how long Giggle's is all you got to do is follow this:

A² + B² = C²

4² + 6² = C²

16 + 36 = C²

C² = 52

The square root of 52 is 7 3/15 or 7 1/3 OR 7.21

THATS ALL FOR NOW :)