873 Math (2007)

Sunday, March 16, 2008

Karla's Pythagoras Growing Post

Part I:Pythagorean Triple

Mr. Jerema is teaching us about the Pythagorean Threom in which it states that if you add both legs of the right triangle(which is labelled a and b) is equal to the hypotenuse(which is labelled c) of the right triangle. (a squared + b squared= c squared.) This is how a Pythagorean theorem looks like:

To test if this theorem is right he taught us the Pythagorean Triple in which it uses a set of numbers (1,2,3,etc.). The numbers indicate the perfect squares which means there's no decimal used. For example: 3 squared + 4 squared= 5 squared

(9 + 16= 25)

a= 3 squared
b= 4 squared

c= 5 squared

3 squared= 9
4 squared= 16
5 squared= 25

But using another set of perfect square numbers we can test if this theorem really works. We could use the numbers 6 squared, 8 squared, and 10 squared.

(36 + 64=100)

a= 6 squared
b= 8 squared

c= 10 squared

6 squared= 36

8 squared= 64
10 squared= 100

Part II:Find the Missing Side

To find the missing side of any right triangle always remember the pythagorean formula (a squared + b squared=c squared). From this formula you can formulate other formulas you could use in finding the sides of a right triangle, like the legs or the hypotenuse.

A. HYPOTENUSE: for finding thre hypotenuse use the original formula. Always remember to find the hypotenuse it is where thew right angle always points.

example
BubbleShare: Share photos - Powered by BubbleShare

B. LEG(it's either a or b): write the original formula then formulate the formula you need for solving the problem. First thing is to write what you know to help you solve the problem.

example:

BubbleShare: Share photos - Powered by BubbleShare

Part III: Word Problems

Example: You've just picked up a ground ball at first base, and you see the other team's player running towards the third base. How far do you have to throw the ball to get it from first base to third base, and throw the runner out?

Baseball Field

Answer: you should throw the ball 127.28 ft far.

Part IV: Make your own Word Problem

Example: If you're climbing up a mountain whose height is 36 m high and the base is 10 m long across. How long would the slope be if you have to roll a ball down to the other side of the mountain from the top of it?

Saturday, March 15, 2008

Anne'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.)

The definition that Mr. Jerema gave us was:
"A Pythagorean Triple is a right triangle that uses a set of whole numbers (1, 2, 3....etc) that satisfy A² + B² = C²"

A pythagorean Triple is a right triangle where the sides are in the ratio of a positive integer or whole number.
Examples are] 3:4:5, 6:8:10, 5:12:13, 9:12:15, 8:15:17 etc.
The formula is simple] a² + b² = c² OR x² + y² = z²
You can invert that formula with the examples like this] 3² x 4² = 5²

perfect square chart
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100

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=?)

The first slides about the missing hypotenuse shows that the straight angle is 3 and the other straight angle is 4, is can be labelled either a or b. But let's say that a = 3 and b = 4. Now we have to find the missing side, since the right angle is in the bottom left corner, pretend to draw a little box to make sure that it is a right angle. Now if you can imagine the box, it would be pointing to the line.. which is the hypotenuse. We have to figure out what the hypotenuse is so we first:
write down what we already know
then write down the pythagorean thereom
then transfer that into the squared numbers
then transfer that into their standard form
then add it together and you get the number
but after you have to figure out the square unit for the number
in this case, the number is 25,
which is easy because the square unit is perfect since 5 squared = 25.

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've just picked up a ground ball at first base, and you see the other team's player runnig towards thrid base. How far do you have to throw the ball to get it from first base to thrid base, and runner out?

I highlighted half the square because it made a right triangle. Since all the sides are 90 squared except for the line running through third base and first base. That was the hypotenuse.

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

Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point?

Angelo's Scribe

Mr. Jerema is teaching us , and he introduced "Pythagoras" to us. We learned that a triangle can also be a right angle.
We first learned about the three basic angles. He showed us that a circle has a 360º angle. If we cut the circle in half it will be 360 divided by 2 and it will turn into a 180º angle, also known as a straight angle. If we cut the semi - circle in half, it will be 180 divided by 2 and it will turn into a 90º angle, also known as a "right angle."

So if we make a right angle and then add the extra line to make it a triangle, it will make a "right angle triangle." In a right angle triangle, there are two legs and a hypotenuse. The legs are the two lines to make a right angle, and the hypotenuse is the longest line.The legs can also be labeled "a" and "b." The hypotenuse will always be a "c."

To find the area of a rectangle, you would have to multiply the length (a) and width (b) together. But if you want to find half of the area, it has to be Length(a) times Width(b) divided by two. If you want, you could also cut the rectangle in a triangular way (it will be the same thing).

Tuesday, February 12, 2008

Lester's Scribe

my scribe is question 4 and 9 in the C66 Paper that mr harbeck gave us

Question Number 4

BubbleShare: Share photos - Green Toys

Question 9

BubbleShare: Share photos - Green Toys

Monday, February 11, 2008

Karla's Scribe Post

Today we were told to anwer 5 questions from the paper that was givento us and we need to answer it into 2 different ways. In this scribe post 2 examples of the word problems are disscussed.

Q1:Andrea cur 62 1/2 inches of ribbon into 4 equal hair ribbons. How long was each hair ribbon?

Answer: Each ribbon would be 15 5/8 inches long.

Solution#1:

1. change mixed fraction to improper fraction

2. get the reciprocal of the divisor which is 4 becomes to 1/4

3. do multiplication

4. simplfy your answer

Solution#2:

1. change mixed faction to improper fraction before doing the ratio table.

2. on the right side divide 4 by 4 or multiply by 1/4 to get 1 as your answer.

3. on the left side do the same thing and simplfy your answer.

Q2:Dawn has 12 yards of silk. She needs 1 1/4 yards of silk to make one skirt. How many skirts can she make?

Answer: She can make 9 3/5 of skirts.

Solution#1:

1. change mixed fraction to improper fraction.

2. then get the reciprocal of the divisor which is 5/4 becomes 4/5.

3. multiply the fractions.

4. simplfy your answer.

Solution#2:

1. change the mixed fraction to improper fraction before doing the ratio table.

2. on the right side multiply 5/4 by 4 which gives you 20/4

3. then divide it by its denominator which is 5 and gives you the answer of 1.

4. do the same thing on the left side and simplfy your answer.

Monday, February 4, 2008

Mya B`s Scribe ,

This scribe is about Ratio tables,How many groups of ___ are in ___ ?. , dividing , and multiplying.
So, the question would be how many groups of 1/8 are in 2/5 ?