Thursday, May 11, 2006

Rainer's Growing Post


------Questions for May 15th------


1. What is meant by the terms "rotation symmetry" and "reflection symmetry?" How does this relate to pentominoes?

Pentominoes are shapes that could be form using 5 squares. The pictures on the left are the 12 unique pentominoes.
Rotation symmetry or rotating any shape makes an identical shape of the original shape. Using the method of rotation symmetry to a pentomino will make a different but still similar pentomino. This does not make the new pentomino unique. Because it has a similar pentomino.
Reflection symmetry or flipping any shape makes a mirror image of the original shape. Also, using this method to a pentomino makes the mirror image of the original pentomino. It doesn't make the pentomino unique because it has a very similar image ^_^ .


2. Create a pattern. You must represent this pattern both pictorially ( i.e. with picture or diagram ) and with numbers. You must show the first 4 steps of your pattern.
shape # 1
shape # 2
shape # 3

shape # 4

3. Describe in words what is occurring with your pattern and if your pattern has an ending or if its continues on indefinately.

This shape is like stairs. It started as a 3 blocks by 3 blocks figure ( shape # 1 ). You keep adding the next set of blocks at the bottom and the bottom-right corner of the shape. So if you add the next set of blocks the shape will be longer at the left side and at the bottom side, like what is happening to the next 3 shapes. This pattern continues on and on forever. It adds more and more set of blocks than anyone could imagine.

4. Create a T-chart that shows what is happening with your pattern.

To get shape 6 and shape 8 you must figure out a formula that works for every shape with or without shape 1. I can't figure out the formula so what I did is count. I'll try to figure out the formula but in the mean time I'm done my post.

------Questions for May 23rd------

1. Solve all 3 parts of the problem below


Jack collects baseball cards. Jack has 180 baseball cards in his collection. At the end of each month Jack buys 25 baseball cards to add to his collection.


a)Create a T-Chart showing how many baseball cards Jack has at the end of the next 4 months.


b)Create an algebraic formula based upon the problem above

For this problem the starting point is 180, the change is +25, and the variable ( n ) is the number of months.

180 + 25n = the number of cards

c)If Jack just turned 8 years old this month and Jack continues to buy the same amount of baseball cards each month, how many baseball cards will jack have when he turns 12?

180 + 25n =

180 + 25(48) =

180 + 1200 = 1380

When he turn 12 years old he would have 1 380 baseball cards.

2. Use the chart to figure out the questions below.

Jackie is planning on having a pizza party with some of her friends. She is trying to figure out how many pizzas to order. She knows that each pizza has six slices of pizza.


a)If Jackie thinks that there will be four people at the party (counting herself) how many pizza’s should she order?

According to the graph, 4 people at Jackie's party ( counting her ) will eat a total of 12 slices of pizza. There are 6 slices in a whole pizza. So, 12/6 = 2 . Jackie will need to order 2 whole pizzas.

b)If two more people show up at the party how many more pizza’s does she need to order?

2 more people is 6. 6 people at Jackie's party ( counting her ) will eat a total of 18 slices of pizza. 18 slices of pizza divided by 6 slices per pizza is equal to 3 whole pizzas ( 18/6 = 3 ).

3. Answer the questions below based upon this information


Kathy has $20 in her savings account. Each month she adds another $15 to her savings account. In order to calculate how much money she will have in one year Kathy has created this algebraic formula: 20 + 15n = Savings amount


a) Calculate how much money Kathy will have in one year

20 is our starting point. +15 is the change of her savings account. Her variable is n It represent the number of months not the number of years.

20 + 15n =

1 year is 12 months. So, our n represents 12.

20 + 15(12) =

20 + 180 = 200

$200 = savings account

Kathy will have $200 in her savings account in 1 year.


b) Suppose Kathy counted wrong and she really has $25 in her account instead of $20. Change the algebraic formula to reflect this miscalculation.

Instead of 20 our starting point is now 25 since Kathy has really $25. The rest of the algebraic formula is still right

25 +15n = savings account

So,

25 + 15n = savings account

25 + 15(12) = savings account

25 + 180 = savings account

$205 = savings account

or

you could just add $5 to the previous answer

200 + 5 = $205

4. Solve the following equations. Show all of the steps that are needed.

We start with working on the equations in the brackets ( ) .

Then, we do the like terms on the same side of the " = " symbol.

Next you combine all the variables ( n ) in one side of the " = " symbol.

By then you have everything you need to know what the variable stand for.


a) 3n + 4n + 7 = 2n + 12

3n + 4n + 7 = 2n + 12

7n + 7 = 14n

14n = 14n

14n = 14

14n/14 = 14/14

n = 1


b) 8n - (4 + 9) = 11

8n - (4 + 9) = 11

8n - 13 = 11

8n - 13 + 13 = 11 + 13

8n = 24

8n/8 = 24/8

n = 3


c) (8 - 3 )n + 7n + 8 = 4n + 40

(8 - 3 )n + 7n + 8 = 4n + 40

5n + 7n + 8 = 4n + 40

5n + 7n + 8 - 8 = 4n + 40 - 40

5n + 7n = 4n

12n = 4n

12 = 4n

12/4 = 4n/4

3 = n




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3 Comments:

At 3:57 PM, Blogger -rain- said...

i'll finish it later....

 
At 8:44 PM, Blogger Mr. Reece said...

The only area that you really need any attention to is reflection and rotation symetry. While you did a good job relating these two terms to the pentominoes you didn't really explain what they are in the first place. Otherwise great job Rain.

Mr. R

 
At 12:39 PM, Blogger Mr. Reece said...

Great job with the first post Rainer. I enjoyed the unique pattern that you decided to create.

The mark for the first post is 19/20

Mr. R

 

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