Well today in class we graded the homework of p. 301 #15-32 and p.310 #15-38 and we discussed about the project. Next Wednesday, the 10th, we will have the presentations to Elementary. You have to go to school that day, becasue it's worth 20% of the project and if you miss, there is no way to make it up. The grades of the projects will be individual, and everything must be in English. There will be three parts of the project for the kids. The history, which Ms. Saatkamp chose the history activity that Mayu, Carin, Pamella, Bernie, and Jenni made (the one in the shape of a tangram). The people that are going to present history to the kids are: Mayu, Lucas, Malena, and Carin. Then there is the story, that the group itself will choose from the three options. The people in the story are: Bernie, Gina, Jenni, Ricardo, Giovanni. And finally the last activity is making games where you will interact with the kids, The games must involve tangrams, and must be fun for 1st graders. The people here are: Javier, Alexandre, Florence, Franklin, Guilherme, Pamella.
The homework was a pain, because we returned to 8th grade subjects, an Ms. Saatkamp wasn’t too happy with our confused faces. In the first homework there is a lot of system of equations, which is when there are two variables in an equation, so when this happens, you have to isolate one of the variables in one of the equations, and then substitute the same letter. For example: if 4x=y+2 and 7x=2y, then you can isolate y in the first equation, which would be y=4x-2. So then you isolate the y in any of the equations, 4x=4x-2+2 (it’s a kindof easy example). The killer today was actually #26, because it went back to the quadratic formula:

#26)

y2 = 49 so y = 7 or -7
x2 = x+6
x2 – x – 6 =0
a x2 +bx+c=0 quadratic formula
a= 1
b= -1
c= -6



so x= (1 +/- square root of 1+24) divided by 2
so x= 3 or -2

The next homework was also very difficult, because the diagrams were hard to read, but most of them used the idea of isosceles triangles, because there are four isosceles triangles made from the diagonals in a rectangle. The idea of exterior angle also comes in useful when reading diagrams.

In the beginning of the class we corrected the homework that was due today:

Most of the questions used the definitions below, that’s why she reviewed them after the homework.

They were:
- Definition of parallelograms: Both pairs of opposite sides are parallel- Theorem 6-1: Opposite sides of a parallelogram are congruent.- Theorem 6-2: Opposite angles of a parallelogram are congruent- Theorem 6-3: Consecutive angles of a parallelogram are supplementary- Theorem 6-4: The diagonals of a parallelogram bisect each other


Many people had problems on doing # 34 and 35, so I’ll explain them now:
34)
N C


Q






M T

And (NQ= 3A + 18) NT=12a QC= a + 2b QM= 3b + 1(that was the given)

NQ=1/2 NT(because the diagonals bisect each other)
So
3a+18=1/2(12a)
3a+18=6a
18=3a
a=6
So if you replace
6+2b=3b+1
5=b












P
35) A B 42
148



S Q



D C


13




Then by using all you know (consecutive angles are supplementary, opposite angles are congruent, etc) you’d find the blue angles. The goal was to get angle APS hint remember the things on the parenthesis.



Then we learned new theorems:

Th 6-6 : If: a quadrilateral has both pairs of opposites angles congruent.
(converse Then: It’s a parallelogram.
of 6-2)

Th 6-7 : If: a quadrilateral has diagonals bisecting each other.
(converse Then: It’s a parallelogram.
of 6-4)

PS: Th 6-3 doesn’t have a converse because it’d affect trapezoids.

Th 6-8 : if: only one pair of opposites sides of a quadrilateral is both parallel and congruent.
Then: it’s a quadrilateral
Ms Saatkamp repeated it like 100 times that is only one PAIR of opposite sides not any side of the figure, she even put stars near this theorem.

Then we learned about rectangles:

Def. It’s a quadrilateral with 4 right angles (PS: it has also the properties of a parallelogram, but the definition still the same, it just needs to be a parallelogram to be a rectangle.)

Th 6-9 : If: a parallelogram is a rectangle
Then: its diagonals are congruent
Th 6-10: If: the diagonals of a parallelogram are congruent
(converse Then: the parallelogram is a rectangle
Of Th 6-9)

Our homework is Page 101 # 15-32 all +page 110 # 15-38 all

In te beggining of the class, as usual, we corrected the homework due today. Number 26 brought lots of difficulties. Ms. Saatkamp corrected it on the board, and showed it is very important to keep what we learned last year in Algebra 1: in this exercise, for example, we use quadratic equations with the quadratic formula (ax²+bx+c=0).


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Afterwards, we reviewed what we had learned until now, and were introduced to our new topic (in red) - lesson 6-3: Notice the rectangles only have one property. That is because they belong to the parallelograms' category, so rectangles has the same traits of the parallelograms plus a special characteristic - 4 right angles.





Defining triangles, we learned that they are QUADRILATERALS with 4 right angles. There is no mention about being a parallelogram: it is something we have to prove, using theorem 6-6.

Further in Lesson 6-3, we learned two new theorems:

• Theorem 6-9: If a parallelogram is a rectangle, then it's diagonals are congruent.
• Theorem 6-10: if a parallelogram has congruent diagonals, then it is a rectangle.

Our homework for this chapter is page 310 #s 15-38 all.

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We also talked about the presentation we are doing next week for the elementary students. he presentation will be divided into 3 categories. Bellow you can see who is in charge of what, and what each category is about:

1. Introduction - brief introduction to Tangram history and explanation of the shapes (what they are, how the game works,...). In here, we decided to use the power point of one of Giulia's group (I'm sorry, I forgot the other members). People in charge of this are Luiza Cristina and Giulia
2. Story - in here, we will choose one of the stories of the origin of Tangram invented by the groups, and present to the children, in an entertaining way. Members of this group are Ana Beatriz, André, Luiza Siqueira, Luis, and Luiza Cristna
3. Playing with kids - people of this group will prepare games, competitions and "gincanas" to interact with the kids. Ms. Saatkamp asked for simple, easy games to be done, since the time these persons will have to present may be very short or very long. One of the options given by Ms. Saatkamp was dividing the kids into groups, with one person in charge of each. We can focus on a theme, like Christmas. People in charge of this are Gabriel, Gustavo, João, Guilherme, Phil - and, as back up, André, Ana Beatri and Giulia.

We do have two very important things to keep in mind in here:

• First of all, we cannot forget to do all the presentations in ENGLISH, which is required by our teacher for the grading - she said if we don't follow this rule, we WON'T be graded
• All of us will present in only one class period, which means we can't have huge presentations. We have to be brief and go directly to the point, but, of course, be sure that the children understand what we are talking about
• We have to pay attention to the language and entonation. THEY ARE FIRST GRADERS! We cannot say "this is a parallelogram", for they won't understand. We have to look for simple words for the explanation
• Last, and extremally important: the key word for all this is INTERACTION. That means we have to interact with the children, be creative so that it doesn't get boring, and teach them with good strategies.

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Well, that was it... See you guys tomorrow ;D

9B - 12 / 2 / 2008

In the beginning of the class we review what we learned yesterday:
- Definition of parallelograms: Both pairs of opposite sides are parallel
- Theorem 6-1: Opposite sides of a parallelogram are congruent.
- Theorem 6-2: Opposite angles of a parallelogram are congruent
- Theorem 6-3: Consecutive angles of a parallelogram are supplementary
- Theorem 6-4: The diagonals of a parallelogram bisect each other
Then we corrected the homework that was due today.

Somethings to remember that we used in the hw and will be on future tests:
1- To check if the diagonals are congruent or bisect each other you will need to calculate FOUR distance formulas.
2- Diagonals are NOT necessarily congruent but BISECT each other.
3- We saw a new method to calculate the possibilities for the forth point of a quadrilateral using logical reasoning and slopes.
4- You have to closely observe the diagrams and look for relations between the angles and the sides in the figure in order to get some of the answers asked.

You might have noticed that until now all theorems of chapter 6 have a given info that is a parallelogram and that leads to a conclusion of other fact. So, today we learned 4 new Theorems that do the opposite: give you the information and leads to the fact that it is a parallelogram.


Today's Lesson:
- Theorem 6-5: If both pairs of sides are congruent, then it is a parallelogram. (converse of T 6-1)
- Theorem 6-6: If both pairs of opposite angles are congruent, then it is a parallelogram. (converse of T 6-2)
- Theorem 6-7: If the diagonals bisect each other, then it is a parallelogram. (converse of T 6-4)
- Theorem 6-8: ONE pair of opposite sides is BOTH congruent AND parallel, then it is a parallelogram.

Notice that there is no converse for Theorem 6-3.
For this chapter you must know all quadrilateral properties in order to succed in quizzes, tests, and the rest of your life!

There is homework due tomorrow: Pg. 301- #15-32 all


Have a great week!
Get better Mrs. Saatkamp!
See you on Monday!
Giovanna Dedini (GD)

In today's class we started chapter 6 which talks about quadrilaterals. We went over lesson 6-1 and one theorem of lesson 6-2 just to predict what we are going to work with tomorow. Lesson 6-1 talks about parallelograns, so we studied the definition of a parallelogram and other four theorems:
Theorem 6-1: if: it's a parallelogram
then: both pairs of opposite sides are congruent

Theorem 6-2: if: it's a parallelogram
then: both pairs of opposite angles are congruent

Theorem 6-3: if: it's a parallelogram
then: consecutive angles are supplementary

Theorem 6-4: if: it's a parellelogram
then: diagonals bisect each other
We also proved theorem 6-1 and 6-2 that was necessary to go back to postulates and theorems related to parallel lines and congruent angles that we have studied already. All the theorems of the lesson 6-1 it's when you know that is a parallelogram and with this given information you can conclude it's characteristcs.
In lesson 6-2 we saw theorem 6-5:
Theorem 6-5: if: a quadrilateral has both pairs of opposite sides
then: it's a parallelogram
In this theorem you know the characteristcs then you can conclude that is a parallelogram. So, the theorems of lesson 6-2 are the converse of the theorems of lesson 6-1. Finally we proved theorem 6-5 that was also necessary to use theorems and postulates related to parallel lines and congruent angles.
HW: pg 295 #17-35 all.

9 A Class summary 1/12

In today’s class we showed our Tangrams presentations.

The 1st group to present was Florence’s, Ricardo’s, Franklin’s and Javier’s group. Activity 1: talked about the different legends of how Tangrams were created because there isn’t a concrete date of when it occurs, rules of the game such as no shape can be overlapping with the other and all of the shapes need to be used. Activity 2: said that the small triangles are congruent and they are isosceles, the parallelogram added to 360 degrees. Activity 3: took them a long time to figure out how to do it but they did manage to do it and they had to turn all shapes around to get the bird. Activity 4: their story was about a shark and a pig and they constructed those animals with Tangrams, their story had a moral.

The 2nd group to present was Cairn’s, Mayu’s, Jenni’s, Pamella’s and Bernie’s group. Activity 1: they all had a different legend written in a shape that made the Tangram puzzle, each one of them talked about the legends they had researched about. Activity 2: had the same answers as the 1st group, but theirs had the two columns proof and all the information was pasted in a poster. Activity 3: same as the 1st group. Activity 4: was about the purple penguin, peter the panda and the pink parrot. The panda wanted to get the information on how to make the perfect puzzle from the penguin.

The 3rd group was Gina’s, Guillerme’s, Giovanni’s, Alexandre’s and my group. We had a problem with the computers so we started off with activity 4, which was about Max the dinosaur, Sophie the little girl and her dog. They end up building a house for Max because he was too big to fit in his parent’s house. Activity 1: showed in the computer lab and was about the same as the other groups. Activity 2: was also a PowerPoint presentation comparing the triangles and said the different combinations of shapes that were made of the smaller shapes. Activity 3: same as the other groups.

After the presentations we got back our test, but we didn’t check them, who ever wanted to see their grades until now were showed their grades. Due to the lack of time we didn’t start chapter 6 nor had any homework. We will start tomorrow on chapter 6.

December 1st

Well, the following was what 9B did today, December 1st:
Presentation Tangrams!
Group 1: Beatriz, André, Phillipe & Luiza M.
History:
· The creation had no exact date
· Invented in Ancient China
· Legend: A man gave the tangrams to his fiancé before marriage
· Legend: Came from the village of the Tancus
Story:
§ There was a Kingdom named Gramland
§ King named Tan, had a son named Tentus
§ A bad wizard wanted to rule the kingdom
§ Cursed Tentus saying that he wouldn’t stop looking at his own image
§ King dies and Tentus becomes king
§ Get obsessed with his image and forget Kingdom
§ Bird destroy all mirrors into 7 pieces
§ Bird tells Tentus to rebuild a mirror so the curse is fired back
§ Tentus rebuild mirror, wizard get cursed and kingdom got happy
§ Tentus named the game after his Kingdom and his father.
§ Shapes created: Crown, Sword, Castle, Mirror and Wizards Pot.

Group 2: João, Giulia, Giovanna & Gabriel
History:
· The creation had no exact date
· Played by women and child
· Legend: The game was created by a God who got the Moon the Sun and some planets as the shape
· Edgard Allan Poe liked playing with it
Story:
§ Bobby appeared in a magical world
§ Meet a new friend named Mr. Tam who was formed by geometrical shapes
§ Bobby starts seeing many animals, such as a Mr. Tam Cat and things formed by geometrical shapes
§ Discovers he is at the Tamgram World
§ Mr. Tam explains the rules of Tamgram
§ Bobby get out of the world in a shuttle and starts creating new friends for Mr. Tam
§ Shapes created: Man(Mr. Tam), Cat and Shuttle.

Group 3: Luis, Gustavo, Luiza S. & Guilherme
History:
· No exact date
· Estimate about 4 thousand years old
· Legend: A King ordered a square of galss which accidently broke into 7 different gemoetrical shapes
Story:
§ Jeremiah was poor and had no human friends
§ His friends were animals, a cat and a bunny
§ Found a strange flower
§ When the flower got into the fire it became a powder
§ The powder transported them to a magical world
§ World had spirits with animals shapes
§ Wizard cursed everything there and turned everything in there into shapes
§ Jeremiah wants to help so he asks his dad to make class figures
§ All of the figures got broken into 7 pieces
§ Shapes created: Bunny, and Running Man
After the presentations Ms.Saatkamp returned our tests that we took last Tuesday.
Then we went over it (had little questions), then we started Chapter 6:

Parallelogram
Definition: A quadrilateral with both pairs of opposite sides parallel

Theorem 6-1
Opposite sides of a parallelogram are congruent.

Theorem 6-2
Opposite angles of a parallelogram are congruent

Theorem 6-3

Consecutive angles of a parallelogram are supplementary

Theorem 6-4
The diagonals of a parallelogram bisect each other

There is also HW =(... It's page 295 numbers 17-35 all
They are easy (no proving!)