Congratulations

Dear Ms. Saatkamp and 9th grade students;

Congratulations on the piloting of your blog! It appears to be a great success by the number of entries and the relevance of your comments. I am so happy to read that you continue with the 1st grade project. It was a highlight of their math studies when I was in elementary, and I'm sure it continues to be.

I wish you continued good luck with your pursuits of integrated technology!

Thank you, Ms. Saatkamp, for taking the initiative to make this happen.

Ms. Mello

Hi Ms. Saatkamp,
Sorry that I'm being late, I totally forgot about posting this yesterday!

I thought the presentation to the 1st grader was a very nice experience. I didn't know that 1st graders would know so much about the shapes! and I was surprized by how smart they were. Even though they couldn't have understood what a parallerogram is or the properties of the shapes, I felt that we were able to teach them somethign new. I think the kids also loved our presentations since they seemed very interested. I'm not sure if all th kids understood the story, but I'm sure that they enjoyed it:) The games were veyr nice as well.
In sum, I thought this presentation was very successful. I hope the 1st graders thought the same way too.

gui bessa

Was pretty good, the children were very concentration on the entire presentation. Didn't had problem for to do the pectures using the tangrans. And were wanted more pictures to try to do. I liked very much of the presentation.

***sorry miss  for I was witer here but I can't use my count.

Our presentation with the first graders was a great oportunity to interact with the kids. I think everybody did a pretty good job. In my opinion we should do this more often because we teached these kids something different, we played with them...An also because they are first graders they didn´t get tire in any moment, because for example when the guys of activity 2 were telling the story, the kids were asking questions, trying to guess what was happening there...like 100% focus on. It was a really good oportunity to interact with them and well try at least to teach them something different.
good job everybody!!!
javier

Presentation with the kids

I think the whole class did a good job, and both the 1st and 9th graders had a good time because we were kind of missing classes ;P. I think that our presentation was very productive for the kids because they got to know some shapes better, for example, the parallelogram. I did activity 3, where we had to entertain the kids, and I think that they were very cooperative in some ways like being quiet when we were doing the story activity.However I could also see that some of them were jealous of the others who got a different shape to do. Besides that everything went fine ;D.

Presentation for the first grade

Well, here I am miss, its one day late but its here. Anyways, presenting about tangrams for the first graders yesterday was pretty good. I was really impresses to notice how the kids really paid attention to us. Well, I was in group #3, entertaining them at the end, and even though some of them were pretty hard to keep behaving, we I think we were able to make a nice job. I was impressed in how the kids really memorized the name of the parallelogram, whenever we asked what were the names of the shapes, they always got it wrong. I guess the only real problem we encountered during our presentation was Travis, who didn't want to obey the rules imposed by us and who was fighting alot with a japanese kid (although it was pretty funny to watch them arguing =P). Anyways, wrapping it all up, I think there were much more positives then negatives in our presentation, as the first grade teacher said, we really had their attention, and that is what you need to have from a first grade child. Summarizing it all in five words: We did a nice job.

Presentation for the kids

I think we did pretty well in our presentation for the first graders yesterday. i was actually surprised over how much the kids knewed already, they are only first graders and they know what a triangle and a diamound is, i was really impressed about that. the think they liked all the three different presentations since they paid attention the whole presentation. they asked questions and they answered the questions we asked them.
I thought that they were going to think that our ( Malena, mayu, Lucas, and mine) presentation should be kind of boring and that they shouldn't listen, but they really did. and i think they Loved the story. they were all laughing when something funny happened. the game part was also fun and they were really serious and they did the figures really fast.
I felt that it was really easy to talk to them and i wasn't nervous at all. since they were soo nice and since they paid soo much attention to what we said, i thought it was really cool:)
see you guys tomorrow and good luck with all our hmwks:) Kisses<3<3

Reflection

It was really nice to present our project to the fisrt grade. We had another chance to remember some stuff that we have learned about tangrams. The best part was to teach, told a story and played with them. At the beggining I was nervous because I didn't know how could be their behavior, but after I saw that the kids were very cooperative and easy to teach (in my case trangram's history).

The Tangram Presentation

I really like the presentation that we gave to the kids because it was nice, nothing bad had happened and etc. At first I believed that while we were presenting the kids would either be fooling around or not really paying attention since they were little, but I was mistaken. Since they were really listening in, making great comments (of course with easy vocabulary words) and raising their hands and joining in the fun. Also I like in the 1st group how they helped out, with naming what shapes are the 7 tangrams and putting them on the board to from a square. While after in group 2, they were listening at the story, making comments when allowed and answering questions that group 2 asked. Last but not least, group 3, in the beginning I was a little nervous and worried thinking that it would be a mess with paper all around and kids fighting for gummy bears. But that really didn't happen, the kids were helping each other, asking us for help and even at one point some were talking to me and asking me name. So in the end, I really like the presentation and I wish that we had more time to play with the kids.

Impressions from 1st Grade Activity

I believe that the whole class did what they were supposed to in the activities, as well as making the whole class an interesting and different experience for the kids. In any of the activities I never saw a single kid not paying attention, they were all very interested and extremely eager to participate. The first group had the kids identifying the shapes that made the tangram (squares, triangles, and "diamonds") as well as having the kids put the seven shapes into a square, which was when the group interacted a lot with the kids. They got the kids prepared very well for the following activities and used simple words with clear pronunciation. I believe that the story showed the kids how many things could be made with tangrams, this got the kids even more interested, as well as enterteining them for a little while. The game group got the kids really excited and involved, it was were there was most interaction. It was a real shame that the game group had to quickly conclude their activity, I think this could be fixed with a bit more communication in between the groups. Overall, the result was excellent and the 1st graders learned a lot as well as having fun.

Bernie

Reflection

I think that the kids got very happy and curious when we went to their class to explain and play with tangrams. They seemed enjoy and presentations and also the games that were played. I think thay learned with this experience and it was really nice to outside the class room and teach other kids about math. The kids payed atention to all the groups and participated really well when they were asked to do so. I liked the experience.

Tangrams Presentation

I think out tangram presentation to the 1st graders went out pretty well. The first group that presented the history did a very good job by interacting with the kids and involving them into makiing the tangram. Most of the kids knew all the geometric shapes but the identified the parallelogram as a diamons. I think the first group also did a good job by using simple vocabulary so the kids could understand and keep paying attention. My group was the fairy tale group and I think we did a good job. the kids were entertained and payed attention. They all answer the questions we asked especially that little girl that kept saying the dinousaur was behind the board. i think our group accomplished our goal by getting the kids attention and explaining a little bit more of tangrams and the shapes you can make with them, like Max´s house that we explained how they used all the pieces of the tangram to build it. The third group who did the games with the kids accomplished their goal by making a fun activity that included tangrams. All the kids were excited and wanted to do the shapes they got, some of them were pretty fast while others needed a little bit of help. In the last minutes it was a little unorganized mainly because all the kids wanted to participate and we had very little time but i think it was fun, especially the jumping over/fire/more jumping each others fairy tale they created. I think it was a very nice experience because we needed to adapt our original presentations to something that would be fun for the first graders and tried to keep them focused on something for a while. Overall I think we all did a very nice job.

Reflection

I think everything went fine when we went to the 1st graders class present the Tangrams to them, and they really enjoy it and so did I to interact with them and they were very cooperative, they liked to learn and to play with the Tangrams. I think they learned about Tangrams and how to play with them very well...

Tangram presentations

The tangram presentations were really good. The 9A class was divided into three goups which were supposed to:

1)tell the history of tangrams;
2)tell a story (Tangram Fairy Tale);
3)play with the kids.

The first group seemed to know what each one had to say and they were asking the kids questions to keep their atention on the presentation. The group also made the kids build a square with the tangram parts, which was very nice.
The second group, which was the one that I was participating, told the kids a short story of a dinossaur, a girl and a big house. The pourpose of it was to show the kids how the tangram parts can be used to build a lot of images. The kids also learn what an isosceles trinagle is.
The third group played with the kids. First the kids had to build some imaged using the tangram. After that they made a circle and created a story using the images that each one og them built. At last they played "lots of corosses" with the kids.
All the presentations were very well organized, every one had their materials and all the groups could keep the kid's atention focused on presentations.

Class Summary- Pam

Hey guys..

today in class Miss Saatkamp began by explaining what we will need for math second semester. We will be required to have a scientific calculator, don't worry, its not too expensive and you can find it in any "papelaria". The thing is though, that for next year we will need a graphic calculator, to buy one in Brazil is very expensive (about 1,400) so if in these vacations or the next you go to the States, its highly recomended that you buy when you are there where it is much cheaper. The one mrs saatkamp prefers is TI 83.

Now, back to math: Today we spent class correcting the homework from page 325 numbers 16-37 (not 36). Some people had trouble with number 21, the answer is 78 and we need to aply the idea of chapter three in which corresponding angles are congruent. Also, many people were in doubt about number 37 because we were expecting an answer as a sole number, but yes the answer is 180-x.

Mrs Saatkamp also reinforced the idea that diagonal are perpendicular it is NOT definate that it is a rhombus.

Guys it is very very important that for the test (not quiz, test) on Friday we know the system of equations, when you have two equations with x and y you isolate y and replace. Also we need to know the main formulas

slope:

distance:

quadratic:

Midpoint:

Thats about it.. Pam

ps to get my formulas i took the images from a site called purple math.. i thought it was really easy to find, if anyone is having trouble.

1st Graders- Pam

I think that presenting our tangram project to the first graders was a great idea. At first I pictured a bunch of kids staring at us and not really getting anything out of it, but I was acctually quite surprised by how much they knew and how well they learnt. I think part 1 (history) was very well explined and I loved that they went up there and acctually put the shapes... i was amazed at the blond boy (who was sitting in the left) he knew all the shapes and was rather amazing. afterwards during part 2 (the story) the kids were interested and acctually really enjoyed Max's story... Part three was my group, the games... I think we did a good job over all, it was nice that each kid got a tangram and they were so exited about it, some girls even asked us if they could have our answer sheets to try it out at home, and i believe the tangram tic-tac-toe was fun and it was a shame we didnt have time to finish. i also loved the tangram story the kids created and although there was a lot of stuff jumping on top of a lot of stuff it was really fun. Next time maybe we could organize better the time tables and not give the kids possibly deadly candy :P.... Overall it was a great expirience.

My reflection- Malena

I think that the presentation went very well and it was a nice experience, also a new one or new to me. Since it's harder to talk to little kids I thought we weren't going to be that good, but it was better than I expected. All the kids were really interested, cooperated well and had fun, which was our goal. I could notice that they were getting what we were talking about because they always answer our questions and were always trying to participate, especially when we ask for volunteers to help us form the tangram. The kids surprised me, since they knew all of the shapes except for the parallelogram but they identify it as a diamond which was a very good guess and they could see the differences between the sizes and shapes. While the other group told the story the kids seem to enjoy it and they seemed entertained. For the games it would had been nicer to have more time in order for them to had played more with tangram, but they did a really good job and had no problem creating the shapes they were given, I also thought that it was very original the part letting the kids make a story with the different shapes they had created. I think that the presentation was worth the time since they all learned something new and were happy with it.

My impression

I thought that the presentations went very well. The kids were super interested and they had a lot of fun. They loved all the parts, the history part, because they could participate to help paste the pieces on the wall, the story was very fun for them and they were very interested in the story, and they loved the games. Everybody was working and everybody did their part in the presentation. I thought it went very well! Not only did it go well, but it was a good learning experience, and best of all, it was fun!
Maybe it would have been nicer if there had been a little more time, so that the children could play a little more, but overall I think it was great.

Jenni

I liked very much presenting to the first grade...

The group that I've got to know was very 

smart, specially a boy named mathias

wich, after 20 seconds at most after we

 tell them to build mr Tan .

They had a little trouble with some of the

 shapes but nothing very confusing or hard.

Idont have much to say...

only that was a very good activity and i liked

it a lot

Impression

Overall I think taht the presentation to teh 1st graders worked out very well. Actually it was better than I expected it to be. The kids cooperated with us through out all the Activities: During the play I think they were interested and interacting by the questions. During the presentations I think they were having fun with the volunteers and effects of the Power Point. I think that my part of the project - the activities with them - worked out nicely and went through good. I was amazed at some of the students that were very fast logicaly and managee to accomplished the tasks we gave them very quickly. I was also surprised to see how much tehy liked teh Tangrams and were paying close attention. I though it would be extra difficult to teach complex conten to children that dont know the vocabulary we were using and have much less knowledge about geometry. It was a challenge but I think it was a very good acitvity that will actually help us, because it is one rtthing to present your project to your classmates and teacher taht know esactly what you are talking about then to first graders taht dont have teh least idea. In my opinion it was constructive and nice. I would do it again anytime.

Giovanna Dedini!*

The Tangram Presentations to the 1st graders

My part of the project, which was the play, worked well and even though we had difficulties at first, we were able to present alot better than I thought we would. Also, the kids seemed to have enjoyed it and most of the time, we had their attention by asking them questions during the story (ex: do you think he'll be able to do it?). The other groups also worked well with interacting with the kids and I especially think we were able to teach them in a fun way what were tangrams. It was a really good experience - for us and for them as well - because it is very different to present our project to the teacher and class and to present it to little kids who don't fully understand geometry and don't know what things like parallelograms are. Overall, I really liked doing it and I think the children also enjoyed it :)

Presenting to people other then class members is always a chalenge, especially with a young first grade audience, where not only does your presentation need to be simple, but it needs to be fun and interactive. I think all the groups did a very good jog because the children's reactions were very good. Especially in Luiza and my presentation, that was the one I really was engaged, they all wanted to participate desperatly, and it seemed like they were having fun. It was also positive to work with someone outside our original group, so we could have new ideas and improve the presentation, especially the images, that Luiza new ways to improve the quality and has better computer skills then I do. Maybe for the next time, we can find new ways to interact with them; this time, we were more concerned in getting the slide show done and improved then accutaly thinking up the presentation. I also think that it was kind of "boring" to stay the last 20 minutes just watching the last group, maybe we could have helped them and even done something more creative or fun. Overall this presentation gave us oral skills, interaction with different people, and sharing knowledge with younger kids. I loved it!! =D

Giuliaa

Well, I really liked presenting to the children: it was a very nice experience. The major problem is that me and my group had issues with organization, and the presentation ended up being a little bit boring.. And confusing. I think that if we had more time, it would have been extremely good, and the "closing" of the project would be amazing. The good thing is we make ourselves learn very well so that we are capable of teaching the children. Also, we deal with the idea ofexplaning things in an easier way and making math a fun thing (not that it isn't!). I would love to have the chance of redoing the presentation, and I know it would be much better.. But for the amount of problems we had and the little time, our theater wasn't THAT bad...

Impression About Presentation

I think we did very well, especially by getting their attention, which is one of the main things to teach first graders. I also think they really got the idea of tangrams, and what they are, but i really like that some of them learned that the parallelogram was a parallelogram not a rectangle. I think we entertained them with the story, they really liked it. The group of what tangrams are and some rules to play with it did really well, mainly when they used the children to be part of it, and it was a really cool experience for them, making them understand better. The group that played with them made it really cool for them because they were really interested in the puzzle and were trying to form new figures. For them this was the funniest part. I liked when we gave them the puzzles, everybody wanted to get it, and they were desperate to have one, which i really had a good impression of the presentations. Another thing that made me realize they were liking the presentation and paying attetion was when i (as prince tantus) went to hadshake them, and every kid wanted to touch me and were saying "Here! Here! Prince tantus!", this made me feel really good about the presentation. I think we did a really good job. They got the idea of tangrams and were really interested in our presentation.

Reflection on Presentation

I believe that the presentations to the first graders were very sucesfull, mainly because we managed to accomplish our objective of teaching them what Tamgrams are. Our class managed to use time wisely, even when some problems (Giulia's and Luiza's PowerPoint not opening)appeared. We also managed to catch their attention, as Ms. Kadlec pointed out. Group 1 strategy of using some of the 1st graders to act out the story was very effective. Group 2, I think managed to entretain them with the story. And Group 3 showed them how to play the game, which was the funnest part for them. After all, the class worked well together, when one group presented, the other were quiet (or at least talking quietly). And in the end, the first graders seemed very satisfied with our little "class". And it was also very copacetic for us to teach them.

Opinion about the Tangram Presentation

I think that the presentations went very well for many reasons. First of all, I think that the 1st graders understood the concept of the tangram. They learned that it is a puzzle that forms a square, and it contains severall shapes within it: triangles, square and parallelogram (they could identify the parallelogram and name it). They also learned that with the shapes that made up the tangram, it is possible to build many different shapes, including a house, a cat, and a running man. I think that by presenting to them the concept of the tangram through a story was a good idea because I think that way understood it better and paid more atention, in the beginning, we needed give them many hints, and the outline, so they could build the different shapes, but after the first and second shape, they were able to build the shapes on there ow and without an outline. I could see that they had lots of fun because they were very excited during the activities and were always focused, and therefore i think it was a good experience for them -and for us because we learned how to handle and interact with small kids - and a good way for them to learn, even a more complex concept like a tangram, without being bored and loosing focus.

Class Summary- Wednesday, December 8th

 

Lesson 6-5-

 
1. Definition of a Trapezoid: It's a quadrilateral with exactly one pair of parallel sides.
 
(Notes: If it has one pair of parallel side that ate also congruent, it is a parallelogram - Theorem 6-8-  and not a trapezoid)

 
2. Bases- the parallel sides (of a trapezoid)
    Legs- The other sides (which are not parallel)
 
3. In a trapezoid, consecutive angles, one from each base, are congruent

4. Two kinds of Trapezoids:
 
Right Trapezoid- has one right angle.

                             - The consecutive angle on the same leg is also right because of Theorem 3-4 (if: the transversal of perpendicular lines is perpendicular to one parallel line, then: it is also perpendicular to the other parallel line.)

Iscosceles Trapezoid- has congruent legs.

5. Median of a Trapezoid: a segment whos endpoints are the midpoints of the legs.

6. Theorems:

T 6-14- if: it is an isosceles trapezoid,

               then: both pairs of base angles are congruent.

T 6-15- if: it is an isosceles trapezoid,

               then: the diagonals are congruent.  (Notes: that doesn't mean they bisect each other.) 

T 6-16- (if) the median of a trapezoid is:

               (then) parallel to the bases,

               AND

               (then) its measure is one-half the sum of the measures of the bases.

The Homework for tomorrow is: Page 325# 16-37 all. 

Also, you have to post your opinion about the presentation to the 1st graders (a paragraph).

1st Grade Presentation Reflection =)

Well, I thought the presentation for the first graders worked well! All three groups got the children entertained and I believe all the first graders learned a little bit. I also felt that some of them really wanted us to clarify what exactly was a parallelogram and even though we didn’t I think they understood it more or less. The entire class collaborated, not only the first graders – that were silent and paying attention – but also the ninth graders for when one group was presenting the others were not making a mess. Furthermore, we were able to deal with the computer that didn’t work at first, what showed that all groups were ready since the second groups presented before the first. In addition, the experience of teaching the first graders was really nice and I believe the first graders themselves thought so too.

1st grade presentation reflection

Overall, the first grade presentations worked out really well. All the kids cooperated more than i would expect, and that should be by the fact that all of them were interacting. They really enjoyed the part of the activities, and my group heard some remarks like "this is too easy", therefore making us challenge them even more by putting the tangram togheter only with the shape's final form shadow only, without the outlines. As that was proven to be too hard, we started challenging them to work in a group and try forming one of the shapes displayed on the television screen. While they were working we started giving them tips and also repeating the Tangram rules: All shapes used, no overlapping and all of the pieces inside the shape's shadow. After they did aboput three of those our time was up. Overall this was a very good experience, since some kids were not cooperating and some were fighting for the tangram pieces (Each kid was given one piece), but that is normal. In the end i think they learned about them in a good way.

Posting for Friday the 5th

Sorry, It's extremely late.

Remember:

• This year postings are only graded for participation, but next year they will be graded. Diagrams and equations are NECESSARY


• Tuesday 9B will present at Jo Mannings 1st grade
  
  

We started class by correcting homework on page 316 and 317

Remember the quadratic equation that we have been using: **Memorize it! There will be a question in the test!!

Exercise 34 and 37 in pg 317 can be solved only by the slope formula. There is no need to do the distance formula. Do first the slope of sides, then the slope of the diagonals. If it is a rectangle and a rhombus, you know it is a square.


Test Firday!!

Giulia

Today's class summary 08/12

1- Today's class started over theorem 6-13 that said:

if: it is a rhombus

then: each diagonal bisects a pair of opposite angles

2- After that we went over the homework (p.317 #4 and 21-47), which was kind of easy for the people that actually did it, with no provings ;D. The question that most people had doubts was #33, because we had to use the quadratic formula(you can see it in Jenni's post). Also, for numbers 34-37, you could solve it using only the idea of slopes without the distance formulas.

Obs. Mrs. Saatkamp won't accept any graphing on quizzes and tests, only algebra.

3- After the homework, we started the lesson 6-5 that is about trapezoids:

Trapezoid's definition: It's a quadrilateral with exactly one pair of opposite sides parallel.

There are two types of trapezoids: Right Trapezoid and Isosceles Trapezoid

Right Trapezoid: It has exactly two right angles

Isosceles: Its legs are congruent


4- After looking over the trapezoids, we went over 3 theorems: theorem 6-14, theorem 6-15 and theorem 6-16.

theorem 6-14: If it is an isosceles trapezoid, then both pairs of bs angles are congruent

theorem 6-15: If it is an isosceles trapezoid, then the diagonals are congruent. Obs. the diagonals don't bisect each other

theorem 6-16: If it is a trapezoid, then the median is the sum of both bases divided by two.

Homework is only due on thursday because tomorrow we are going to work on the projects and on wednesday we are going to present for the little kids. Hw: p.325 #16-37 except for 36.

PS. 33-35 requires algebra

guilherme bessa

Today we started correct the homework from page 301, #15-32 all and page 310, #15-38 all. After Ms. Saatkamp explain soome questions in the homework, and we started learning about two other type of quadrilateral, Rhombi  (rhombus), and square.

And  some other theorem 

Theorem 6-11:   If It´s a rhombus, them the diagonals are perpendicular

Theorem 6-12: if a parallelogram has perpendicular diagonals, them it's a rhombus

the square don't heve a expecific theorem, but it have a definition: 

Square definition

it's a quadrilateral with four sides and four right angles 

Class Summary 4/12/08 by Guilherme

Today we started things off by going over the homework from page 301, #15-32 all. After Ms. Saatkamp corrected some diagram questions in the homework, we started learning about another type of quadrilateral, Rectangles.

Rectangles

Definition: A quadrilateral with four right angles.
There are two theorems on chapter 16 regarding rectangles especifically, and those are:

Theorem 6-9: If a parallelogram is a rectangle then it's diagonals are congruent.
Explanation: For example, if a parallelogram being a rectangle is given as information then it can be stated than all the diagonal lines in that rectangle is congruent, or equal to each other.

Theorem 6-10: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Explanation: A parallelogram can be considered a rectangle if its diagonals are congruent.


After we got over Rectangles we moved on to Rhombi (Rhombus).

Rhombus

Definition: It's a quadrilateral with all sides congruent.
Unlike Rectangles, they have three theorems especifically for them, and those are:

Theorem 6-11: If it is a rhombus then the diagonals are perpendicular.
Explanation: If the figure given is rhombus then it can be said that its diagonals are perpendicular to each other, eventually forming 90 degree angles.

Theorem 6-12: If a parallelogram has perpendicular diagonals then it is a rhombus.
Explanation: If the figure given is said to be a parallelogram and if that parallelogram has perpendicular diagonals then it is correct to assume that the figure is a rhombus.

Theorem 6-13: If it is a rhombus then each diagonals bisect a pair of opposite angles.
Explanation: If the rhombus is given then its diagonals will bisect (pass through the middle) of a pair (2) of opposite angles in that rhombus.

Then went on to Squares, however we didn't have any theorems on them. Instead, Ms. Saatkamp drew us a very helpful diagram about Quadrilaterals.

PARALLELOGRAMS-

RECTANGLES - RHOMBI


SQUARES


This basically states then all the properties used to identify Parallelograms can also be used to identify Rectangles and Rhombi, apart from their own. Squares are the Quadrilaterals that can be identified with any of the properties used on all the three of the Quadrilaterals above.

Finally we finished it off by copying the homework pages

Page 316 #4
Page 317 #'s 21 through 47 ALL

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).


----------------------------------------------------------------------------------------------

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.

------------------------------------------------------------------------------------------------

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.

-----------------------------------------------------------------------------------------------

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!)