Answers to your questions

Dear Giulia

Yes, I'm much better. Thank you for your concern.
About your questions:

1. In activity one you need to explain briefly the history of tangrams, and you should have noticed already that there aren't clear records about that, only legends. you don't need at this point explain details of the shapes.

2. In activity two, it is time for you to detail as much as possible your shapes.

3. In the last activity, you again don't need to explain about your shapes, just create a story that will cativate the kids.

I hope it helped you.

Mrs. Saatkamp

Ms. Saatkamp,

Are you better? I have a question abou the project. In the story, do we need to include how the tangrams were created? Or only what tangrams are? And is it basic, or do we need to explain what type o triangle each one is?
Question number 2: Is there a correct history of tangrams? Or are there many legends?

Thank-you,

Giulia, João, Giovanna and Gabriel

Wednesday's work

FRANKLIN'S GROUP:
During class were working in Activity 3 and 4,
Alredy did Activity 1,
Need to do Activity 2 still.

PAMELA'S GROUP:
During class were working in Activity 4,
Alredy did Activity 1 and 2,
Karen missed school and was doing Activity 3 at home.

GINA'S GROUP:
During class were doing Activity 3 and 4,
Alredy did Activity 1 and 2.

Answers to your Questions

Drawing Diagrams: if you have numbered your 7 pieces of your tangram, instead of drawing anything you can just use the numbers. Example: shapes 1 and 2 form shape 5. (note that those numbers don't any correlation to possible answers for your project) The purpose of this is to give the reader of your projects an idea of what was your reasoning through your solution.


Properties of Quadrilaterals: you are only expected to explain the properties of the quadrilaterals that appear at your tangrams.

See you on Monday.

Question about Activity #2

Hey, Ms Saatkamp! How are you?
In activity two of the project, do we have to find out the propertities of all types of quadrilaterals or only of the one present in the Tangram?
Thank you!

Ana Beatriz, André, Luiza Cristina and Phil

Question about the math project

Hi Ms. Saatkamp!
I have question about the Activity 2 in the project.
It says: Compare the pieces between themselves. Which combinations of pieces could form others? Draw diagrams to exemplify your answers.
What do you mean by draw diagrams to exemplify your answers?
thanks!

Hi! this monday, november 24, Ms. saatkampgave us the only calss

in this week that she will be teached, due to a health problem in her

eye.

Today we went over homework of the page 282 questions 11~36

without the proovings. many people had problems on questions 31

32 34 and 30. In this homework we had to use the content learned on

chapter one (distance formula in this case), and it will be more needed

from now on. Today we also went over our quizes, that in general everyone

did well.

Remember!!!

Tomorrow test about chapter six

wednesday: We will have time to work on our project.

Lets all hope ms. Saatkamp get better soon

João

Class Summery of 9a ( November 21)

In today’s math class, Ms. Saatkamp first gave us our quizzes back that we took last Friday and we went over the questions. From number 7 to 10, we were to look carefully in the diagram and use the theorems that we learned previously. Some questions that were asked were number 6 and 8. On number 6, you had to subtract one number to the other to find the smallest possible number of X and you also had to add the two numbers to find the biggest possible number of X. On number 8, you had to use Theorem 5-14 to find the inequality.
Next we went over our review questions which were #11- 36 from page 282 (all questions except proving). Ms. Saatkamp taught us that on number 16, we were suppose to calculate ∟A+ ∟Z= 90. On number 9, you had to look at the big triangle to find the answer. On #30 and 31, you had to use distance formula. Number 34 was a very tricky question because segment AO was not a straight line!! If you were careful enough on those things, you should have got the questions right=)
Then we had rest of the class to work on our tangram project. Remember, it is due next Monday and we’ll also present the project that day. Some thing else for those who doesn’t know, OUR CHAPTER 5 TEST WILL BE TOMORROW! And on Wednesday, we’ll have the entire class to work on our project.
Well I guess that’s all that we did today=) Study hard for tomorrow’s test and see you tomorrow!!

Hope you get better Ms. Saatkamp!
Mayu
p.s. no math hw for tomorrow*

1st post

Gina and Malena!!! (math project)

9B - 11 / 19 / 2008

In today's class first we started by going to the Computer Lab and finishing the activity in Geogebra about Theorem 5-14 (SSS Inequalities).
Then we went back to the classroom and started working on Pg. 276 #5-10 all and Pg. 277 #14-29 all. We spent the rest of the class working on these exercises, whoever didn't finish has to do it for homework.
Remember: Today's homework is about applying Theorems 5-13 and 5-14
Remember(2): For this hw you must look carefully at all the diagrams, and remember the theorems and postulates from before, they will be very useful.
Remember (3): The exterior angle is used very often.

Tomorrow we will go over these pages and after (since Mrs. Saatkamp is such a nice teacher) we will have a study hall. You will be allowed to do work for any subject but if and only if you have the material with you! YOU WILL NOT BE ALLOWED TO GO TO YOUR LOCKERS!

Reminder:
Friday Nov. 21st - Quiz (lessons 5.4 - 5.6)
Friday, Nov. 21st - Show one activity completed
Wed, Nov 26th - Test on chapter 5

Love you all!
Giovanna Dedini!

Since we didn't have homework for today's class, we were given exercises to do and if you didn't finish them, then they are for homework. For all the people who didn't finish in math class. The pages are 276, #5-10 all and page 277 # 14-29 all.

Remember that in this homework look carefully at the diagrams!! Then tomorrow we are checking this homework and with the remaining time its a study hall so bring anything that you need to work on, study...etc.

Also, just a reminder that we have a quiz THIS friday, a test this wednesday and that our projects are coming closer and closer to the due date (December 1st).
So keep up the good work and study hard for this week!

Have a good day and see you tomorrow ;3,

Florence

In today's class, we started by correcting yesterday's homework, which mainly involved Theorem 5-12, which we learned yesterday.

Afterwards, we went to geogebra to understand SAS Inequality and the SSS Inequality.

Theorem 5-13: SAS Inequality: If two sides sides of a triangle are congruent to two sides of another triangle and if the included angle in one triangle is greater than the included angle of the other triangle, then the 3rd side of the first triangle is greater than the 3rd side of the second triangle.

Theorem 5-14: SSS Inequality: If two sides of the first triangle are congruent to two sides of the second triangle and the third side in the first triangle is greater than the other third side, then the angle between the pair of congruent sides in the first triangle is greater than the corresponding angle in the second triangle.

Majority of the class didn't finish the both theorems, so we should finish the geogebra activity tomorrow.

No homework is due tomorrow but please keep in mind that on Friday (the 21st) we have a quiz and our test will be on Wednesday, next week (the 26th).

That's all. :)

Today we started the class by checking the homework, in which Mrs. Saatkamp remained us what was the theorem 5-12 (inequality of triangles).

Theorem 5-12: The sum of the lenghts of any two sides of atriangle is greter than the lenght of the third side.

Then we went to the computers to work in the geogebra. There we learned two new theorems:

Theorem 5-13 (SAS inequality): If two sides of one triangle are congruent to two sides of another triangle, and the included angle in one triangle is greater than the included angle in the other, then the third side of the first triangle is longer than the third side in the second triangle.

Theorem 5-14 (SSS inequality): If two sides of one triangle are congruent to two sides of another triangle and the third side in one triangle is longer than the third side in the other, then the angle between the pair of congruent sides in the first triangle is greater than the corresponding angle in the second triangle.

Today we don't have homework! But remain on friday we have a quiz, and next week on wednesday I think we have a test...so everybody has to STUDY!!!!

javier (ODPSF)

Today’s Class – November 17th

Today we went over our homework from last week and learned a new theorem. And, as usual, were assigned more homework… ^^

To start off, we corrected the worksheet Inequalities of Sides and Angles of a Triangle, what involved some algebra. (By the way, don’t forget that, from now own, algebra will be very important– it will be worth at least 50% of the grade!)

After we finished correcting it, we went to the computer lab to work with Geogebra – this time with Theorem 5-12. However, we were not able to look at our Theorems’ paper before working in the computer.
The Geogebra activity involved analyzing the relation of the three sides of one triangle by using one inequality. After that, we had to solve three questions regarding that same theorem.

Theorem 5-12: (Triangle Inequality Theorem) If the addition of the lengths of any two sides is greater than the length of the third side, then a triangle is formed.
Hint: In this theorem, for a triangle to be formed the sum of every two sides must be greater than the third side; however, an easier way to find that out is by comparing the two smallest sides with the biggest side (small side + small side > biggest side).

And here is our homework for tomorrow: Page 270, # 14 – 30 (even) and # 32 – 40 (all).

Just a reminder: on this Friday we must show Miss Saatkamp at least one more acitivity of the Tangram Project done.

Well, I guess that's it! =)

Summary of 9A´s class on Monday

Today we started our class by correcting the Worksheet about Inequalities for sides and Angles of a triangle, that was Due for Today. In the first four Questions we just needed to looking at a diagram and answer some question about the shortes and the longest segment. questinons 5,6 and 7 were also answering questions and listing the greatest to shortest. But in these last question we needed to show ALGEBRA. From now and on, in every question were you can use Algebra, we need to show our work. in quizes and tests, 25% of the question will be for the right answer, the rest 75% will be for showing algebra work.

After that, we took our notebooks and went to the math computer lab. We were doing an activity in geogebra. the Activity were conected to Theorem 5-12.

Theorem 5-12:the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

This means: side+side>3rd side. See pict.

In the Activity there were Two circles and one Triangle. you were able to change the measurement of all of them.

Ms. Saatkamp asked us Three Questions that we needed to answer;

What happens if:

1) the measures of the two sides is Greater than the Third?

2) the measures of the two sides is Less than the Third?

3) the measure of the two sides is Equal to the Third side?

the answers were:

1) This is the only way you can have a triangle, the two circles overlaped each other.

2) in this way you can't form a Triangle, and now, the Circles don't even touch each other.

3) when they are Equal, you can't form a triangle, the two circles touch each other, but they don't ever lap, they just touch on one of the segments.

That was what we did in class.. and for tomorrow we have homework.

P. 270 # 14-30 even and 32-40 all.- it sounds much but they are really easy..

And don't forget, on friday, we need to have one Whole activity for the project done.

Good luck with all our Homeworks ans Projects.

See you tomorrow=)

Summary of Friday class (9B)

(Ms Saatkamp I'm so so sorry! I totally forgot about this yesterday so i'm posting today)

We stared class by corecting number 32 of thursday's homework ( Pg 263 15-32 [no 30] ) It was a proving exercise very similar to number 31 involving the idea of linear pair and acute and obtuse angles. Instead of giving us the answers, we were given the first stpes and some hints then tried by ourselves.

Then we worked on a Practice sheet with 7 exercises regarding Shortest and longest sides and angles of triangles. If you didn't finish in class remember it's Homework.

VERY IMPORTANT-->> from now on, algebra will be graded in quizzes and tests along with the answer. So remember to show your work!!

Have a nice weekend and good luck on reading log and science project!

Giuliaa

Hey!
today we started class by correcting the prooving 32 from yesterdays homework (pg. 263 #15-32) it was a 12-step prooving and we used the idea of substituting <90>90 to obtuse and acute... it also used corrollary 4-1.
After we checked the prooving Miss Saatkamp gave us a worksheet on the same lesson the homework was about. The worksheet wasn't too hard, just be careful in using algebra, especially for numbers 5-7. Also, for number 6 you are NOT allowed to switch it to decimal form you need to leave it as fraction, and dont freak out if your fraction is huge, thats how its supposed to be. we had a lot of time during class for the worksheet and if you finished during class there is no homework.
Beijos!! and have a nice half day!
Pam :P
ps. (does the word proving have one or two letter O's?)

Class Summary 9B 13/11

Today we started the class with Mrs. Saatkamp checking what the groups had done for the project.
After we revised the theorems 5-8, 5-9, 5-10 and 5-11 and corollary 5-1.

• Theorem 5-8: The exterior angle is greater than each of the remote interior angles
• Theorem 5-9: If one side is longer than another side then the angle opposite to the longer side is greater than the angle opposite to the shorter side.
• Theorem 5-10: (converse of T 5-9) If one angle is greater than another angle then the side opposite to the bigger angle is longer than the side opposite to the smaller angle.
• Theorem 5-11: The shortest path from one point to a line is a perpendicular segment.
• Corollary 5-1: The shortest path from one point to a plane is a perpendicular segment.

After Mrs. Saatkamp revised each of these theorem and corollary she started to correct the homework from page 263 # 15 - 32, except 30 (i think)

We correct everything even proovngs.

Prooving number 29 was easy and had 4 steps.

But prooving 31 was really difficult and we had to use corollary 4-2 that we never thought we would have to use and it was 12 steps.

Although we had to do prooving number 32 we didn't correct it in class because we didnt have enough time to do it. I think we starting the class tomorrow by correcting it and Mrs. Saatkamp said it is also 12 steps. And tomorrow i think we are learning a new lesson.

P.S.: No homework for tomorrow because we didn't learn a new lesson yet.

Today's class 13/11/08

1. In today's class we fisrt started with Mrs. Saatkamp checking if the groups had something of the project already done, because the groups should have at least a something to show today.



2. After that we went over the homework (pag. 263 #15-32) solving all the exercises exept for #32 because we didn't had time to. Here are some tips about the exercises:



- From #15-25, you should compare the triangles in order to find the least or the greates angle or segment asked. In the question 23 for exemplo if you don'i compare the three triangles of the diagram you can't find the correct answer because you need to compare one triangle with the other.



3. The provings were quite hard, exept for 29. The Proving #31 involves 13 steps and you also need to replace measures for it's term:

Ex.: 90 >

4. We don't have homework for tomorrow (14/11/08) and we'll start tomorrow's class correcting proving #32.

Volunteer

Mrs. I can be volunteer for tomorrow or thursday or even friday this week.
But then tell me when I'll have to post the summary. Thank You.

Great posts and great start. This is the way I want us to go. Keep like this!
And a very Big Thank You to our volunteers of today.
Remember that the first two weeks you will volunteer, after that I'll give a list to follow.
9A has a huge list of volunteers. What about 9B?????

Pô Bia, também não precisa humilha né ;P

Class of Today

Today we started class by reading theorems 5-9 and 5-10, and going to the computer lab to explore and understand it in GeoGebra.

After that, we came back to class and analyzed the differences between theorems 5-8 and 4-3. While the first states the exterior angle is greater than EACH of the remote interior angles, the other states the exterior angle is equal than the sum (can we call it union?) of BOTH remote interior angles.

Then we made the correction of our howemork (I can't recall the page at the moment, and forgot my notebook at the school).

The major part of the class, though, was about Lesson 5-4 (Inequalities for sides and angles of a triangle), which we came back to discuss afterwards. Theorems 5-8, 5-9, and 5-10 and Corollary 5-1 were what we looked at.

1. With Theorem 5-9, if we have the sides, we are able to compare the angles. It states that if there are two sides, and one longer than the other, the angle opposite the longer side is bigger than the one opposite the shorter side.
2. Theorem 5-10 is the converse of Theorem 5-9. If we have two angles, one bigger than the other, the side opposite the bigger angle is longer than the side opposite the smaller one.
3. Theorem 5-11 states that the shortest possible segment between a line segment and a point not on it is a segment that connects them in 90º - in other words, a perpendicular segment. We learned an extension of it in right triangles, which, unfortunatly, cannot be used in provings (just if you take all steps needed). In those, sides which have the right angles are smaller than the hypothenuse.
4. Corollary 5-1: this is just another kind of extension of Theorem 5-11,which replaces the line segment with a plane. That means, the shortest possible segment between a plane and a point not on the plane is a perpendicular line segment.
   

So, I think that was it.

Just some reminders:
*TOMORROW, we have a QUIZ on lessons 5-1, 5-2 and 5-3
*Also, DON'T forget to start doing the project for thursday ( we are going to have a class on wednesday, in which we can decide to study or develop our projects, but it is nice to start)

Today's class 10/11/08

1.Today's class began with a small discussion about theorems 5-8 and 4-3 and then we went over the homework to vary a little bit. After that we went to the computer lab to visualize theorems 5-9 and 5-10. When everbody finished, we went back to class and Mrs. Saatkamp went over theorem 5-11 and corollary 5-1.

Theorems 5-9 and 5-10 talk about the measures of the angles due to the measures of the sides and vice-versa.

Theorem 5-11 says that the perpendicular segment from a point to line is the shortest segment from the point to the line. The only difference between Theorem 5-11 and Corollary 5-1 is that the theorem talks about lines, while the corollary talks about planes.

Today's hw: p. 263 #15-32 all, except for 30

PS: The hw is due only on thursday because we have a quiz tomorrow and wednesday we are working on the projects or in the homework.

PSS: VAMOS CRUZEIRO QUERIDO DE TRADIÇÃO! O BRASILEIRO, SER CAMPEÃO!^^

Class Summary

In today's class we corrected exercises from page 249. After that we had a small introduction to lesson 5-3, about inequalities. We then moved to the computer lab to work at geogebra. For that students needed to have clear the concept of: Remote Interior Angles. If you don't remember it, STUDY !

Students needed to explore the relation of each exterior angle to each remote interior angle and write their conclusions. Who had the correct answers, could go back to the classroom and start on their hw.

Homework assigned is: page 256 # 23 to 36. Take a special attention to exercise 28. Make sure you don't use the appearance of the diagram in order to find the answer. Remember, in geometry diagrams are not up to scale. I'll require reasons for your answers. For questions 31 and 34 you need to remember a property learned in grade 6: the comparison property (When comparing 2 numbers in math there are 3 possibilities: those numbers are equal or the first is greater than the second or the first is lesser than the second)

Even though some students that are missing a lot of classes are doing fine in terms of assessments, don't forget about the importance of being in the classroom daily. You are missing an important part: class participation as well as the computer experience.


Don't forget to start working on your projects. Next week, on Thursday (Nov. 13th) I'll require all the groups to present something done already.

Class Summary

Today both classes went over lesson 5-2, about Right Triangles. We covered theorems: 5-5 (LL), 5-6 (HA), 5-7 (LA - and no, it's not Los Angeles neither Language Arts), and postulate 5-1 (HL). The purpose for those theorems and postulate was to prove the congruence of right triangles. We proved all the theorems together, and the proofs were based into postulates and theorems of chapter 4: SSS, SAS, ASA, AAS.

HW: page 249, # 14 to 25 ALL

Tomorrow we will have an activity at geogebra.