How to use Rootmaths Virtual Classroom

For teachers, you can redirect to our new course management system with one click:

1.Logon into zz.rootmaths.com, select Tutoring Management->Class List, Click the big button "Redirect To Course Management" from the top left corner:

You will be redirect into the course management system immediately:

2. Click into your course ("here our course is 2022 AMC 10 Summer Camp 18L"),then choose  Virtual Classroom Links->Join Classroom-...->Join Session, you just started the Virtual Classroom, wait there for the students to join your classroom:

3.Like Zoom, you can use the correspondent buttons to control Voice,Video,Screen Sharing,Recording:

4.For the recordings, you just click Start Recording, Stop Recording.

You do not need to upload the videos anymore, the recording files will be presented automatically after you close Rootmaths Classroom.

That's it, Enjoy!

We are looking for passionate and professional math teacher to join us!

Qualifications

• Master's or Doctor's Degree or Certified teacher
• Be good at math tutoring with  more than 1 year experiences
• Better with math competition awards in Middle school or High school

Responsibilities

• Reports to the Senior Educator
• Be familiar with online class platform and procedures
• Teach students with designed courseware and homework
• Check students homework before next lesson
• Record and upload the lecture video if students ask
• Attend staff meetings

Work remotely:Yes

Job Type: Part-time

Salary: Negotiable

Please send your CV to: hr#rootofroot.com.

How to send the SAME Join Steps email for the whole class

1.Click "EDIT" button to input the Join Steps email content in the "Join Steps in English" field:

2.Check the class you want to send the email for Join Steps, then click "Email Join Steps" button:

3.Done. The system will pop a successful message.

How to send individual exam codes 

1.Finish the Join Steps in English above first;

2.COPY this class' Join Steps in English to all students. Check the class you want to copy Join Steps to all students, then click "Join Steps To All" button:

3.Choose Class List->Contest Users from the management system:

4. Here click Edit for specific student to change the Exam Codes individually, then click Update to save. Here you can also change score for this student:

5.Check the class you want to send the email for Exam Codes, then click "Email Exam Codes" button:

6.Done. The system will pop a successful message.

For some reason some students might be absent from the lecture, here are steps on how to record the video and upload for them

1.When you start the lecture for the students, choose the Console Menu: More->Record to start recording the video, please check the Settings to see where the recording file stored：

2.Quit Zoom after you finish the lecture, Zoom will take some time to compress and save the MP4 video file. After it is ready, please login into our Backend system and find the corresponding lesson in the Lesson List menu, check this lesson then click "Choose File"  to locate the recorded MP4 file then click "Upload Lesson Video". There is a progress bar in the bottom left corner, please wait until it is done. Please click "Open it" to verify it is successfully uploaded before assigning it to the student：

2A.Reuse the same Video for the classes with same courseware

To save the storage space in the server, we can share the video link between  classes with same courseware.

For example, if you teach 2 classes of AMC 10, you can upload the video once and share the video link for the second class lecture.

After you finish the uploading process in the previous Step 2,click Edit button on the lesson you just uploaded the video,

you will see the video link you just uploaded, press Ctrl +C to copy it into clipboard;

Find the lesson of the second class with the same courseware content, click Edit again and press CTRL+V to Paste the copied video link,  then click Update to save it.

3.Locate the student's homework to whom you want to assign the video file by click "Student Homework" in the backend system, open the access right for this student.

Please note: our class rule is that we only record the video for the absent students who asked to record the video, which will deduce one time from their tuition;

When the student asks for leave without deducing the lesson time, we do not need to record the video for them.

4.All done for video uploading and sharing.

Thanks for your good work to guarantee the absent students stay in the lesson by Video！

Here are the steps to open a new lecture from the online class back-end system.

1.Create New Lesson each time you want to open a new lecture:

Tutoring Management->Class List->Check the Specific Class->Click "Create New Lesson" Button,new lesson will be created below Tutoring Management->Lesson List.

2.Edit the lecture name and set homework ID and Courseware ID:

Tutoring Management->Lesson List->Select the row for the newly created Lesson->Click "Edit" button, Add the lecture name in Title and Description edit box after the "-",the click "Update" button to save.Do NOT remove the "-" as this is sign for computer recognition.

3.Set Homework ID and Courseware ID:

Find the Homework ID and Courseware ID from Database Management->Paper Management->Homework List or Courseware List->ID column:

Set the Homework ID or Courseware ID for specific Lesson by Tutoring Management->Lesson List->Select the row for the newly created Lesson->Click "Edit" button, Input the Homework ID or Courseware ID,the click "Update" button to save.

3-1.For Math Teachers ONLY

Choose one Lesson from Lesson List:

Click each Student's Name in the Student's Writing column to  open their personal handwriting window to interact;

Click  Homework Summary to get all students homework summary to see the common mistakes and explain it in the next lesson,

on this homework summary page you can just Click the rightmost  Open It! in the solution column to open the solution to this question if you need it;

Click "Start Math Class" to start the lesson, the system will load the courseware content for you.

Click Next to go to the next page;

Click Save! to save the notes of this lesson for the students to review;

Click Send  to send  the current question to all the students laptop window, then all the students will receive the question and write the steps 

to interact with you;

Click F11 to maximize this window to let students see the writing easier;

Click the Right Scroll Bar to scroll down if you want more spaces to write;

4.Assign homework to students in one click:

Tutoring Management->Lesson List->Select the row for the specific Lesson to assign homework->Click "Assign Homework" button->Click "Assign with NO pay" or "Assign with PAY".For assessment lesson just click "Assign with NO pay";For the lesson we want to deduce the class time from the student, please click  "Assign with PAY". The student's homework will be assigned and you review it below Tutoring Management->Student Homework;

5.Filter out the lessons only for a specific class:

Find the class ID from Tutoring Management->Class List->ID,remember the number;

Set the class ID 219 in the edit box before "Set Class ID" button,then click"Set Class ID" button；

 6.Set outer assignment link like Google Docs:

Set the Google Docs link by Tutoring Management->Student Homework->Select Specific Student Row->Click "Edit" Button->Copy Google Docs link into the edit box below "Link For Assignment"->Click "Update" to save;

If the assignment link and comments link is different,just input the comments link in the edit box below "Link for Comments"->Click "Update" to save.

7.Students do the homework in their account:

The students can do the homework in their account by My Account->My VIP Practices->Choose the specific assignment->Click "Do It!" to start.

This is the same for the assignment with Google Docs,the student will be redirected to the Google Docs link you set in their homework.

8.For teachers creating homework by yourself without previous course-wares:

Select the specific lesson from Tutoring Management->Lesson List->Check the lesson, and then click "Create Homework", the system will generate

a new homework bound to this lesson as template,which you can see under the directory of  Tutoring Management->Student Homework.

If you want to copy this homework to all the students in the class,just click 'Assign Homework' the same as in Step 4;

If you want to add more questions into this homework sample,please go to the directory Tutoring Management->Student Homework,do it in Step 9.

9.Add questions into sample homework:

Will add here later......

Thanks for your work!

In order to grade the students English writing work,which is submitted by students with hand-writing steps or uploading pictures, the teachers need to grade the hand-writing work and send out the comments and score。

Now this functionality is already provided by our online class back-end system,here are the detailed steps:

1.Click Tutoring Management->Student Homework, Choose the student's homework you want to grade and click "Submitted Homework"：

2.Here you will see all the answers of this practice from the student,click "Grading" in the row of that question which you want to grade:

3.Here you can write anything for the comment of this question in the same way you do the handwriting in the class (You need to use the hand-writing device or tablet):

4.After you finish your comments, click "Save" to save your comments ,then close the handwriting page and go back to the question list;

5.(optional)Click the "Edit" button to input the score for this question,and then click "Update"：

6.Repeat the step 3-4 to grade and score all the questions.

7.(optional)Sometimes if the student submits the answers by uploading photographs with mobile devices,you might need to click "Rotate" to rotate

the answer image before grading:

8.Thanks very much for your hard work to make students the best in English Writing!

In order to let professional teacher to share the ideas and ways of solving problems,also make some profits for the teacher,we developed the electronic book editing system.

Here are the steps to edit the contents for a book.

1.Overview architecture for the book

Generally speaking, a book includes many chapters, a chapter includes many topics, a topic includes many topic questions;

2.Create a new book:EBook Management->Book List->Add New, input all the information for the book,click "SAVE" to save the information into the database;

3.Create a new Chapter for a book:EBook Management->Book List, check the book you want to create the chapter for, then click "Create New Chapter":

The system will generate a new chapter for this book in the EBook Management->Chapter List directory;

4.Edit Chapter information: EBook Management->Book List,find the chapter you want to edit and then click "Edit Info" button,

input all the information for this chapter then click "SAVE" to save the information into the database:

5.Create a new topic for a chapter:EBook Management->Chapter List,check the chapter you want to create the topic for, then click "Create New Topic":

The system will generate a new topic for this chapter in the EBook Management->Topic List directory;

6.Edit Topic information: EBook Management->Topic List,find the Topic you want to edit and then click "Edit Info" button,

input all the information for this topic then click "SAVE" to save the information into the database:

7.Create a new topic question for a topic:EBook Management->Topic List,check the topic you want to create the question for, then click "Create New Question":

The system will generate a new topic question  for this topic in the EBook Management->Topic Question List directory;

8.Edit Topic Question information: EBook Management->Topic Question List,find the Topic Question  you want to edit and then click "Edit Info" button,

input all the information for this topic then click "SAVE" to save the information into the database:

Set the Content Type In Topic for this question:

Textbook Example:this question will show up as an example in this topic;

Workbook Practice:this question will show up as a workbook practice in this topic;

9.Input Latex: Click "Edit Info" in EBook Management->Chapter List or Topic List or Topic Question List,

in the corresponding editor you just need to input the LATEX,the system will show the real formula below to verify.

10.Copy questions  of other papers in database into this topic: 

Set the target topic by EBook Management->Topic List ->Check the target Topic, then Click "Copy Question To This Topic" to save the target;

Choose the source questions from 试卷管理->试卷列表->题目->Check the questions to copy, then Click "复制到当前练习试卷" to

copy the selected questions to the target topic.

11.Preview the whole chapter: Will add this functionality later.

1.For all the questions which accept handwriting steps, there is a "Write Steps" button just to the right of the "Submit Answer" button. Please login www.rootofmath.com with your PAD and click "Write Steps"：

2.The system will redirect you to the handwriting page after waiting for a while:

3.Do remember to click "Save" button to save your handwriting steps；

4.If you can not finish all the steps in one single page, you can continue to write after you click "Save" button to save the previous one；

5.Click "Finish" to return to your previous question page，click "Submit Answer" to finish all the answers for the current question;

6.Keep doing step 1- step 5 for all your handwriting questions;

7.If you want to write steps on paper, just use your iPad or tablet device or mobile phone to click "Upload" button to take photographs then upload onto the website. Your teacher will see you photographs in the backend system.

1、System Requirement

1) A  desktop computer or Laptop with Microphone and Camera.  This computer is used to create the video conference with teacher and classmates. This is your whiteboard in the class;

2) An iPad or Android Tablet. This is your electrical notebook in your class. Anything you write on this screen can be shared to the teacher and all of your classmates. The teacher can also send some questions  onto this screen thus you can finish it by yourself.

3) A screen touch Pen(Optional). You need to write with this pen to complete detailed steps. The teacher will help you  fix the issues in your steps hand by hand.

4) Consistent good internet connection.

2、Class Preparation

1)Install Zoom. On your computer browser please access:  https://zoom.us/download#client_4meeting ,finish all the steps as system prompted.

 Open Zoom then click Join Meeting,input your teacher's Zoom Meeting ID to join the class.

The details for your teacher's zoom ID and join steps please click the "Join Steps" link of your class on the www.rootofroot.com homepage,

you can get all the information on the Pop Up window;

2).Open the browser on your PAD and access http://www.rootofroot.com/ , click "Join Class" button on the home page, input your  email and password if you did not login. The system will redirect you to the handwriting page like this:

3、Additional Information

1)For the writing pen,you can buy some pen like this:

Active Stylus Pen for Touch Screens

2) If you do NOT have a iPAD or Tablet device,you can use the mouse to do the questions on your computer for short term.

However, for long-term and better learning effect,please buy Graphics Drawing Tablet connecting to your computer like this:

VEIKK S640 Ultra-Thin 6x4 Inch Graphics Drawing Tablet

4、How to do the homework

Generally speaking, each lesson will have related homework, you can see it on the next day after the lesson date by My Account->My VIP Practices:

Just click "Do It!" to start practising:

5、How to review the lesson notes

Generally speaking, each lesson will have related notes from the teacher, you can see it by My Account->My Notes and Videos after the lesson;

6、How to review the detailed solution to questions

In order to guarantee the learning effect, our system only displays the detailed solution after students submit their homework.

Just click My Account->My VIP Practices->...->Details->...->Solution to review the detailed solution to each question;

7、How to watch video after you ask the teacher to record

For some reason, if you can not join the lesson, you can ask the teacher to record the video for you in advance.

You can watch the video by My Account->My Notes and Videos->Videos->Watch:

The lesson times will be deducted as normal and the video is only open for the students in leave.

The videos will be reserved in the system for one month.

All done!

You are good to start your class.

Pythagorean Theorem

The theorem states that:

"The square on the hypotenuse of a right triangle is equal to the sum of the squares on the two legs" (Eves 80-81).

This theorem is talking about the area of the squares that are built on each side of the right triangle. 

Accordingly, we obtain the following areas for the squares, where the green and blue squares are on the legs of the right triangle and the red square is on the hypotenuse.

area of the green square is 

area of the blue square is 
area of the red square is 

From our theorem, we have the following relationship:

area of green square + area of blue square = area of red square or

Pythagoras' Proof

"Let a, b, c denote the legs and the hypotenuse of the given right triangle, and consider the two squares in the accompanying figure, each having a+b as its side. The first square is dissected into six pieces-namely, the two squares on the legs and four right triangles congruent to the given triangle. The second square is dissected into five pieces-namely, the square on the hypotenuse and four right triangles congruent to the given triangle. By subtracting equals from equals, it now follows that the square on the hypotenuse is equal to the sum of the squares on the legs" (Eves 81).

Consider the following figure. 

The area of the first square is given by (a+b)^2 or 4(1/2ab)+ a^2 + b^2.
The area of the second square is given by (a+b)^2 or 4(1/2ab) + c^2.
Since the squares have equal areas we can set them equal to another and subtract equals. The case (a+b)^2=(a+b)^2 is not interesting. Let's do the other case. 
4(1/2ab) + a^2 + b^2 = 4(1/2ab)+ c^2
Subtracting equals from both sides we have

concluding Pythagoras' proof.

Bhaskara's First Proof

Bhaskara's proof is also a dissection proof. It is similar to the proof provided by Pythagoras. Bhaskara was born in India. He was one of the most important Hindu mathematicians of the second century AD. He used the following diagrams in proving the Pythagorean Theorem. 

In the above diagrams, the blue triangles are all congruent and the yellow squares are congruent. First we need to find the area of the big square two different ways. First let's find the area using the area formula for a square. 
Thus, A=c^2.
Now, lets find the area by finding the area of each of the components and then sum the areas.
Area of the blue triangles = 4(1/2)ab
Area of the yellow square = (b-a)^2
Area of the big square = 4(1/2)ab + (b-a)^2
= 2ab + b^2 - 2ab + a^2
= b^2 + a^2

Since, the square has the same area no matter how you find it
A = c^2 = a^2 + b^2,
concluding the proof. 

Bhaskara's Second Proof of the Pythagorean Theorem

In this proof, Bhaskara began with a right triangle and then he drew an altitude on the hypotenuse. From here, he used the properties of similarity to prove the theorem.

Now prove that triangles ABC and CBE are similar.
It follows from the AA postulate that triangle ABC is similar to triangle CBE, since angle B is congruent to angle B and angle C is congruent to angle E. Thus, since internal ratios are equal s/a=a/c.
Multiplying both sides by ac we get
sc=a^2.

Now show that triangles ABC and ACE are similar.
As before, it follows from the AA postulate that these two triangles are similar. Angle A is congruent to angle A and angle C is congruent to angle E. Thus, r/b=b/c. Multiplying both sides by bc we get
rc=b^2.

Now when we add the two results we get
sc + rc = a^2 + b^2.
c(s+r) = a^2 + b^2
c^2 = a^2 + b^2,
concluding the proof of the Pythagorean Theorem.

Garfield's Proof

The twentieth president of the United States gave the following proof to the Pythagorean Theorem. He discovered this proof five years before he become President. He hit upon this proof in 1876 during a mathematics discussion with some of the members of Congress. It was later published in the New England Journal of Education.. The proof depends on calculating the area of a right trapezoid two different ways. The first way is by using the area formula of a trapezoid and the second is by summing up the areas of the three right triangles that can be constructed in the trapezoid. He used the following trapezoid in developing his proof.

First, we need to find the area of the trapezoid by using the area formula of the trapezoid.
A=(1/2)h(b1+b2) area of a trapezoid

In the above diagram, h=a+b, b1=a, and b2=b.

A=(1/2)(a+b)(a+b)
=(1/2)(a^2+2ab+b^2).

Now, let's find the area of the trapezoid by summing the area of the three right triangles.
The area of the yellow triangle is
A=1/2(ba).

The area of the red triangle is
A=1/2(c^2).

The area of the blue triangle is 
A= 1/2(ab).

The sum of the area of the triangles is 
1/2(ba) + 1/2(c^2) + 1/2(ab) = 1/2(ba + c^2 + ab) = 1/2(2ab + c^2).

Since, this area is equal to the area of the trapezoid we have the following relation:
(1/2)(a^2 + 2ab + b^2) = (1/2)(2ab + c^2).

Multiplying both sides by 2 and subtracting 2ab from both sides we get

concluding the proof.