Difference between revisions of "PhET-Simulations-for-Mathematics/C2/Number-Line---Distance/English"

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(Created page with "Title: Number Line: Distance Keywords: PhET simulation, number line, integers, subtraction, variables, absolute value, directed distance, spoken tutorial, video tutorial. {|...")
 
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'''Title Slide'''
 
'''Title Slide'''
 
||Welcome to this '''Spoken Tutorial''' on '''Number Line: Distance'''.
 
||Welcome to this '''Spoken Tutorial''' on '''Number Line: Distance'''.
−
 
  
 
|-
 
|-
Line 20: Line 19:
 
||In this tutorial, we will learn how to:
 
||In this tutorial, we will learn how to:
  
−
* Represent integers on the number line
+
* Represent integers on the '''number line'''
  
 
* Subtract integers
 
* Subtract integers
  
 
* Calculate the distance between two integers
 
* Calculate the distance between two integers
−
 
−
 
  
 
|-
 
|-
Line 34: Line 31:
 
||This tutorial is recorded using,
 
||This tutorial is recorded using,
  
−
* macOS Catalina version 10.15.7
+
* '''macOS Catalina''' version 10.15.7
−
 
+
−
* Google chrome version 101.0.49
+
−
 
+
  
 +
* '''Google Chrome''' version 101.0.49
  
 
|-
 
|-
Line 47: Line 42:
  
 
'''https://spoken-tutorial.org'''
 
'''https://spoken-tutorial.org'''
−
 
−
 
  
 
||To follow this tutorial,
 
||To follow this tutorial,
  
−
Learners should be familiar with topics in basic Mathematics.
+
*Learners should be familiar with topics in basic Mathematics.
−
 
+
−
 
+
−
Please use the link below to access the tutorials on '''PhET simulations'''.
+
−
 
+
  
 +
*Please use the link below to access the tutorials on '''PhET simulations'''.
  
 
|-
 
|-
Line 66: Line 56:
  
 
'''https://phet.colorado.edu/en/simulations/number-line-distance'''
 
'''https://phet.colorado.edu/en/simulations/number-line-distance'''
−
||Please use the given link to download the '''PhET''' '''simulation'''.
+
||Please use the given link to download the '''PhET simulation'''.
 
|-
 
|-
 
||'''Slide Number 6'''
 
||'''Slide Number 6'''
Line 72: Line 62:
 
'''PhET simulations'''
 
'''PhET simulations'''
  
−
 
+
||In this tutorial, we will use the '''Number Line: Distance PhET simulation'''.
−
 
+
−
||In this tutorial, we will use the '''Number Line: Distance''' '''PhET simulation'''.
+
  
 
|-
 
|-
Line 81: Line 69:
  
 
'''Number Line: Distance simulation'''
 
'''Number Line: Distance simulation'''
 +
||I have already downloaded the '''simulation''' to my '''Downloads''' folder.
  
−
 
−
||I have already downloaded the '''simulation''' to my '''Downloads''' folder.
 
 
|-
 
|-
 
||Double click on the '''number-line-distance_en.html''' file
 
||Double click on the '''number-line-distance_en.html''' file
Line 89: Line 76:
  
  
−
The file will open in your default browser.
+
The file will open in your default '''browser'''.
−
 
+
−
 
+
  
 
|-
 
|-
Line 98: Line 83:
 
|-
 
|-
 
||Point to each screen
 
||Point to each screen
−
||The interface has two screens,
+
||The interface has two screens - '''Explore''' and  '''Generic'''.
−
 
+
−
'''Explore''' and  '''Generic'''.
+
−
 
+
−
 
+
  
 
|-
 
|-
 
||Click on '''Explore''' screen
 
||Click on '''Explore''' screen
 
||Click on the '''Explore''' screen.
 
||Click on the '''Explore''' screen.
−
 
  
 
|-
 
|-
 
||Point to the number line
 
||Point to the number line
 
||The screen has a '''number line WE'''.
 
||The screen has a '''number line WE'''.
−
 
  
 
It is used to represent numbers at equal intervals and perform operations.
 
It is used to represent numbers at equal intervals and perform operations.
−
 
−
 
  
 
|-
 
|-
 
||Point to the top left corner.
 
||Point to the top left corner.
 
||On the top left corner, there are two options.
 
||On the top left corner, there are two options.
−
 
  
 
We can switch between them.
 
We can switch between them.
Line 127: Line 103:
  
 
'''Absolute Value''' radio button is selected by default.
 
'''Absolute Value''' radio button is selected by default.
−
 
−
 
  
 
|-
 
|-
 
||Point to the '''Absolute Value''' radio button
 
||Point to the '''Absolute Value''' radio button
 
||'''Absolute Value ''' is the magnitude of a number without regard to its sign.
 
||'''Absolute Value ''' is the magnitude of a number without regard to its sign.
−
 
−
 
  
 
|-
 
|-
Line 141: Line 113:
  
 
Select '''Absolute Value''' radio button.
 
Select '''Absolute Value''' radio button.
−
||'''Directed Distance'''.
+
||'''Directed Distance''' shows the difference between two numbers along with the sign.
−
 
+
−
It shows the difference between two numbers along with the negative sign.
+
−
 
+
−
 
+
  
 
|-
 
|-
 
||Point to the bottom left corner swap button
 
||Point to the bottom left corner swap button
−
||At the bottom, we have two variables represented as '''x1''' and '''x2'''.
+
||At the bottom, we have two '''variables''' represented as '''x1''' and '''x2'''.
  
 
We can swap them using the swapping arrow button.
 
We can swap them using the swapping arrow button.
−
 
−
 
  
 
|-
 
|-
 
||Point to the '''Objects''' box.
 
||Point to the '''Objects''' box.
 
||We can drag and place the objects from the''' Objects '''box on the number line.
 
||We can drag and place the objects from the''' Objects '''box on the number line.
 +
 
|-
 
|-
 
||Point to the different scenarios.
 
||Point to the different scenarios.
 
||We can view this '''simulation''' in different scenarios.
 
||We can view this '''simulation''' in different scenarios.
  
−
 
+
#The first one is the distance between a house and a person.
−
The first one is the distance between a house and a person.
+
#The second is the temperature difference between two climates.
−
 
+
#The last is the vertical distance between a fish and a bird.
−
The second is the temperature difference between two climates.
+
−
 
+
−
The last is the vertical distance between a fish and a bird.
+
−
 
+
−
 
+
  
 
|-
 
|-
Line 178: Line 140:
  
  
−
||On the top right we have,
+
||On the top right we have:
−
 
+
−
'''Point Labels'''
+
−
 
+
−
'''Distance Labels'''
+
−
 
+
−
'''Distance Description '''and''' '''
+
−
 
+
−
'''Tick Marks''' checkboxes.
+
−
 
+
−
 
+
−
We can use these check boxes to show and hide the details.
+
  
 +
#'''Point Labels'''
 +
#'''Distance Labels'''
 +
#'''Distance Description '''and''' '''
 +
#'''Tick Marks''' checkboxes.
  
 +
We can use these checkboxes to show and hide the details.
  
 
|-
 
|-
 
||Point to the '''Distance Statement '''on the top center of the screen
 
||Point to the '''Distance Statement '''on the top center of the screen
−
||At the top, is the '''distance statement'''.
+
||At the top is the '''distance statement'''.
−
 
+
  
 
It can be minimised.
 
It can be minimised.
 +
  
 
We can again maximise it when required.
 
We can again maximise it when required.
Line 206: Line 162:
  
 
|-
 
|-
−
||Point to the '''number line'''.
+
||Point to the right of the '''number line'''.
−
||From the origin, positive numbers are represented on the right of the number line.
+
 
 +
Point to the left of the '''number line'''.
 +
||From the origin, positive numbers are represented on the right of the '''number line'''.
  
  
Line 216: Line 174:
 
|-
 
|-
 
||Point to the '''Objects''' box.
 
||Point to the '''Objects''' box.
−
||Let us put the house and the person on the number line.
+
||Let us put the house and the person on the '''number line.'''
  
  
Line 223: Line 181:
 
Let us use the following values for demonstration.
 
Let us use the following values for demonstration.
  
−
 
+
|-
 +
||Point to the '''House''' >> then to the '''number line'''
 +
||The house is represented by '''variable x1''' whose value is -4.
  
 
|-
 
|-
−
||Point to the '''House'''
+
||Point to the '''Person''' >> then to the '''number line'''
−
||The house is represented by variable x1 whose value is -4.
+
||The person is represented by '''variable x2''' whose value is 5.
  
−
 
−
|-
 
−
||Point to the '''Person'''.
 
−
||The person is represented by variable '''x2''' whose value is 5.
 
 
|-
 
|-
 
||Point to the '''Distance Statement'''.
 
||Point to the '''Distance Statement'''.
Line 243: Line 199:
  
 
Select '''Absolute Value ''' radio button.
 
Select '''Absolute Value ''' radio button.
−
 
−
 
−
 
 
||'''Directed distance''' also remains the same.
 
||'''Directed distance''' also remains the same.
−
 
−
 
  
 
|-
 
|-
Line 260: Line 211:
 
||Drag the '''Person ''' towards right on the number line.
 
||Drag the '''Person ''' towards right on the number line.
 
||If the person moves to the right, the distance increases.
 
||If the person moves to the right, the distance increases.
−
 
  
 
|-
 
|-
Line 268: Line 218:
 
|-
 
|-
 
||Point to the '''Distance Statement'''
 
||Point to the '''Distance Statement'''
−
||The difference between '''x2''' and '''x1''', also changes simultaneously.
+
||The difference between '''x2''' and '''x1''' also changes simultaneously.
−
 
+
−
 
+
−
Hence, distance between two integers is the absolute value of their difference.
+
  
  
 +
Hence, distance between two integers is the '''absolute value''' of their difference.
  
 
|-
 
|-
 
||Point to the bottom left swap button
 
||Point to the bottom left swap button
  
−
 
+
||If we swap the '''variables x1''' and '''x2''', the '''absolute value''' remains the same.
−
 
+
−
||If we swap the variables '''x1''' and '''x2''', the absolute value remains the same.
+
−
 
+
−
 
+
  
 
|-
 
|-
Line 290: Line 234:
  
 
'''x2-x1''' is (-4-3) which is equal to -7.
 
'''x2-x1''' is (-4-3) which is equal to -7.
−
 
−
 
  
 
|-
 
|-
Line 299: Line 241:
 
|-
 
|-
 
||Point to the number line
 
||Point to the number line
−
||On the number line, the person that is variable '''x1''' is the reference point.
+
||On the number line, the person that is''' variable x1''' is the reference point.
  
  
 
The arrowhead points west in the direction of the house.
 
The arrowhead points west in the direction of the house.
−
 
−
 
  
 
|-
 
|-
 
||Point to the bottom left swap button
 
||Point to the bottom left swap button
−
||If we swap the variables again, the directed distance is 3-(-4) which is 7.
+
||If we swap the '''variables''' again, the directed distance is 3-(-4) which is 7.
  
  
Line 314: Line 254:
  
  
−
The person is 7 metres East of the house.
+
The person is 7 metres east of the house.
−
 
+
−
 
+
  
 
|-
 
|-
Line 340: Line 278:
  
 
It is the difference of their distance from the sea level.
 
It is the difference of their distance from the sea level.
−
 
−
 
  
 
|-
 
|-
Line 349: Line 285:
  
 
We can place these objects wherever we want on the number line.
 
We can place these objects wherever we want on the number line.
−
 
−
 
  
 
|-
 
|-
 
||Point to the '''Bird'''.
 
||Point to the '''Bird'''.
−
||The bird is represented by the variable '''y1''' whose value is -2.
+
||The bird is represented by the '''variable y1''' whose value is -2.
−
 
+
−
 
+
  
 
|-
 
|-
 
||Point to the '''House'''
 
||Point to the '''House'''
−
||The fish is represented by the variable '''y2''' whose value is -13.
+
||The fish is represented by the '''variable y2''' whose value is -13.
 
|-
 
|-
 
||Point to the '''Distance Statement'''
 
||Point to the '''Distance Statement'''
Line 370: Line 302:
  
 
Hence, they have a vertical distance of 11 meters.
 
Hence, they have a vertical distance of 11 meters.
−
 
  
 
|-
 
|-
Line 378: Line 309:
  
 
The '''Generic''' screen has some new tools.
 
The '''Generic''' screen has some new tools.
−
 
−
 
  
 
|-
 
|-
 
||Point to the '''Scale'''.
 
||Point to the '''Scale'''.
−
||From this list, we can select the '''scale''' of the number line.
+
||From this list we can select the '''scale''' of the '''number line'''.
  
  
 
-10 to 10 is chosen by default.
 
-10 to 10 is chosen by default.
−
 
−
 
  
 
|-
 
|-
  
 
||Point to the number line representations.
 
||Point to the number line representations.
−
||We can choose between a '''horizontal''' or '''vertical '''representation of the number line.
+
||We can choose between a '''horizontal''' or '''vertical '''representation of the '''number line'''.
  
  
Line 404: Line 331:
  
 
We can use the '''Generic''' screen to generalise and understand these concepts.
 
We can use the '''Generic''' screen to generalise and understand these concepts.
−
 
  
 
|-
 
|-
 
||Point to the '''colored balls'''.
 
||Point to the '''colored balls'''.
−
||Let us put the colored balls on the number line.
+
||Let us put the colored balls on the '''number line'''.
−
 
+
  
 
|-
 
|-
 
||Point to the number line
 
||Point to the number line
−
||The variable '''x1''' represents the pink ball.
+
||The '''variable x1''' represents the pink ball.
−
 
+
−
 
+
−
The variable '''x2''' represents the blue ball.
+
  
  
 +
The''' variable x2''' represents the blue ball.
  
 
|-
 
|-
Line 426: Line 349:
  
 
x2-x1 is 2-(-4) which is equal to 6.
 
x2-x1 is 2-(-4) which is equal to 6.
−
 
−
 
  
 
|-
 
|-
Line 433: Line 354:
 
||Select the '''directed distance''' option.
 
||Select the '''directed distance''' option.
  
−
Here the '''distanc'''e''' description''' tells us that '''x2''' is 6 units more positive than '''x1'''.
+
Here the '''distance description''' tells us that '''x2''' is 6 units more positive than '''x1'''.
−
 
+
−
 
+
  
 
|-
 
|-
Line 450: Line 369:
 
|-
 
|-
 
||Point to the bottom left swap button
 
||Point to the bottom left swap button
−
||If we swap the variables, the arrowhead points towards the left.
+
||If we swap the '''variables''', the arrowhead points towards the left.
−
 
+
−
 
+
  
 
|-
 
|-
Line 460: Line 377:
 
|-
 
|-
 
||Point to the bottom left swap button
 
||Point to the bottom left swap button
−
||Let us swap the variables once again.
+
||Let us swap the '''variables''' once again.
  
 
|-
 
|-
 
||Point to the '''Distance Statement'''
 
||Point to the '''Distance Statement'''
−
||Let us change the variable values using the buttons in the '''distance statement'''.
+
||Let us change the '''variable''' using the buttons in the '''distance statement'''.
  
  
−
The position of the colored balls on the number line changes accordingly.
+
The position of the colored balls on the '''number line''' changes accordingly.
  
 
|-
 
|-
 
||Point to the number line
 
||Point to the number line
−
||Hence, the absolute value of the difference between two integers is their distance.
+
||Hence, the '''absolute value''' of the difference between two integers is their distance.
−
 
+
−
 
+
  
 
|-
 
|-
Line 484: Line 399:
 
||In this tutorial, we have learnt how to:
 
||In this tutorial, we have learnt how to:
  
−
Represent integers on the number line
+
*Represent integers on the '''number line'''
  
−
Subtract integers
+
*Subtract integers
  
−
Calculate the distance between two integers
+
*Calculate the distance between two integers
 
|-
 
|-
 
||'''Slide number 8'''
 
||'''Slide number 8'''
Line 495: Line 410:
 
||As an assignment,
 
||As an assignment,
  
 +
*Open the second scenario in the '''Explore''' screen.
  
−
Open the second scenario in the '''Explore''' screen.
+
*Find the average temperature of winter and summer months in your city.
−
 
+
−
 
+
−
Find the average temperature of winter and summer months in your city.
+
−
 
+
−
 
+
−
Represent them on the number line and calculate the difference between them.
+
−
 
+
−
 
+
−
Find out how this has changed over the years.
+
  
 +
*Represent them on the number line and calculate the difference between them.
  
 +
*Find out how this has changed over the years.
  
 
|-
 
|-
Line 516: Line 425:
  
 
Please download and watch it.
 
Please download and watch it.
−
 
−
 
  
 
|-
 
|-
Line 530: Line 437:
  
 
* For more details, please write to us.
 
* For more details, please write to us.
−
 
−
 
  
 
|-
 
|-
Line 541: Line 446:
  
 
* Please visit this site.
 
* Please visit this site.
−
 
  
 
* Choose the minute and second where you have the question.
 
* Choose the minute and second where you have the question.
−
 
  
 
* Explain your questions briefly.
 
* Explain your questions briefly.
−
 
  
 
* The Spoken tutorial project will ensure an answer.
 
* The Spoken tutorial project will ensure an answer.
−
 
  
 
* You will have to register to ask questions.
 
* You will have to register to ask questions.
−
 
−
 
  
 
|-
 
|-
Line 560: Line 459:
  
 
'''Acknowledgement'''
 
'''Acknowledgement'''
−
 
−
 
−
 
 
||The Spoken Tutorial project is funded by the Ministry of Education, Government of India.
 
||The Spoken Tutorial project is funded by the Ministry of Education, Government of India.
−
 
−
 
  
 
|-
 
|-
Line 575: Line 469:
  
 
Thanks for joining.
 
Thanks for joining.
−
 
  
 
|-
 
|-
 
|}
 
|}

Revision as of 17:18, 15 December 2022

Title: Number Line: Distance

Keywords: PhET simulation, number line, integers, subtraction, variables, absolute value, directed distance, spoken tutorial, video tutorial.

Visual Cue Narration
Slide Number 1

Title Slide

Welcome to this Spoken Tutorial on Number Line: Distance.
Slide Number 2

Learning Objectives

In this tutorial, we will learn how to:
  • Represent integers on the number line
  • Subtract integers
  • Calculate the distance between two integers
Slide Number 3

System Requirements

This tutorial is recorded using,
  • macOS Catalina version 10.15.7
  • Google Chrome version 101.0.49
Slide Number 4

Pre-requisites


https://spoken-tutorial.org

To follow this tutorial,
  • Learners should be familiar with topics in basic Mathematics.
  • Please use the link below to access the tutorials on PhET simulations.
Slide Number 5

Link for PhET simulation


https://phet.colorado.edu/en/simulations/number-line-distance

Please use the given link to download the PhET simulation.
Slide Number 6

PhET simulations

In this tutorial, we will use the Number Line: Distance PhET simulation.
Point to the simulation in the Downloads folder.


Number Line: Distance simulation

I have already downloaded the simulation to my Downloads folder.
Double click on the number-line-distance_en.html file To open the simulation, double click on the number-line-distance_en.html file.


The file will open in your default browser.

Point to the simulation interface This is the interface of the Number Line: Distance simulation.
Point to each screen The interface has two screens - Explore and Generic.
Click on Explore screen Click on the Explore screen.
Point to the number line The screen has a number line WE.

It is used to represent numbers at equal intervals and perform operations.

Point to the top left corner. On the top left corner, there are two options.

We can switch between them.


Absolute Value radio button is selected by default.

Point to the Absolute Value radio button Absolute Value is the magnitude of a number without regard to its sign.
Select Directed Distance radio button.


Select Absolute Value radio button.

Directed Distance shows the difference between two numbers along with the sign.
Point to the bottom left corner swap button At the bottom, we have two variables represented as x1 and x2.

We can swap them using the swapping arrow button.

Point to the Objects box. We can drag and place the objects from the Objects box on the number line.
Point to the different scenarios. We can view this simulation in different scenarios.
  1. The first one is the distance between a house and a person.
  2. The second is the temperature difference between two climates.
  3. The last is the vertical distance between a fish and a bird.
Point to the information checkboxes.

Point Labels, Distance Labels, Distance Description, and Tick Marks.


On the top right we have:
  1. Point Labels
  2. Distance Labels
  3. Distance Description and
  4. Tick Marks checkboxes.

We can use these checkboxes to show and hide the details.

Point to the Distance Statement on the top center of the screen At the top is the distance statement.

It can be minimised.


We can again maximise it when required.

Point to the reset button The reset button takes us back to the starting point.
Point to the right of the number line.

Point to the left of the number line.

From the origin, positive numbers are represented on the right of the number line.


The negative numbers are represented on the left.


Hence, the numbers on the right are greater than the numbers on the left.

Point to the Objects box. Let us put the house and the person on the number line.


We can place them at any point on the line.

Let us use the following values for demonstration.

Point to the House >> then to the number line The house is represented by variable x1 whose value is -4.
Point to the Person >> then to the number line The person is represented by variable x2 whose value is 5.
Point to the Distance Statement. The absolute difference between x2 and x1 is x2-x1.

5-(-4) which is equal to 9.

Select Directed Distance radio button.


Select Absolute Value radio button.

Directed distance also remains the same.
Point to the Distance Description. See the distance description.


It tells us the distance between the two objects is 9 metres.

Drag the Person towards right on the number line. If the person moves to the right, the distance increases.
Drag the Person towards left on the number line. If the person moves to the left, the distance decreases.
Point to the Distance Statement The difference between x2 and x1 also changes simultaneously.


Hence, distance between two integers is the absolute value of their difference.

Point to the bottom left swap button If we swap the variables x1 and x2, the absolute value remains the same.
Select Directed Distance radio button However, the directed distance is now -7.


x2-x1 is (-4-3) which is equal to -7.

Point to the Distance Description. The distance description tells us the house is 7 metres west of the person.
Point to the number line On the number line, the person that is variable x1 is the reference point.


The arrowhead points west in the direction of the house.

Point to the bottom left swap button If we swap the variables again, the directed distance is 3-(-4) which is 7.


The house becomes the reference point now.


The person is 7 metres east of the house.

Click on the third scenario Let us select the third scenario.
Point to the number line


Point to all the features

Here we have a vertical number line.


All other features remain the same.

Point to the Objects box Let us place the bird in the sky and the fish in the water.
Point to the number line The vertical distance between them is calculated.


It is the difference of their distance from the sea level.

Drag the Bird inside the water to catch the Fish. Let us drag the bird inside the water to catch the fish.


We can place these objects wherever we want on the number line.

Point to the Bird. The bird is represented by the variable y1 whose value is -2.
Point to the House The fish is represented by the variable y2 whose value is -13.
Point to the Distance Statement The difference between y2 and y1 is y2-y1.


(-13) - (-2) equal to 11 is the absolute value.


Hence, they have a vertical distance of 11 meters.

Click on Generic screen. Click on the Generic screen.


The Generic screen has some new tools.

Point to the Scale. From this list we can select the scale of the number line.


-10 to 10 is chosen by default.

Point to the number line representations. We can choose between a horizontal or vertical representation of the number line.


Horizontal is chosen by default.

Click on reset button. Let us reset our screen.


We can use the Generic screen to generalise and understand these concepts.

Point to the colored balls. Let us put the colored balls on the number line.
Point to the number line The variable x1 represents the pink ball.


The variable x2 represents the blue ball.

Point to the Distance Description The distance description tells us that x2 and x1 are 6 units apart.


x2-x1 is 2-(-4) which is equal to 6.

Select Directed Distance radio button Select the directed distance option.

Here the distance description tells us that x2 is 6 units more positive than x1.

Point to the number line. Here, x1 is the reference point.


Notice that the arrowhead points towards the right in the direction of x2.

Point to the Distance Description

The description here tells us that x2 is more positive.
Point to the bottom left swap button If we swap the variables, the arrowhead points towards the left.
Point to the Distance Description The description tells us that x2 is more negative.
Point to the bottom left swap button Let us swap the variables once again.
Point to the Distance Statement Let us change the variable using the buttons in the distance statement.


The position of the colored balls on the number line changes accordingly.

Point to the number line Hence, the absolute value of the difference between two integers is their distance.
Only Narration With this, we have come to the end of this tutorial. Let us summarise.
Slide number 7

Summary

In this tutorial, we have learnt how to:
  • Represent integers on the number line
  • Subtract integers
  • Calculate the distance between two integers
Slide number 8

Assignment

As an assignment,
  • Open the second scenario in the Explore screen.
  • Find the average temperature of winter and summer months in your city.
  • Represent them on the number line and calculate the difference between them.
  • Find out how this has changed over the years.
Slide number 9

About the Spoken Tutorial project

The video at the following link summarises the Spoken Tutorial project.

Please download and watch it.

Slide number 10

Spoken Tutorial workshops

The Spoken Tutorial Project team:
  • conducts workshops using spoken tutorials and
  • gives certificates on passing online tests.
  • For more details, please write to us.
Slide number 11

Forum for specific questions

  • Do you have questions in THIS Spoken Tutorial?
  • Please visit this site.
  • Choose the minute and second where you have the question.
  • Explain your questions briefly.
  • The Spoken tutorial project will ensure an answer.
  • You will have to register to ask questions.
Slide number 12

Acknowledgement

The Spoken Tutorial project is funded by the Ministry of Education, Government of India.
Slide number 13

Thank you

This is Radhika Yadav, a FOSSEE summer fellow 2022, IIT Bombay signing off.


Thanks for joining.

Contributors and Content Editors

Madhurig, Nancyvarkey, RadhikaYadav

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