View source for PhET-Simulations-for-Mathematics/C2/Number-Line---Distance/English

Title: Number Line: Distance

Author: Radhika Yadav

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


{| border=1
|| '''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 W E'''.

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.

# 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.

|-
||Point to the information checkboxes.

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


||On the top right we have:

# '''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
||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.

|-
|}