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

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Title: Number Line: Distance
 
Title: Number Line: Distance
 +
 +
Author: Radhika Yadav
  
 
Keywords: PhET simulation, number line, integers, subtraction, variables, absolute value, directed distance, spoken tutorial, video tutorial.
 
Keywords: PhET simulation, number line, integers, subtraction, variables, absolute value, directed distance, spoken tutorial, video tutorial.
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{| border=1
 
{| border=1
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||To follow this tutorial,
 
||To follow this tutorial,
  
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*Learners should be familiar with topics in basic Mathematics.
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* Learners should be familiar with topics in basic Mathematics.
  
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*Please use the link below to access the tutorials on '''PhET simulations'''.
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* Please use the link below to access the tutorials on '''PhET simulations'''.
  
 
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|-
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'''https://phet.colorado.edu/en/simulations/number-line-distance'''
 
'''https://phet.colorado.edu/en/simulations/number-line-distance'''
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||Please use the given link to download the '''PhET simulation'''.
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|| Please use the given link to download the '''PhET simulation'''.
 
|-
 
|-
 
||'''Slide Number 6'''
 
||'''Slide Number 6'''
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|-
 
|-
 
||Point to the number line
 
||Point to the number line
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||The screen has a '''number line WE'''.
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||The screen has a '''number line W E'''.
  
 
It is used to represent numbers at equal intervals and perform operations.
 
It is used to represent numbers at equal intervals and perform operations.
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|-
 
|-
 
||Point to the '''Objects''' box.
 
||Point to the '''Objects''' box.
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||We can drag and place the objects from the''' Objects '''box on the number line.
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||We can drag and place the objects from the ''' Objects ''' box on the number line.
  
 
|-
 
|-
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||We can view this '''simulation''' in different scenarios.
 
||We can view this '''simulation''' in different scenarios.
  
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#The first one is the distance between a house and a person.
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# The first one is the distance between a house and a person.
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#The second is the temperature difference between two climates.
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# The second is the temperature difference between two climates.
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#The last is the vertical distance between a fish and a bird.
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# The last is the vertical distance between a fish and a bird.
  
 
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|-
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'''Point Labels''', '''Distance Labels''', '''Distance Description''', and ''' Tick Marks'''.
 
'''Point Labels''', '''Distance Labels''', '''Distance Description''', and ''' Tick Marks'''.
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||On the top right we have:
 
||On the top right we have:
  
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#'''Point Labels'''
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# '''Point Labels'''
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#'''Distance Labels'''
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# '''Distance Labels'''
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#'''Distance Description '''and''' '''
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# '''Distance Description '''and''' '''
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#'''Tick Marks''' checkboxes.
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# '''Tick Marks''' checkboxes.
  
 
We can use these checkboxes to show and hide the details.
 
We can use these checkboxes to show and hide the details.
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|-
 
|-
 
||Point to the number line
 
||Point to the number line
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||On the number line, the person that is''' variable x1''' is the reference point.
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||On the number line, the person that is ''' variable x1''' is the reference point.
  
  
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||In this tutorial, we have learnt how to:
 
||In this tutorial, we have learnt how to:
  
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*Represent integers on the '''number line'''
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* Represent integers on the '''number line'''
  
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*Subtract integers
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* Subtract integers
  
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*Calculate the distance between two integers
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* Calculate the distance between two integers
 
|-
 
|-
 
||'''Slide number 8'''
 
||'''Slide number 8'''

Latest revision as of 16:46, 14 February 2023

Title: Number Line: Distance

Author: Radhika Yadav

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 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.
  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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