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

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Title: Number Line: Operations
 
Title: Number Line: Operations
 +
 +
Author: Radhika Yadav
  
 
Keywords: PhET simulation, number line, integers, addition, subtraction, additive inverse, assets, debts, spoken tutorial, video tutorial.
 
Keywords: PhET simulation, number line, integers, addition, subtraction, additive inverse, assets, debts, spoken tutorial, video tutorial.
Line 11: Line 13:
  
 
'''Title Slide'''
 
'''Title Slide'''
−
||Welcome to this Spoken Tutorial on '''Number Line: Operations.'''
+
||Welcome to this Spoken Tutorial on '''Number Line: Operations'''.
  
 
|-
 
|-
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||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
  
 
|-
 
|-
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||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 56: Line 58:
  
 
'''PhET simulations'''
 
'''PhET simulations'''
−
||In this tutorial, we will use the '''Number Line: Operations PhET simulation.'''
+
||In this tutorial, we will use the '''Number Line: Operations PhET simulation'''.
  
 
|-
 
|-
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||The interface has four screens:
 
||The interface has four screens:
  
−
'''Chips''', '''Net Worth''', '''Operations''', and '''Generic'''
+
'''Chips''', '''Net Worth''', '''Operations''', and '''Generic'''.
  
 
|-
 
|-
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|-
 
|-
 
||Point to the number line
 
||Point to the number line
−
||The screen has a '''number line '''to represent the total amount of chips or coins.
+
||The screen has a '''number line ''' to represent the total amount of chips or coins.
  
 
|-
 
|-
 
||Point to the '''Total''' box
 
||Point to the '''Total''' box
−
||The total can also be viewed at the top of the screen in the '''Total '''box.
+
||The total can also be viewed at the top of the screen in the '''Total ''' box.
  
 
|-
 
|-
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−
'''Operation Descriptions, Operation Labels, '''and''' Tick Marks'''
+
'''Operation Descriptions''', '''Operation Labels''', and ''' Tick Marks'''.
  
  
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|-
 
|-
 
||Point to the '''Total '''box.
 
||Point to the '''Total '''box.
−
 
−
 
−
 
−
 
  
 
Add annotation while editing.
 
Add annotation while editing.
 
||The total amount is now 0 as 1 + (-1) is 0.
 
||The total amount is now 0 as 1 + (-1) is 0.
−
 
  
 
This means -1 is the additive inverse of 1.
 
This means -1 is the additive inverse of 1.
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|-
 
|-
 
||Point to the left panel next to the '''Negatives''' bag
 
||Point to the left panel next to the '''Negatives''' bag
−
||Let us put the -5 chip in the '''Negatives '''bag.
+
||Let us put the -5 chip in the '''Negatives ''' bag.
  
 
|-
 
|-
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|-
 
|-
−
||Click on the '''Net Worth '''screen
+
||Click on the '''Net Worth ''' screen.
 
||Click on the '''Net Worth''' screen.
 
||Click on the '''Net Worth''' screen.
  
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−
Assets are items that a person owns which have value.
+
'''Assets''' are items that a person owns which have value.
  
 
|-
 
|-
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||See the following table.
 
||See the following table.
  
−
*Pause the video here and perform these transactions using the '''Net Worth''' screen.
+
Pause the video here and perform these transactions using the '''Net Worth''' screen.
−
*Calculate the net worth of a person.
+
 
−
*:(Note: See table 1)
+
It will calculate the net worth of a person.
 +
 
  
 
|-
 
|-
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||After performing these operations, the final net worth of a person is $100.
 
||After performing these operations, the final net worth of a person is $100.
 
|-
 
|-
−
||Click on the '''Operations''' screen
+
||Click on the '''Operations''' screen.
 
||Click on the '''Operations''' screen.
 
||Click on the '''Operations''' screen.
  
 
|-
 
|-
 
||Point to the number line
 
||Point to the number line
−
||The screen has a '''number line '''to represent net worth.
+
||The screen has a '''number line ''' to represent net worth.
  
 
|-
 
|-
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|-
 
|-
 
||Point to the top right box.
 
||Point to the top right box.
−
 
−
 
  
 
Point to the up and down arrow buttons.
 
Point to the up and down arrow buttons.
−
 
  
 
||On the top right, there is an option to perform two transactions.
 
||On the top right, there is an option to perform two transactions.
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Click the down arrow.
 
Click the down arrow.
−
 
−
 
−
 
  
 
Scroll the right arrow to move to right slide.
 
Scroll the right arrow to move to right slide.
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||Point to the '''Net Worth''' box
 
||Point to the '''Net Worth''' box
  
 +
Point to Simplify button.
  
−
Point to Simplify button
+
Point to equals button.
−
 
+
−
 
+
−
 
+
−
Point to equals button
+
 
||The '''Net Worth''' box next to it displays the net worth amount.
 
||The '''Net Worth''' box next to it displays the net worth amount.
  
  
−
We can click the Simplify button to simplify negative signs in the expression.
+
We can click the '''Simplify''' button to simplify negative signs in the expression.
  
  
−
We can click the equals button to evaluate the expression.
+
We can click the '''equals''' button to evaluate the expression.
  
 
|-
 
|-
−
||Point to the information checkboxes
+
||Point to the information check boxes
−
||On the top left, we have the following checkboxes.
+
||On the top left, we have the following check boxes.
  
  
−
'''Operation Descriptions, Operation Labels, Point Labels '''and''' Tick Marks'''
+
'''Operation Descriptions''', '''Operation Labels''', '''Point Labels ''' and ''' Tick Marks'''.
  
−
 
+
We can use these check boxes to show and hide the details.
−
We can use these checkboxes to show and hide the details.
+
  
 
|-
 
|-
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We have already learned this concept.
 
We have already learned this concept.
  
−
Adding a negative number has the same effect as subtracting its additive inverse
+
Adding a negative number has the same effect as subtracting its additive inverse.
  
 
|-
 
|-
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|-
 
|-
 
||Point to the '''Net Worth''' box
 
||Point to the '''Net Worth''' box
−
||The net worth is now 200 + (-300) +500.
+
||The net worth is now 200 + (-300) + 500.
  
 
|-
 
|-
 
||Click and hold the '''Simplify''' button
 
||Click and hold the '''Simplify''' button
 
||Click and hold the '''Simplify''' button again.
 
||Click and hold the '''Simplify''' button again.
−
 
  
 
This expression is equal to 200 - 300 + 500.
 
This expression is equal to 200 - 300 + 500.
  
 
|-
 
|-
−
||Click and hold the '''equals '''button
+
||Click and hold the '''equals '''button.
 
||Click and hold the '''equals''' button.
 
||Click and hold the '''equals''' button.
  
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|-
 
|-
−
||Point to the information checkboxes
+
||Point to the information check boxes
−
||On the top left, we have the following checkboxes.
+
||On the top left, we have the following check boxes.
  
  
−
'''Operation Labels, Point Labels '''and''' Tick Marks'''
+
'''Operation Labels''', '''Point Labels ''' and ''' Tick Marks'''.
  
  
Line 471: Line 458:
  
 
|-
 
|-
−
||
+
||Only Narration.
−
||With this, we have come to the end of this tutorial. Let us summarise.
+
||With this, we have come to the end of this tutorial.  
 +
 
 +
Let us summarise.
  
 
|-
 
|-
−
||'''Slide number 8'''
+
||'''Slide Number 8'''
  
 
'''Summary'''
 
'''Summary'''
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* Add integers on the '''number line'''
 
* Add integers on the '''number line'''
 
* Subtract integers on the '''number line'''
 
* Subtract integers on the '''number line'''
−
* Calculate the additive inverse
+
* Calculate the additive inverse.
  
 
|-
 
|-
Line 488: Line 477:
 
'''Assignment'''
 
'''Assignment'''
  
 +
||As an assignment,
  
 +
1. Use the '''Operations''' screen to calculate the net worth in different scenarios.
 +
2. Open the '''Generic''' screen and choose the two numerical expressions option.
 +
3. Then perform the steps shown in this table.
 +
4. Compare the different operations on integers.
  
−
||As an assignment,
 
−
 
−
*Use the '''Operations''' screen to calculate the net worth in different scenarios.
 
−
*Open the '''Generic''' screen and choose the two numerical expressions option.
 
−
*Then perform the steps shown in this table.
 
−
*Compare the different operations on integers.
 
−
*:(Note: See table 2)
 
  
 
|-
 
|-
Line 512: Line 499:
 
|| The Spoken Tutorial Project team:
 
|| The Spoken Tutorial Project team:
  
−
*conducts workshops using spoken tutorials and
+
* conducts workshops using spoken tutorials and
−
 
+
* gives certificates on passing online tests.
−
*gives certificates on passing online tests.
+
* For more details, please write to us.
−
 
+
−
For more details, please write to us.
+
  
 
|-
 
|-

Latest revision as of 11:43, 15 February 2023

Title: Number Line: Operations

Author: Radhika Yadav

Keywords: PhET simulation, number line, integers, addition, subtraction, additive inverse, assets, debts, spoken tutorial, video tutorial.


Visual Cue Narration
Slide Number 1

Title Slide

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

Learning Objectives

In this tutorial, we will learn how to:
  • Add integers on the number line
  • Subtract integers on the number line
  • Calculate the additive inverse
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-operations

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

PhET simulations

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


Number Line: Operations simulation

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


The file will open in your default browser.

Point to the simulation interface This is the interface of the Number Line: Operations simulation.
Point to each screen The interface has four screens:

Chips, Net Worth, Operations, and Generic.

Click on Chips screen Click on the Chips screen.
Point to the number line The screen has a number line to represent the total amount of chips or coins.
Point to the Total box The total can also be viewed at the top of the screen in the Total box.
Point to the right panel next to the Positives bag We can put chips in the Positives bag from the panel on the right.


This will increase chips in the total amount.

Point to the left panel next to the Negatives bag


We can put chips in the Negatives bag from the panel on the left.


This will decrease chips in the total amount.

Point to the information checkboxes On the top left, we have the following checkboxes.


Operation Descriptions, Operation Labels, and Tick Marks.


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

Point to the reset button The reset button takes us back to the starting point of the simulation.
Point to the right panel next to the Positives bag Let us put the +1 chip in the Positives bag.
Point to the number line The description tells us we have added a positive 1 to the total amount.


The mark on the number line moves one place to the right.

Point to the Total box The total amount is now 1.
Point to the left panel next to the Negatives bag Let us now put the -1 chip in the Negatives bag.
Point to the number line The description tells us we have added a negative 1.


The mark on the number line moves one place to the left.

Point to the Total box.

Add annotation while editing.

The total amount is now 0 as 1 + (-1) is 0.

This means -1 is the additive inverse of 1.


Additive inverse of a number x, is a number that results in 0 when added to x.

Point to the number line However, we know 1 - 1 is also equal to 0.


This means adding -1 to 1 has the same effect as subtracting 1 from 1.


Let us try this with other combinations of chips.

Point to right panel next to the Positives bag Let us put +2 in the Positives bag.
Point to the number line The mark on the line moves two places to the right.
Point to right panel next to the Positives bag Let us further put +4 in the Positives bag.
Point to the number line The mark on the line now moves four places to the right.
Point to the Total box The total is now 0 + 2 + 4 which is 6.
Point to the left panel next to the Negatives bag Let us put the -5 chip in the Negatives bag.
Point to the number line The description tells us we have added a negative 5.


The mark on the line moves five places to the left.

Point to the Total box Hence, the total is 6 + (-5) which is 1.


This is also equal to 6 - 5.


Observe that adding -5 to 6 has the same effect as subtracting 5 from 6.

Point to the Negatives bag Let us now remove the -1 chip from the Negatives bag.
Point to number line The description tells us we have removed a negative 1.


The mark on the line moves one place to the right.

Point to the Total box The total amount is now 1 - (-1) which is 2.


We already know 1 + 1 is also equal to 2.


This means subtracting -1 from 1 has the same effect as adding 1 to 1.

Click on the Net Worth screen. Click on the Net Worth screen.
Point to the right panel next to the Positives bag In the right panel, we have different assets.


Assets are items that a person owns which have value.

Point to the left panel next to the Negatives bag


In the left panel, we have debts.


Debt is money that a person owes to someone.

Point to the Net Worth box Using the Net Worth box on the top, we can calculate the net worth.


It is all the assets and debts added together.

Slide number 7

Assets and Debts table

See the following table.

Pause the video here and perform these transactions using the Net Worth screen.

It will calculate the net worth of a person.


Point to the number line After performing these operations, the final net worth of a person is $100.
Click on the Operations screen. Click on the Operations screen.
Point to the number line The screen has a number line to represent net worth.
Point to the Initial Net Worth box


Click and show the net values.

At the bottom, there is an Initial Net Worth box.


Using the up and down arrows we can set a starting point.

Point to the top right box.

Point to the up and down arrow buttons.

On the top right, there is an option to perform two transactions.


We can select an amount using the up and down arrows.


A positive amount is an asset and a negative amount is a debt.

Point to the plus button.


Point to the minus button.


Click the down arrow.

Scroll the right arrow to move to right slide.

We can add an asset or debt using the plus button.

We can remove an asset or debt using the minus button.


Let us click the down arrow to add it to the net worth.


We can scroll right using the right arrow to perform the second transaction.

Point to the Net Worth box

Point to Simplify button.

Point to equals button.

The Net Worth box next to it displays the net worth amount.


We can click the Simplify button to simplify negative signs in the expression.


We can click the equals button to evaluate the expression.

Point to the information check boxes On the top left, we have the following check boxes.


Operation Descriptions, Operation Labels, Point Labels and Tick Marks.

We can use these check boxes to show and hide the details.

Point to the eraser button The eraser button takes us back to the initial net worth.
Click the reset button Let us reset our screen.
Point to the Initial Net Worth box Let us set an initial net worth of $200.
Point to the top right box Now let us add debt of $300 to the net worth of $200.
Point to the Net Worth box The net worth is now 200 + (-300).
Click and hold the Simplify button Click and hold the Simplify button.


This expression is equal to 200 - 300.


We have already learned this concept.

Adding a negative number has the same effect as subtracting its additive inverse.

Click and hold the equals button Click and hold the equals button.


The net worth is now -$100.

This means the person is in debt of $100.

Point to the top right box Let us add assets of $500.


Scroll right in the top right box to add the asset.

Point to the Net Worth box The net worth is now 200 + (-300) + 500.
Click and hold the Simplify button Click and hold the Simplify button again.

This expression is equal to 200 - 300 + 500.

Click and hold the equals button. Click and hold the equals button.


The net worth is now $400.

This means the person has assets of $400.

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 net worth representations We can choose between representing one or two numerical expressions.


For two expressions, two number lines will be displayed.


One is chosen by default.

Point to the information check boxes On the top left, we have the following check boxes.


Operation Labels, Point Labels and Tick Marks.


We can use these check boxes to show and hide the details.

Point to the number line You can explore the Generic screen yourself.
Only Narration. With this, we have come to the end of this tutorial.

Let us summarise.

Slide Number 8

Summary

In this tutorial, we have learnt how to:
  • Add integers on the number line
  • Subtract integers on the number line
  • Calculate the additive inverse.
Slide Number 9

Assignment

As an assignment,

1. Use the Operations screen to calculate the net worth in different scenarios. 2. Open the Generic screen and choose the two numerical expressions option. 3. Then perform the steps shown in this table. 4. Compare the different operations on integers.


Slide number 10

About the Spoken Tutorial project

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

Please download and watch it.

Slide number 11

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 12

Forum for specific questions

Please post your timed queries in this forum.
Slide number 13

Acknowledgement

The Spoken Tutorial project is funded by the Ministry of Education, Government of India.
Slide number 14

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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