Difference between revisions of "PhET/C2/Graphing-Lines/English-timed"

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|-  
 
|-  
 
|00:05
 
|00:05
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| In this tutorial, we will demonstrate, '''Graphing Lines, an interactive '''PhET simulation'''.  
+
| In this tutorial, we will demonstrate '''Graphing Lines''', an interactive '''PhET simulation'''.  
  
 
|-  
 
|-  
 
|00:12
 
|00:12
−
| To follow this tutorial,  
+
| To follow this tutorial, learner should be familiar with topics in high school mathematics.  
−
 
+
−
Learner should be familiar with topics in high school mathematics.  
+
  
 
|-  
 
|-  
 
|00:20
 
|00:20
−
| Here I am using,
+
| Here I am using:
  
−
Ubuntu Linux OS version 14.04  
+
'''Ubuntu Linux OS''' version 14.04  
  
−
Java version 1.7  
+
'''Java''' version 1.7  
  
−
Firefox Web Browser version 53.02.2  
+
'''Firefox Web Browser''' version 53.02.2  
  
 
|-  
 
|-  
 
|00:35
 
|00:35
−
| Using this simulation we will learn,
+
| Using this simulation, we will learn:
  
 
1. About Cartesian coordinate system  
 
1. About Cartesian coordinate system  
  
−
2. How to calculate the slope of a graphed line  
+
2. How to calculate the '''slope''' of a graphed line  
  
−
3. To save the plotted lines  
+
3. To '''save''' the plotted lines  
  
 
|-
 
|-
 
|00:48
 
|00:48
−
|4. How to change the slope and intercept of the line  
+
|4. How to change the '''slope''' and '''intercept''' of the line  
  
−
5. How, changing variables in a linear equation will affect the line.  
+
5. How changing '''variable'''s in a '''linear''' equation will affect the line.  
  
 
|-  
 
|-  
 
|00:58
 
|00:58
−
| An equation with two variables x and y is a Linear equation. y=mx+b Here m is slope of the line and b is intercept.  
+
| An equation with two variables x and y is a linear equation. y=mx+b Here, '''m''' is '''slope''' of the line and '''b''' is '''intercept'''.  
  
 
|-  
 
|-  
 
|01:12
 
|01:12
−
| Slope signifies rate of change of y value with respect to x value. y-intercept is y value when x=0  
+
| Slope signifies rate of change of '''y''' value with respect to '''x''' value. '''y-intercept''' is y value when x=0.
  
 
|-  
 
|-  
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|-  
 
|-  
 
|01:29
 
|01:29
−
| Use the given link to download the simulation.  
+
| Use the given '''link''' to download the '''simulation'''.  
  
 
|-  
 
|-  
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|-  
 
|-  
 
|01:39
 
|01:39
−
| To open the simulation, right click on '''graphing-lines_en.html''' file.
+
| To open the simulation, right-click on '''graphing-lines_en.html''' file.  
−
 
+
−
Select the option, '''Open With Firefox Web Browser'''.  
+
  
−
File opens in the browser.  
+
Select the option '''Open With Firefox Web Browser'''. File opens in the browser.  
 
   
 
   
 
|-  
 
|-  
 
|01:53
 
|01:53
−
| This is the interface of '''Graphing Lines''' simulation.  
+
| This is the '''interface''' of '''Graphing Lines''' simulation.  
  
 
|-  
 
|-  
 
|01:57
 
|01:57
−
|The interface has four screens,
+
|The interface has four '''screen'''s-'''Slope, Slope-Intercept, Point-Slope''' and  
−
 
+
−
'''Slope'''
+
−
 
+
−
'''Slope-Intercept'''
+
−
 
+
−
'''Point-Slope''' and  
+
−
 
+
 
'''Line Game'''.
 
'''Line Game'''.
  
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|-  
 
|-  
 
|02:10
 
|02:10
−
|Screen has a Cartesian coordinate system with x and y axes.  
+
|Screen has a '''Cartesian coordinate system''' with '''x''' and '''y''' axes.  
  
 
|-  
 
|-  
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|-
 
|-
 
|02:23
 
|02:23
−
|To calculate the slope, we can input values for y2, y1 and x2, x1.  
+
|To calculate the slope, we can input values for '''y2, y1''' and '''x2, x1'''.  
  
 
|-  
 
|-  
 
|02:31
 
|02:31
−
| Default values of y2, y1 are 4 and 2.  And x2, x1 are 3 and 1.  
+
| Default values of y2, y1 are 4 and 2, and x2, x1 are 3 and 1.  
  
 
|-  
 
|-  
 
|02:41
 
|02:41
−
| A graph is plotted using the default values. Here we can see, Slope is 1.  
+
| A graph is plotted using the default values. Here we can see '''Slope is 1'''.  
  
 
|-
 
|-
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|-
 
|-
 
|03:02
 
|03:02
−
|We can hide the formula box, by clicking on red minus sign. To show the box click on green plus button.  
+
|We can hide the formula box by clicking on red minus sign. To show the box, click on green plus button.  
  
 
|-  
 
|-  
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|-  
 
|-  
 
|03:19
 
|03:19
−
| If we click on, '''Hide lines''' and '''Hide grid''' check boxes, graph and grid are hidden.  
+
| If we click on '''Hide lines''' and '''Hide grid''' check-boxes, '''graph''' and '''grid''' are hidden.  
−
 
+
Automatically '''Slope''' check-box is disabled.  
−
Automatically, '''Slope''' check box is disabled.  
+
  
 
|-
 
|-
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|03:40
 
|03:40
 
| Notice that graph displays value of the slope.   
 
| Notice that graph displays value of the slope.   
−
 
 
Observe that on moving purple and yellow points, x1, y1 and x2, y2 values can be changed.  
 
Observe that on moving purple and yellow points, x1, y1 and x2, y2 values can be changed.  
  
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|03:54
 
|03:54
 
|As we move the points, slope of the line changes.  
 
|As we move the points, slope of the line changes.  
−
 
 
Observe the change in values of x and y in the formula box.  
 
Observe the change in values of x and y in the formula box.  
  
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|04:24
 
|04:24
 
| Drag the purple point to coincide with origin (0, 0).   
 
| Drag the purple point to coincide with origin (0, 0).   
−
 
 
Drag one of the '''Point''' tool and place it on the origin.  
 
Drag one of the '''Point''' tool and place it on the origin.  
  
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|04:49
 
|04:49
 
| Drag the yellow point to (2,8).  
 
| Drag the yellow point to (2,8).  
−
 
 
Drag the '''point''' tool and place it on yellow point.  
 
Drag the '''point''' tool and place it on yellow point.  
 
This confirms that yellow point is at(2,8).  
 
This confirms that yellow point is at(2,8).  
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|-  
 
|-  
 
|05:11
 
|05:11
−
| Drag the yellow point to (-5,5). Drag and place Point tool on yellow point.  
+
| Drag the yellow point to (-5,5). Drag and place '''Point''' tool on yellow point.  
  
 
|-
 
|-
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|-  
 
|-  
 
|05:39
 
|05:39
−
| Click on '''Save Line'''. Line is saved  
+
| Click on '''Save Line'''. Line is saved.
  
 
|-  
 
|-  
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|-  
 
|-  
 
|05:53
 
|05:53
−
| As an assignment,
+
| As an assignment:
  
 
1. Find when slope is zero and when it is undefined.  
 
1. Find when slope is zero and when it is undefined.  
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|-  
 
|-  
 
|06:04
 
|06:04
−
| Now let us explore '''Slope-Intercept''' screen at the bottom of the interface.  
+
| Now, let us explore '''Slope-Intercept''' screen at the bottom of the interface.  
  
 
|-
 
|-
 
|06:10
 
|06:10
−
||Click on '''Slope-Intercept''' screen. Screen opens with a line y= 2/3x+1.  
+
||Click on '''Slope-Intercept''' screen. Screen opens with a line y= 2/3x+1 (2 by 3 x plus 1).  
 
|-
 
|-
 
|06:21
 
|06:21
−
|Here intercept value is 1.  
+
|Here '''intercept''' value is 1.  
  
 
|-  
 
|-  
 
|06:25
 
|06:25
−
| In this screen we can change the values of 'm' and 'b'.  
+
| In this '''screen''', we can change the values of 'm' and 'b'.  
  
 
|-  
 
|-  
 
|06:30
 
|06:30
−
| Drag the purple point on y axis. Notice that purple point represents the intercept.  
+
| Drag the purple point on y-axis. Notice that purple point represents the intercept.  
−
 
+
 
When we move the purple point, intercept for the line changes.  
 
When we move the purple point, intercept for the line changes.  
  
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|06:44
 
|06:44
 
| The blue point is free to move across the graph.  
 
| The blue point is free to move across the graph.  
−
 
 
When we move the blue point, slope of the line changes.  
 
When we move the blue point, slope of the line changes.  
  
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|06:53
 
|06:53
 
| Click on '''Reset''' button to reset the simulation.
 
| Click on '''Reset''' button to reset the simulation.
−
 
 
Click on '''Save Line'''. Line is saved.  
 
Click on '''Save Line'''. Line is saved.  
  
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|07:02
 
|07:02
 
|Change the numerator value of '''m''' from 2 to 3 in the formula box.  
 
|Change the numerator value of '''m''' from 2 to 3 in the formula box.  
−
 
 
Notice that slope is 1 while '''Intercept''' still remains 1.  
 
Notice that slope is 1 while '''Intercept''' still remains 1.  
  
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| Now adjust '''m''' again to 2/3 and increase b value to 4.  
 
| Now adjust '''m''' again to 2/3 and increase b value to 4.  
  
−
Notice that, the new line is parallel to the first line but intercepts y-axis at 4.  
+
Notice that the new line is parallel to the first line but intercepts y-axis at 4.  
  
 
|-  
 
|-  
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|-  
 
|-  
 
|07:35
 
|07:35
−
| Change '''b''' value to -2 Click on '''Save Line'''. Line is saved.  
+
| Change '''b''' value to -2, click on '''Save Line'''. Line is saved.  
  
 
|-
 
|-
 
|07:43
 
|07:43
−
|We have 3 parallel lines intercepting y axis at 3 different points.  
+
|We have 3 parallel lines intercepting y-axis at 3 different points.  
  
 
|-  
 
|-  
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|-  
 
|-  
 
|07:55
 
|07:55
−
|Let us change b value to zero. Notice that purple point is at the origin.  
+
|Let us change '''b''' value to zero. Notice that purple point is at the origin.  
  
 
|-
 
|-
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|-  
 
|-  
 
|08:19
 
|08:19
−
| Now let us now move on to '''Point-Slope''' screen.  
+
| Now, let us now move on to '''Point-Slope''' screen.  
  
 
|-  
 
|-  
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|-
 
|-
 
| 08:53
 
| 08:53
−
|The Generic point '''(x1,y1)''' is represented by the purple point.  
+
|The Generic point '''(x1, y1)''' is represented by the purple point.  
  
 
|-
 
|-
 
|08:59
 
|08:59
−
|Drag the '''Point''' tool to the purple point to see its coordinates.  
+
|Drag the '''Point''' tool to the purple point, to see its coordinates.  
  
 
|-
 
|-
Line 357: Line 337:
 
|-  
 
|-  
 
|09:45
 
|09:45
−
|Now let us move on to '''Line Game''' screen.  
+
|Now, let us move on to '''Line Game''' screen.  
  
 
|-  
 
|-  
Line 365: Line 345:
 
|-  
 
|-  
 
|09:52
 
|09:52
−
| '''Line Game''' screen has 6 difficulty levels, to play.  
+
| '''Line Game''' screen has 6 difficulty levels to play.  
  
 
These games will test the knowledge gained using this simulation.  
 
These games will test the knowledge gained using this simulation.  
Line 383: Line 363:
 
|-  
 
|-  
 
|10:22
 
|10:22
−
|In this tutorial, we have learnt,
+
|In this tutorial, we have learnt about '''Graphing Lines''', an interactive '''PhET simulation'''.  
−
 
+
−
About '''Graphing Lines''', an interactive '''PhET simulation'''.  
+
  
 
|-  
 
|-  
 
|10:29
 
|10:29
−
| Using this simulation, we have learnt,
+
| Using this simulation, we have learnt:
  
 
1. About Cartesian coordinate system with x and y axes.  
 
1. About Cartesian coordinate system with x and y axes.  
Line 395: Line 373:
 
2. How to calculate the slope of a graphed line.  
 
2. How to calculate the slope of a graphed line.  
  
−
3. To save the plotted lines  
+
3. To '''save''' the plotted lines  
 
   
 
   
 
|-
 
|-
Line 403: Line 381:
 
|-  
 
|-  
 
|10:47
 
|10:47
−
|5. How changing variables in a linear equation will affect the line.  
+
|5. How changing variables in a '''linear''' equation will affect the line.  
  
 
|-  
 
|-  
 
|10:53
 
|10:53
−
| As an assignment,
+
| As an assignment:
  
 
1. Using '''Slope-Intercept''' screen, find when the value of slope is 1.  
 
1. Using '''Slope-Intercept''' screen, find when the value of slope is 1.  
Line 415: Line 393:
 
|-  
 
|-  
 
|11:09
 
|11:09
−
| The video at the following link summarizes the Spoken Tutorial project. Please download and watch it.  
+
| The video at the following link summarizes the '''Spoken Tutorial''' project. Please download and watch it.  
  
 
|-  
 
|-  
 
|11:17
 
|11:17
−
|The Spoken Tutorial Project team: conducts workshops using spoken tutorials and  
+
|The '''Spoken Tutorial''' Project team conducts workshops using spoken tutorials and  
 
gives certificates on passing online tests. For more details, please write to us.  
 
gives certificates on passing online tests. For more details, please write to us.  
  
Line 432: Line 410:
 
|-  
 
|-  
 
|11:41
 
|11:41
−
| Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. More information on this mission is available at this link.  
+
| Spoken Tutorial Project is funded by '''NMEICT, MHRD,''' Government of India. More information on this mission is available at this link.  
  
 
|-  
 
|-  
 
|11:53
 
|11:53
−
| This tutorial is contributed by Spoken tutorial team IIT Bombay. Thank you for joining.  
+
| This tutorial is contributed by Spoken tutorial team, IIT Bombay. Thank you for joining.  
 
|-
 
|-
 
|}
 
|}

Latest revision as of 22:19, 10 August 2018

Time Narration
00:01 Welcome to this tutorial on Graphing Lines simulation.
00:05 In this tutorial, we will demonstrate Graphing Lines, an interactive PhET simulation.
00:12 To follow this tutorial, learner should be familiar with topics in high school mathematics.
00:20 Here I am using:

Ubuntu Linux OS version 14.04

Java version 1.7

Firefox Web Browser version 53.02.2

00:35 Using this simulation, we will learn:

1. About Cartesian coordinate system

2. How to calculate the slope of a graphed line

3. To save the plotted lines

00:48 4. How to change the slope and intercept of the line

5. How changing variables in a linear equation will affect the line.

00:58 An equation with two variables x and y is a linear equation. y=mx+b Here, m is slope of the line and b is intercept.
01:12 Slope signifies rate of change of y value with respect to x value. y-intercept is y value when x=0.
01:26 Let us begin the demonstration.
01:29 Use the given link to download the simulation.
01:33 I have already downloaded Graphing Lines simulation to my Downloads folder.
01:39 To open the simulation, right-click on graphing-lines_en.html file.

Select the option Open With Firefox Web Browser. File opens in the browser.

01:53 This is the interface of Graphing Lines simulation.
01:57 The interface has four screens-Slope, Slope-Intercept, Point-Slope and

Line Game.

02:06 Click on Slope screen.
02:10 Screen has a Cartesian coordinate system with x and y axes.
02:16 On the right side, formula box shows formula to find slope of the line.
02:23 To calculate the slope, we can input values for y2, y1 and x2, x1.
02:31 Default values of y2, y1 are 4 and 2, and x2, x1 are 3 and 1.
02:41 A graph is plotted using the default values. Here we can see Slope is 1.
02:49 We can change the values of y2, y1 and x2, x1 using up and down arrow buttons.
02:57 Plotted line can be saved using Save Line button.
03:02 We can hide the formula box by clicking on red minus sign. To show the box, click on green plus button.
03:11 Below the formula box, we have Slope, Hide lines and Hide grid check boxes.
03:19 If we click on Hide lines and Hide grid check-boxes, graph and grid are hidden.

Automatically Slope check-box is disabled.

03:32 Let's uncheck Hide lines and Hide grid check boxes to enable Slope check box.
03:40 Notice that graph displays value of the slope.

Observe that on moving purple and yellow points, x1, y1 and x2, y2 values can be changed.

03:54 As we move the points, slope of the line changes.

Observe the change in values of x and y in the formula box.

04:04 At the bottom of the screen, we have gray boxes to display coordinates of a point. These gray boxes are called as Point tools.
04:14 Drag and place Point tools on purple and yellow points to see the coordinates.
04:20 Drag the Point tools to the bottom.
04:24 Drag the purple point to coincide with origin (0, 0).

Drag one of the Point tool and place it on the origin.

04:33 Drag yellow point to coincide with (5,5). Observe that slope of the line is 1.
04:42 Click on Save Line button in the formula box. Line is saved.
04:49 Drag the yellow point to (2,8).

Drag the point tool and place it on yellow point. This confirms that yellow point is at(2,8).

05:02 Now Slope is 4.
05:05 Click on Save Line in the formula box. Line is saved.
05:11 Drag the yellow point to (-5,5). Drag and place Point tool on yellow point.
05:19 Now Slope is -1.
05:22 Click on Save Line in the formula box. Line is saved.
05:28 Drag the point tool back to place. Drag the yellow point to (-2,8).
05:36 Here Slope is -4.
05:39 Click on Save Line. Line is saved.
05:44 We have drawn 4 lines with different slopes. Notice that steepness is related to slope.
05:53 As an assignment:

1. Find when slope is zero and when it is undefined.

2. Give an explanation.

06:04 Now, let us explore Slope-Intercept screen at the bottom of the interface.
06:10 Click on Slope-Intercept screen. Screen opens with a line y= 2/3x+1 (2 by 3 x plus 1).
06:21 Here intercept value is 1.
06:25 In this screen, we can change the values of 'm' and 'b'.
06:30 Drag the purple point on y-axis. Notice that purple point represents the intercept.

When we move the purple point, intercept for the line changes.

06:44 The blue point is free to move across the graph.

When we move the blue point, slope of the line changes.

06:53 Click on Reset button to reset the simulation.

Click on Save Line. Line is saved.

07:02 Change the numerator value of m from 2 to 3 in the formula box.

Notice that slope is 1 while Intercept still remains 1.

07:14 Now adjust m again to 2/3 and increase b value to 4.

Notice that the new line is parallel to the first line but intercepts y-axis at 4.

07:31 Click on Save Line. Line is saved.
07:35 Change b value to -2, click on Save Line. Line is saved.
07:43 We have 3 parallel lines intercepting y-axis at 3 different points.
07:50 Click on Reset button to reset the simulation.
07:55 Let us change b value to zero. Notice that purple point is at the origin.
08:03 Line now passes through the origin.
08:06 Click on y=x and y=-x check boxes below the slope.

Notice that we have three lines passing through the origin.

08:19 Now, let us now move on to Point-Slope screen.
08:23 Click on Point-Slope at the bottom of the interface.
08:28 In Point-Slope screen, a set of (x,y) values are substituted in the equation.

In this method, x and y values are defined.

08:41 For a given value of (x, y), m can be calculated using the formula, y-y1 = m(x-x1)
08:53 The Generic point (x1, y1) is represented by the purple point.
08:59 Drag the Point tool to the purple point, to see its coordinates.
09:04 Drag the Point tool back to its place.
09:07 Drag the purple and blue points freely across the graph to modify the equation of the line.

Drag and place purple point to (5,0).

09:20 Then drag the blue point to (5,5).
09:24 Notice that line is parallel to y-axis and slope is undefined.
09:31 Click on Save line. Line is saved.
09:35 Drag the purple point along the x-axis.

Notice that Slope is undefined all along the x-axis.

09:45 Now, let us move on to Line Game screen.
09:49 Click on Line Game screen.
09:52 Line Game screen has 6 difficulty levels to play.

These games will test the knowledge gained using this simulation.

10:02 It has a Timer and Sound buttons at the bottom of the screen.
10:08 Click on each game and explore.
10:20 Lets summarize.
10:22 In this tutorial, we have learnt about Graphing Lines, an interactive PhET simulation.
10:29 Using this simulation, we have learnt:

1. About Cartesian coordinate system with x and y axes.

2. How to calculate the slope of a graphed line.

3. To save the plotted lines

10:43 4. How to change the slope and intercept of the line
10:47 5. How changing variables in a linear equation will affect the line.
10:53 As an assignment:

1. Using Slope-Intercept screen, find when the value of slope is 1.

2. Using Point-Slope screen, find in which quadrants slope is positive.

11:09 The video at the following link summarizes the Spoken Tutorial project. Please download and watch it.
11:17 The Spoken Tutorial Project team conducts workshops using spoken tutorials and

gives certificates on passing online tests. For more details, please write to us.

11:29 Please post your timed queries in this forum.
11:32 This project is partially funded by Pandit Madan Malaviya National Mission on Teachers and Teaching.
11:41 Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. More information on this mission is available at this link.
11:53 This tutorial is contributed by Spoken tutorial team, IIT Bombay. Thank you for joining.

Contributors and Content Editors

Madhurig, Pratik kamble, Sandhya.np14

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