Difference between revisions of "PhET/C2/Graphing-Lines/English-timed"
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| − | | In this tutorial, we will demonstrate | + | | In this tutorial, we will demonstrate '''Graphing Lines''', an interactive '''PhET simulation'''. |
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|00:12 | |00:12 | ||
| − | | To follow this tutorial, | + | | To follow this tutorial, learner should be familiar with topics in high school mathematics. |
| − | + | ||
| − | + | ||
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|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 | + | 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 | + | | 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 | + | Select the option '''Open With Firefox Web Browser'''. File opens in the browser. |
| − | + | ||
| − | File opens in the browser. | + | |
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|01:53 | |01:53 | ||
| − | | This is the interface of '''Graphing Lines''' simulation. | + | | This is the '''interface''' of '''Graphing Lines''' simulation. |
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|01:57 | |01:57 | ||
| − | |The interface has four | + | |The interface has four '''screen'''s-'''Slope, Slope-Intercept, Point-Slope''' and |
| − | + | ||
| − | ''' | + | |
| − | + | ||
| − | '''Slope-Intercept | + | |
| − | + | ||
| − | + | ||
| − | + | ||
'''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 | + | | 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 | + | | 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 | + | |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 | + | | If we click on '''Hide lines''' and '''Hide grid''' check-boxes, '''graph''' and '''grid''' are hidden. |
| − | + | Automatically '''Slope''' check-box is disabled. | |
| − | Automatically | + | |
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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. |
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|06:21 | |06:21 | ||
| − | |Here intercept value is 1. | + | |Here '''intercept''' value is 1. |
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|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'. |
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Revision as of 20:48, 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. |
| 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. |
