Overview:
The goal of this activity is to understand why graphs of linear equations are parallel, perpendicular, or the same. Simulations are used to get a more exact visual of lines on a coordinate plane. Comparison of two lines will be much more clear for students using the simulations, and they will be able to draw conclusions about parallel and perpendicular lines. The activity involves SOL A6, where the student will apply an appropriate technique to graph linear functions, and A7, where the student will determine the slope of a line when given an equation of the line. I decided that no graphing calculators will be used because students can use simulations and graph paper.
Advantage of Using Technology: It is difficult to teach this type of lesson without technology. When students draw graphs on paper they are never perfect. A teacher cannot draw perfect graphs either. So, technology comes to the rescue. In this activity, students will draw the graphs first, so that they can practice plotting points, using the slope and y-intercept to draw a line, etc. But if they do not draw their graphs perfectly, they may struggle with answering questions. For example, two lines drawn messily on graph paper may not look parallel. But when they are created on the simulation, it is very clear that they are parallel. The students can look at the simulation so they are less likely to make mistakes. They can also compare their graphs to the ones on the computer to make sure they are drawing them correctly.
Before this activity, some students may already know about this lesson and some may not. However, the way it is set up allows for students to practice finding slopes and y-intercepts, drawing graphs, using simulations, and describing visual elements no matter what they already know. It is also a "self-taught" activity. It is meant to teach students about parallel and intersecting lines without giving them a straightforward lecture on it. So both students can use it: those that already understand the topic can practice with this activity, and those that do not already understand it can learn through this activity.
The activity can help with preconceptions because it paints a clear picture of what certain graphs look like. If students have any false ideas about graphs, they can be corrected by seeing it on the computer. When the teacher goes over the activity at the end of class, she is making sure that these preconceptions have disappeared.
Students will be in groups of two for this activity. They will each draw their own graphs, but will probably have to share one computer. This will emphasize cooperative learning. They can either take turns using the simulation, or have one person use it while the other observes. I think the teacher should encourage taking turns, but essentially this decision is up to the students.
Procedure:
1. Students will pair up and find a computer to work at. The teacher will set up the simulation on a computer/projector so that the class can see it. She will demonstrate how to use it and ask if anyone has any questions.
2. Once every student understands how to use the simulation, the teacher will hand out worksheets.
3. Though the students are working in pairs, each student must complete the worksheet and show their own work. The teacher will be walking around the room, available to answer any questions.
4. When all of the students have completed the worksheet, they will turn their attention to the teacher, who will briefly go through it with them.
5. Towards the end of the class, the teacher will ask about what they learned. The class will come up with a list of everything they learned that day (for example, lines with the same slope different y-intercepts are parallel).
6. If there is time, the teacher will ask what the students thought of the activity: if it was helpful, if it was fun, if they would like to do it again, etc.
Assessment:
The worksheet itself will act as the assessment. Students will be expected to complete the worksheet and hand it in at the end of class. If they make mistakes, they should catch them at the end when the teacher is going through the activity. If a student marks that they made a mistake and attempts to fix it, they will still get full credit. In other words, the student will be assessed based on effort, completeness, and honesty. I am a huge supporter of showing all work possible and never leaving any questions blank, which is portrayed in this activity.
Product:
Here is a rough example of what a worksheet may look like: Completed Worksheet.
The students will hand in the graphs they drew on paper as well.
The goal of this activity is to understand why graphs of linear equations are parallel, perpendicular, or the same. Simulations are used to get a more exact visual of lines on a coordinate plane. Comparison of two lines will be much more clear for students using the simulations, and they will be able to draw conclusions about parallel and perpendicular lines. The activity involves SOL A6, where the student will apply an appropriate technique to graph linear functions, and A7, where the student will determine the slope of a line when given an equation of the line. I decided that no graphing calculators will be used because students can use simulations and graph paper.
Advantage of Using Technology:
It is difficult to teach this type of lesson without technology. When students draw graphs on paper they are never perfect. A teacher cannot draw perfect graphs either. So, technology comes to the rescue. In this activity, students will draw the graphs first, so that they can practice plotting points, using the slope and y-intercept to draw a line, etc. But if they do not draw their graphs perfectly, they may struggle with answering questions. For example, two lines drawn messily on graph paper may not look parallel. But when they are created on the simulation, it is very clear that they are parallel. The students can look at the simulation so they are less likely to make mistakes. They can also compare their graphs to the ones on the computer to make sure they are drawing them correctly.
Before this activity, some students may already know about this lesson and some may not. However, the way it is set up allows for students to practice finding slopes and y-intercepts, drawing graphs, using simulations, and describing visual elements no matter what they already know. It is also a "self-taught" activity. It is meant to teach students about parallel and intersecting lines without giving them a straightforward lecture on it. So both students can use it: those that already understand the topic can practice with this activity, and those that do not already understand it can learn through this activity.
The activity can help with preconceptions because it paints a clear picture of what certain graphs look like. If students have any false ideas about graphs, they can be corrected by seeing it on the computer. When the teacher goes over the activity at the end of class, she is making sure that these preconceptions have disappeared.
Students will be in groups of two for this activity. They will each draw their own graphs, but will probably have to share one computer. This will emphasize cooperative learning. They can either take turns using the simulation, or have one person use it while the other observes. I think the teacher should encourage taking turns, but essentially this decision is up to the students.
Materials:
graph paper
worksheet: blank worksheet
pencil
Procedure:
1. Students will pair up and find a computer to work at. The teacher will set up the simulation on a computer/projector so that the class can see it. She will demonstrate how to use it and ask if anyone has any questions.
2. Once every student understands how to use the simulation, the teacher will hand out worksheets.
3. Though the students are working in pairs, each student must complete the worksheet and show their own work. The teacher will be walking around the room, available to answer any questions.
4. When all of the students have completed the worksheet, they will turn their attention to the teacher, who will briefly go through it with them.
5. Towards the end of the class, the teacher will ask about what they learned. The class will come up with a list of everything they learned that day (for example, lines with the same slope different y-intercepts are parallel).
6. If there is time, the teacher will ask what the students thought of the activity: if it was helpful, if it was fun, if they would like to do it again, etc.
Assessment:
The worksheet itself will act as the assessment. Students will be expected to complete the worksheet and hand it in at the end of class. If they make mistakes, they should catch them at the end when the teacher is going through the activity. If a student marks that they made a mistake and attempts to fix it, they will still get full credit. In other words, the student will be assessed based on effort, completeness, and honesty. I am a huge supporter of showing all work possible and never leaving any questions blank, which is portrayed in this activity.
Product:
Here is a rough example of what a worksheet may look like: Completed Worksheet.
The students will hand in the graphs they drew on paper as well.