Possible issues: - Ambiguous case – geogebra only works on IE, not on firefox, chrome - maybe use more than one technology tool – youre using geogebra twice - do students have to print the geogebra triangle on the handout? - lots of rules and memorization. Maybe this is unavoidable. - lots of activities to do in 70 minutes
1. For real-life applications, you can have students find angle lengths for pendulum questions or other physics questions. You could incorporate geography by finding the shortest path length. 2. Student discussion – think about giving students a worked example and putting them in groups to talk about the problem and solution. 3. I think the summary handout is a little too wordy, but that might just be the nature of the topic. 4. I think the teacher should introduce and have control of the geogebra application. Students might not be comfortable with the software.
-Timing for the first activity isn't enough. The ambiguous case will take much longer - I think you should include an activity in the consolidation or have them do more questions then consolidate. You can incorporate a class discussion in this.
Visual Appeal on Handout: - make the underline go all the way across in the title - use o instead of 0 for your degree sign (these things distract the easily distracted)
Some things to consider: - the online activities are great but some students may be easily distracted and just play around without understanding the point of the lesson, just consider this (it's probably unavoidable) - seems like a lot to do in 75 minutes, timing may have to be very precise
Plan your "work through example" Work through one or two examples of the ambiguous triangles handout Verbally and visually show them how to use geogebra (zooming, panning, etc) What is your ticket out the door question?
I think you're missing part of the explanation of why the ambiguous case occurs- I would use it as an opportunity to teach that supplementary angles have the same sine.
I think this is a really good lesson one things to consider, it sort of struck me as something that may not work quite as you expected: - consider for your hook having very structured questions for using the GeoGebra activity, otherwise you may lose their interest very quickly.
- I really enjoy the apps used on the smart board because it gives the kids a good visual of what the triangles should look like, what the relationships between the sides are and what happens if you change the variables.
- You might want to have the kids fill out the summary sheet, so give them some information and go over the sheet with them and allow them to fill out the rest of the material. This allows them to focus on the lesson and the various rules that they need to know and review them during the lesson as well.
- A great idea to write your learning goals, success criteria and agenda on the board for your students to reference throughout the lesson - Do the students already know that the angle gamma is related to side c - Consider having a fill-in the blank handout to ensure that students are paying attention during the lesson - A great idea for guided learning and review for the students - are you going to go over the answer and full solution to ensure that all students have the correct answer/process? - If this was done in a computer lab - are all students able to participate in the 1st geogebra applet, instead of just having one student going to the board - A very interactive lesson!
The ambiguous case activity is a nice interactive way of getting students to explore the concepts of trigonometry. I like how you can change the triangle properties and see how that affects the other measurements/angles. I like the idea of giving students the handout summaries, but you could also get them to make ones for themselves. I think this is more a matter of personal preference.
- I like the idea of using the worksheet that goes along with GeoGebra. It makes it more engaging to the students. - The simple chalk and talk portions of the lesson where you did review or consolidation, etc. I feel there may be a better way to make it engaging for the students, as your 'ambiguous case' activity is - Students should create their own summary sheet as Bryan mentioned I agree whole heartedly
- *Shudders* UOIT lesson plan templates… - Nice little applet that demonstrates the equality of the Sine Law - Worksheet has the lengths on the top and bottom for the equalities -> obvious but students don’t realize that, so that was a nice touch - Visual on the worksheet for the ambiguous case is kind of hard to make out due to the black background - The content seems kind of crammed... - Overall, I think it’s a strong lesson but just watch out for too much information; spreading this out might be beneficial
I really like how you have the learning goals and the agenda stated at the beginning of the lesson! The GeoGebra activity is a great way to grab students’ attention and I think it’s great that you can get students up to the board to manipulate it as well. During your lesson, I think that you should further explain the ambiguous case at some point so that they are not just discovering it on their own. During the ‘Ambiguous Case Activity’, how will you know if the students have learned the concepts? I really like your handouts that you are giving the students but I think that sometimes having the students create their own summary sheets is more beneficial. For the consolidation/homework section you could have the students create their own summary sheet with one or two examples so you can determine if they have learned the concepts. You could then include the peer assessment into the lesson by having them go over a partner’s summary sheet the following day. Great lesson!
I definitely think you should have a summary sheet so they can always review the content any time afterwards, but give them more time to process the information they just learned before giving the summary sheet out. The only downfall of the peer assessment depends on how engaged the students are in actually reading someone else's summary sheet. If they're not, they're going to pretend to read it and just hand it back and you can't really assess what they really learned or still have yet to learn.
- If you're handing out laptops for students to use, you need to include that transition in your lesson plan (if you don’t already have it). From experience laptop distribution and setting up TAKES FOREVER, and I found it easier to have one laptop per pair (less laptops to fix) - Keep the hook short and done on the projector rather than have the students do it individually, I don’t think you want to spend too much time on this. - I feel that even though they have seen this before, they may need an example given to them before they try on their own (or even in a group) - The activity is good, but definitely will need a class discussion or something to ensure they understand what the turning point for the ambiguous case is. - Perhaps include some blanks on the summary sheet that they have to fill in - In the ticket out the door make the student sketch out the triangles (as best as they can)
- I love the idea of allowing students with ADD, ADHD, etc, to come up to the board (will get them out of their seats) - Giving students time to make their own summary sheet has been proven to be extremely successful (proven in research) - Law of Sines activity is a great visual and demonstrates how the law works - Not sure if you would be able to do this lesson in one class, probably going to take two (at least) - Guided practice sounds like something that would work out nicely - Not sure if students would be motivated by GeoGebra - Ticket-out-the-door could be a different problem that better reflects your learning goals and success criteria - Overall, well thought out. Great job girls!
I think the ambiguous case is a very difficult case for students to understand. They probably need a day to first review the sine law, and then on the second day, have the opportunity to discover that there could be two possible triangles formed. I think that using manipulatives instead of the applet may be beneficial and more realistic (having 15 laptops in the class is probably not very likely).
- the hook with Geogebra is a great way of showing the sine law without actually getting into the law itself - you might want to give students a simpler example to start, even though this is a refresher (you’re essentially starting them with a word problem) - asking them to put a screen shot in the handout restricts them from handing the work in during class (many wouldn’t want to be forced to do the work at home) - maybe define in the lesson what you mean by “The Ambiguous Case” – make sure the students know what ‘ambiguous’ means (I would bet some don’t). - there is a lot of content here. You may want to break this into a few lessons. -having students come up with their own summary sheet may be a better idea (Supportive Learning Environment, Alfie Kohn)
Always good to have solutions to the problems in case you get nervous up front
Handout is a good idea, especially if there are students who write slower, and it seems that students write slower than when we were in school (not based on research, just observation). You could make it a fill in the blanks sheet, where they get it at the beginning of the lesson and fill in the key points.
The GeoGebra is a good way to visually show the different examples, however, I don't think it is going to hook the students into the lesson. For a student who is having a hard time understanding the sin law, this program might just appear to be a bunch of numbers with an equation. I do like how you take the time to go through an example question with the class. This will give students a chance to ask questions. I like how you have an activity and sheet for them to work on. However, I think there are too many questions. What will you do when the students start getting bored? How are you going to make sure they aren't surfing the web? Are you going to be collecting the sheet at the end? You could possibly sign off on every students worksheet at the end of the period so you know what they completed in class and what they completed as homework. This could be used for Learning Skills and Work Habits in the report card.
Good hook. I think that the sine law should have more of a review, so simpler questions first to access their prior knowledge then that big triangle. Group work for the 1st handout is a good idea, how will you assess that they all know what they’re doing? I think it would be easier to give the students a hardcopy of the handout and draw the triangle on would be easier than taking a screen shot of geogebra. Maybe have students work in groups to write their summary and then have a class discussion as you write a summary on the board instead of just giving them a handout.
Would students use the GeoGebra individually or take turns coming up to the board to try? (one has physical limitations and the other has timing limitations)
Is the ambiguous case something that you would put on the test/exam? (I know often it is omitted) If not, why spend a whole lesson based on it rather than just mention it more briefly and then just focus on regular sine law problems?
Intro -Great idea of writing the success criteria, learning goals and the day’s agenda on the board -You can do a quick check either at the beginning or through the lesson, just get the students to say
Activity Sheet -Geogebra is an excellent addition in your lesson. -I like the idea that you get the students to figure out on their own, how many triangles they can make. -Hands-on work for the students is great, they get to learn on their own and see how the change of side lengths changes the amount of triangles you can make. -Great tips on using geogebra in class, the fact that you can modify activities that are uploaded. -Get the teacher to show first on the smart board, so the students would see what is need to be done rather than just blindly letting them ‘figure’ things out on their own. -I really like how you’re using formal assessment throughout, providing them with some hints for which direction to look at next. -The use of smart board is good, it’s more interactive, gets some students thinking out of the box.
Consolidation -Great idea to provide them with a handout. -I think I would have the students write down something rather than just get a handout, writing something out will help them retain more information. -You could have the handout as something they would have to go through for each case, and fill out the missing information so they know and understand the criteria for the cases. -Ticket out the door, assessment for learning, good idea. You can assess what the students have learned, if they learned. Get the students to write their names on it, just so you know where students are at in the learning process.
what conclusions are you going to make with the hook. Not sure what your going to say when a student plays with the triangle. What are you trying to hook them on exactly? Might be too long for one class. I suggest a two day lesson. Consolidation doesn't match your learning goals.
•I like the (side) detail comments on the lesson plan write up •GeoGebra activity is a good hook to get students to engage. •I think the summary sheet is great to solidify their learning and definitely helpful for review for a test. •The ambiguous case needs a little more explanation, ie show more example questions and solve it in class. •Overall, it is a great lesson.
Possible issues:
ReplyDelete- Ambiguous case – geogebra only works on IE, not on firefox, chrome
- maybe use more than one technology tool – youre using geogebra twice
- do students have to print the geogebra triangle on the handout?
- lots of rules and memorization. Maybe this is unavoidable.
- lots of activities to do in 70 minutes
1. For real-life applications, you can have students find angle lengths for pendulum questions or other physics questions. You could incorporate geography by finding the shortest path length.
2. Student discussion – think about giving students a worked example and putting them in groups to talk about the problem and solution.
3. I think the summary handout is a little too wordy, but that might just be the nature of the topic.
4. I think the teacher should introduce and have control of the geogebra application. Students might not be comfortable with the software.
-Timing for the first activity isn't enough. The ambiguous case will take much longer
ReplyDelete- I think you should include an activity in the consolidation or have them do more questions then consolidate. You can incorporate a class discussion in this.
Visual Appeal on Handout:
ReplyDelete- make the underline go all the way across in the title
- use o instead of 0 for your degree sign
(these things distract the easily distracted)
Some things to consider:
- the online activities are great but some students may be easily distracted and just play around without understanding the point of the lesson, just consider this (it's probably unavoidable)
- seems like a lot to do in 75 minutes, timing may have to be very precise
Plan your "work through example"
ReplyDeleteWork through one or two examples of the ambiguous triangles handout
Verbally and visually show them how to use geogebra (zooming, panning, etc)
What is your ticket out the door question?
During the second 20 min block in the instruction section you mention that you are summarizing what the students have just discovered. You include:
ReplyDeleteIf < A is obtuse and
a>b, one triangle exists
a<b or a=b, no triangles exist
but during the work sheet 'Triangle Activity Sheets" there is no point where the students work on a triangle with an obtuse angle.
I think you're missing part of the explanation of why the ambiguous case occurs- I would use it as an opportunity to teach that supplementary angles have the same sine.
ReplyDeleteI think this is a really good lesson one things to consider, it sort of struck me as something that may not work quite as you expected:
ReplyDelete- consider for your hook having very structured questions for using the GeoGebra activity, otherwise you may lose their interest very quickly.
- I really enjoy the apps used on the smart board because it gives the kids a good visual of what the triangles should look like, what the relationships between the sides are and what happens if you change the variables.
ReplyDelete- You might want to have the kids fill out the summary sheet, so give them some information and go over the sheet with them and allow them to fill out the rest of the material. This allows them to focus on the lesson and the various rules that they need to know and review them during the lesson as well.
-
- A great idea to write your learning goals, success criteria and agenda on the board for your students to reference throughout the lesson
ReplyDelete- Do the students already know that the angle gamma is related to side c
- Consider having a fill-in the blank handout to ensure that students are paying attention during the lesson
- A great idea for guided learning and review for the students - are you going to go over the answer and full solution to ensure that all students have the correct answer/process?
- If this was done in a computer lab - are all students able to participate in the 1st geogebra applet, instead of just having one student going to the board
- A very interactive lesson!
The ambiguous case activity is a nice interactive way of getting students to explore the concepts of trigonometry. I like how you can change the triangle properties and see how that affects the other measurements/angles.
ReplyDeleteI like the idea of giving students the handout summaries, but you could also get them to make ones for themselves. I think this is more a matter of personal preference.
- I like the idea of using the worksheet that goes along with GeoGebra. It makes it more engaging to the students.
ReplyDelete- The simple chalk and talk portions of the lesson where you did review or consolidation, etc. I feel there may be a better way to make it engaging for the students, as your 'ambiguous case' activity is
- Students should create their own summary sheet as Bryan mentioned I agree whole heartedly
- *Shudders* UOIT lesson plan templates…
ReplyDelete- Nice little applet that demonstrates the equality of the Sine Law
- Worksheet has the lengths on the top and bottom for the equalities -> obvious but students don’t realize that, so that was a nice touch
- Visual on the worksheet for the ambiguous case is kind of hard to make out due to the black background
- The content seems kind of crammed...
- Overall, I think it’s a strong lesson but just watch out for too much information; spreading this out might be beneficial
I really like how you have the learning goals and the agenda stated at the beginning of the lesson! The GeoGebra activity is a great way to grab students’ attention and I think it’s great that you can get students up to the board to manipulate it as well. During your lesson, I think that you should further explain the ambiguous case at some point so that they are not just discovering it on their own. During the ‘Ambiguous Case Activity’, how will you know if the students have learned the concepts? I really like your handouts that you are giving the students but I think that sometimes having the students create their own summary sheets is more beneficial. For the consolidation/homework section you could have the students create their own summary sheet with one or two examples so you can determine if they have learned the concepts. You could then include the peer assessment into the lesson by having them go over a partner’s summary sheet the following day. Great lesson!
ReplyDeleteI definitely think you should have a summary sheet so they can always review the content any time afterwards, but give them more time to process the information they just learned before giving the summary sheet out. The only downfall of the peer assessment depends on how engaged the students are in actually reading someone else's summary sheet. If they're not, they're going to pretend to read it and just hand it back and you can't really assess what they really learned or still have yet to learn.
ReplyDelete- If you're handing out laptops for students to use, you need to include that transition in your lesson plan (if you don’t already have it). From experience laptop distribution and setting up TAKES FOREVER, and I found it easier to have one laptop per pair (less laptops to fix)
ReplyDelete- Keep the hook short and done on the projector rather than have the students do it individually, I don’t think you want to spend too much time on this.
- I feel that even though they have seen this before, they may need an example given to them before they try on their own (or even in a group)
- The activity is good, but definitely will need a class discussion or something to ensure they understand what the turning point for the ambiguous case is.
- Perhaps include some blanks on the summary sheet that they have to fill in
- In the ticket out the door make the student sketch out the triangles (as best as they can)
- I love the idea of allowing students with ADD, ADHD, etc, to come up to the board (will get them out of their seats)
ReplyDelete- Giving students time to make their own summary sheet has been proven to be extremely successful (proven in research)
- Law of Sines activity is a great visual and demonstrates how the law works
- Not sure if you would be able to do this lesson in one class, probably going to take two (at least)
- Guided practice sounds like something that would work out nicely
- Not sure if students would be motivated by GeoGebra
- Ticket-out-the-door could be a different problem that better reflects your learning goals and success criteria
- Overall, well thought out. Great job girls!
I think the ambiguous case is a very difficult case for students to understand. They probably need a day to first review the sine law, and then on the second day, have the opportunity to discover that there could be two possible triangles formed. I think that using manipulatives instead of the applet may be beneficial and more realistic (having 15 laptops in the class is probably not very likely).
ReplyDelete- the hook with Geogebra is a great way of showing the sine law without actually getting into the law itself
ReplyDelete- you might want to give students a simpler example to start, even though this is a refresher (you’re essentially starting them with a word problem)
- asking them to put a screen shot in the handout restricts them from handing the work in during class (many wouldn’t want to be forced to do the work at home)
- maybe define in the lesson what you mean by “The Ambiguous Case” – make sure the students know what ‘ambiguous’ means (I would bet some don’t).
- there is a lot of content here. You may want to break this into a few lessons.
-having students come up with their own summary sheet may be a better idea (Supportive Learning Environment, Alfie Kohn)
Always good to have solutions to the problems in case you get nervous up front
ReplyDeleteHandout is a good idea, especially if there are students who write slower, and it seems that students write slower than when we were in school (not based on research, just observation). You could make it a fill in the blanks sheet, where they get it at the beginning of the lesson and fill in the key points.
The GeoGebra is a good way to visually show the different examples, however, I don't think it is going to hook the students into the lesson. For a student who is having a hard time understanding the sin law, this program might just appear to be a bunch of numbers with an equation.
ReplyDeleteI do like how you take the time to go through an example question with the class. This will give students a chance to ask questions.
I like how you have an activity and sheet for them to work on. However, I think there are too many questions. What will you do when the students start getting bored? How are you going to make sure they aren't surfing the web? Are you going to be collecting the sheet at the end? You could possibly sign off on every students worksheet at the end of the period so you know what they completed in class and what they completed as homework. This could be used for Learning Skills and Work Habits in the report card.
Good hook. I think that the sine law should have more of a review, so simpler questions first to access their prior knowledge then that big triangle. Group work for the 1st handout is a good idea, how will you assess that they all know what they’re doing? I think it would be easier to give the students a hardcopy of the handout and draw the triangle on would be easier than taking a screen shot of geogebra. Maybe have students work in groups to write their summary and then have a class discussion as you write a summary on the board instead of just giving them a handout.
ReplyDeleteWould students use the GeoGebra individually or take turns coming up to the board to try? (one has physical limitations and the other has timing limitations)
ReplyDeleteIs the ambiguous case something that you would put on the test/exam? (I know often it is omitted) If not, why spend a whole lesson based on it rather than just mention it more briefly and then just focus on regular sine law problems?
Intro
ReplyDelete-Great idea of writing the success criteria, learning goals and the day’s agenda on the board
-You can do a quick check either at the beginning or through the lesson, just get the students to say
Activity Sheet
-Geogebra is an excellent addition in your lesson.
-I like the idea that you get the students to figure out on their own, how many triangles they can make.
-Hands-on work for the students is great, they get to learn on their own and see how the change of side lengths changes the amount of triangles you can make.
-Great tips on using geogebra in class, the fact that you can modify activities that are uploaded.
-Get the teacher to show first on the smart board, so the students would see what is need to be done rather than just blindly letting them ‘figure’ things out on their own.
-I really like how you’re using formal assessment throughout, providing them with some hints for which direction to look at next.
-The use of smart board is good, it’s more interactive, gets some students thinking out of the box.
Consolidation
-Great idea to provide them with a handout.
-I think I would have the students write down something rather than just get a handout, writing something out will help them retain more information.
-You could have the handout as something they would have to go through for each case, and fill out the missing information so they know and understand the criteria for the cases.
-Ticket out the door, assessment for learning, good idea. You can assess what the students have learned, if they learned. Get the students to write their names on it, just so you know where students are at in the learning process.
what conclusions are you going to make with the hook. Not sure what your going to say when a student plays with the triangle. What are you trying to hook them on exactly? Might be too long for one class. I suggest a two day lesson. Consolidation doesn't match your learning goals.
ReplyDelete•I like the (side) detail comments on the lesson plan write up
ReplyDelete•GeoGebra activity is a good hook to get students to engage.
•I think the summary sheet is great to solidify their learning and definitely helpful for review for a test.
•The ambiguous case needs a little more explanation, ie show more example questions and solve it in class.
•Overall, it is a great lesson.