I really like your idea on how you have peer to peer learning. Your idea on having the students go to different areas in the classroom to identify the amplitude, domain, range, and period of a function. Though, I think 30 minutes might be too much time to do this. This idea would work well where you do a Jigsaw group as well. If you create groups of four students, you can have them each go to a different property and become an expert in this. After about 5 minutes in their expert groups, students will go back to their home groups and share their knowledge. This will take a bit of time as well but it will reduce the shuffling around the class which will put students in and out of focus. You can also provide a graphic organizer for students to use when recording their findings.
- Tribes, yeah! - Strong minds-on - Consider trying to user the jig-saw set-up to have one student be a master of each topic, and pull their knowledge to solving a difficult task. - For the consolidation activity, give them a starting base (example y = 4sin[2(x+pi)]+3, and have them play with the numbers. It could be better than have them think of an equation themselves. - Solid work folks!
- Great warm-up activity, having groups work in tribes and asking what they think the definitions of the words may be is an excellent idea - Not all the activities have times on them (consider putting the times in the left hand column to make it easier to see how long each activity will take - Are you able to show the change in the graph (at the beginning of the graph) on a smart board using an app, it might be more accurate and students may enjoy the use of technology - Ensure that students have a note to copy down for their lesson for future references - Consider giving students a second example of a cosine and sine function to make sure they fully understand the content
- Avoid underlines - Great idea with warm up activity! It's a great idea to have them dig and come up with what they think each of the term means. You could try having a Jigsaw, where you have experts for each term, they can come up with their definition, visual, and example. They would then have to share it with their home group and have an opportunity to teach their peers (helps drill it into their head).
- Use of Desmos is great, students can visually see the transformations, and change the variables as they wish. - Great idea to have students work with cosine, as we tend to focus on sine a lot more throughout our lessons. - Are they handing in anything at all? How are you going to assess that they've caught onto the idea and how much they understand?
I like the idea of using expert groups to learn about amplitude, period, etc... When students come back together in their groups as experts on each individual transformation, students need to know which transformations should be applied first (what makes it easier in terms of graphing).
My last post didn't make it... Here's a brief summary:
Graphing calculators are used often in classrooms and referenced to in textbook examples so they might be a good option. Some students might prefer them and departments usually have class sets. Maybe use a short video of waves being used in science for a hook?
I like the way you've split the main components of the lesson (period, amplitude, domain, etc...) and used the idea of expert groups for students to learn about these. This is also a good way of getting students to work together to produce their final result (for the transformations).
I like that you had activities that reflected the students in your class - allowing them time to talk, but keep this short (5 min). Is there handouts or visuals to go with the activities? It would make it easier to understand. For such a visual topic there seems to be a lack of visuals in your lesson. I like that you incorporated desmos into the consolidation, yet this may take a bit of time for a consolidation. Jigsaw is a good idea, but it is time consuming - have graphic organizers to help students keep on task. The ticket out the door is a great assessment tool, but this is a very full lesson - consider making it into two. Overall a lot of great strategies used here.
Expert groups as a warm-up activity is a great idea, and 20 mins is more than enough time! The KWL like Jason said is also a great suggestion. Content: is there any way that you can let students discover what each parameter does on its own, and THEN put it all together? Class activity: using expert groups is a good idea in theory, but do you really trust that students are able to teach each other in a way that everybody will understand concepts?
I thought your expert activity was really good. I think it might be a bit much for one lesson- exploring new definitions, playing around with parameters, and graphing. I might save the graphing activity for the next class because there are a whole new set of things that need to be emphasized for graphing (how to set up the axes when graphing trig functions, labeling points, etc).
- Great to see the expectations from the curriculum document, gives a link to what is being touched upon exactly. - Formal assessment...the brainstorming in Tribe groups at the beginning is the great, gets the students to dig and pull out what they already know of these terms and relate it to real-life situations. - Use a KWL chart maybe to help students - Use of Desmo app is great in the activity, get the students to use the app to help them understand what their parameter is, and visualize it so they can explain it better to their peers. - For the activity, since they have Desmo app, get the equations to be cosine, since we all always usually focus on sine function. - Ticket-out-the-door: Get the students to explain how each parameter changes, now just draw out a graph only.
Groups should probably be varied periodically so students get to work with different people.
8 minutes is probably too long for each group to brainstorm at the beginning of the lesson. 3 minutes would probably suffice. Use KWL chart for each topic.
Relate transformations of trig functions to quadratic transformations - tie in past knowledge because they would have already seen all those parameters in the quadratics unit.
Continuing on the graphing calculator thing, I know that a lot of high schools have their students learn how to transform functions using their graphing calculators. I've tutored students who have this activity where they have to use transformed functions to make a picture on their calculator. This might be a good homework activity to use for your lesson-- its kind of a creative and different math assignment so its a cool break from what the students are used to.
- I liked your hook having them simply brainstorming what they know about each of the parameters - I really like your class activity with Desmos, that will offer discovery based learning - I would use the main Jigsaw activity right off the bat as the hook and then do the brainstorming activity of what each parameter means after they have worked with it - I would (as Caroline said) relate it back to the transformations used with quadratic equations because they have already seen that
I find it useful to use the transformations of quadratic functions as a starting point because of how much time is spent with that in grade 10. Most students are able to draw the connection between a(x-h)^2+k and a*sin[k(x-d)]+c and eventually they can see the way transformations can then be expressed generally as a*f [b(x-c)]+d regardless of the function. Good use of Desmos to bring visuals into the lesson.
- Very organized presentation - A handout perhaps would be better than copying the note out in their notebook - It would be beneficial for students to discover the affect of amplitude on the graph rather than being told (like you later did using Desmos) - Desmos is an awesome app..I believe it would be highly effective in your lesson. Ultimately, it's user-friendly and highly visual - Jigsaw is also a great strategy
-I like your idea of getting the definitions out of the way first, and doing some group brainstorming -Using Desmos is a great idea, its a solid resource to use -For the ticket out the door, I might want to see how well they do without Desmos. -Really solid lesson overall!
Keep the warm up activity, that is fantastic! Maybe provide the groups some chart paper and markers so they can record their brainstorming and make it easier for them to present to the class. Don’t stress over the timing for this activity, as a teacher you would be walking the room, and could cut the brainstorm portion shorter if you notice off task conversations.
Starting off the content by adding in all the new parameters at the same time is a little daunting. Perhaps only show the a general equation for each parameter ( amplitude: f(x) = a sin x), and then later on after you have presented each parameter individually you can start making general equations that have two or more parameters, and then finally the general equation that has all transformations.
I like the suggestion of doing the instruction content after the jigsaw. Maybe allow the students to use the desmos in the expert groups. If the expert groups are assigned a single parameter maybe provide more structure to the activity by requiring them to specifically identify if their parameter modifies the phase, domain, range, amplitude, and how it visually changes the graph.
I know you guys planned to do graphing separately, but I really think it goes hand and hand with sine functions.
-I like the 5 mins at the beginning to review expectations are let the class settle. -Maybe students should be given less time to talk about the different concepts; they are not likely to spend more than 3-5 minutes on a certain topic. -If students have already seen graphs, maybe it would be of benefit to show how the graph transforms when various numbers are added to the "base equation" (or at least plot the "base equation" and the "transformed equation" on the same axes) to give a visual demonstration of the concept you are explaining. -The jigsaw technique is used well, but the Desmos thing seems like too much for one lesson. -Maybe it would be optimal for the students to explore the different parameters of the sine function and formalizing it on their own before giving them the answers in a summary.
I think the students should be able to explore the sine graph using desmos by changing the parameters to find out what each one does on their own. They can try to come up with the properties of the parameters as they explore. Good lesson overall.
-I think it is better not to start with the whole formula of f(x) = asin(k(x-d)) + c, it might confused them - I like the idea of using the Desmos activity
- students may not know enough or be interested enough in the beginning of the lesson to talk about domain/range/etc for 8 minutes (it really depends on the group) - as Jason mentioned, using KWL might be a better alternative - I like how you’re encouraging them to play with the functions and determine what they look like and what transformations do - the jigsaw activity (and switching an ‘expert’ for each aspect) is very well thought-out. - it could be challenging for students to graph at the end of the lesson, and you might want to give feedback to the students for the next lesson
I really like your idea on how you have peer to peer learning. Your idea on having the students go to different areas in the classroom to identify the amplitude, domain, range, and period of a function. Though, I think 30 minutes might be too much time to do this. This idea would work well where you do a Jigsaw group as well. If you create groups of four students, you can have them each go to a different property and become an expert in this. After about 5 minutes in their expert groups, students will go back to their home groups and share their knowledge. This will take a bit of time as well but it will reduce the shuffling around the class which will put students in and out of focus. You can also provide a graphic organizer for students to use when recording their findings.
ReplyDelete- Tribes, yeah!
ReplyDelete- Strong minds-on
- Consider trying to user the jig-saw set-up to have one student be a master of each topic, and pull their knowledge to solving a difficult task.
- For the consolidation activity, give them a starting base (example y = 4sin[2(x+pi)]+3, and have them play with the numbers. It could be better than have them think of an equation themselves.
- Solid work folks!
- Great warm-up activity, having groups work in tribes and asking what they think the definitions of the words may be is an excellent idea
ReplyDelete- Not all the activities have times on them (consider putting the times in the left hand column to make it easier to see how long each activity will take
- Are you able to show the change in the graph (at the beginning of the graph) on a smart board using an app, it might be more accurate and students may enjoy the use of technology
- Ensure that students have a note to copy down for their lesson for future references
- Consider giving students a second example of a cosine and sine function to make sure they fully understand the content
- Avoid underlines
ReplyDelete- Great idea with warm up activity! It's a great idea to have them dig and come up with what they think each of the term means. You could try having a Jigsaw, where you have experts for each term, they can come up with their definition, visual, and example. They would then have to share it with their home group and have an opportunity to teach their peers (helps drill it into their head).
-
- Use of Desmos is great, students can visually see the transformations, and change the variables as they wish.
ReplyDelete- Great idea to have students work with cosine, as we tend to focus on sine a lot more throughout our lessons.
- Are they handing in anything at all? How are you going to assess that they've caught onto the idea and how much they understand?
I like the idea of using expert groups to learn about amplitude, period, etc...
ReplyDeleteWhen students come back together in their groups as experts on each individual transformation, students need to know which transformations should be applied first (what makes it easier in terms of graphing).
My last post didn't make it... Here's a brief summary:
ReplyDeleteGraphing calculators are used often in classrooms and referenced to in textbook examples so they might be a good option. Some students might prefer them and departments usually have class sets.
Maybe use a short video of waves being used in science for a hook?
I like the way you've split the main components of the lesson (period, amplitude, domain, etc...) and used the idea of expert groups for students to learn about these. This is also a good way of getting students to work together to produce their final result (for the transformations).
ReplyDeleteI like that you had activities that reflected the students in your class - allowing them time to talk, but keep this short (5 min). Is there handouts or visuals to go with the activities? It would make it easier to understand. For such a visual topic there seems to be a lack of visuals in your lesson. I like that you incorporated desmos into the consolidation, yet this may take a bit of time for a consolidation. Jigsaw is a good idea, but it is time consuming - have graphic organizers to help students keep on task. The ticket out the door is a great assessment tool, but this is a very full lesson - consider making it into two. Overall a lot of great strategies used here.
ReplyDeleteExpert groups as a warm-up activity is a great idea, and 20 mins is more than enough time! The KWL like Jason said is also a great suggestion.
ReplyDeleteContent: is there any way that you can let students discover what each parameter does on its own, and THEN put it all together?
Class activity: using expert groups is a good idea in theory, but do you really trust that students are able to teach each other in a way that everybody will understand concepts?
Overall: a solid lesson with great ideas!
I thought your expert activity was really good. I think it might be a bit much for one lesson- exploring new definitions, playing around with parameters, and graphing. I might save the graphing activity for the next class because there are a whole new set of things that need to be emphasized for graphing (how to set up the axes when graphing trig functions, labeling points, etc).
ReplyDelete- Great to see the expectations from the curriculum document, gives a link to what is being touched upon exactly.
ReplyDelete- Formal assessment...the brainstorming in Tribe groups at the beginning is the great, gets the students to dig and pull out what they already know of these terms and relate it to real-life situations.
- Use a KWL chart maybe to help students
- Use of Desmo app is great in the activity, get the students to use the app to help them understand what their parameter is, and visualize it so they can explain it better to their peers.
- For the activity, since they have Desmo app, get the equations to be cosine, since we all always usually focus on sine function.
- Ticket-out-the-door: Get the students to explain how each parameter changes, now just draw out a graph only.
Groups should probably be varied periodically so students get to work with different people.
ReplyDelete8 minutes is probably too long for each group to brainstorm at the beginning of the lesson. 3 minutes would probably suffice. Use KWL chart for each topic.
Relate transformations of trig functions to quadratic transformations - tie in past knowledge because they would have already seen all those parameters in the quadratics unit.
Continuing on the graphing calculator thing, I know that a lot of high schools have their students learn how to transform functions using their graphing calculators. I've tutored students who have this activity where they have to use transformed functions to make a picture on their calculator. This might be a good homework activity to use for your lesson-- its kind of a creative and different math assignment so its a cool break from what the students are used to.
ReplyDelete- I liked your hook having them simply brainstorming what they know about each of the parameters
ReplyDelete- I really like your class activity with Desmos, that will offer discovery based learning
- I would use the main Jigsaw activity right off the bat as the hook and then do the brainstorming activity of what each parameter means after they have worked with it
- I would (as Caroline said) relate it back to the transformations used with quadratic equations because they have already seen that
I find it useful to use the transformations of quadratic functions as a starting point because of how much time is spent with that in grade 10. Most students are able to draw the connection between a(x-h)^2+k and a*sin[k(x-d)]+c and eventually they can see the way transformations can then be expressed generally as a*f [b(x-c)]+d regardless of the function.
ReplyDeleteGood use of Desmos to bring visuals into the lesson.
- Very organized presentation
ReplyDelete- A handout perhaps would be better than copying the note out in their notebook
- It would be beneficial for students to discover the affect of amplitude on the graph rather than being told (like you later did using Desmos)
- Desmos is an awesome app..I believe it would be highly effective in your lesson. Ultimately, it's user-friendly and highly visual
- Jigsaw is also a great strategy
-I like your idea of getting the definitions out of the way first, and doing some group brainstorming
ReplyDelete-Using Desmos is a great idea, its a solid resource to use
-For the ticket out the door, I might want to see how well they do without Desmos.
-Really solid lesson overall!
Using Desmos as a visual is good. I think the timing may need to be adjusted. I think these activities will take longer.
ReplyDeleteKeep the warm up activity, that is fantastic! Maybe provide the groups some chart paper and markers so they can record their brainstorming and make it easier for them to present to the class. Don’t stress over the timing for this activity, as a teacher you would be walking the room, and could cut the brainstorm portion shorter if you notice off task conversations.
ReplyDeleteStarting off the content by adding in all the new parameters at the same time is a little daunting. Perhaps only show the a general equation for each parameter ( amplitude: f(x) = a sin x), and then later on after you have presented each parameter individually you can start making general equations that have two or more parameters, and then finally the general equation that has all transformations.
I like the suggestion of doing the instruction content after the jigsaw. Maybe allow the students to use the desmos in the expert groups. If the expert groups are assigned a single parameter maybe provide more structure to the activity by requiring them to specifically identify if their parameter modifies the phase, domain, range, amplitude, and how it visually changes the graph.
I know you guys planned to do graphing separately, but I really think it goes hand and hand with sine functions.
-I like the 5 mins at the beginning to review expectations are let the class settle.
ReplyDelete-Maybe students should be given less time to talk about the different concepts; they are not likely to spend more than 3-5 minutes on a certain topic.
-If students have already seen graphs, maybe it would be of benefit to show how the graph transforms when various numbers are added to the "base equation" (or at least plot the "base equation" and the "transformed equation" on the same axes) to give a visual demonstration of the concept you are explaining.
-The jigsaw technique is used well, but the Desmos thing seems like too much for one lesson.
-Maybe it would be optimal for the students to explore the different parameters of the sine function and formalizing it on their own before giving them the answers in a summary.
I think the students should be able to explore the sine graph using desmos by changing the parameters to find out what each one does on their own. They can try to come up with the properties of the parameters as they explore.
ReplyDeleteGood lesson overall.
-I think it is better not to start with the whole formula of f(x) = asin(k(x-d)) + c, it might confused them
ReplyDelete- I like the idea of using the Desmos activity
- students may not know enough or be interested enough in the beginning of the lesson to talk about domain/range/etc for 8 minutes (it really depends on the group)
ReplyDelete- as Jason mentioned, using KWL might be a better alternative
- I like how you’re encouraging them to play with the functions and determine what they look like and what transformations do
- the jigsaw activity (and switching an ‘expert’ for each aspect) is very well thought-out.
- it could be challenging for students to graph at the end of the lesson, and you might want to give feedback to the students for the next lesson