Unit7 L1
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Unit7 L1 as PDF for free.
More details
- Words: 1,836
- Pages: 5
UMF Unit-Wide Lesson Plan Template
Name: Nicole Brewer Program: Secondary Ed. Math Course: EDU 460 Lesson Topic / Title: Graphing Exponential Functions Lesson Date: 3/5/2019 Lesson Length: 80 min Grade/Age: Grades 9-11 Learning Objectives & Content Standard Alignment - Selects, creates, and sequences learning experiences and performance tasks that support learners in reaching rigorous curriculum goals based on content standards. Learning Objective(s) Instructional Decisions / Reasoning • I can graph exponential growth and decay • Being able to graph functions. exponential growth and decay allows you to see how the functions change over time. Seeing that in one direction they go forever and in the other they plateau. Content Standard(s) Instructional Decisions / Reasoning • Understands how to graph a function and • Students will need to be able to determine key features. interpret a graph and understand what it is telling CCSS.MATH.CONTENT.HSF.IF.C.7.E them.
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. CCSS.MATH.CONTENT.HSF.LE.A.1.C
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Assessment - Uses assessment flexibly to expand and deepen understanding of learner performance and determines best supports for continued learner growth. Assessment Instructional Decisions / Reasoning • Pre-Assessment to check their understanding on • The pre-assessment will be graphing and solving exponential equations. used to show me if students have the intuition to solve the • Notice and Wonder looking at graphs of logarithmic and exponential exponential equations. equations because it is content • Desmos Activity that they haven’t been taught. • The notice and wonder activity allows me to get an idea about what they understand about exponential graphs and if they know what it tells you.
Revised 07/19/2018
•
Desmos allows the teacher to see on each problem what students answered or look at a certain student and what they did for all the problems. It also gives you a list of the class and a checkmark an x or a blank for each question for each student. This breaks down the work and identifies students who are struggling or problems that stumped multiple people. Instructional Materials and Resources - Stays current in content knowledge and expands expertise in reviewing instructional materials from the perspectives of both the discipline and individual learner needs. Materials, Resources, and / or Technology Instructional Decisions / Reasoning Materials • The students use their iPads to take notes and work on • Worksheet worksheets in an app called • Notes Notability. This allows them to • Sticky Notes always have their notes with Technology them if they have their iPad. • iPads Notes are done in slide shows • Laptop so that students can use them • Desmos Link and Code as guided notes and can focus https://teacher.desmos.com/dashboard/5c7697c more on what’s being said. a33a3cf0c66182d9f • Sticky notes as an exit ticket allows them to put it up on the board and make it more anonymous. • Using Desmos is a fun way to get students engaged and thinking but it feels more like a game. Instructional Methods: Selects, creates, and sequences learning experiences and performance tasks by using a variety of instructional approaches, strategies, and technologies that make learning accessible to all learners and support learners in reaching rigorous curriculum goals. Teaching and Learning Sequence Instructional Decisions / Reasoning 1. Go over Unit Outline (5) • Showing the students the 2. Notice and Wonder (5) outline gives them a picture of 3. Notes (20) where we are going and tells 4. Look at graph of y=2^x (10) them what targets this unit 5. Desmos Activity (30) will give them an opportunity 6. Reminders about homework (5) to hit again. 7. Exit Ticket (5) • Looking at graphs of Exponential Growth and Decay • Notice and wonder looking at the graphs of before the students know what exponential growth and decay. Ask students if it is allows them to connect they see any differences or similarities. what they already know to • Pull up Desmos and type in y=2^x twice. Keep one these graphs. It also gives them but change parts of the other, asking students a chance to see if something is what they think will happen. Such as the fact that different. The students also the asymptote changes when you add or subtract.
Revised 07/19/2018
•
• •
Have students go to the Desmos link posted on the board. Explain to them that they will be doing an activity where they have to manipulate something in the equation to change the graph to what they want it to be. At the end of the activity tell them that they have to do at least 4 problems from the worksheet for homework. Hand out exit ticket (sticky note) and ask the questions, “What did you think of this activity, what did you learn, would you like to do something like this again?” have students write their answers, they don’t have to include their name. Have them post the sticky note on the white board as they leave the room.
•
•
•
•
•
Meeting students’ needs (differentiation, extensions, modifications, accommodations) • I added in section 4, manipulating a graph on Desmos together, to support students who didn’t see initially from the notes what shifts occur when. • Limited the Desmos activity to just the first 14 problems.
Having the notes be in slideshow form makes them guided notes that allows students to focus more on listening than on writing. Not all students will see how different parts of the equation impact the graph so pointing it out to them is a way to avoid misconceptions. The Desmos activity gives the students something new to try which they said they wanted. Content wise it is also a strong activity because it forces students to think about how changing one part of the equation will change the graph. I only assigned four of the problems for the worksheet because they did they activity but I still wanted them to practice making a table and graph themselves. The exit ticket will help me to see if they found value in the activity or if it was something that didn’t help them learn.
Instructional Decisions / Reasoning • Not all students can pick up on those shifts or even realize that they are their unless they are prompted. Showing them allows them to see and hear those associations in a way that includes everyone. This also allows students who already see and understand it to share their knowledge. • I didn’t think that the other parts of the activity would be beneficial for this unit as the students are never required to look at a graph and write the equation.
Field Courses Only – Post lesson
Revised 07/19/2018
Reflection Over all I think that the lesson went well. The students were actively engaged and participating during the notice and wonder. This allowed me to see what they already knew and adjust what I would emphasize during the notes. The Desmos activity seemed to go well, students were engaged and looking at the graph beforehand definitely allowed them more confidence in their decisions and understanding. The Desmos activity allowed me to see a trend that most students weren’t making the connection that changing the base number in the equation would change the rate at which the graph was growing. This was easy to address and point out to students in the moment. From the exit tickets I gathered that most of the class enjoyed doing something outside of the normal routine. Some didn’t like it, those were the students who struggled with understanding or thought it was too easy. I learned that the students are more engaged when you ask them direct questions and give them time to think and respond. I will use this to help me plan my other lessons by trying to incorporate more time for them to think about and respond to the content. On 3/7/2019 they took a formative covering graphing exponential functions. Of the 17 students who took it, 8 got a 3, 5 got a 2.5 and 4 got a 2. No students received a 1 on this assignment so they all attempted it and knew mostly what they were doing. Many of the 2 and 2.5 scores came from students not reading the directions to identify domain, range and whether it was growth or decay, as well as making a simple mistake. While not all students met the objective they all showed progress towards meeting the objective. To help all students meet the objectives I will remind them that they need to read the directions and give them more opportunity to practice.
Revised 07/19/2018
Teaching Standards and Rationale Standard #2 Learning Differences Notice and Wonder Rationale: Some students already understand and can see how adding a number to an equation will change the graph but others don’t. Adding in discussion around this allows me to see who already understands it. It also allows the students who might not automatically see it to hear it explained by me or another student, so this will allow them to learn without targeting them. Standard #6 Assessment Desmos Activity Rationale: Desmos collects all the student responses and gathers them in a way that teachers can look at one student or at one question in particular. This allows me to gauge the level of understanding, directly after direct instruction, that students have. I looked at problem questions and their answers to free response options. Standard #8 Instructional Strategies Notice and Wonder Rationale: The notice and wonder activity had the students engaging with me, their peers, and the content directly. This got them to use and learn vocabulary that they will see in the unit. It was an easy way to question them but let them feel like they were just sharing ideas. It also got them questioning each other to figure out commonalities in ideas. Standard #10 Collaborations Discussion with Mentor Rationale: During discussion with my mentor about the unit he pointed out that most students had never seen a graph with an asymptote or learned what it is. This lead me to realize that I needed to emphasize the asymptote concept during notes. It also made me think about the fact that most students wouldn’t realize how parts of an equation create shifts and changes to the graph. This lead to the decision to incorporate an emphasis on those shifts into the lesson. Standard #11 Technology Desmos Activity Rationale: The Desmos Activity challenged students to think about the relationship between the graph and the equation in ways that they don’t normally have to. They had to think about how changing the equation would change the graph. The technology allows them to instantly check their ideas to see if they work. They don’t have to take the time to do all the calculations for the graphs but can still get the information out of them. Revised 07/19/2018
Name: Nicole Brewer Program: Secondary Ed. Math Course: EDU 460 Lesson Topic / Title: Graphing Exponential Functions Lesson Date: 3/5/2019 Lesson Length: 80 min Grade/Age: Grades 9-11 Learning Objectives & Content Standard Alignment - Selects, creates, and sequences learning experiences and performance tasks that support learners in reaching rigorous curriculum goals based on content standards. Learning Objective(s) Instructional Decisions / Reasoning • I can graph exponential growth and decay • Being able to graph functions. exponential growth and decay allows you to see how the functions change over time. Seeing that in one direction they go forever and in the other they plateau. Content Standard(s) Instructional Decisions / Reasoning • Understands how to graph a function and • Students will need to be able to determine key features. interpret a graph and understand what it is telling CCSS.MATH.CONTENT.HSF.IF.C.7.E them.
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. CCSS.MATH.CONTENT.HSF.LE.A.1.C
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Assessment - Uses assessment flexibly to expand and deepen understanding of learner performance and determines best supports for continued learner growth. Assessment Instructional Decisions / Reasoning • Pre-Assessment to check their understanding on • The pre-assessment will be graphing and solving exponential equations. used to show me if students have the intuition to solve the • Notice and Wonder looking at graphs of logarithmic and exponential exponential equations. equations because it is content • Desmos Activity that they haven’t been taught. • The notice and wonder activity allows me to get an idea about what they understand about exponential graphs and if they know what it tells you.
Revised 07/19/2018
•
Desmos allows the teacher to see on each problem what students answered or look at a certain student and what they did for all the problems. It also gives you a list of the class and a checkmark an x or a blank for each question for each student. This breaks down the work and identifies students who are struggling or problems that stumped multiple people. Instructional Materials and Resources - Stays current in content knowledge and expands expertise in reviewing instructional materials from the perspectives of both the discipline and individual learner needs. Materials, Resources, and / or Technology Instructional Decisions / Reasoning Materials • The students use their iPads to take notes and work on • Worksheet worksheets in an app called • Notes Notability. This allows them to • Sticky Notes always have their notes with Technology them if they have their iPad. • iPads Notes are done in slide shows • Laptop so that students can use them • Desmos Link and Code as guided notes and can focus https://teacher.desmos.com/dashboard/5c7697c more on what’s being said. a33a3cf0c66182d9f • Sticky notes as an exit ticket allows them to put it up on the board and make it more anonymous. • Using Desmos is a fun way to get students engaged and thinking but it feels more like a game. Instructional Methods: Selects, creates, and sequences learning experiences and performance tasks by using a variety of instructional approaches, strategies, and technologies that make learning accessible to all learners and support learners in reaching rigorous curriculum goals. Teaching and Learning Sequence Instructional Decisions / Reasoning 1. Go over Unit Outline (5) • Showing the students the 2. Notice and Wonder (5) outline gives them a picture of 3. Notes (20) where we are going and tells 4. Look at graph of y=2^x (10) them what targets this unit 5. Desmos Activity (30) will give them an opportunity 6. Reminders about homework (5) to hit again. 7. Exit Ticket (5) • Looking at graphs of Exponential Growth and Decay • Notice and wonder looking at the graphs of before the students know what exponential growth and decay. Ask students if it is allows them to connect they see any differences or similarities. what they already know to • Pull up Desmos and type in y=2^x twice. Keep one these graphs. It also gives them but change parts of the other, asking students a chance to see if something is what they think will happen. Such as the fact that different. The students also the asymptote changes when you add or subtract.
Revised 07/19/2018
•
• •
Have students go to the Desmos link posted on the board. Explain to them that they will be doing an activity where they have to manipulate something in the equation to change the graph to what they want it to be. At the end of the activity tell them that they have to do at least 4 problems from the worksheet for homework. Hand out exit ticket (sticky note) and ask the questions, “What did you think of this activity, what did you learn, would you like to do something like this again?” have students write their answers, they don’t have to include their name. Have them post the sticky note on the white board as they leave the room.
•
•
•
•
•
Meeting students’ needs (differentiation, extensions, modifications, accommodations) • I added in section 4, manipulating a graph on Desmos together, to support students who didn’t see initially from the notes what shifts occur when. • Limited the Desmos activity to just the first 14 problems.
Having the notes be in slideshow form makes them guided notes that allows students to focus more on listening than on writing. Not all students will see how different parts of the equation impact the graph so pointing it out to them is a way to avoid misconceptions. The Desmos activity gives the students something new to try which they said they wanted. Content wise it is also a strong activity because it forces students to think about how changing one part of the equation will change the graph. I only assigned four of the problems for the worksheet because they did they activity but I still wanted them to practice making a table and graph themselves. The exit ticket will help me to see if they found value in the activity or if it was something that didn’t help them learn.
Instructional Decisions / Reasoning • Not all students can pick up on those shifts or even realize that they are their unless they are prompted. Showing them allows them to see and hear those associations in a way that includes everyone. This also allows students who already see and understand it to share their knowledge. • I didn’t think that the other parts of the activity would be beneficial for this unit as the students are never required to look at a graph and write the equation.
Field Courses Only – Post lesson
Revised 07/19/2018
Reflection Over all I think that the lesson went well. The students were actively engaged and participating during the notice and wonder. This allowed me to see what they already knew and adjust what I would emphasize during the notes. The Desmos activity seemed to go well, students were engaged and looking at the graph beforehand definitely allowed them more confidence in their decisions and understanding. The Desmos activity allowed me to see a trend that most students weren’t making the connection that changing the base number in the equation would change the rate at which the graph was growing. This was easy to address and point out to students in the moment. From the exit tickets I gathered that most of the class enjoyed doing something outside of the normal routine. Some didn’t like it, those were the students who struggled with understanding or thought it was too easy. I learned that the students are more engaged when you ask them direct questions and give them time to think and respond. I will use this to help me plan my other lessons by trying to incorporate more time for them to think about and respond to the content. On 3/7/2019 they took a formative covering graphing exponential functions. Of the 17 students who took it, 8 got a 3, 5 got a 2.5 and 4 got a 2. No students received a 1 on this assignment so they all attempted it and knew mostly what they were doing. Many of the 2 and 2.5 scores came from students not reading the directions to identify domain, range and whether it was growth or decay, as well as making a simple mistake. While not all students met the objective they all showed progress towards meeting the objective. To help all students meet the objectives I will remind them that they need to read the directions and give them more opportunity to practice.
Revised 07/19/2018
Teaching Standards and Rationale Standard #2 Learning Differences Notice and Wonder Rationale: Some students already understand and can see how adding a number to an equation will change the graph but others don’t. Adding in discussion around this allows me to see who already understands it. It also allows the students who might not automatically see it to hear it explained by me or another student, so this will allow them to learn without targeting them. Standard #6 Assessment Desmos Activity Rationale: Desmos collects all the student responses and gathers them in a way that teachers can look at one student or at one question in particular. This allows me to gauge the level of understanding, directly after direct instruction, that students have. I looked at problem questions and their answers to free response options. Standard #8 Instructional Strategies Notice and Wonder Rationale: The notice and wonder activity had the students engaging with me, their peers, and the content directly. This got them to use and learn vocabulary that they will see in the unit. It was an easy way to question them but let them feel like they were just sharing ideas. It also got them questioning each other to figure out commonalities in ideas. Standard #10 Collaborations Discussion with Mentor Rationale: During discussion with my mentor about the unit he pointed out that most students had never seen a graph with an asymptote or learned what it is. This lead me to realize that I needed to emphasize the asymptote concept during notes. It also made me think about the fact that most students wouldn’t realize how parts of an equation create shifts and changes to the graph. This lead to the decision to incorporate an emphasis on those shifts into the lesson. Standard #11 Technology Desmos Activity Rationale: The Desmos Activity challenged students to think about the relationship between the graph and the equation in ways that they don’t normally have to. They had to think about how changing the equation would change the graph. The technology allows them to instantly check their ideas to see if they work. They don’t have to take the time to do all the calculations for the graphs but can still get the information out of them. Revised 07/19/2018
