Lesson Plan for Implementing NETS•S—Template I

[Pages:8]Lesson Plan for Implementing NETS?S--Template I

(More Directed Learning Activities)

Template with guiding questions

Teacher(s) Name

Erin Benson

Position

Mathematics Teacher

School/District Etowah High School/Cherokee County School District

E-mail

Erin.benson@cherokee.k12.ga.us

Phone

1-770-852-0028

Grade Level(s) 9-10

Content Area Algebra 1 (3rd period) and Algebra 1 Support (4th period) both in an ELL setting

Time line

3rd and 4th period for 7 consecutive days (54 minute periods)

Standards (What do you want students to know and be able to do? What knowledge, skills, and strategies do you expect students to gain? Are there connections to other curriculum areas and subject area benchmarks? ) Please put a summary of the standards you will be addressing rather than abbreviations and numbers that indicate which standards were addressed.

Content Standards

After completing this section, students will be able to graph exponential equations by hand and by using technology, identify characteristics of exponential functions, and use exponential equations to model real world problems. The GSE Algebra 1 standards for this section are listed and described below.

MGSE9-12.A.CED.2 Create exponential equations in two or more variables to represent

relationships between quantities; graph equations on coordinate axes with labels and

scales. (The phrase "in two or more variables" refers to formulas like the compound interest

formula, in which

=

(1

+

)

has multiple

variables.)

MGSE9-12.F.BF.3 Identify the effect on the graph of replacing () by () + , (), (), and ( + ) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (Focus on vertical translations of graphs of linear and exponential functions. Relate the vertical translation of a linear function to its y-intercept.)

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MGSE9-12.F.IF.1 Understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range, i.e. each input value maps to exactly one output value. If f is a function, x is the input (an element of the domain), and f(x) is the output (an element of the range). Graphically, the graph is y = f(x).

MGSE9-12.F.IF.4 Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior.

MGSE9-12.F.IF.7 Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.

MGSE9-12.F.IF.7e Graph exponential functions, showing intercepts and end behavior.

NETS*S Standards: 1C Students use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways

1D Students understand the fundamental concepts of technology operations, demonstrate the ability to choose, use and troubleshoot current technologies and are able to transfer their knowledge to explore emerging technologies

2B Students engage in positive, safe, legal, and ethical behavior when using technology, including social interactions online or when using networked devices

2C Students demonstrate an understanding of and respect for the right and obligations of using and sharing intellectual property

3A Students plan and employ effective research strategies to locate information and other resources for their intellectual or creative pursuits.

3B Students evaluate the accuracy, perspective, credibility and relevance of information, media, data or other resources

3C Students curate information from digital resources using a variety of tools and methods to create collections of artifacts that demonstrate meaningful connections or conclusions

5A Students formulate problem definitions suited for technology-assisted methods such as data analysis, abstract models and algorithmic thinking in exploring and finding solutions

5C Students break problems into component parts, extract key information, and develop descriptive models to understand complex systems or facilitate problem-solving

6B Student create original works or responsibly repurpose or remix digital resources into new creations.

6C Students communicate complex ideas clearly and effectively by creating or using a variety of digital objects such as visualizations, models, or simulations

6D Students publish or present content that customizes the message and medium for their intended audiences

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7C Students contribute constructively to project teams, assuming various roles and responsibilities to work effectively toward a common goal

Overview (a short summary of the lesson or unit including assignment or expected or possible products)

In Algebra 1: Students will learn how to graph exponential equations both by hand and by using technology (traditional graphing calculator, a graphing calculator app, and a graphing calculator website). To begin students will spend a day exploring exponential functions by graphing them by hand using a table of values. We will discuss what they notice about these graphs ? why do some increase why others decrease (growth/decay), what is happening at the ends of the graphs (end behavior), do they look the same/follow the same rule as linear equations, etc. Students will work in collaborative pairs for the opening days of this section. Students will learn how to use a graphing calculator. They will discover the rules for horizontal and vertical translations. Students will work in groups of 3 to discover what happens when coefficient is introduced (). This will lead them to the discovery of transformations (stretch/shrink/reflections). Students will activate prior knowledge using warm ups and complete guided notes on the characteristics of exponential equations (domain, range, intercepts, asymptote, increase/decrease, growth/decay, end behavior, transformations). Students will explore real-world applications of exponential functions (compound interest, population growth/decay, and half-life).

In Algebra 1 Support: Students will continue their exploration of exponential applications by completing the following activities on Desmos: Avi and Benita's Repair Shop, What Comes Next?, Polygraph: Exponentials, Card Sort: Exponentials, Extensions ? Marbleslides: Exponentials & Predicting Movie Ticket Prices

Students will complete an Office Mix presentation as a class. Each student will be responsible for a slide and its screen recording. Students will be able to choose their topic by a random drawing. Students will work simultaneously on the presentation through Office365. Students will research their topic using the internet and will collaborate with their peers virtually and in person. The final product will be shared will all Algebra 1 students at our school to help them prepare for the summative assessment. It will also be used as a remediation/reteaching tool to prepare students for the end of unit test, final exam, and GA Milestone Algebra 1 Assessment. The final product will be shared on Canvas Commons where any teacher with access to Canvas can download a copy and import it into his/her class and will be shared on the teacher's twitter page. This activity is meant to help ELLs enhance their ability to write and speak using proper academic language (CALP).

Essential Questions (What essential question or learning are you addressing? What would students care or want to know about the topic? What are some questions to get students thinking about the topic or generate interest about the topic? Additionally, what questions can you ask students to help them focus on important aspects of the topic? (Guiding questions) What background or prior knowledge will you expect students to bring to this topic and build on?) Remember, essential questions are meant to guide the lesson by provoking inquiry. They should not be answered with a simple "yes" or "no" and should have many acceptable answers.

What are exponential functions and how do they occur in the real world? How do you graph an exponential equation and determine its domain and range? What are the characteristics of exponential functions? What are exponential transformations? How do I use exponential functions to model exponential behavior? How do I use exponential models to solve problems?

Assessment (What will students do or produce to illustrate their learning? What can students do to generate new knowledge? How will you assess how students are progressing (formative assessment)? How will you assess what they produce or do? How will you differentiate products?) You must attach copies of your assessment and/or rubrics. Include these in your presentation as well.

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Students will complete homework assignments daily, they will check their answers for accuracy, and will be given opportunities to ask questions on these assignments. Some homework assignments are modified for ELLs (less problems, different words ? no contradictions, word swaps i.e. car for convertible, etc.). Informal formative assessments such as Ticket Out the Door/Exit Tickets will be used to assess student understanding (informal formative assessments). Desmos will be used as formative assessments. At the end of this section, students will take a section test (quiz). ELLs will be given a modified version of the test and be given the use of bilingual dictionaries, word wall, and word cloud. All students will have access to the GA Milestone Algebra 1 Formula Sheet for this section test.

Support students will create an Office Mix using Office365. Each student will be responsible for a slide and its slide recording. They will be evaluated on this assignment with a rubric. Differentiation on this assignment will occur in multiple ways. ELLs will use Google Translate to help throughout the process when teacher intervention is not enough. Newcomers will be given a scaffolded handout to help guide them through the process as well as sentence frames to help them with the script that they will read for their slide recording. Students will be given choice as to which topic they pick, and how they set up their slide. Students will collaborate through this process and cultural preferences of pairs will be encouraged even though each student is responsible for his/her own slide.

Resources (How does technology support student learning? What digital tools, and resources--online student tools, research sites, student handouts, tools, tutorials, templates, assessment rubrics, etc--help elucidate or explain the content or allow students to interact with the content? What previous technology skills should students have to complete this project?)

Desmos ? I love using this resource. Desmos has an exponentials bundle, which helps students gradually move through discovery activities. I chose to complete many of these assignments during the course of this section to help enrich the content and to help my students use their critical thinking and problem solving skills. These activities really help students get a deeper understanding of the concepts as they are asked to complete tasks that have a higher depth of knowledge (DOK) level. In many of the tasks, students are able to experiment/manipulate graphs and equations that deepens their level of understanding on how different elements of an equation can affect its graph. Students need no prior knowledge before using Desmos. This Web 2.0 tool is very user friendly and walks students and teachers through tutorials when needed.

Socrative ? The exit ticket of this resource was used to help drive instruction. Students use a "room number" to login using their learning their device (phone/tablet/laptop) and answer 3 questions: How well did you understand today's material? What did you learn today? And answer the teacher's question. I post a question on the board for them to respond to for the third question. This gives me immediate feedback on the lesson and what needs to be addressed the following day.

PowerPoint/Office Mix ? Each student was responsible for his or her slide. The use of screen recordings using Office Mix increased student engagement. Students knew that the final product would be shared and viewed by all Algebra 1 students at our school and shared online with the world. This made them take ownership of their slide and gave them the incentive to do their best. Using PowerPoint Online through Office365 I could see how each student was progressing in real time. They could also look at each other's slides and collaborate with each other to improve the overall presentation. I set up each slide with the title and completed the first slide as an exemplar for students. They were also given a rubric on how they would be graded on this assignment. This really helped them understand the expectations. Completing this assignment really helped the ELLs develop their CALP and get a deeper understanding of their chosen topic. To complete this task, it would be beneficial if students have knowledge of PowerPoint. Students who had no prior knowledge of PowerPoint were encouraged to work in collaborative cultural pairs to help each student learn about the different features. I worked with each student individually when they made their screen recording. Newcomer ELLs as well as ELL with low WIDA scores were given sentence frames to help them with their script for the screen recording.

Many of my ELLs are also low SES. Many of them do not always have consistent/regular access to internet at home. For this reason, all Desmos activities and the Office Mix Presentation were completed in class to ensure digital equity for all students.

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Google Translate ? This resource was used frequently to help ELLs understand assignment directions. All ELLs had prior knowledge of how to use this tool. It was extremely helpful when completing the Office Mix presentation. Students also utilized this tool when working on the Desmos activities.

Graphing Calculator ? None of my students had used a graphing calculator for anything other than basic computations. I went through and showed students the basic key strokes and settings for the first half of class the first time we used the graphing calculator to graph exponential functions. This was necessary for students to know how to input a function into a graphing calculator and how to access its table of values. Students without access to graphing calculators at home were shown how to access free apps and online graphing calculators on their learning devices.

Khan Academy and Problem Attic ? These resources were used to help remediate, reteach, and review. Students who did not proficiently master the content were assigned a module in our learning management system, Canvas. In this module, students watched Khan Academy videos on the concepts they were still struggling to master. They then took a skills check (practice test) to see how they were progressing with these skills. The skills check was created using Problem Attic. Canvas automatically grades this assignment to give the student immediate feedback on their progress. As the teacher, I am able to input comments for each answer they give to help guide their learning. These resources together really help students take ownership of their own learning. Students need to know how to access the LMS to utilize this resource.

SMART Notebook/Guided Notes/Word Cloud ? Students were given guided notes to complete when direct instruction was given. I displayed the guided notes on the SMART Board with SMART Notebook. Each day a Word Cloud was displayed on the SMART Board as students entered the room as an activating strategy. We began each lesson discussing the words that the students knew and which ones they were going to learn about that day. The SMART Notes were converted to PDF files and uploaded to the LMS. This is incredibly helpful for ELLs and students with disabilities. They are able to go back and review the teacher copy of the notes at all times on their learning devices (phone/tablet/etc.) at school and at home. Students need to know how to access the LMS to be able to access this resource.

Instructional Plan Preparation (What student needs, interests, and prior learning provide a foundation for this lesson? How can you find out if students have this foundation? What difficulties might students have?)

ELLs need to practice speaking in English using academic language. This is a part of the ELL testing process, which is administered in the spring. Completing the Office Mix presentation gave ELLs an opportunity to practice their speaking skills to help them grow in this area and move towards proficiency.

Students are always interested when you have a conversation about money. Many of the real world applications that we explored used students' prior knowledge of money. We were able to have conversations about savings accounts, interest rates, car depreciation, credit cards, student loans, and population. These conversations happened around students' prior knowledge of these topics and their interests in them.

To be successful with graphing exponentials, it is important that students know the fundamentals of graphing ordered pairs on a coordinate plane, domain and range, functions, graphing lines, end behavior, and intercepts. These concepts were taught in previous units this school year were assessed with both formative and summative assessments. Students who did not meet proficiency with these standards were given remediation and these skills have been continually reviewed through the use of warm ups.

In years past, students have struggled with graphing exponentials when adding in transformations. This year I changed the way I delivered instruction by including the discovery lessons and using the Desmos activities. Despite remediation and review, difficulties may still include the concepts of domain, range, and end behavior.

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Management Describe the classroom management strategies will you use to manage your students and the use of digital tools and resources. How and where will your students work? (Small groups, whole group, individuals, classroom, lab, etc.) What strategies will you use to achieve equitable access to the Internet while completing this lesson? Describe what technical issues might arise during the Internet lesson and explain how you will resolve or trouble-shoot them? Please note: Trouble-shooting should occur prior to implementing the lesson as well as throughout the process. Be sure to indicate how you prepared for problems and work through the issues that occurred as you implemented and even after the lesson was completed.

In this section, students will spend a lot of time working in collaborative pairs/groups of 3. They will work together during the discovery activities and Office Mix presentation in the classroom. During this time, I will walk around, work with pairs/groups, and redirect/reteach as needed. Direct instruction will be delivered to the class as a whole group in the classroom. I have a laptop cart in my classroom for student use, which helps to ensure digital equity. As stated previously, all Desmos and Office Mix components will be completed in class to guarantee equitable access.

When students use Desmos or PowerPoint, I will be able to see what they are doing on their screens on my computer screen. This will allow me to help students who are "stuck" or to check on students that are not working at the class pace. I will also be able to manage students by frequently circulating the room and checking in on each student throughout the period.

Some technical issues that may arise could include a student not knowing their username and password into the school server. To solve this problem, I have printed out the directions on how a teacher can find a student's username and reset their password to get them access. Students may not receive the invite to the shared PowerPoint. I will share the PowerPoint to each students' Office365 account. If there is still a glitch, I will display a QR code of the link on my SMART Board to get them access. The class set of graphing calculators may be on different settings, which would cause their graphs and tables to be different. To fix this problem, I will show students how to reset the calculator as well as how to adjust a calculator's window, zoom, and table set up.

I had to reset one password during this lesson but I was able to easily follow the instructions to do so. Since the class set of graphing calculators is shared with an Algebra 2 class, all of the calculators were set to different settings as expected. I showed students how to reset the calculators and how to adjust their settings. They were able to pick up these directions very quickly. One issue that occurred that I did not plan for was the lack of math type in PowerPoint Online. I was able to overcome this issue by typing that the students needed on my computer and use a snipping tool to paste it into their slide upon their request. Students also took advantage of taking pictures of their work and posting that to their slides as well.

Instructional Strategies and Learning Activities ? Describe the research-based instructional strategies you will use with this lesson. How will your learning environment support these activities? What is your role? What are the students' roles in the lesson? How can you ensure higher order thinking at the analysis, evaluation, or creativity levels of Bloom's Taxonomy? How can the technology support your teaching? What authentic, relevant, and meaningful learning activities and tasks will your students complete? How will they build knowledge and skills? How will students use digital tools and resources to communicate and collaborate with each other and others? How will you facilitate the collaboration?

I will use activating strategies such as warm ups, the word cloud, and word wall. Each day we will discuss the words in the word cloud the ones that students have learned and the ones that they will learn that day. I also have a word wall on my white board with large cards with the vocabulary word and picture on one side and the definition on the back. I refer to the word wall during instruction and students will frequently go to the word wall and look at the definitions during Support or while students are working in collaborative pairs/independently. The warm ups will help students review and active prior knowledge needed for the lesson.

Students will spend a lot of time working in collaborative pairs (or groups of 3). This is important when students are working on student-centered discovery activities. They are able to use their academic vocabulary and experiment with possibilities while working in a low-risk environment.

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During times of whole group direct instruction, I will use the "Think-Pair-Share" strategy when looking into a new concept. I will also have students complete a "Try This" problem on their own and then have them check their answer with their neighbor. If they have different answers they need to figure out which answer is correct and why. If they do not have an answer or do not complete the problem, they need to ask their neighbor for help. When students are working on this, I walk around the room and help pairs as needed. I give students the opportunity for productive struggle to help them work together to come to the conclusion on their own. This helps them take ownership of their own learning.

I will frequently use the Socrative Exit Ticket to check for student understanding after each lesson. I will use the data collected from these exit tickets to drive my instruction for the next day. Through the use of formal and informal formative assessments throughout this section, I will be able to provide quicker feedback to students using the technological resources. This will help students gage their understanding of the material. During direct instruction, guided notes will be used which helps ELLs and SWDs. Students that have a strong understanding of the topic are also able to move ahead of the class and complete the notes at their own pace.

When homework is assigned, students have a mandatory challenge question. This question has a higher DOK level than the rest of the homework, as it usually requires students to extend their thinking. This helps push all students to grow and improve their critically thinking and problem solving skills.

Students will engage in student-centered discovery based activities in collaborative pairs in class when they use Desmos and when creating the Office Mix. As the teacher, I will interact which each pair during these times. I will allow them to experience productive struggle and work together to draw their own conclusions. Students will also receive direct instruction as a whole group, during this time I will lead the class and students will complete the guided notes, be an active learner and participant in class discussions and work with a neighbor when "Think-PairShare" and "Try This" problems are completed.

Students will engage in higher order thinking skills throughout this entire process. They will analyze and evaluate when working through the discovery and Desmos activities and they will create when completing the Office Mix presentation. As previously stated, the Desmos activities are rich in higher order thinking skills and help promote an active learning environment. Using Socrative as an exit ticket will give me immediate feedback on the lesson and product data that can drive my future instruction. Students will work through real world examples featuring compound interest. They will create an Office Mix Presentation that will be shared with all Algebra 1 students at our school, as well as on the Canvas Commons, and my twitter feed.

Differentiation (How will you differentiate content and process to accommodate various learning styles and abilities? How will you help students learn independently and with others? How will you provide extensions and opportunities for enrichment? What assistive technologies will you need to provide?)

As stated previously, differentiation will occur during all aspects of this section. PDFs of the guided notes are posted on my Canvas page to help ELLs and SWDs. When presenting the material, I use a different color to represent each element. For example, I use red when discussing the transformations from a coefficient, I use green for horizontal translations, purple for vertical translation and asymptote (both are from the value), I use orange for domain and blue for range, etc. This helps visual learners keep track of all of the different characteristics that come into play.

ELLs will be given a modified version of the test and be given the use of bilingual dictionaries, word wall, and word cloud. ELLs are able to use their learning devices during class for translation purposes. Some ELLs are given modified homework assignments based on ability and need. Through the use of informal formative assessments, I am able to see where individual students have gaps, meet them where they are, and meet their diverse needs. Based on their WIDA levels, ELLs will be given sentence frames to help them with the script for their screen recording. The LMS Canvas, helps students take ownership of their own learning by allowing them to review, remediate, and move ahead as they need/are able to. During this time, I will be able to work with students individually, in small groups, and as a whole. Students will be provided enrichment activities on Canvas ? I will include the extension Desmos activities listed above. Students will also have enrichment opportunities by completing the in class Desmos activities and mandatory challenge questions on their homework. Google Translate, bilingual dictionaries, and laptops are assistive technologies that will be utilized by students.

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Reflection (Will there be a closing event? Will students be asked to reflect upon their work? Will students be asked to provide feedback on the assignment itself? What will be your process for answering the following questions?

? Did students find the lesson meaningful and worth completing? ? In what ways was this lesson effective? ? What went well and why? ? What did not go well and why? ? How would you teach this lesson differently?)

The Office Mix presentation is the closing event. Students will be need to reflect on what they have learned to complete their slide. When this assignment is over, we will discuss how they liked the assignment and if they found it meaningful. I will ask them if it is something that they would like to do for future units. Students will reflect after lesson when they answer the questions on the Socrative exit ticket. This will provide me with instant feedback on if the lesson/strategies are effective and help me improve my instruction for the next day. The Desmos activities will also allow me to see what students understand and what they are struggle to master. It will give me the opportunity to notice any gaps my students may have and check in with those students. Through the use of multiple formative assessments I will have the data I need to see what strategies are successful and which ones are not. It will also allow me to properly instruct my students to meet their diverse needs to prepare them for the summative assessment, final exam, and GA Milestone EOC Algebra 1 Assessment.

Closure: Anything else you would like to reflect upon regarding lessons learned and/or your experience with implementing this lesson. What advice would you give others if they were to implement the lesson? Please provide a quality reflection on your experience with this lesson and its implementation. In the future, I would like to be able to have more time to implement this lesson. When completing the Office Mix with ELLs I would give sentences frames for all ELLs as well as have them complete a paper template before using technology. This will truly help them to see what they have mastered before asking Google for help. I would also have the slide set up for them (type of layout) to help with overall appearance of the presentation. It would be helpful if PowerPoint Online allowed math type and the Office Mix add ins. I hope that in future versions, these will be included. I found that student have a stronger understanding of the material this year than in previous years. They performed better on the section test (quiz) than previous years as well. I hope to complete a similar lesson on our quadratics unit next semester.

I knew that I really wanted to revamp this section when teaching it this year. In previous years, many students struggled with these concepts because of the way it was taught. By using discovery activities and ensuring the use of higher order thinking skills, student were able to master graphing exponentials functions on a much deeper level. The Web 2.0 tools used enhanced the experience and helped with student engagement, enthusiasm, and achievement. Through this process, my ELLs not only gained important mathematical knowledge and academic vocabulary but they were also able to practice creating voice recordings ? something that they will do on in the spring during ELL testing. The speaking aspect of the test is something that our students really struggle with. I was excited to create a meaningful activity that will help prepare them for that experience.

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