UDL Lesson Plan Template Instructor: Josh Karr Learning Domain: Algebra II/Geometry Grade: 10 th Lesson Objective/s: Students will learn to apply the concepts of transformations to an algebraic context (graphing parabolas). Assessment/s: Discovering Transformations Activity, Station Work, Pre/Post Test State Standards Correlation: M.2HS.QFM.4, M.2HS.QFM.8 UDL Applications Key: Representation Engagement Expression Pre-planning Activities : Create packet and questions for Discovering Transformations Activity ; Graphing Calculators, Coloring Utensils Graphic Organizer for rules; paper for foldables; create pre/post test; For Station 1 will need: rope, life size coordinate plane, questions, and answers so they can check themselves; For Station 2 will need: 3 graphing calculators, CBR Motion Detectors, Ball Bounce activity (questions and directions), 3 balls; For Station 3 will need: multiple tables, word descriptions, and graphs that will have students write the equation for each based on the transformations. Lesson Element Lesson Setup & Lesson Opening Lesson Body Procedures *Lesson will begin on Friday; Stations will begin on the following Wednesday* 1. To get students excited about the lesson, I m going to introduce them to mathematics, in the form of quadratic equations, in the real world. They have already experienced some quadratics that take place in the real world through previous investigations, so we hope to build upon them. In this next section of study we are going to continue to focus on quadratics, but now we will be emphasizing the equation of the quadratic. Who can tell me what the explicit equation for the quadratic looks like? We will also getting a look into where quadratics can be in the real world. Who can name some of the situations that we have already seen? Can you think of any other places that you ve seen quadratics? 2. I want to make the goals of this lesson explicit, so I want to begin by briefly introducing the topic. This is just to give students an idea of what we will be studying. Next, I want to tell them my goals for them as a collective class, which are: 1. To find and explore multiple examples of quadratics in the real world, 2. Become fluent with the new technology and methods that we will be using, 3. To find how they learn mathematics the best, and 4. Bridge the gap between Algebra and Geometry through transformations. 3. Now I want to ask students what their goals are for themselves. We will take 5 minutes to come up with ideas and discuss them. Teacher Input We will first take a pre-test. This will enable us to see what we know, and at the end it will allow us to see how much you ve grown. Time What is the teacher doing? 10 mins Talking Facilitating What are the students doing? Listening Answering Questions 10 mins Circulating Answering test questions Materials Smart Board to jot notes Pre-Test
Students will take the pre-test. After the pre-test, I will hand students the Discovering Transformations Activity. Two volunteers will help me by distributing a calculator and three coloring utensils to each student. Through this activity, students will a) learn to graph quadratics using technology and b) develop rules or patterns that are happening within the equations. I will have to guide them through the first couple of graphs to ensure that there are no questions and that all students understand how to use the calculators. Through this investigation, you are going to learn to graph using the calculators and you are to look for patterns within the graphs as you work through the activity. To get you started I am going to demonstrate the first couple of graphs. I d like you to read the first prompt to yourself and identify what it is that we are to do. Who can tell me what it is that we need to do? Good. We need to graph f(x)=x^2. Does anybody know the first step to do this? In order to type in functions we first push the y= button which is in the top left. Once you have this pushed, type x^2. Now, in order to graph it in a nice window, I usually start by pressing ZOOM and then choose option 6. This is ZSTANDARD. What this does is sets the x and y axes from [-10,10] which gives you a nice picture of the origin. Once you press this, your equation will be graphed. Has everyone been able to reach this step? What do we need to do next? Right, we need 5 exact points for our hand graph. In order to get exact points we push TRACE. This brings up a cursor that we can move along our graph and in the bottom of the screen it gives us the x and y values for where our cursor is. Try that out. Are you able to get exact points? No, when you move this cursor around it gives you crazy decimal points which are not realistic to graph. In order to get nice values, we need to type in x values and the calculator will tell us the corresponding y values. Can anyone think of 5 reliable x values that we will be able to type in? That s right! Old Reliable will work for this one. We can type in the x values from -2 to 2 and find this y values. We can then put these on our graph. The last thing to do is the domain and range. How far left and right will this graph go? How far down and up? Your task for the remainder of today and tomorrow is to complete this activity. Should you get stuck and have a question, ask your neighbors first. If you are still stuck, then ask me. 15 mins Demonstrati ng Replicating Directions; Answering and asking questions Graphing Calculators; Discoverin g Transformat ions Activity ; Coloring Utensils; Overhead Calculator Students will work to complete the activity. I will circulate to prompt students. After the task has been completed, we will summarize our findings. Students will have 3 options on how to organize this information. They can take regular notes. They can make a foldable. They also may use a graphic organizer that I have made. 50 mins Circulating Independent Practice
We are now going to go over the patterns that we have found in the graphs based on the given equations. To do this, you have three options for your notes: typical notes, a foldable you will need three pieces of paper for this one, or a graphic organizer. Whichever you would like, you may get the materials now. There are 4 basic types of transformations that you have studied before (6 th /7 th grade). Can anybody name one? (Translation, Rotation, Reflection, and Dilation). Now, did we see all of these in our graphing activity? That s right. We did not see a rotation. Why do you think that is? What happens to a parabola if it were to be rotated? That s correct. If we were to rotate a parabola, it would no longer be a function. Through this summary, we will discuss which part of the equation translates/reflects/and dilates. *Writing on SmartBoard* If we were given an equation that look like this, f(x)=(x-h)^2, what happened to our graph? That s right. If we had -h it moved right h units and if it was +h it moved left h units. Let s do an example. What would happen to our parent function if we were given the equation (x-4)^2? Yes, it would move right 4 units. Let s graph that in your notes. *Writing on SmartBoard* If we were given an equation that look like this, f(x)=ax^2, what happened to our graph? That s right. a makes our graph skinnier or wider. We will call this stretching or compressing. Now, which values does it effect, the x s or y s. At first we may think it is the x s, but when we graphed them in our activity, were we still able to use Old Reliable? Yes, so did our x values change? No, then it had to of been our y values. When you multiply by this a, you are stretching (numbers larger than 1) your graph vertically or compressing (numbers between 0 and 1) your graph vertically. Let s do an example. What would happen to our parent function if we were given the equation 3x^2? Yes, it would make the graph 3 times as tall. Let s graph that in your notes. *Writing on SmartBoard* If we were given an equation that look like this, f(x)=-x^2, what happened to our graph? That s right. If we had a negative in front of our equation, if flips the graph over the x axis. Let s do an example. What would happen to our parent function if we were given the equation (x+3)^2? Yes, it would move left 3 units and also flip it. Let s graph that in your notes. *Writing on SmartBoard* If we were given an equation that look like this, f(x)=(x^2)+k, what happened to our graph? That s right. If we had +k it moved up k units. If we had -k it moved down k units. Let s do an example. What would happen to our parent function if we were given the equation (x^2)-6? Yes, it would move down 6 units. Let s graph that in your notes. So we have 4 different moves that we can enact on our parent function. If we put all of these together into one Mega equation we get an equation that is called vertex form. f(x)=a(x-h)^2+k. Now it looks scary, but what we are looking at are the values of a, h, and k. What does a do to your graph? How about h? And k? Based upon these three values, you transform your parent function accordingly. Lastly, we have a few simple definitions that you probably already know. We can draw a 30 mins Demonstrati ng; Facilitating Note Taking; Listening; Answering Questions Graphic Organizer; Construction Paper
picture and write a few words for each. The first one is vertex. In terms of our focus, which is quadratics, what do you think vertex means? The vertex is the point on a parabola that marks the middle. Let s draw a picture and/or write some words that describe a vertex. Next is axis of symmetry. What do you think this is? This axis of symmetry is the line of symmetry. Where will the axis of symmetry be? *Someone will probably say Through the vertex *. Will the axis of symmetry always go through the vertex? Yes, it will. Think of what these two things mean. The vertex is a point that marks the middle and since the parabola is symmetric, won t the axis of symmetry always be in the middle? Lastly we have maximum and minimum. What do you think this means? If the parabola opens up, does it have a maximum or minimum? That s right. It has a minimum. That means a parabola that opens down will have a maximum. Guided Practice: I will then explain to students their task for the next three days. I will also give them their group assignments. Beginning tomorrow you will work through three stations. The first station will have you use the CBR Motion detector in order to experiment with falling objects. You will use the graphing calculators to help you find the vertex form. You will then answer questions about what you re a, h, and k mean in the real world. There are 3 CBR Motion Detectors so you can split up into smaller groups. In the second station, you will use yourself as points on a parabola in order to create Person-abolas. You will be given multiple equations. You will have to identify the a, h, and k. This will help you identify the transformations needed to be done on the parent function. You will move yourselves to the correct points. Check your points using a graphing calculator. You will then take a picture of your Person-abola using a Galaxy Tablet. You will save your picture and using the app Skitch you will write your corresponding equation on the picture. You will do this for as many equations as you can during the period. In the final station you will be given graphs, tables, and word descriptions of equations. You and your group members will have to analyze the given representation, identify the correct value of a, h, and k, and then write the equation. 10 mins Giving Directions Listening; Taking Notes on Group Assignment Prezi with Details and Group Assignments Ask students work on the stations, I will circulate to prompt, ask questions, and answer questions. Before they ask me a question though, they must first speak with their group members. 3 Days Circulating Individual Station Work Directions for each station;
Extended Practice Lesson Closing Over the weekend students will complete a review of the skills they practiced in the station. This will be comprised of six questions. The first two will have students identify the a, h, and k of given equations and describe the transformations. The next two will give students equations and ask them to graph them without technology. The final two questions will give them a graph and a table and ask them to come up with an equation. This will allow me to assess their individual understandings. To finalize the lesson we will discuss the perks of having a quadratic equation in vertex form. What is good about vertex form? What is not so convenient? I also want to touch on what we have learned and I will also address any questions and misconceptions that I saw in the extended practice. 15-20 mins Facilitating Homework Discussion; Listening Calculators and CBR; balls; Handout for each station; rope; life size coordinate plane; extra graphing calculators 6 Problems Smart Board Students will then take the post test. Circulating Post Test
Possible Learner Barriers: WHAT CHALLENGES MIGHT THE STUDENTS FACE Possible Solutions WHAT ACCOMMODATIONS OR ADAPTATIONS ARE YOU GOING TO CREATE SO THE CHILD CAN BE SUCCESSFUL? Lack of Prior Knowledge Getting all students motivated to work in stations Struggles using CBR Completing Homework Group students appropriately; Try and put students together that will work well and help each other out. Circulate as much as possible; Prompt students; Praise those doing well; Hand out Karr Cash as rewards Make sure that directions are complete and as thorough as possible; Make myself available for quesitons Give assignment early that way they can complete it as they go; Reward for those that complete the assignment. Representation Engagement Possible UDL Applications for Extension Giving options for note taking; Algebraic / Word / and Graphical representation of rules for transformations; Pictures and words for definitions; Using technology to aid graphing Engaging with hands on activity; Technology (calculators and Galaxy Tablet) Expression Three separate stations with very different tasks in order to express understanding
Level III: A few students will Be able to do Level II. They will also be fluent in converting tables and word descriptions into vertex form. Level II: Some students will Be able to do Level I. They will also be fluent in converting graphs into equations. They will be able to identify a, h, and k from a given graph. Level I: All students will Be able to identify a, h, and k in vertex form of a quadratic. They will be able to list the transformations for the given values and graph the parabola. Also, they will find more ways that mathematics is found in the real world.