My goal for this lesson is to arm my students with additional resources when they present information to their peers. Through these presentations I want the students to be able to showcase their analysis based on the graph I have assigned them. By making the graphical analysis, my students are analyzing and interpreting data (SP4) and through plotting the data given, making a statement about the written relationship between variables, and stating the mathematical model from the graph, the students are demonstrating a use of mathematics and computational thinking (SP5). Finally, through their whiteboard presentations the students are communicating important scientific information (SP8).
To begin class, students take out their work for the Graphing Practice Worksheet from the previous day and their Chromebooks. They have finished the graphing practice worksheet for homework the night before in their notebooks. While doing their homework they used Plolty and their summary graphing page to help them. Then I go through how to make a whiteboard online using Google Drawings.
I have students create a digital copy of their whiteboards in part because of the requirement to use Chromebooks in the classroom in our district. I also like to use these digital whiteboards because it gives students a different way to present their information in addition to presenting in front of the class, it helps to show all of the explanations of their work in written form. Whiteboarding is very important in my classroom because it helps the students to talk out how they got to their answers and do more explaining and teaching to help them learn better. I also find that many of students' misconceptions come out in the whiteboard presentations when they are talking about the problems. By presenting it helps me to point out misconceptions and address concepts that I may have not encountered otherwise in class.
I tell them to make a Google Drawing Whiteboard for the problems on this worksheet they must include a properly labeled graph and the properly substituted mathematical model that goes with it. I go through the process of inserting both the graph and the mathematical model for the first problem that I present on the front projector screen. To insert the graph into the Drawing, they must make their Plotly graph first. For instructions on creating graph, please refer to the instructions here. Then I ask them take a screen shot of their graph and paste it into the Drawing. To insert the mathematical model into the Drawing, they must insert a text box below and type in their equation. I tell students to remember to replace the x and y variables with the variable names and to include appropriate units to the numbers.
I assign students the problems based on the numbers of their tables (#1-7). Once students know their problem number, I allow them to have time as a group to complete their Google Drawing Whiteboard and prepare to present in front of the class. I give them about 15 minutes to prepare their whiteboards and figure out what each member will be presenting. I do this so that they have time to prepare what they need to present so they are experts on their problem when they are presenting.
Each group presents their problem to the class. I assign problems to each group for this whiteboard session. They come up to the front projector screen and project their Google Drawing. The goal of the whiteboard session is to help students to verbally express the process they used to complete the problem and show how much they understand the problem they were assigned. During their presentation, I expect them to explain what their graph and mathematical model mean and how they got to that answer. When they are done presenting, the floor is opened up for questions from the teacher and the students. When they have answered all of the questions, we move onto the next group.
In order to make sure that students understand the expectations of how to present and what they need to include in their presentations, I give a sample presentation using problem #8. When I present the problem, I talk about the graph and how I plotted the points and why I chose not to use a trendline. Then I talk about how the shape of the graph led me to identify what equation to use to create the mathematical model. I discuss how I replace x and y with the variable names. Since it is not a line I talk about how I don't answer the slope and y-intercept questions because we only look at these when it is a line. Finally, I talk about the written relationship and how I determined the correct relationship based on the shape. These student examples show a linear graph (Google Whiteboard Student Example #2) and a non-linear graph (Google Whiteboard Student Example).
While other groups present, I expect the students in the audience to be looking over their work to identify similarities and differences between their own work and the group's work on the screen. After the group has finished presenting, I expect the students in the audience to be asking questions about any differences that they see. I like to run the presentations this way because it give the students presenting a chance to talk about their thought process when solving problems. This activity gives the students in the audience a chance to look at someone else's work and check to see if they agree. Finally, it helps them to be able to start asking questions if they don't agree. If students do not ask questions, I have 1-2 questions ready to ask students so they also get used to answering questions.
Once students have completed their presentations, I provide an exit slip that students should be able to complete after going through the graphing worksheet and discussing it during the whiteboard discussions. These questions are made for students to do on their own without their group. My goal for this checkpoint is to gauge where students are with the skills and targets that we used in the graphing packet to see if we need more extension before moving on to the next unit. I chose this problem because both graphs turn out linear and most of our data in the following units will be in linear form so I want to check and see what they have learned after going through the worksheet and discussing the problems in whiteboard sessions.
This Graphical Analysis Worksheet students will work on in their groups to extend their practice with graphing and analysis of graphs. It is an opportunity for students to get more practice with problems that are asking different questions that may be a bit more challenging. Any questions that they do not finish in class are homework to finish for the next day. I expect that by the end most of my students should be able to answer all of the questions. Some of these questions are questions that they have answered in the previous worksheet. The difference with these questions is the phrasing of the questions and some questions are brand new concepts. I will not be collecting this homework assignment but I will use it in a jigsaw activity in the next class for students to gain more confidence with the content.