Description:
This end of the unit project asks grade eight students to think of an everyday object or item they use in their lives or a real-world problem. I give them some examples:
phone and battery life
which cell phone company to go with
Creating a grocery store scenario figuring out how much you can buy with a fixed amount
As long as the math is feasible, they get complete freedom. Their task is to create a systems of linear equations that represent two possible trends for the item. For example, battery life of their cell phone versus the battery life of their computer. They then have to solve the systems of linear equations by choosing three of the four methods we learned:
table method
elimination method
substitution method
graphical method
Once they notice all three methods produce the same answer, they must explain which method they prefer and explain the advantages and disadvantages of each method, paying close attention to math vocabulary. I provide the students with many resources, but will generally not help them with any calculations. Relying on their problem solving skills is a strong component of this project. The last piece is a presentation of their work and project. Students will be asked to describe their scenario and defend their methods choice in front of the class. Showing their work, using graphs, and relating their answer back to the scenario will show their true understanding.
Questions of Inquiry:
How can we use systems of linear equations to solve real world problems?
Why is it important to understand how to solve a problem using multiple methods?
What is a big advantage of using the graphical method is a job setting?
Open Inquiry:
All students have the ability to pick their own project topic. Students will use the same methods to solve the systems of equations, however how they apply and present the information will vary from student to student. Some may use a video, oral presentation with visuals, and some may choose to simply provide a handout. However they decide to present the material will help them gain knowledge moving forward in the workforce. They learn effective presentation skills as well as problem solving skills from this project. No two students will have the same end result, which provides many learning opportunities during the presentation phase.
Standards Being Assessed:
8.EE.8: Analyze and solve pairs of simultaneous linear equations
8.EE.8a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
8.EE.8b: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
8.EE.8c: Solve real-world and mathematical problems leading to two linear equations in two variables
Rubric:
The school I was student teaching at follows proficiency based grading and uses the Exceeds (E), Meets (M), Partially Meets (P), and Does Not Meet (D) system. I decided to use a rubric with a similar structure.
Teacher Resources:
I chose my Desmos screencast-o-matic tutorial because it would be a great resource for teachers to show their students when solving the systems of equations by graphing. The resource is interactive and allows students to check their work, or provide a great presentation opportunity. This could also be a great resource for students.
I chose to provide educators with examples of how students should approach real-world problems. Students find these problems tricky as their is not an algorithm that works perfectly for every problem. By teachers researching and exploring how to effectively solve word problems they will be able to explain the process much easier.
I chose to provide educators with information on inquiry. This project I would find to be most successful with structured inquiry, but can also be successful with many methods of inquiry. Allowing educators to research which inquiry method is best for them and provide examples of the different methods, teachers can find what works best for their classroom and this project.
- Teaching Strategies
- Guided Note Sheet Example
There are many ways to teach systems of linear equations, but I find it difficult to find creative and fun ways to introduce the methods of solving systems of linear equations. This resource recommends what teachers can do to create fun activities and how supplements guide student understanding. I create a guided notes sheet with every lesson I teach and have found them to be very successful. The guided note sheet I provided above follows the book’s guided practice so students will be able to follow along easily during my lesson and when they study.
Student Reference Tools:
Khan Academy is my go-to resource for students to use to practice a concept. The link I provided brings students to a full unit of videos on the multiple methods of solving systems of equations, as well as extra practice. They can use this tool to practice and learn how to apply their answer to the problem before they work on their project.
Wolfram Alpha is a free online calculator that shows the answer in many different forms. It shows all the possible forms, e.g. graphical, numerical, etc. Students can use this resource to check their work. There is also a step-by-step solution option that is available if they decide to upgrade to pro, which has a fee.
This resource provides definitions and step-by-step solutions for solving systems of linear equations. If students forget or are unsure of what step to do next, this resource should help them work through the problem. The math vocabulary in this resource will also help them when explaining their method choices.
Student Technology Tools:
Prezi is a great presentation tool that allows students to make an interactive presentation. They will be able to upload videos, graphs, their work easily and make the presentation more engaging. Part of the assignment is to learn effective presentation skills, and learning how to use Prezi effectively will accomplish that goal. Math is generally one-dimensional, and encouraging students to use Prezi for their presentation fits the redefinition phase of the SAMR model.
Google sites is another presentation option for students. Google sites is an easy to use resource that can elevate any presentation, especially since math presentations can generally become mundane to listen to. Google sites would also fall under the redefinition phase of the SAMR model by creating a more visual presentation of student work.
Some students have anxiety about presenting in front of a live audience. Utilizing screencast-o-matic by recording and editing videos of them explaining their steps and solution will be a good option for them. Students have the option to hide the video and can narrate instead. The presentation will still be elevated and would fit under the redefinition phase in the SAMR model.
Discussion:
Provide a reflection about how you have planned for real-world, collaborative and learner-centered experience
My project encompasses real-world problems and experiences stemming from the essential questions stated above. My project involves collaboration by asking students to share their project topic with me, where we can discuss how feasible the topic is and how they plan to solve the problem. This project is also very learner-centered where I will not be offering any help after they select a topic. They will need to use their classwork, notes, and resources I provide to solve the problem on their own. They will also have to decide which presentation method is best for their project.
What barriers might you, or learners face in this experience? How might you address them?
I will be facing instances where I want to help the students through their project. It is my first instinct to help anyone I see struggling, but I have to remember this is an inquiry project and they have all the tools they need to succeed. I think many students will struggle on the presentation side of the project. Creating an organized presentation is difficult and many students are afraid of public speaking. I am hopeful that the presentation resources I have provided will address this problem and students will be able to find the perfect platform for themselves.
What are you most excited about with the plan you’ve created?
This project has me excited about many things. I am most excited for the presentations. I want to see how well the students understand the material, how well they problem solve, and how creative they are with their presentations. I am also excited to see the look of accomplishment on many of my students’ faces. My classroom is not generally inquiry centered. I generally like to guide my students throughout class addressing problems instantly. Instead, students are going to be asked to answer their questions on their own. I am excited to see how well they persevere!
EDT 520 Blog 