The Context for My Lesson
This lesson on graphing proportional relationships is part of a unit covering lines, linear equations and simultaneous linear equations. The lesson is designed for the students I described in my post on teaching scientific notation which is linked here. The year before, in 7th grade, the students would have studied proportional relationships and unit rates in preparation for connecting them to graphing and linear equations in 8th grade. The lesson prior to the one that this lesson was created for would have included a thorough review of the concepts that were covered in 7th grade about proportional relationships. After completing this lesson, students will complete other standards that explore linear equations that are not proportional and more abstract understandings of slope and graphing.
Another important part of the foundation of this lesson is that students would have been working with Google Docs and other google products all over the course of the class, and so would be fluent with how they work and the expectations about them. A lesson that requires technology skills to complete is only feasible when students are confident with the media that the lesson is based on. The lesson teaches a math standard directly, but also helps students learn the broader 21st century skill of proficiency with technology.
The Standard(s) this Lesson Meets
The Google Slides presentation lesson is intended to teach the first part of North Carolina Public Schools’ Standard Course of Study for Mathematics (2016) standard 8.EE.5: “Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.” (p. 22). This standard breaks down into three skills:
1) Graphing proportional relationships
2) Understanding the slope of the graph of a proportional relationship is the unit rate
3) Compare proportional relationships expressed as graphs with proportional relationships expressed as an equation
The interactive online lesson focuses on the first of these three skills–graphing proportional relationships–and the collaborative aspect of the lesson results in a collection of student-generated examples of proportional relationships that will be used to teach the last two skills. Students will learn about graphing, and then research a proportional relationships to graph (such as how fast a tree grows or how much a subscription to Spotify costs each month.) This will help them make connections to the second part of the standard: understanding that the slope is also the unit rate. Working in groups, they will determine the equations for lines generated by their peers as well as interpreting the real-world meaning of the slopes of those lines. The third part of the standard–comparing proportional relationships that are expressed in different ways– would build on the skills taught in this lesson and be part of a separate lesson taught on a different day.
The Media or Technology I am Integrating
I utilized several cloud-based products offered by Google to create an interactive lesson that has collaborative practice and sharing documents embedded in it as well as other multi-media instruction and practice available on the web. The main lesson is a Google Slides presentation that actively guides students through the instruction elements of the lesson. It begins with a visual with an introductory question posed to the students and answers the question using two videos from Khan Academy that demonstrate how to graph two different proportional relationships. Then the students are directed to visit a link that takes them to the collaborative graphing assignment that I created using Google Sheets. After graphing a line as a group, the slide show presents another video from Khan academy that goes over a higher-level practice problem and more thorough explanation of the meaning of the slope of the line. The slideshow then links to a 10-question practice quiz from IXL.com that lets the students know immediately if they did not get a question right. When the students return to the slidehow, they are presented with an assignment to use the internet to find their own example of a proportional relationship. Then they are linked to a Google Doc that they can copy and edit to graph their example independently. Finally, they copy and paste their example into a collaborative document that will be used for group practice in the classroom. I blended independent and collaborative learning in this lesson in the hopes that students would benefit from seeing the work of their peers while still moving at their own pace through the lesson.
The collaborative graph, shown above, instructs students to add one or two points on the graph of a proportional relationship by calculating an x-y coordinate point to the table. As more and more points are added, the linear shape of the graph becomes clear and answers the question that was posed at the beginning, “What does the graph of a proportional relationship look like?”
The Rationale for Integrating the Media or Technology into this Lesson
This lesson integrates several layers of technology: the presentation of information in a multi-media context with videos, interactive practice problems that provide immediate feedback, and student-edited digital documents. The lesson is placed in the context of a traditional classroom with the direct support of a teacher. I integrated Google Slides, Docs, and Sheets into the lesson because technology-based learning increases student engagement and prepares them for life in the digital age. Franklin and Peng (2008) present a case study about integrating technology, specifically videos created for presentation on an iPod Touch, benefit students learning algebra in the 8th grade. They review theory and research to support their claim and summarize that “…educational theorists…advocated that classroom experiences must mirror the complexity of society in order to develop collaboration skills, gain proficiency in working with incomplete information and concepts, manage decision making, and create and share new knowledge—part of being a productive member of society.” The researchers summarize that experts in the field “called for the integration of technology into the teaching of content, as students become more proficient in using the various technologies. Use of technology to investigate problems and design solutions improved their understanding of the process and also the content.” (p. 70) These statements support the idea that integration of technology benefits the students both in the short term while they learn the math standard and in the long term as they live and learn in a digital age.
Collaboration and cooperative learning are best-practices for middle grades students, as well as an essential 21st century skill. (Framework for 21st Century Learning, para. 3) This technology integration is intended to incorporate elements of collaboration into the learning process, and to set the stage for face-to-face collaboration between students at the conclusion of the technology-based portion of instruction. Johnson and Johnson (2009) state that “few instructional practices have been more successfully implemented in the past 60 years than cooperative learning.” (p. 365) They give an overview of the established psychological theories that support the use of collaboration in the classroom, as well as the successful track record of collaboration in the classroom over the past 50 years. I designed this interactive multi-media lesson to have some collaborative elements so that students would reap the benefits of working with other student within the online lesson as well as in the face-to-face portion of the lesson.
In addition, working with cloud-based technology is an important skill for students in the 21st century. In this lesson, students are directly interacting with and editing digital expressions of math. They are using spreadsheets and editable illustrations to create the kinds of products that they will most likely have to use later in their education and in life.
The Integration of the Media or Technology Into the Lesson
The Google Slides presentation (that incorporates the use of Google Docs and Google Slides) is meant to be used at the beginning of a lesson on graphing but after the warm up. Here is how it would be integrated into the lesson:
- A warm up reviewing all the big concepts about proportional relationships that had been learned
- A brief class discussion about the warm up and what students think the graph of a proportional relationship might look like, which ties into the question asked at the beginning of the Google Slides lesson.
- Students complete the Google Slides lesson independently while the teacher circulates, including graphing a line as a class using the collaborative graphing document in Google Sheets as well as contributing an example to a collaborative
- As students finish the slide show, they are put into groups to work together to answer questions about the examples in the collaborative document. They are asked to work together to write equations for some of the examples, and to interpret the slope of the lines as unit rates for the real-world examples. For example, students should be able to look at the graph of the distance traveled by a cheetah and be able to write an equation like y=65x and express that the 65 means that the cheetah can run 65 miles per hour.
- Students who have not finished writing equations and interpreting slopes would finish independently at home for homework.
My Evaluation of the Media or Technology Integration
Cloud-based documents and spreadsheets are a powerful way for students to collaborate using technology. In a traditional classroom, students might work together in groups, have a class discussion, or work one-by-one on an example math problem on the board. Google Docs and Google Sheets used within a multi-media presentation of a lesson are a way for students to see and interact with the work of other students. Simply graphing a line together will allow a student to see how the points added by their peers collectively create the linear shape of the graph of a proportional relationship. And the students can self-correct if the point that they graphed is not in line with the points graphed by their peers. In addition, student-generated examples generated by the class create a collection of examples that are of interest to the students in the class and that they are more likely to relate to than teacher-generated questions. Middle-grades students benefit from having choices in what they are learning and with curriculum that relates to their lives. Because they are at varying developmental stages, the ability to progress through the content at their own pace, and to learn from and with peers, is a benefit to them as well.
The complex nature of this technological integration makes careful planning and clear directions imperative for the success of a lesson like this. Permissions on documents, a clear plan for formative and summative assessments, and careful monitoring of the collaborative documents to ensure safe digital spaces are all challenging elements that need to be considered carefully for the lesson to work. Another challenge is ensuring the students have the background skills and vocabulary to understand the directions for navigating and completing the online lesson. To copy and paste, edit, and move between documents and presentations in the cloud are skills that can be challenging to anyone who is not fluent with that technology. In creating collaborative documents, there is the possibility of student interference in the work of others so clear accountability structures need to be in place and clear to the students to ensure an environment that is conducive to learning for all students.
Cox, Victoria. (2016). Proportional Relationship Image.
Framework for 21st Century Learning – P21. (n.d.). Retrieved June 18, 2016, from http://www.p21.org/our-work/p21-framework
Franklin, T., & Peng, L. (2008). Mobile Math: Math Educators and Students Engage in Mobile Learning. Journal Of Computing In Higher Education, 20(2), 69-80.
Johnson, D. W., & Johnson, R. T. (2009). An Educational Psychology Success Story: Social Interdependence Theory and Cooperative Learning. Educational Researcher, (3).
Khan, S. (2013, August 09). Graphing proportional relationships example 1| 8th grade | Khan Academy. Retrieved August 01, 2016, from https://youtu.be/1F7LAJEVp-U
Khan, S. (2013, August 09). Graphing proportional relationships example 2| 8th grade | Khan Academy. Retrieved August 01, 2016, from https://youtu.be/1F7LAJEVp-U
Khan, S. (2013, August 09). Graphing proportional relationships example 3| 8th grade | Khan Academy. Retrieved August 01, 2016, from https://youtu.be/1F7LAJEVp-U
Practicing Eighth grade math: ‘Graph proportional relationships’ (n.d.). Retrieved August 01, 2016, from https://www.ixl.com/math/grade-8/graph-proportional-relationships
Public Schools of North Carolina. Standard Course of Study for Mathematics. Retrieved from: http://www.ncpublicschools.org/docs/curriculum/mathematics/scos/k-12%20Standards.pdf. 22-24