What do those numbers mean? Graphical representation helps students "see" the story that is told by the numbers collected as data in scientific investigations. Graphs are visual models that illustrate relationships among variables, including those that are not observable but predict observable phenomena (SP2).
In this lesson, students identify independent and dependent variables (SP3) and construct graphical displays of data sets to identify linear and nonlinear relationships (SP4).
In order to ENGAGE students in this lesson, students are invited to "get in" the graph:
This experience is fun, but also provides a view into what students already know. While this group modeling of coordinate graphing does not replace an individual pretest, an engaging prompt to start students thinking about graphing is:
What did I (the teacher) learn about what you (the students) know about line graphing?
In this instance, I learned that students generally understand where the title of a graph goes, where labels and units are placed and how to plot simple data points. From here, the progression of the lesson can be tailored more effectively for individual students.
The EXPLORE stage of the lesson is to get students involved in the topic so that they start to build their own understanding. To help students explore coordinate graphing, a pretest to gauge current graphing skills is prudent during a skills-based lesson like this one: Graphing Pretest. If students are proficient graphical artists, they move on to the EXTEND stage of this lesson. If students are not proficient, they continue on in further exploration of graphing using the Graphing Student Handout.
Using whole group or small group instruction, students work through graphing practice. Alternately, a favorite strategy for this stage of the lesson is to encourage proficient students to act as "Master Tutors" for students who need additional practice (Mastery Learning in Science: Students as Teachers). These peer tutors use the Graphing Tutor Instructions to guide their proteges through the process.
As students complete the practice activities, a great strategy to model is using the Graphing Checklist to help students self assess their own graphs (or the graphs of their proteges). Using the checklist also helps recognize, and hopefully remember, the different components required in a coordinate graph. Other than the checklist, students check their work with an expert continuously to avoid practicing inaccurate or incomplete graphing. Upon successful completion of the practice graphing, students move on to the EVALUATE stage of the lesson.
Teacher Note: There are several sticking points with coordinate graphing. The idea of scale, positive and negative numbers on a number line, plotting data points and identifying independent and dependent variables in a controlled scientific experiment (Exploring Controlled Experiments Part 1/2 and Part 2/2) can throw serious monkey wrenches into the process. A pretest can help identify some of these challenges. Additionally, being familiar with your students' math curriculum can help predict challenges. If students need additional practice, this document offers additional opportunity: Graphing - Additional Practice.
The EXTEND stage allows students to apply new knowledge to a novel situation. The novel situation in this case is by student choice:
1) Students can extend their learning of graphing by acting as a Master Tutor - Mastery Learning in Science: Students as Teachers. Master tutors work with another student or small group of students to model, teach, guide and coach until those students are able to show proficiency with regard to coordinate graphing. This extension opportunity rests on the assumption that if you can effectively teach someone else, your own understanding is fortified by the process and most likely represents advanced understanding.
2) Students can extend their learning by completing a more advanced graph and data analysis challenge like this one: Graphing Extension - Challenge Graph. A student example can be seen here: Coordinate Graph Extension Student Work.
3) Students can complete an investigation that generates data to graph like: Dunking for Density (Part 1/2) and Dunking for Density (Part 2/2). Graphing real, messy data can be a real challenge that fits the extension criteria: Dunking for Density Investigation Student Work.
The EVALUATION stage is for both students and teachers to determine how much learning and understanding has taken place. To assess student learning, students need to complete a Graphing Check Out Quiz. This quiz requires students identify variables in an investigation and successfully graph data given in a data table like this: Coordinate Graphing Student Assessment.
If students need additional practice, they can access a resource like: Graphing - Additional Practice. This additional practice can be used for independent learning or in a small group setting to additional support. After more instruction, students can show their skills on the Graphing Check Out Quiz - Retake.