Authentic Assessment: Graphing Functions

As "21st Century Skills" has entered the education sphere, we have been exploring ways to make students content creators. Such opportunities give students the chance to teach their peers and a digital record gives them content which to use in their portfolios.

The following is a project based authentic assessment which takes place of a traditional assessment but does measure and include all learning benchmarks:

1. Which best represents the graph of y = 2x − 5? Standard 3.3
2. Students solve simple linear equations and inequalities over the rational numbers Standard 4.2
3. Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph. Standard 3.3
4. Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the ratio of the quantities. Standard 3.4 
5. Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. Standard 4.1
6. Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. Standard 3.1 
7. Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph. Standard 3.3

 What I did was turn the solving of a function into the final assessment as I felt that the project targeted them well, and I could debrief some of the minor points of slope afterwards. (Some project only hit a minor swath of standards so this is why I still favor traditional tests in some regards)

In this case though, students recorded themselves using the document camera while solving a function. The project rubric was at their side for reference which included some target vocabulary and some of the things I wanted them to do while working with functions. The document was in a quiet section of the room where students could "rotate through" over a period of two weeks. Here is an example of a student recording:



After the recording, I met with the student to discuss how well they met the objectives, and if they wanted to, could resubmit their work. The video was great content for their digital portfolios which they worked on at the end of the year.

Graphing Linear Functions Rubric





I'm tinkering with the rubric a bit before we start this year's projects, but the students said that they quite liked the experience. I don't always use projects as summative assessment, but through good design principles, an authentic summative assessment can bring applications to life.