Graphing
***As a topic to be supplemented in this course, graphing in general needs to be emphasized throughout the curriculum. Students need to be able to interpret and use the data they encounter every day in the world around them. ***
It has been noted that students in Math 111 are not prepared to draw or interpret graphs. In order to enrich our text and support our instructors while increasing student understanding and competence in this area, we are implementing a list of minimum standards for the presentation of graphs in Math 60-95. Each Math 60-95 instructor, whether in class or online, must assign and assess some graphs (application problems being the most empowering) that the student must create by hand. For those instructors charged with this important task, please let us know if there is anything you need in addition to the packet material in meeting this challenge.
Included in this section are supplementary materials on graph construction, graph analysis, vocabulary terms, general concepts for depth of student understanding, student graphing expectations, and examples of acceptable graphs. We encourage you to incorporate these materials into your curriculum as you see fit. If you have any additional materials or projects that you would like to share, please feel free to do so.
Math 60, 65, 95
Graphing Fundamentals for Instructors
The following skills, terms, and concepts are appropriate for our developmental students. Please include some instruction or review of these fundamentals (in addition to the graphing material presented in the text) during these courses.
Skills to Apply
Graph Construction:
a)Determining appropriate independent and dependent axes.
b)Scaling each axis consistently while using the majority of the grid.
c)Labeling each axis with appropriate units.
d)Installing an appropriate title at the top.
e)Plotting the data points accurately.
f)Drawing a line of best fit, where appropriate.
Graph Analysis:
a)Determining the subject matter of the graph.
b)Finding the units used in the data.
c)Locating the x and y intercepts and determining what these points represent.
d)Finding slopes (if linear) and determining what the slope represents.
e)Given one data coordinate (x or y value), find its matching coordinate partner (y or x value).
f)For pairs of lines, determine the point of intersection and what this point represents.
Vocabulary Terms to Emphasize
grid / graph / x-axis / y-axisscale / title / independent / dependent
plot / units / line of best fit / intercept
slope / intersect point / Cartesian plane / coordinate plane
General Concepts for Depth of Student Understanding
1)Graphing is one of many ways to represent data.
2)The independent variable is displayed on the horizontal axis; dependent on the vertical axis.
3)The axes may be scaled independently (different units are ok).
4)The title should explain the nature of the data displayed in the graph and, when appropriate, the axes should be labeled (for word problems particularly).
5)Not all graphs are linear.
6)Data may not lend itself to a best fit linear regression, there are other functions that may model the data more accurately.
7)Not all data sets lend themselves to regression analysis.
8)(0,0) may not be the lower left corner of a graph. Read each scale carefully.
9)Any change in scale, along either axis is indicated by or
Additional Talking Points
1)The x- and y- intercepts should be named as points. Naming the point helps strengthen the connection between the intercept and 0.
Do not accept x=k as an answer to the x-intercept question since this is the equation of a vertical line (similarly for the y-intercept).
2)In the course of teaching graphing it is important to periodically pick a point from the graph (different from those used to create the picture) and show that it works in the equation.
3)Line segments should have endpoints not arrows on the ends.
Student Graphing Expectations
To Receive Full Credit, Graphs:
- Must be on Graph Paper
- Arrows on Graphed Lines and Axes
- Label Axes
- Show Scale (label tick marks or points)
-Label 3 Ordered Pairs (Initially)
OR Label Significant Points
- Show Table of Significant Points
3.2 Graphing by Tables
3.2 Graphing Application Problems
3.3 Graphing by Intercepts
3.6 Graphing using y = mx + b
4.1 Graphing Systems