A Lesson in Basic Graphing With Parabolic Curves

For the last few years I've had the privilege of being a Technician, Fabricator and Teaching Artist for the Children's Museum of Pittsburgh. One of my favorite things to do with our learners is Math Art- anything from drawing Celtic knots to paper engineering to what we're exploring today- parabolic curves.

This is intended to be covered as a single day lesson plan to teach the absolute basic fundamentals of graphing through plotting points and making connections with lines. This will teach X and Y axis, understanding coordinates, and positive and negative values on a graph. The first part of the lesson the students will learn about parabolic curves. Then they'll have to demonstrate plot points by writing out the coordinates of each line. Then students will be presented with a blank graph and a list of coordinates to draw out their own lines. If they are successful they should have a beautifully drawn a parabolic curve. This shows students how graphing works in both directions of interpreting information. To add complexity to the lesson, the next step introduces a negative value on one axis. Starting with a single axis can introduce the idea without quadrupling the complexity right away. Finally, the last lesson is a full four quadrant graph with a complex range of positive and negative values that will ultimately create a full parabolic design.

For further student collaboration the instructor can have students draw out the lines and coordinates of their own design and then copy just the coordinates onto another sheet of paper. Then just the coordinates are given to a different student to be drawn. The drawings can then be compared. This gives students a fun way to test their comprehension.

Art Teachers- if you are interested in a less-math oriented approach to parabolic curves check out my other Instructable where you can doodle or embroider similar shapes!

Supplies

There are only a few basic supplies that are needed for this project-

-graph paper

-the provided printable PDFs (pictured with the supplies)

-pencil (preferably with eraser!)

-a ruler

-colored pencils or pens if you want to get fancy (so, optional)

-patience

Now let's get started!

Step 1: Explaining the Basics and Our First Curve

In this first part of the lesson students should understand X and Y axis, how to draw out a coordinate point, how to use a ruler to connect two points to make a line and what a parabolic curve is.

A parabolic curve is a group of straight lines that, when drawn together, give the illusion that a curve has formed.

As seen in my example above, I chose to make a curve out of six lines, for a total of twelve points that need to be plotted. I wanted to start with just positive numbers to get students used to plotting points. This first exercise can be done on graph paper or on my provided PDF single quadrant WS blank. The benefit of using the worksheet is that I wrote in all the numbers to help students get used to counting.

To solidify plotting points and lines the next steps would be using PDF single quadrant WS lines, which provides a parabolic curve that the students have to write in the number coordinates, and then PDF single quadrant WS coordinates, which is the opposite- the worksheet gives the number coordinates and the students have to draw the lines to make a curve.

The PDFs in this step are the same as the ones in the supply list.

Step 2: Adding Negatives Along the Y Axis

After establishing the basics in all positive numbers, it's time to start plotting in the negative.

For this part of the lesson I've provided PDF two quadrants WS lines, which has a curve that the students need to pull the numeric coordinate points from, and two quadrants WS coordinates, which provides the points that students need to connect to draw their own curve. In these two worksheets I did not number the X axis, so students will have to count themselves, but I did number the Y axis in both the positive and negative direction to get them used to counting in both directions.

The PDFs in this step are the same as the ones in the supply list.

Step 3: All the Quadrants

By the end of this part of the lesson students should have a full understanding of the X and Y axis in both the positive and negative direction.

I've drawn out a little hint to help students remember which parts of our coordinates are positive and which are negative in each of the four quadrants. To solidify this concept use PDF four quadrants WS lines and then PDF four quadrants WS coordinates. With these I've provided the positive/negative hint pictured above, but I've not numbered either axis so students will need to count out their points.

The PDFs in this step are the same as the ones in the supply list.

Step 4: Colaboration

For a collaborative and fun way for students to test their comprehension print two copies of PDF four quadrants WS blank per student. Have each person draw a parabolic curve and map out the coordinates in the provided space. Then have the student copy just the coordinates onto the second piece of paper. Have the students trade and see if they can draw a friend's parabolic curve with the points provided.

The PDF in this step is the same as the one in the supply list.

Step 5: Advanced Curve Examples

It's easy to go crazy coming up with more advanced curves. Starting on a 45 degree line can make fun shapes or students can try adding color. The possibilities are endless!

I hope this lesson plan has provided a cool and fun way to start building a graphing framework for your students. My goal is that this will create a solid foundation that they will be able to build on in future endeavors while being playful and artistic.