Personal Learning Path #2

Background

I am working from the New York State Teacher Certification Examinations (NYSTCE) standards, Field 004: Mathematics. This week, we will be discussing a topic from Competency 0002 - Algebra. Within this Competency, I have chosen the following performance indicator: "solves systems of linear and quadratic equations using a variety of methods." More specifically, I will be focusing on the discriminant of the quadratic formula.

Here are the NY State Common Core Learning Standards for Mathematics which align with my selected topic:

My goal is to create an engaging activity for students to practice working with quadratic equations. More specifically, the activity will require students to work with the discriminant of the quadratic formula.

It will be assumed that students already understand how to use the quadratic formula as well as how to calculate the discriminant of a quadratic equation. For reference, the discriminant is highlighted in orange below.

For reference, when the discriminant is greater than zero, there will be two real roots of the quadratic equation. When the discriminant is equal to zero, there will be exactly one real root of the quadratic equation. When the discriminant is less than zero, there will be zero real roots (and two imaginary roots) of the quadratic equation.

The Activity

This activity has two components: (1) A worksheet filled with fifteen quadratic equations and (2) a coloring sheet which corresponds to the problems. I have created the worksheet myself, though my quadratic equations were retrieved from the sources listed at the end of this post. I numbered the coloring sheet myself, but the original drawing was likewise retrieved from a source listed at the end of this post. Here is the worksheet:

Students will first place the quadratic equations in standard form and then use the discriminant to determine whether each one contains 0, 1, or 2 real roots. Their answer will correspond to a color which they will use to fill in the corresponding section of the coloring sheet. Here is the coloring sheet:

In theory, all students should obtain a turtle with the same coloring. Teachers can offer students any colored utensils (though I recommend colored pencils) so long as they have the colors used in the activity: yellow, orange, red, green, light green, blue, light blue, purple, pink, brown. These colors can be found in most colored pencil sets. Here is a solution key:

Reflection

The goal of this post was to provide educators (and myself) with an engaging activity for students to practice working with the discriminant of quadratic equations. I believe the activity above is simple and easy to implement for teachers. The activity has a number of potential modifications. For one, teachers can choose to create their own worksheets using other quadratic equations to suit their purposes. Beyond that, teachers may even use this structure for other math activities. One could imagine this template being used for other sorts of problems students may encounter; this activity has implications far beyond the discriminants of quadratic equations. Another area where teachers can improvise is the chosen image. I have chosen this turtle, because I found the image to be adorable, but teachers may choose images that are more simple or complex. Again, the central idea here is that this activity can be modified in many ways. One idea for differentiation is that teachers could create two or three coloring sheets of varying difficulty. The equations could remain the same, though some worksheets would have extra equations. This way, students could choose to work on a worksheet with only 5-10 questions, while more advanced students could choose to work on a worksheet with 20+ problems. The options for modifications to this activity are endless.

References

Quadratic equations have been retrieved from the following links:

• https://alissakitchens.weebly.com/uploads/5/7/5/2/57524903/discriminant-worksheet.pdf
• https://www.humbleisd.net/cms/lib/TX01001414/Centricity/Domain/3513/Discriminant%20Worksheet.pdf

The image of the turtle was retrieved from the following link:

• https://www.coloring-pages-kids.com/coloring-pages/animal-coloring-pages/turtles-coloring-pages/turtles-coloring-pages-images/turtle-coloring-page-04.gif