INTRODUCTION

This WebQuest is designed as a review of quadratics for a pre-calculus course and can also be used to introduce important algebraic concepts behind quadratics and polynomials in general.

Have you ever thought about how interconnected basketball and math really are? Notice the graph showing how a basketball rises until it reaches its maximum height and then falls down? This is modelled by a parabola. The latter is the graph of a quadratic equation and has numerous applications in the modern world of technology. Supersonic planes are also parabolic in shape to reduce air resistance.

Do you think there is the only way to solve quadratic equations? In this WebQuest, you will see that there are several methods to do so and for you to master and learn to select the one that most efficiently solves the problem at hand. Get ready to become a PRO at Math and basketball for that matter!

TASK

Your task is to understand the most basic properties of quadratic functions and parabolas, how to solve quadratic equations, and how to model real-world problems with quadratics.

In this WebQuest, you will use a variety of resources to:

• examine the characteristics of the graph of a parabola and determine how these characteristics relate to the quadratic equation;
• investigate the various methods of solving quadratic equations, which include graphing, factoring, using the quadratic formula, and completing the square;
• discover various real-world applications, and develop some guidelines for determining the most efficient method to use to solve the problems posed in these applications.

All your findings should be recorded in your "Quadratic Padlet".

PROCESS

This WebQuest is meant to be conducted in groups but it also involves a lot of work on your own.

Before starting WebQuest, you are suggested to go and create a free account for your learning diary on Padlet. Padlet is a great tool to reflect on learning.

After completing each module, you will write in your Padlet. Share a link to your learning diary within your group after finishing each module.

Go to Padlet and create your free account now!

Section 1: Basics

After your account is created, take a look at the following articles to learn the basics about quadratic functions and parabolas including the most important term and definitions, Math dictionary with illustrations, history of the parabola, quadratis projects and quadratic functions and their graphs. You will need this information to lay the grounds for the next step to be taken in your WebQuest!:

1. Important Terms and Definitions

Math Words Dictionary

Math Is Fun - Definitions

Formal Math Dictionary

2. Illustrating Vocabulary

Mathematics Dictionary with Illustrations

3. History of the Parabola

General Timeline for Mathematics

History of the Parabola

4. Quadratics Basics Project

Graphing Quadratics Overview

Graphing Quadratics Lesson

Quadratics in the Real World

More Examples of Real World Quadratics

5. Quadratic Functions and Their Graphs

Quadratic Functions and Their Graphs

Section 2: Solutions

Investigate each method by using the websites listed down below (and others!) and create a presentation of max. 4 slides where you make a summary of one method you chose in your Drive.

You will then share it with members of your group.

Finally, together as a group, complete each part and problem in your padlet as you look at your group members‘ presentations.

1. Graphing Method

Solving Quadratics by the Graphing Method

2. Factoring Method

Solving Quadratics by the Factoring Method

3. Square Root Method

Solving Quadratics by the Square Root Method

4. Completing the Square Method

Solving Quadratics by Completing the Square

5. Quadratic Formula Method

Solving Quadratics by using the Quadratic Formula

6. Deciding on the Best Method

Which Method to Use?

7. The Discriminant and the Nature of Roots

Information on the Discriminant

*** General Guidelines for Solving Quadratic Equations

Solving Equations Quadratic in Form

8. Check your abilities

Go to Match My Parabola

Section 3: Real-World Applications

As you already know, quadratics are everywhere. The resources below will give you a detailed overview of the types of real-world problems where quadratic modelling can be applied. Watch the videos full of examples and then work with your partners to fill Section 3 of your Padlet.

Parabolas in Real Life

Real-Life Examples of Parabolas

Real-World Applications of Parabolas

Quadratics in Games

Super Mario Quadratics

CONCLUSION

Congratulations!!! You should now feel like a real quadratics master who can tackle any problem!

Evaluation of learning achievements

In this section we will not dive very deep into the underlying educational theories about evaluation and testing: there’s too much out there than we could possibly cover in this small project report.

Instead, we want to concentrate on procedures that enable both students/pupils and their teachers to establish if the learning goals of the Webquest were achieved and, if so, to what extent. We recommend teachers make use of a combined evaluation procedure, that consists of:

1. Statements by learners (after being asked to do so)
   • telling what they learned about the subject (knowledge-oriented self-evaluation): now (after going through the Webquest) I know that …
   • telling what he/she learned about herself/himself (formative evaluation, in this case, diagnostic self-evaluation): now (after going through the Webquest) I know about myself that I …
     This pair of basic statements add up to a so-called learner report, in which the pupil/student reflects on what the Webquest brought him/her in terms of acquired knowledge and new personal views and attitudes concerning the subject.

   For instance:

   • ‘I learned that in medieval times the hygiene of people was hardly a concern which helped to let epidemic diseases like the Plague cause so many casualties’ Or:
   • ‘I learned the facts and I know the earth is warming, but I cannot understand why people were so stupid to pollute the world and let it warm up so much.
   • ‘I learned from the information about diseases that this subject is more appealing to me than I would expect in advance: maybe I should consider a medical career’. Or:
     ‘The Webquests confirms what I thought already: I could not care less about the climate and global warming. In fact, I thought it was all a hoax and I still do!’

   This kind of assessment seems more subjective than it actually is: in his standard work on testing and evaluation (and much more), simply called Methodology (1974), Prof. A.D. de Groot described how consistent the student’s self-evaluations appeared to be: when asked again after 5 or 10 years, their evaluation would almost be the same. De Groot advised teachers to use the learner report as a start for joint evaluations, striving for consensus between teacher and student/pupil about the learning outcomes and their value for the learner, but also compared with the learning objectives as stated in the curriculum.

2. The learning achievements are visible in the output produced by the students: it is physical evidence: reports, answers to questions asked in the Webquest, presentations, and performance during presentations (preferably recorded). The teacher completes an evaluation grid stating clearly what the learning outcomes for the student/pupil are. The categories in the grid can be modified by the teacher to cover more precisely the content of a Webquest.

   >We advise teachers to use the grid to start a joint evaluation discussion, aiming at consensus or at least understanding between the teacher and the student/pupil about the learning outcomes: were they achieved (as planned in the curriculum and communicated before the Webquest started) and to what extent? To communicate the learning goals clearly before any learning activity starts, is a transparency requirement that is widely acknowledged in the educational community. The history of making learning objectives explicit goes back to the evaluation ‘Bible’ by Bloom, Hastings and Madaus: ‘Handbook on formative and summative evaluation of student learning’ (1971), a standard work that also served as inspiration for the earlier mentioned Prof. De Groot.

The procedure also applies when students/pupils have worked together on a Webquest. The teacher will ask questions about individual contributions: ‘What did you find? What part did you write? How did you find the illustrations? Who made  the final presentation?’

All the evidence (of learning efforts and outcomes plus joint evaluations) is preferably stored in the learning portfolio of the student, or in any other suitable storage system (folders with written or printed documents, online collection of files, etcetera ).

Changes in personal points of view and feelings are harder to value and here the consensus between teacher and student/pupil about experiences during the learning process provides essential insights.

The grid below gives an example of how the evaluation of the learning process and achievements can be shaped: what kind of reactions to the Webquest does the teacher expect and how valuable are they? Is the teacher capable to explain the value or score allocated to answers or presentations given by pupils? Does the pupil/student understand the evaluation outcomes, and does he/she agree? If an agreement (consensus is not possible, it is still the teacher who decides how to value the student’s work.

Please note that the text in the grid addresses the pupil/student directly: this is important and it is in fact a prerequisite for using such an evaluation grid: it is specifically meant to enable a discussion of learning results between teacher and student and not to communicate learning achievements of learners to others who had no direct role in the Webquest.

Evaluation Grid