INTRODUCTION

Welcome to the world of rational inequalities!

This WebQuest is designed as a review of rational inequalities. However, it can also be used to introduce important algebraic concepts behind rational inequalities and the inequalities of the second degree in general.

You are going to explore the quadratic inequalities most specifically, master different methods related to them and learn to select the one that most efficiently solves the problem at hand.

TASK

Your task is to understand how to solve quadratic inequations, and how to model real-world problems with inequalities of the second degree.

In this WebQuest, you are going to research inequalities and their graphs to gain an understanding, solve graph inequalities, apply what you have learned to everyday situations and solve problems of your own.

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

PROCESS AND RECOURSES

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 create a free account for your learning diary on Padlet.

Padlet is a useful tool to improve collaboration and reflect on learning.

After completing each module, you will write in your Padlet and share the link of your learning diary within your group.

Now start your journey with Padlet!

Section 1: Basics

After your account is created, take a look at the following articles to learn the basics on quadratic inequalities, solving them, practising solving them and checking your abilities. You will need this information to lay the grounds for the next step to be taken in your WebQuest!:

Important Terms and Definitions

Math Words Dictionary

Math Is Fun - Definitions

Inequality (mathematics)

Quadratic Inequalities Basics Project

Solving Quadratic Inequalities: Concepts

Solving Quadratic Inequalities: Examples

Solving Quadratic Inequalities: More Examples

Solving quadratic Inequalities

Methods used to solve Quadratic Inequalities

Solving Quadratic Inequalities

Quadratic Inequalities_Video

Practice page

Solve quadratic inequalities

Graph solutions to quadratic inequalities

Solutions of a Quadratic Inequalities

Check your abilities

Question Database

Section 2: Real-World Applications

The resources below will give you a detailed overview of the types of real-world problems where quadratic inequations modelling can be applied. Watch the example videos and then work with the others in the group to fill Section 2 of your Padlet.

Quadratic inequalities in the Real World

Application of quadratic inequation in a real-life situation

Quadratic inequalities in Games

Quadratic Inequalities - MathsPad

Section 3: Solutions

Investigate each method by using the abovementioned websites (and others!) and create your own "Algorithm for solving quadratic inequations" video. Be as creative as you would like - just make sure you are also appropriate. Make sure you use your math vocabulary and get the algorithm correct for you!!!

Finally, together as a group, complete each other‘s parts and problems in your Padlets as you also look at the other group members’ created videos.

CONCLUSION

Congratulations!!! You now know how to use quadratic inequalities to help you solve everyday problems!

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