Module 5: Module 5 | MoodleHUB 🎓

1. Module 5

Mathematics 20-2 M5 Introduction

Module 5 Introduction

Have you ever looked up at the sky at night and wondered why the stars don’t fall down? Or have you wondered how the newscaster knows that there will be an eclipse of the moon tomorrow night? The latter isn’t just a hunch; there is solid mathematics behind the prediction.

This image shows a photo of a telescope and stars.

This image shows a watch used as a pendulum.

Radicals, including the square root sign you are familiar with, are used in many of the laws governing the universe. Different laws can be used to model and predict the behaviour of stars and planets and can also be used for predicting the swinging motion of a pendulum or determining the outcome of a collision by analyzing the tire skid marks at the scene.

This module gives you the chance to learn more about radical expressions. You will see how they are used in sports and other everyday situations. Such differing activities as cliff diving, sky diving, and accident reconstruction will be used as opportunities for you to practise working with radical equations.

In this module you will investigate the following inquiry questions:

What mathematical operations are appropriate for radical expressions?

How can problems involving radical equations be solved?

To investigate these module questions, you will focus on the lessons and corresponding inquiry questions shown in the following table.

Lesson	Title	Lesson Inquiry Questions
1	Mixed and Entire Numerical Radicals	How do you express a mixed radical with a numerical radicand as an entire radical and vice versa?
		How do you compare and order radical expressions in a given set of mixed and entire radicals?
2	Mixed and Entire Radicals that Include Variables	How do you express a mixed radical that includes variables in the radicand as an entire radical?
		How do you express an entire radical with a variable coefficient as a mixed radical?
		How do you identify values of the variable for which the radical expression is defined?
3	Adding and Subtracting Radicals	How do you add radical expressions?
		How do you subtract radical expressions?
4	Multiplying and Dividing Radicals	How do you multiply radical expressions?
		How do you divide radical expressions?
5	Rationalizing Radical Expressions	How do you simplify a fractional radical by rationalizing the denominator?
		How do you explain, using examples, the rules for writing positive and negative roots?
6	Solving Radical Equations	How do you determine the solutions (also known as roots) of a radical equation algebraically?
		How do you verify that the values determined in solving a radical equation are not extraneous roots of the equation?
7	Modelling Problems with Radical Equations	How do you use radical equations to model situations when solving problems?

Module 5 Project

You will work with dot paper in the Module 5 Project. It is difficult to visualize a line that is or long. This project will give you a greater understanding of lengths that include radicals. Drawing straight and tilted squares and calculating their areas and side lengths will help you to see that are numbers as real and definite as 2 or 5.

This shows 1-cm dot paper with three squares.

For specific instructions, refer to the Module 5 Project.

Strategies for Success

You may find the following strategies useful to support your success in this module.

Strategy 1: Course Glossary

Recall from the course introduction that you will be building your own version of a glossary in Mathematics 20-2. As you encounter new terms in the lesson, you can add them to your Glossary Terms document. For a full description, refer to Glossary Terms.

Strategy 2: Notes Organizer

A notes organizer is a tool for recording key concepts, terms, formulas, examples, or tips from each lesson in one place to refer to as you work through the course. Notes can be organized in a variety of formats. If you have not done so already, take a look at the Notes Organizer document for some ideas.

Strategy 3: Supplementary Resources

You will be referring to Chapter 4 (pages 172 to 233) of the Principles of Mathematics 11 textbook for Module 5. Take time to flip through these textbook pages. Look at illustrations, margin features, and main titles to get a sense of the concepts you will be covering in this module.

There are also resources available on LearnAlberta.ca. Your teacher can provide you with a username and a password to access content on LearnAlberta. An Internet search can also provide you with useful information. Just remember to consider the source of the information.

This illustration is of a puzzle with the letter w on three puzzle pieces.

Hemera/Thinkstock

Are you ready to begin Module 5: Radicals? Lesson 1 starts you off with an exploration of mixed and entire radicals.