1. Lesson 1

Mathematics 20-1 Module 7

Module 7: Absolute Value and Reciprocal Functions

 

Lesson 1: Absolute Value

 
Focus

 

This shows an image of the painting Adele Bloch-Bauer’s Portrait by Gustav Klimt.

Adele Bloch-Bauer's Portrait by Gustav Klimt.

The image here is a reproduction of a famous painting by Gustav Klimt, who created it in 1907. The painting features the wife of a wealthy businessman and was created out of oil paints and gold. If you had the financial resources, how much would you pay to own this painting?

 

This painting sold in 2006 for $135 million! Some may say that this is a fair price to pay for a rare and beautiful piece of artwork, while others may see it as grossly overpaying for what amounts to a simple portrait.

 

Paintings, like other investments, generally increase in value over time. Aspects of the painting such as its composition (oil or acrylic), subject, condition, and rarity all contribute to its market value. In the end, a painting is worth what someone will pay for it. Nevertheless, wouldn’t it be great to be able to determine the absolute value of a painting—the one true value of a piece of artwork that neither shortchanges the seller nor gouges the buyer?

 

In this lesson you will study the concept of absolute value in the context of mathematics. You will learn how to apply the absolute value of numbers in different situations, including the world of art.

 

Outcomes

 

At the end of this lesson you will be able to

  • determine the distance of two real numbers of the form ±a, a ∈ , from 0 on a number line, and relate this to the absolute value of a or

  • determine the absolute value of a positive or negative real number

  • explain, using examples, how distance between two points on a number line can be expressed in terms of absolute value

  • determine the absolute value of a numerical expression

  • compare and order the absolute values of real numbers in a given set
Lesson Questions

 

In this lesson you will investigate the following questions:

  • How can you determine the absolute value of a mathematical expression?

  • Under what circumstances is the absolute value of an expression used to solve a problem?
Assessment

 

Your assessment may be based on a combination of the following tasks:

  • completion of the Lesson 1 Assignment (Download the Lesson 1 Assignment and save it in your course folder now.)

  • course folder submissions from Try This and Share activities

  • additions to Module 7 Glossary Terms and Formula Sheet

  • work under Project Connection

Self-Check activities are for your own use. You can compare your answers to suggested answers to see if you are on track. If you are having difficulty with concepts or calculations, contact your teacher.