Module 3 Introduction

Module 3: Polynomials

 

Module 3 Introduction

 

Some of the designs behind the most successful children’s toys are very simple. Barbie dolls and LEGO building blocks have always been popular with kids of all ages. One of the more popular toys since the 1980s is a Transformer, or a toy robot whose limbs can be manipulated to form a vehicle or a toy gun or a cellphone (as in the photo). The ingenuity of the design cannot be overstated. These transformable robots not only serve as two toys in one, but they are also like puzzles to challenge the child.

 

The design of these toys is similar to the design of codes. For every one of these toys, there is a particular way to form both the robot and the other object. You can form the one and then reverse the steps to form the other. In this way, the transformable toy is like a code that is enciphered and then deciphered. A code can be encoded according to an algorithm and then decoded by reversing the steps in the algorithm. In other words, encoding and decoding are inverse processes.

 

Mathematics lends itself very well to code construction because there are many concepts in math that involve inverse processes. In this module you will look at the inverse processes of multiplying polynomials and factoring them. Multiplying polynomials involves building larger expressions out of smaller ones. Factoring polynomials does the opposite—breaking larger expressions into smaller ones.

 

In this module you will learn different strategies for multiplying polynomials. You will see how multiplying polynomials is like multiplying two-digit numbers. You will also discover different ways to approach the factoring of polynomials. These approaches will be based on the nature of the polynomial. You will learn that factoring polynomials is similar to factoring integers.

 

Throughout this module you will learn to work with algebra tiles, both by watching demonstrations and by using an interactive applet. You will see that algebra tiles can be an effective tool to help you multiply and factor polynomials. You will also explore several algebraic approaches and see how these approaches tie into previously learned concepts, such as perfect squares and their roots.

 

You will also continue to work on creating systems of coding and decoding based on the math that you will learn. You will discover creative ways to use math to encrypt secret messages. Above all, you will have an opportunity to practise reversing algorithms in order to decrypt secret codes!

 

You will investigate the following lesson questions in this module.

 

Lesson	Title	Lesson Questions
1	Multiplying Binomials	How is multiplying binomials similar to multiplying two-digit numbers? How is the process of multiplying binomials similar to encoding a message?
2	Multiplying Polynomials	How is the distributive property extended to solve multiplication problems and other types of problems? How can you tell if two polynomials have been multiplied correctly?
3	Common Factors	How are polynomial-factoring strategies similar to strategies used to obtain the prime factorization of a whole number? How can you tell if a polynomial is factored correctly?
4	Factoring Trinomials of the Form ax2 + bx + c	How is a multiplication array similar to a cipher? How are the coefficients of a trinomial related to the coefficients of its binomial factors?
5	Factoring Special Polynomials	How are perfect squares involved in the factoring of polynomials? How do you select appropriate strategies for factoring polynomials?

 

As in previous modules, you will learn the outcomes in this module in a variety of ways. You will have the opportunity to perform Math Labs, experiment with interactive applets, and watch videos that demonstrate how to solve problems. You will have the opportunity to crack secret codes and to create them. You will apply the concepts you learn to real-life problems. You will undertake hands-on activities as well as virtual ones. Keep your calculator handy throughout the module, as you will find that some calculations are much easier to complete that way.

 

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