# Math Bridge Resources

This collection of lessons was developed to bridge the learning gap for students who have successfully completed Math CST 4 and would like to pursue the Math Science (SN) stream. These resources include interactive videos, as well as supporting documents that identify and explore topics that are not covered in the CST 4 program. *(Additional lessons are in development.)*

PLEASE NOTE: No sign-in is required to view these lessons. Simply click the arrow on the lower left-hand side of the slide to play. Use the arrows on the lower right-hand side of the slide to advance the slides.

LEARN Design and Development Team: Author/Lead Teacher: Peggy Drolet, BEd; Editor: Tasha Ausman, PhD; and Instructional Designer: Kristine Thibeault, MEd.

# Factoring 5: Factoring trinomials with a value of ‘a’ that is greater than 1

In this lesson, the decomposition method is introduced whereby trinomials in general form with an a value greater than 1 can be factored. The approach is to first find any GCFs and remove them, multiply the first and last terms to find a desired target value, and then determine which combination of integers results in the value of b using addition or subtraction. This video relies on prior knowledge of factoring by grouping.

**Learning Goal:**

-To be able to factor polynomials that contain decomposable second degree trinomials

# Long Division: Dividing polynomials by monomials and binomials

The purpose of this video is to learn how to employ the principles of long division, originally taught in elementary school, to polynomials. This lesson first reminds you how to divide a polynomial by a monomial, and then draws upon the steps in long division to divide a binomial into larger polynomials (second and third degree).

**Learning Goal:**

-To be able to divide a polynomial by another polynomial (with or without a remainder)

**Related Textbook Pages:**

*Visions, Science, Student Book Volume 1, Secondary Cycle Two, Year Two*, Les Editions CEC Inc, 2009, **pp 148-177**

**Additional Resources:**

**Dividing a Polynomial by a Binomial**

# Rational Expressions 1: Simplifying rational expressions

In this introductory lesson to Rational Expressions (REs), students will build upon their knowledge of factoring to, firstly, define rational expressions, and secondly, understand basic simplification. Using the concept of Greatest Common Factor (GCF), several examples are worked through, emphasizing how a common term can be removed, leaving a final answer that cannot be reduced further.

**Learning Goal:**

-To be able to manipulate rational expressions

**Related Textbook Pages:**

*Visions, Science, Student Book Volume 1, Secondary Cycle Two, Year Two*, Les Editions CEC Inc, 2009, **pp 148-177**

**Additonal Resources:**

**Khan Academy: Intro to Rational Expression Simplification**

**Khan Academy: Simplifying Rational Expressions: Common Binomial Factors**

# Rational Expressions 2: Multiplying and dividing rational expressions

Beginning with an introduction on multiplying fractions, this lesson first focuses on factoring out terms in the numerators and denominators of polynomial fractions. Once again, reminding ourselves that common factors can be cancelled top-to-bottom, these are removed, leaving us with a final, non-reducible solution. In division, the same method is employed, but with a poignant reminder that when dividing fractions, including polynomial ones, one must reciprocate the second term.

**Learning Goal:**

-To be able to manipulate rational expressions

**Related Textbook Pages:**

*Visions, Science, Student Book Volume 1, Secondary Cycle Two, Year Two*, Les Editions CEC Inc, 2009, **pp 148-177**

**Additional Resources:**

**Khan Academy: Multipying and dividing rational expressions (Video Series)**

# Rational Expressions 3: Adding and subtracting rational expressions

In this lesson, we learn about adding and subtracting rational expressions (polynomials in fraction form). Students are reminded about the basics of arithmetic, whereby a common denominator must be found before any two fractions can be added or subtracted. Special emphasis is placed upon distributing the negative (subtraction sign) in the numerator when subtracting rational expressions.

**Learning Goal:**

-To be able to manipulate rational expressions

**Related Textbook Pages:**

*Visions, Science, Student Book Volume 1, Secondary Cycle Two, Year Two*, Les Editions CEC Inc, 2009, **pp 148-177**

**Additional Resources:**

**Khan Academy: Adding & Subtracting Rational Expressions: Like Denominators**

# Rational Expressions 4: Adding and subtracting rational expressions

In this lesson, the steps for adding and subtracting rational expressions are reviewed and emphasized, and several difficult examples are worked through. Try these examples alongside the step-by-step instructions, and check your work as you proceed. If you can do these questions, you have an excellent grasp of adding and subtracting rational expressions.

**Learning Goal:**

-To be able to manipulate rational expressions

**Related Textbook Pages:**

*Visions, Science, Student Book Volume 1, Secondary Cycle Two, Year Two*, Les Editions CEC Inc, 2009, **pp 148-177**

**Addtional Resources:**

**Khan Academy: Adding Rational Expressions: Unlike Denominators**

# The Greatest Integer Function (Step Function): An Introduction

This lesson introduces the concept of a new mathematical operation that involves [ ]. Students will have the opportunity to explore a situation that requires this new operation. As a result, students will learn about the Basic Greatest Integer Function by building a table of values, constructing the graph and analyzing this Basic Greatest Integer Function

# The Role of Parameters a and b in the Greatest Integer Function

# The Role of Parameters h and k in the Greatest Integer Function

In this lesson, students will review the basic Greatest Integer Function. Then, students will explore the effects of changing parameters h and k. As a result, they will learn how to build a table of values and learn how to construct a graph of a Greatest Integer Function when parameters h and k are introduced in the basic rule.