# 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 1: Introduction and review of Greatest Common Factors (GCFs)

This video introduces students to the building blocks of polynomials for the Math SN4 option. Geared toward students who already have a solid grasp of polynomials and exponents from Secondary 3, this video reviews Greatest Common Factor (GCF).

**Learning Goal:**

-To be able to factor polynomials by finding the common factor

**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: Factoring Polynomials - Common Factor 1**

**Khan Academy: Factoring Polynomials - Common Factor 2**

# Factoring 2: Factoring by differences of two perfect squares

This video continues the methods of factoring necessary for the Math SN4 option: factoring the difference of two perfect squares.

**Learning Goal:**

-To be able to factor polynomials by using second degree algebraic identity: the difference of two perfect squares.

**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: Factoring Differences of Squares with Two Variables**

# Factoring 3: Factoring by grouping

This video continues the methods of factoring necessary for the Math SN4 option: factoring by grouping.

**Learning Goal:**

-To be able to factor polynomials by grouping terms

**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: Factor by Grouping**

# Factoring 4: Factoring trinomials with a value of 'a’ equal to 1 (“easy” trinomials)

In this lesson, students are introduced to “easy” trinomials. Building upon students’ knowledge of the process of FOIL from Secondary 3, students will learn how to work backwards to find two binomials leading to a simple trinomial with an a value of 1. As well, this lesson reminds students to remove any GCFs first, so that factoring might take place.

**Learning Goal:**

-To be able to factor second degree trinomials

**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: Factoring Quadratics Examples**

# 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**