Variables and Algebra

BIG IDEAS:

(taken from “Big Ideas by Dr. Small”):

1. Algebra is a way to represent and explain mathematical relationships and to describe and analyze change.

2. Using variables is a way to efficiently and generally describe relationships that can also be described using words.

STUDENT LEARNING GOALS:

GOAL #1: I can write algebraic expressions and equations from words.

• VIDEO: What is a Variable? (Source: Khan Academy)

• VIDEO: Why we don’t use the multiplication symbol (Source: Khan Academy)

• VIDEO: Writing Basic Expressions involving Variables (Source: Khan Academy)

• VIDEO: Writing Expressions involving Variables (Source: Khan Academy)

• VIDEO: Writing Algebraic Expressions involving Brackets (Source: Khan Academy)

• VIDEO: Interpreting Algebraic Expressions (Source: Khan Academy)

• VIDEO: Consecutive Integers (Source: Khan Academy)

• PRACTICE: Writing Algebraic Expressions (Source: Khan Academy)

• LESSON: Algebraic Expressions (Source: PBSLearningMedia)

• GIZMO: Using Algebraic Expressions (Source: ExploreLearning Gizmo)

• GAME: Writing Algebraic Expressions Millionaire (Source: math-play.com)

• GAME: Rags to Riches (Source: Quia)

• GAME: Algebra Expressions Basketball (Source: Algebra4Kids)

GOAL #2: I can evaluate algebraic expressions using substitution.

• VIDEO: Substituting Values into Algebraic Expressions? (Source: Khan Academy)

• VIDEO: Evaluating Expressions with two variables (Source: Khan Academy)

• VIDEO: Evaluating Expressions with Decimals and Fractions (Source: Khan Academy)

• VIDEO: Evaluating Expressions with Exponents (Source: Khan Academy)

• PRACTICE: Evaluating Expressions (Source: Khan Academy)

• PRACTICE: Algebra Substitution (Source: ThatQuiz)

• GAME: Substitution Matching (Source: Flash Maths)

GOAL #3: I can solve one- and two-step algebraic equations.

• VIDEO: Balance Model (Source: Khan Academy)

• VIDEO: Balance Model – add/subtract (Source: Khan Academy)

• VIDEO: One-Step Equations – add/subtract (Source: Khan Academy)

• VIDEO: Balance Model – multiply/divide (Source: Khan Academy)

• VIDEO: One-Step Equations – multiply both sides (Source: Khan Academy)

• VIDEO: One-Step Equations – divide both sides (Source: Khan Academy)

• VIDEO: Balance Model – two step equations (Source: Khan Academy)

• VIDEO: Two-Step Equations (Source: Khan Academy)

• VIDEO: Two-Step Equations involving Decimals (Source: Khan Academy)

• VIDEO: Writing and Solving Equations from Word Problems (Source: Khan Academy)

• MODEL: One- and Two-Step Equations (Source: MathPlayground)

• GAME: Swimming Otters – solving by inspection (Source: Arcademics)

• GAME: Shuttle Mission Math – balance model (Source: MathPlayground)

• GAME: Noodle Board Game (Source: LearnAlberta)

GOAL #4: I can simplify algebraic expressions.

• VIDEO: What is a Polynomial? (Source: Math Antics)

• VIDEO: Collecting Like Terms (Source: Khan Academy)

• VIDEO: Collecting Terms Example (Source: Khan Academy)

• VIDEO: Distributive Property (Source: Khan Academy)

• VIDEO: Solving System of Equations – advanced topic (Source: Khan Academy)

• INFO: Collecting Like Terms (Source: mathisfun)

• PRACTICE: Collecting Like Terms (Source: IXL Math)

• PRACTICE: Distributive Property (Source: IXL Math)

• GAME: Matching Action (Source: Math Warehouse)

• GAME: Like Term Invaders (Source: XP Math)

• GAME: Jeopardy (Source: Jeopardy Labs)

CURRICULUM EXPECTATIONS:

• describe different ways in which algebra can be used in real-life situations (e.g., the value of $5 bills and toonies placed in a envelope for fund raising can be represented by the equation v = 5f + 2t);

• translate statements describing mathematical relationships into algebraic expressions and equations (e.g., for a collection of triangles, the total number of sides is equal to three times the number of triangles or s = 3n);

• evaluate algebraic expressions with up to three terms, by substituting fractions, decimals, and integers for the variables (e.g., evaluate 3x + 4y = 2z, where x = 1/2, y = 0.6, and z = –1);

• solve and verify linear equations involving a one-variable term and having solutions that are integers, by using inspection, guess and check, and a “balance” model (Sample problem: What is the value of the variable in the equation 30x – 5 = 10?)

• model linear relationships graphically and algebraically, and solve and verify algebraic equations, using a variety of strategies, including inspection, guess and check, and using a “balance” model.