# Variables and Algebra

**BIG IDEAS****:**

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

- Algebra is a way to represent and explain mathematical relationships and to describe and analyze change.
- 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)*

**CURRICULUM EXPECTATIONS:**

- Model real-life linear relationships graphically and algebraically, and solve simple algebraic equations using a variety of strategies, including inspection and guess and check;
- Translate phrases describing simple mathematical relationships into algebraic expressions (e.g., one more than three times a number can be written algebraically as 3
*x*+ 1), using concrete materials (e.g., algebra tiles, pattern blocks, counters); - Evaluate algebraic expressions by substituting natural numbers for the variables;
- Solve linear equations of the form
*ax*=*c*or*c*=*ax*and*ax*+*b*=*c*or variations such as*b*+*ax*=*c*and*c*=*bx*+*a*(where*a*,*b*, and*c*are natural numbers) by modelling with concrete materials, by inspection, or by guess and check, with and without the aid of a calculator (e.g., “I solved*x*+ 7 = 15 by using guess and check. First I tried 6 for*x*. Since I knew that 6 plus 7 equals 13 and 13, is less than 15, then I knew that*x*must be greater than 6.”). - Model real-life relationships involving constant rates (e.g., speed, heart rate, billing rate), using algebraic equations with variables to represent the changing quantities in the relationship (e.g., the equation
*p*= 4*t*represents the relationship between the total number of people that can be seated (*p*) and the number of tables (*t*), given that each table can seat 4 people [4 people per table is the constant rate]).