- 1. Generalising with Words and Tiles
Understand the concept of a variable and generalise patterns from numbers to algebraic symbols.
- 2. The Language of Algebra: Expressions
Define expression, term, and constant. Confidently write algebraic expressions without multiplication signs and translate algebra tiles into written symbols.
- 3. Simplifying by Combining Like Terms (Addition Only)
Define like terms and coefficients. Use algebra tiles and mathematical rules to simplify expressions by adding like terms together.
- 4. Simplifying with Subtraction and Zero Pairs
Define and use a zero pair. Use positive and negative algebra tiles to simplify expressions that include subtraction.
- 5. Collecting Like Terms
Transition from algebra tiles to abstract symbolic algebra. Collect like terms by carrying the sign with its term. Simplify expressions with multiple different variables and preview finding the value of a simplified expression.
- 6. Introduction to Substitution
Understand that variables represent unknown numbers. Learn to evaluate algebraic expressions by substituting specific known values for variables using proper mathematical notation involving brackets.
- 7. Substitution with Negatives and Multiple Variables
Extend substitution skills to handle negative integers and expressions containing two or more different variables. Evaluate algebraic expressions by substituting each variable with its matching value, using brackets as a protective shield against sign errors.
- 8. Exploring Equivalence and Always True/Sometimes True
Use substitution to test whether mathematical statements represent equivalent expressions (Always True) or equations that only work for specific values (Sometimes True).
- 9. What is an Equation?
Distinguish between algebraic expressions and equations. Use the balance scale model to understand that an equation uses an equals sign to show two quantities have the exact same value.
- 10. Solving One-Step Equations with Tiles (Addition/Subtraction)
Use the balance scale and algebra tile models to solve one-step addition and subtraction equations by isolating the variable and maintaining equality.
