- Students will learn the distributive property of multiplication over addition for real numbers.
- Students will verify that algebraic expressions involving the distributive property are equivalent both graphically and algebraically.
- Apply the properties of operations to generate equivalent expressions (CCSS).
- Identify when two expressions are equivalent (CCSS).
- Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients (CCSS).
- Reason abstractly and quantitatively (CCSSM Mathematical Practice).
- Look for and make use of structure (CCSSM Mathematical Practice).
- Distributive Property of Multiplication over Addition
- real numbers
- equivalent expressions
- coinciding lines
About the Lesson
This lesson involves using the graphs of two lines to create equivalent expressions.
As a result, students will:
- Change the values of a and b in the second line until the graphs coincide and explain why this shows that they now have equivalent expressions.
- Generate several other examples and derive a rule for generating equivalent algebraic expressions using the distributive rule, i.e. a(x + c) = ax + ac.
- Change the values of a and c so that the graph a(x + c)matches the graph of one of the form ax + b.
- Generate several other examples and derive a rule for generating equivalent algebraic expressions using the distributive rule in reverse, i.e. ax + ac = a(x + c).