Representing Algebraic Relationships: Creating Equivalent Representations

This lesson teaches how to create equivalent representations by identifying variables and their relationships. It covers the definition of variables, the distinction between independent and dependent variables, and how to represent algebraic relationships in different forms. The core lesson involves a practical example with Stephanie's necklace, where students learn to determine variables, form an equation, and create a table and graph. The lesson concludes with a summary of key concepts.

What is a variable in the context of algebra?

• A letter or symbol representing an unknown number

• A fixed number

• A type of graph

• A mathematical operation

In an equation involving x and y, which variable is typically the independent one?

• Neither x nor y

• x

• Both x and y

• y

What is the independent variable in the example of Stephanie's necklace?

• The total length of the necklace

• The number of links

• The length of the clasp

• The color of the necklace

What is the equation representing the total length of Stephanie's necklace?

• y = 4 + 2x

• y = 2 + 4x

• y = 4x + 2

• y = 2x + 4

What does the point (2, 8) represent in the graph of Stephanie's necklace?

• The clasp length is 8 cm

• The necklace has 8 links

• 8 links result in a total length of 2 cm

• 2 links result in a total length of 8 cm