Variables

Definition

Variables are symbolic representations of values or quantities that can change or vary within the context of a problem or mathematical expression. They serve as placeholders for unknown or changing information, allowing for the manipulation and analysis of data.

5 Must Know Facts For Your Next Test

1. Variables can represent different types of values, such as numbers, measurements, or even abstract concepts.
2. The value of a variable can be assigned, changed, or determined through calculations or problem-solving.
3. Variables are essential in algebra and pre-algebra for modeling real-world situations and solving for unknown quantities.
4. The choice of variable names can provide context and clarity to the problem being solved.
5. Variables are often denoted using single letters, such as x, y, or z, but can also be represented by more descriptive names.

Review Questions

• Explain how variables are used in the problem-solving strategy described in 9.1 'Use a Problem Solving Strategy'.
  • Variables play a crucial role in the problem-solving strategy outlined in 9.1. They allow you to represent unknown or changing quantities within the problem, enabling you to set up equations, expressions, or models to find the solution. By assigning variables to the unknown values, you can manipulate and solve for them using the given information and the problem-solving steps, such as identifying the goal, creating a plan, and executing the plan.
• Describe how the use of variables can help you analyze and interpret the information presented in a problem related to 9.1 'Use a Problem Solving Strategy'.
  • Variables allow you to break down a problem into its essential components and represent the relationships between them. By identifying the variables in a problem, you can determine what information is known and what is unknown, helping you create a plan to solve the problem. Variables also enable you to represent the problem in a more general, abstract form, making it easier to apply problem-solving strategies and recognize patterns that can be used to solve similar problems in the future.
• Evaluate how the use of variables can enhance your ability to communicate and justify your problem-solving approach in the context of 9.1 'Use a Problem Solving Strategy'.
  • The use of variables in problem-solving allows you to communicate your thought process and solution steps more clearly and concisely. By representing unknown quantities with variables, you can express the relationships between the given information and the desired solution in a more universal and transferable way. This can help you justify your approach, as variables enable you to demonstrate the logical flow of your problem-solving strategy and the reasoning behind your steps, making it easier for others to understand and evaluate your work.

Related terms

Constant:

A fixed value that does not change within the given context or problem.

Expression: A combination of variables, constants, and operations that represents a value or quantity.

Equation:

A mathematical statement that shows two expressions are equal, often using variables to represent unknown values.