6th Grade Math

Ratios, proportions, and algebraic thinking for sixth grade students.

Understanding RatiosIntroduction to ProportionsAlgebraic Thinking: Expressions and Variables
Solving Ratio and Proportion ProblemsUsing Variables to Write and Solve EquationsRecognizing Patterns and Relationships
Using Ratios in Cooking and RecipesProportions in Maps and ModelsAlgebra in Everyday Decisions
Breaking Down Word ProblemsChecking Your Answers
Understanding RatiosIntroduction to Prop...Algebraic Thinking: ...Solving Ratio and Pr...Using Variables to W...Recognizing Patterns...Using Ratios in Cook...Proportions in Maps ...Algebra in Everyday ...Breaking Down Word P...Checking Your Answer...
Basic Concepts

Algebraic Thinking: Expressions and Variables

What Are Expressions and Variables?

An expression is a math sentence with numbers, variables (like \(x\) or \(y\)), and operations. A variable stands in for a number you don't know yet.

Why Use Variables?

Variables let us describe patterns, solve puzzles, and write rules. They're like mystery boxes!

Writing Expressions

You can write an expression like \(2x + 5\) (which means "2 times a number plus 5").

Real-Life Connections

Algebra helps you figure out things like "How many tickets can I buy with \$20 if each ticket costs \(x\) dollars?"

Examples

  • If you have \(x\) apples and buy 3 more, you have \(x + 3\) apples.

  • If each t-shirt costs \$8, the cost for \(n\) shirts is \(8n\).

In a Nutshell

Variables and expressions help describe unknowns and solve real-world problems.

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Solving Ratio and Proportion Problems