Algebraic Expressions and Fair Budgets Vocabulary Review

How to Use

• Review each term and example before your quiz.
• Study how math, real-life, and fairness examples connect to understand how algebra helps communities make fairer financial decisions.
• Keep this sheet in your Equity in Numbers Student Journal as a math + equity reference page.
• Remember: Expressions tell a story about how money flows — who has enough and who might need more support.

Algebraic Expression

• Definition: A combination of numbers, variables, and operations that shows a relationship, but doesn’t have an equal sign.
• Math Examples:
  • (E = 1,000 + 400 + 300 + 0.1I)
  • (R = I – E)
  • (T = 2x + 3y + 100)
• Real-Life Example: Representing a family’s total monthly expenses as an expression.
• Fairness Example: Expressions help compare budgets fairly, showing which families face higher basic costs.

Variable

• Definition: A symbol (usually a letter) that represents an unknown or changeable number.
• Math Examples:
  • (I) = income; (E) = expenses; (S) = savings.
  • (E = 800 + 300 + 0.15I)
• Real-Life Example: Variables help model budgets that change each month.
• Fairness Example: Using variables shows flexibility — because not all families have fixed, equal incomes.

Income (I)

• Definition: The total money earned or received.
• Math Examples:
  • (I = 3,000) or (I = 4,000)
  • (R = I – E)
• Real-Life Example: A parent’s paycheck or school’s funding grant.
• Fairness Example: Comparing incomes helps us see how earning differences affect opportunities.

Expenses (E)

• Definition: The total amount of money spent on needs and wants.
• Math Examples:
  • (E = 1,000 + 400 + 300 + 0.1I)
  • (E = 800 + 200 + 0.05I)
• Real-Life Example: Rent, groceries, transportation, or bills.
• Fairness Example: When expenses take up most of income, families have less left to save — showing unequal financial stability.

Savings

• Definition: The portion of income that is set aside instead of being spent.
• Math Examples:
  • Savings = 10% of income → (0.1I)
  • (I – E = R) (Remaining money includes savings.)
• Real-Life Example: Putting money in a savings account each month.
• Fairness Example: Not every family can save — showing how unequal resources impact future security.

Remaining Balance (R)

• Definition: The money left after subtracting expenses from income.
• Math Examples:
  • (R = I – E)
  • (R = 3,000 – (1,000 + 400 + 300 + 0.1I))
• Real-Life Example: The amount left after paying rent, groceries, and transportation.
• Fairness Example: Remaining balances show who can afford extras (like tutoring or vacations) and who can’t.

Percent of Income

• Definition: The fraction or decimal that shows what part of income goes to a specific category.
• Math Examples:
  • 10% of income = (0.10I)
  • 15% of income = (0.15I)
• Real-Life Example: Families often spend a percent of income on rent or savings.
• Fairness Example: If low-income families spend a higher percent on basic needs, it reveals inequity.

Budget

• Definition: A plan for how income will be used to pay for expenses and savings.
• Math Examples:
  • Income: (I = 3,500); Expenses: (E = 1,950 + 0.10I); Remaining: (R = I – E)
• Real-Life Example: A school budget divides money between supplies, salaries, and student activities.
• Fairness Example: Budgets reveal how resources are distributed — showing whether funds are shared equitably.

Fixed Expense

• Definition: A cost that stays the same every month.
• Math Examples:
  • Rent = $1,000; Internet = $100.
  • (E = 1,000 + 100 + 0.05I)
• Real-Life Example: Monthly rent or a car payment.
• Fairness Example: Families with lower income feel fixed expenses more sharply than wealthier households.

Flexible Expense

• Definition: A cost that can change from month to month.
• Math Examples:
  • Groceries = $300 → sometimes $350.
  • (E = 800 + 0.15I) changes as needs change.
• Real-Life Example: Food, clothing, or school supplies.
• Fairness Example: When budgets are tight, families may need to cut flexible expenses — a sign of financial inequity.

Equity in Budgeting

• Definition: Making sure resources are distributed so that everyone gets what they need to live well — not just equal amounts.
• Math Examples:
  • School A: (I – E = 100); School B: (I – E = 1,000).
  • Adjusting budgets for need = equity.
• Real-Life Example: A district gives more funding to schools with fewer local resources.
• Fairness Example: Equity ensures fairness by meeting different needs, not treating everyone identically.

Summary of Math + Fairness Connections

Concept	Math Focus	Fairness Connection
Expression	Combines numbers & variables	Models real budgets clearly
Income & Expenses	Use operations to find totals	Show gaps in opportunity
Savings	Percent of income	Reveals differences in financial security
Remaining Balance	(I – E)	Measures who has extra vs. who struggles
Equity in Budgeting	Applies math to fairness	Promotes just resource distribution