Understanding Integers and Fairness in Education Vocabulary Review

How to Use

• Read each word carefully before your quiz or journal activity.
• Review the math, real-life, and fairness examples to see how numbers describe progress, balance, and need.
• Focus on patterns—how positive, negative, and zero values connect to real-world fairness.
• Keep this page in your Equity in Numbers Student Journal for independent practice.

Integer

• Definition: A whole number that can be positive, negative, or zero.
• Math Examples:
  • (−3) + (+5) = +2
  • (+8) − (+10) = −2
  • |−4| = 4
• Real-Life Example: A school gains (+) or loses (−) teachers or funding.
• Fairness Example: Integers help compare progress and reveal which schools need more support.

Positive Integer (+)

• Definition: A number greater than zero; shows increase or gain.
• Math Examples:
  • +4 + (+3) = +7
  • (+5) − (+2) = +3
  • (+2) × (+6) = +12
• Real-Life Example: A school receives 12 new computers.
• Fairness Example: Positive values show growth and improvement in opportunity.

Negative Integer (−)

• Definition: A number less than zero; shows decrease or loss.
• Math Examples:
  • −2 + (−3) = −5
  • (−6) + (+2) = −4
  • (−8) − (−3) = −5
• Real-Life Example: A district loses five teachers after budget cuts.
• Fairness Example: Negative numbers reveal disadvantages and unmet needs.

Zero

• Definition: The balance point between positive and negative numbers.
• Math Examples:
  • +5 + (−5) = 0
  • (−2) + (+2) = 0
  • (+3) − (+3) = 0
• Real-Life Example: A school’s gains and losses even out—no overall change.
• Fairness Example: Zero represents equality and balance among schools.

Gain

• Definition: A positive change or increase in value.
• Math Examples:
  • (−2) + (+6) = +4
  • (+3) + (+5) = +8
  • (+7) − (+2) = +5
• Real-Life Example: A school gains five new tutors this semester.
• Fairness Example: Gains signal progress toward equitable learning conditions.

Loss

• Definition: A negative change or decrease in value.
• Math Examples:
  • (+4) + (−9) = −5
  • (−3) + (−2) = −5
  • (+6) − (+8) = −2
• Real-Life Example: A community loses two after-school programs.
• Fairness Example: Losses highlight where extra support is needed for balance.

Balance

• Definition: When gains and losses are equal; total = 0.
• Math Examples:
  • (+5) + (−5) = 0
  • (+3) + (+2) + (−5) = 0
  • (−4) + (+4) = 0
• Real-Life Example: Two schools receive the same funding amount.
• Fairness Example: Balance represents stability—every student has an equal chance.

Equity

• Definition: Giving everyone what they need to succeed (not always the same).
• Math Examples:
  • (+6) + (−4) = +2 → needs +2 more to balance
  • (−5) + (+5) = 0
  • (+3) + (+1) + (−4) = 0
• Real-Life Example: One school receives extra resources so both reach equal goals.
• Fairness Example: Equity adjusts differences so every student can succeed.

Gap

• Definition: The difference or distance between two values or groups.
• Math Examples:
  • |+6 − (−2)| = 8
  • |−3 − (+4)| = 7
  • |+2 − 0| = 2
• Real-Life Example: The funding gap between two schools is $8,000.
• Fairness Example: The larger the gap, the more inequity exists.

Resource

• Definition: Anything measurable that supports learning or growth.
• Math Examples:
  • (+10) + (−7) = +3
  • (−4) + (+9) = +5
  • (+6) − (+3) = +3
• Real-Life Example: Teachers, books, and laptops that support students.
• Fairness Example: Fair distribution of resources creates equal opportunity.