Numbers and Operations

Numbers

• Types of Numbers:
  • Natural Numbers: 1, 2, 3, ... (counting numbers)
  • Whole Numbers: 0, 1, 2, 3, ... (including zero)
  • Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (including negative numbers)
  • Rational Numbers: fractions, decimals, percentages (can be expressed as a ratio)
  • Irrational Numbers: cannot be expressed as a ratio (e.g. π, e, sqrt(2))
• Number Operations:
  • Addition: combining two or more numbers to get a total or a sum
  • Subtraction: finding the difference between two numbers
  • Multiplication: repeated addition of a number
  • Division: sharing or grouping a number into equal parts
• Properties of Operations:
  • Commutative Property: order of numbers does not change the result
  • Associative Property: grouping numbers does not change the result
  • Distributive Property: multiplying a number by a sum is the same as multiplying by each addend separately

Time

• Units of Time:
  • Second (s)
  • Minute (min) = 60 s
  • Hour (h) = 60 min
  • Day = 24 h
  • Week = 7 days
  • Month = 28-31 days
  • Year = 12 months
• Time Conversions:
  • 1 h = 60 min = 3600 s
  • 1 day = 24 h = 1440 min = 86400 s
• Time-Related Concepts:
  • AM/PM: morning (AM) and afternoon/evening (PM)
  • Time zones: regions with uniform standard time

Distance

• Units of Distance:
  • Meter (m)
  • Kilometer (km) = 1000 m
  • Centimeter (cm) = 0.01 m
  • Millimeter (mm) = 0.001 m
• Distance Conversions:
  • 1 km = 1000 m = 100,000 cm = 1,000,000 mm
  • 1 m = 100 cm = 1000 mm
• Distance-Related Concepts:
  • Perimeter: distance around a shape
  • Circumference: distance around a circle

Numbers

• Natural Numbers are counting numbers, starting from 1, such as 1, 2, 3, ...
• Whole Numbers include zero, in addition to Natural Numbers, such as 0, 1, 2, 3, ...
• Integers include negative numbers, whole numbers, and zero, such as ..., -3, -2, -1, 0, 1, 2, 3, ...
• Rational Numbers can be expressed as a ratio, including fractions, decimals, and percentages
• Irrational Numbers cannot be expressed as a ratio, such as π, e, and sqrt(2)
• Addition is the process of combining two or more numbers to get a total or a sum
• Subtraction is the process of finding the difference between two numbers
• Multiplication is the repeated addition of a number
• Division is the process of sharing or grouping a number into equal parts
• The Commutative Property states that the order of numbers does not change the result
• The Associative Property states that grouping numbers does not change the result
• The Distributive Property states that multiplying a number by a sum is the same as multiplying by each addend separately

Time

• A Second (s) is a unit of time
• A Minute (min) is equal to 60 seconds
• An Hour (h) is equal to 60 minutes
• A Day is equal to 24 hours
• A Week is equal to 7 days
• A Month is equal to 28-31 days
• A Year is equal to 12 months
• 1 hour is equal to 60 minutes, which is equal to 3600 seconds
• 1 day is equal to 24 hours, which is equal to 1440 minutes, which is equal to 86400 seconds
• AM/PM refers to morning (AM) and afternoon/evening (PM)
• Time zones are regions with uniform standard time

Distance

• A Meter (m) is a unit of distance
• A Kilometer (km) is equal to 1000 meters
• A Centimeter (cm) is equal to 0.01 meters
• A Millimeter (mm) is equal to 0.001 meters
• 1 kilometer is equal to 1000 meters, which is equal to 100,000 centimeters, which is equal to 1,000,000 millimeters
• 1 meter is equal to 100 centimeters, which is equal to 1000 millimeters
• Perimeter refers to the distance around a shape
• Circumference refers to the distance around a circle