First lesson

• What are natural numbers?

  Counting numbers starting from 1
• Why are natural numbers used?

  To count objects or order items
• What is an example of a natural number?

  The number of cars in a parking lot
• What are the key characteristics of natural numbers?

  • Positive numbers greater than zero
  • Ordered in ascending order
  • Infinite, continuing without end
• What characteristic does the number 25 exhibit?

  It is positive, ordered, and infinite
• What do whole numbers include?

  Zero and all natural numbers
• How do whole numbers differ from natural numbers?

  Whole numbers include zero, natural numbers do not
• What is an example of a whole number?

  The number of books on a shelf
• What is the relationship between natural numbers and whole numbers?

  Whole numbers encompass all natural numbers plus zero
• What are integers?


  Whole numbers and their negative counterparts
• What is an example of an integer?

  The temperature of -5°C
• What are the types of integers?

  • Positive integers: 1, 2, 3, ...
  • Negative integers: -1, -2, -3, ...
  • Zero: Neutral integer separating positive and negative
• What type of integer represents a profit of $6$ million dollars?


  Positive integer
• What type of integer does a depth of $-20$ meters represent?


  Negative integer
• How are whole numbers and integers represented on a number line?

  • Whole numbers: Numbers to the right of zero including zero
  • Integers: All numbers on the number line including those to the left of zero
• What distinguishes integers from whole numbers on a number line?

  Integers include negative numbers, whole numbers do not
• What are whole numbers on a number line?

  Numbers to the right of zero, including zero
• What are integers on a number line?

  All numbers on the number line, including negatives
• How do whole numbers differ from integers?

  Whole numbers include zero and positives; integers include negatives
• If a number line extends from $-5$ to $5$, which integers are positive whole numbers?


  $1, 2, 3, 4, 5$
• What is the correct representation of whole numbers on a number line?

  Whole numbers are represented to the right of zero
• What do the blue dots represent on a number line?

  Positive whole numbers greater than zero
• How is the set of whole numbers ${0, 1, 2, 3}$ represented on a number line?


  Zero and all positive integers to the right of zero are marked
• What operators are used to compare and order integers?

  Greater than, less than, equal to
• Which operator correctly compares -2 and 5?

  $-$2 < 5
• What is the result of adding two positive natural numbers?


  The result is always a larger natural number
• What are the operations with natural numbers, whole numbers, and integers?

  1. Addition:

  • Natural numbers: Larger natural number
  • Whole numbers: Includes zero
  • Integers: Consider signs

  
  

  1. Subtraction:

  • Natural numbers: Larger minus smaller
  • Whole numbers: Subtracting zero unchanged
  • Integers: Use sign rules

  
  

  1. Multiplication:

  • Natural numbers: Product of two numbers
  • Whole numbers: Includes zero
  • Integers: Consider signs

  
  

  1. Division:

  • Natural numbers: How many times one goes into another
  • Whole numbers: Dividing by zero is undefined
  • Integers: Use sign rules
• What is an example of addition with natural numbers?

  5 + 3 = 8
• What is an example of subtraction with integers?

  10 - 4 = 6
• What is an example of multiplication with whole numbers?

  7 × 2 = 14
• What is an example of division with natural numbers?

  15 ÷ 3 = 5
• What happens when you subtract zero from a whole number?


  It does not change the number
• What is the result of dividing by zero in whole numbers?

  It is undefined