Description I. Structure and Calculation of Natural Numbers 01 Structure of Natural Numbers 1. Natural numbers are made from 10 digits and place value. Decimal system | Place value and the value each digit represents | Place value of large numbers | Comparing the size of numbers 2. A natural number is the sum of the values represented by each digit. Expanded form of the decimal system 3. Natural numbers increase by 1 starting from 1. Consecutive natural numbers | Integers 02 Calculation with Natural Numbers (1) 1. A 1 in a higher place is 10 in the place below it. Addition and subtraction | Addition and subtraction of large numbers 2. Multiplying by 10 adds one digit. Multiplying by 10, 100, 1000, … 3. Dividing by 10 removes one digit. Quotients when dividing by 10, 100, 1000, … 4. A natural number is the sum of the values represented by each digit. Multiplication (1) - Multiplying by a one-digit number | Multiplication (2) - Multiplying by numbers with two or more digits | Division (1) - Calculating with long division | Division (2) - Remainders | Division (3) - Checking your answer 03 Calculation with Natural Numbers (2) 1. Addition and subtraction, multiplication and division are opposites of each other. Relationship between addition/subtraction and multiplication/division 2. Repeated operations are calculated in order. Order of operations for addition and multiplication | Order of operations for addition, subtraction, multiplication, and division | Order of operations with parentheses | Calculating with consecutive natural numbers 3. An expression can be rewritten as a different expression with the same value. Commutative property | Associative property | Distributive property | Equal signs and equations II. Properties of Natural Numbers 01 Multiples and Divisors 1. A natural number is either even or odd. Even and odd numbers 2. Multiples are found through multiplication, and divisors are found through division. Multiples | Rules for determining multiples | Divisors | Relationship between multiples and divisors | Prime numbers | Prime factorization 3. Two or more natural numbers share common divisors. Common divisors and the greatest common divisor | Finding the greatest common divisor | Finding the greatest common divisor of three numbers | Solving problems using the greatest common divisor 4. Two or more natural numbers share common multiples. Common multiples and the least common multiple | Finding the least common multiple | Finding the least common multiple of three numbers | Solving problems using the least common multiple 5. Two natural numbers can be expressed using their greatest common divisor and least common multiple. Relationship between two numbers and their greatest common divisor | Relationship between two numbers and their greatest common divisor and least common multiple 02 Estimating Numbers, Ranges, and Sequences 1. Numbers can be estimated to a nearby value. Rounding down | Rounding up | Rounding 2. A range of numbers can be expressed by setting a standard. Greater than and at least | Less than and at most | Ranges with two standards | Overlapping ranges 3. The next number can be found from the pattern in a sequence. Sequences 4. The next number can be found from the relationship between neighboring numbers. Sequences with a constant difference between neighboring numbers | Sequences with a constant ratio between neighboring numbers