Description I. Structure and Calculation of Natural Numbers 01 The Structure of Natural Numbers 1. Natural numbers are made of 10 digits and place values. Decimal system | Place value and the value each digit represents | Place values 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 with large numbers 2. Multiplying by 10 adds one place. Multiplying by 10, 100, 1000, … 3. Dividing by 10 removes one place. 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 of two digits or more | 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. The 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. Every natural number is either even or odd. Even and odd numbers 2. Multiples are found through multiplication, and divisors through division. Multiples | Rules for identifying multiples | Divisors | The relationship between multiples and divisors | Prime numbers | Prime factorization 3. Two or more natural numbers can 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 can 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 through their greatest common divisor and least common multiple. The relationship between two numbers and their greatest common divisor | The relationship between two numbers, their greatest common divisor, and least common multiple 02 Estimation, 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 conditions | 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