Page 2: Number Line and Integer Properties

This page explores the properties of integers and their representation on a number line.

Vocabulary: Absolute value refers to a number without its sign.

Definition: Natural numbers are positive integers starting from 1, while integers include positive, negative numbers, and zero.

Highlight: The number line shows negative numbers to the left of zero and positive numbers to the right.

Example: When comparing integers:

• Positive numbers are greater than negative numbers
• Among positive numbers, the larger value is greater
• Among negative numbers, the value closer to zero is greater

Page 3: Prime and Composite Numbers

This page delves into the classification of numbers and their properties.

Definition:

• Prime numbers have exactly two divisors: 1 and themselves
• Composite numbers have more than two divisors

Example: Number classification:

• 41 is prime (divisors: 1, 41)
• 35 is composite (divisors: 1, 5, 7, 35)
• 72 is composite (multiple divisors)

Highlight: Two numbers are coprime when their greatest common divisor is 1.

Vocabulary: LCM problems often involve timing (coincidence) scenarios, while GCD problems typically involve grouping or distribution.

Page 4: Combined Operations and Problem Solving

This page focuses on complex mathematical operations with integers.

Highlight: Order of operations must be followed: parentheses, brackets, multiplication/division (left to right), addition/subtraction (left to right).

Example: Combined operations:

• 9·$5-8$-2 = 9·$-3$-2 = -27-2 = -29
• 28÷4·$-7-(-6)$ = 7·$-7+6$ = 7·$-1$ = -7

Definition: When solving problems with integers, maintain careful attention to signs and order of operations.

Vocabulary: Combined operations (operaciones combinadas) involve multiple mathematical operations that must be solved in a specific order.

Page 1: Divisibility Rules and Prime Factorization

This page introduces fundamental mathematical concepts related to divisibility and prime factorization.

Definition: Divisibility rules are criteria that help determine if a number is divisible by another without performing division.

Example: A number is divisible by:

• 2 if it ends in 0 or an even digit
• 3 if the sum of its digits equals 3, 6, or 9
• 4 if its last two digits are in the 4 times table or are 00
• 5 if it ends in 0 or 5
• 6 if it's divisible by both 2 and 3
• 9 if the sum of its digits equals 9
• 10 if it ends in 0

Highlight: Prime factorization is expressing a number as a product of prime numbers.

Definition: Least Common Multiple (LCM) uses the highest power of each prime factor, while Greatest Common Divisor (GCD) uses the lowest power of common prime factors.