Building Blocks of 7th Grade Math equips students with fundamental mathematical concepts and problem-solving skills. This course focuses on number theory and exponents, providing a solid foundation for more advanced mathematical studies. By the end of this course, students will confidently manipulate numbers, understand the properties of exponents, and apply these skills to solve equations and real-world problems.

Prime Factorization

• Learn to break down composite numbers into their prime factors — essential for simplifying fractions and solving number theory problems.
• Use factor trees and division methods to find prime factors efficiently.
• Apply prime factorization to determine the number of divisors of a given number.

Greatest Common Factor (GCF)

• Understand the concept of common factors and the GCF — the largest factor shared by two or more numbers.
• Calculate the GCF using prime factorization and listing methods.
• Apply the GCF to simplify fractions and solve real-world problems involving division.

Least Common Multiple (LCM)

• Define multiples and the LCM — the smallest multiple that two or more numbers share.
• Determine the LCM using prime factorization and listing methods.
• Solve problems involving the LCM, such as scheduling events and comparing fractions.

Introduction to Exponents

• Grasp the basic definition of exponents — representing repeated multiplication of a base number.
• Identify the base and exponent in exponential expressions.
• Understand and apply exponent notation to simplify expressions.

Evaluating Powers

• Calculate the value of exponential expressions with positive integer exponents.
• Work with exponents of 0 and 1 — understanding their unique properties.
• Practice evaluating powers to build fluency and accuracy.

Exponents with Variables

• Substitute numerical values into expressions with variables and exponents.
• Simplify expressions with variables raised to powers.
• Evaluate algebraic expressions involving exponents.

Working with Negative Exponents

• Understand the meaning of negative exponents — representing reciprocals of positive powers.
• Rewrite expressions with negative exponents as fractions.
• Simplify expressions involving both positive and negative exponents.