United University

Algebra Grade 7. Integer expressions. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 30 hrs
Language version

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   An engaging, interactive course designed for children, featuring interactive tests and exercises.

This interactive course introduces students to integer expressions, focusing on understanding fundamental algebraic concepts and developing problem-solving skills through hands-on activities. The course offers a structured and fun approach to learning, helping students build confidence and fluency in algebraic manipulations. Designed for independent and collaborative study, it emphasizes critical thinking and a deeper comprehension of mathematical principles.

Key Concepts Covered in the Course

  • Expressions with Variables: Numeric and algebraic expressions
  • Identities and Transformations: Simplification and proof of identities
  • Powers: Natural exponents and their properties
  • Polynomials: Addition, subtraction, multiplication, and factoring
  • Special Products: Squares and cubes of sums and differences

Course Modules

Module 1: Integer Expressions

  • Lesson 4: Expressions with variables. Integer rational expressions. Numerical value of an expression.
    Practice Problems and Exercises
  • Lesson 5: Equivalent expressions. Identity.Equivalent transformation of an expression.
    Practice Problems and Exercises
  • Lesson 6: Powers with Natural Exponents
    Practice Problems and Exercises
  • Lesson 7: Properties of Powers
    Practice Problems and Exercises
  • Lesson 8: Monomials: Standard Form and Operations
    Practice Problems and Exercises
  • Lesson 9: Multiplication and Powers of Monomials
    Practice Problems and Exercises
  • Lesson 10: Introduction to Polynomials: Combining Like Terms
    Practice Problems and Exercises
  • Lesson 11: Adding and Subtracting Polynomials
    Practice Problems and Exercises
  • Lesson 12: Multiplying Monomials and Polynomials
    Interactive Activities
  • Lesson 13: Factoring Polynomials by Grouping and Common Factors
    Practice Problems and Exercises
  • Lesson 14: Multiplying Polynomials
    Practice Problems and Exercises
  • Lesson 15: Advanced Factoring Techniques
    Practice Problems and Exercises
  • Lesson 16: Special Products: Squares and Differences
    Practice Problems and Exercises
  • Lesson 17: Factoring Using Special Product Formulas
    Practice Problems and Exercises
  • Lesson 18: Multiplying the Sum and Difference of Two Terms
    Practice Problems and Exercises
  • Lesson 19: Factoring Differences of Squares
    Practice Problems and Exercises
  • Lesson 20: Sum and Difference of Cubes
    Practice Problems and Exercises
  • Lesson 21: Applying Multiple Factoring Techniques
    Practice Problems and Exercises
    Homework Assignment 4
    Exercises to Check Understanding of Paragraphs 16-21

Expected Learning Outcomes

By the end of this course, students will:

  • Understand the fundamental concepts of numeric and variable expressions
  • Identify, simplify, and transform algebraic expressions
  • Master operations with powers and polynomials
  • Apply special product formulas to solve complex problems
  • Analyze and factor polynomials using multiple strategies
  • Develop logical reasoning and systematic problem-solving skills
  • Collaborate effectively in group settings and complete independent tasks

This interactive course combines engaging exercises with a structured learning path, enabling students to explore algebra with curiosity and confidence. Through practical examples and challenging tasks, students will gain the skills needed for advanced mathematical studies.

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