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Integrated Math I

Course Overview

  • Introduction to Integrated Mathematics: Importance and Application

  • Role of Algebra, Geometry, and Data Analysis in Real-Life Problem Solving

  • The Concept of Mathematical Thinking and Problem Solving

  • The Structure of Integrated Math: Combining Various Disciplines

Algebraic Concepts

  • Solving Linear Equations and Inequalities

  • Understanding and Applying Functions

  • Graphing Linear Equations and Functions on the Coordinate Plane

  • Systems of Equations and Methods of Solving (Substitution, Elimination)

  • Exponents and Powers: Laws of Exponents

  • Solving and Graphing Quadratic Equations

Geometry

  • Geometric Shapes and Properties (Lines, Angles, Triangles, Polygons, Circles)

  • Congruence and Similarity: Transformations and Symmetry

  • Perimeter, Area, and Volume Calculations for Various Shapes

  • The Pythagorean Theorem and Its Applications

  • Coordinate Geometry: Slope, Distance, Midpoint Formula

  • The Basics of Trigonometry (Sine, Cosine, Tangent)

Data Analysis & Probability

  • Descriptive Statistics: Mean, Median, Mode, Range

  • Probability Theory and Counting Principles

  • Graphing and Interpreting Data: Bar Graphs, Histograms, Box Plots

  • Analyzing and Interpreting Scatter Plots and Correlations

  • Measures of Central Tendency and Variability

  • Introduction to Conditional Probability and Events

Functions & Modeling

  • Understanding Functions and Their Notation

  • Linear Functions: Graphing and Interpreting Slopes and Y-Intercepts

  • Introduction to Non-Linear Functions (Quadratic, Exponential)

  • Creating and Interpreting Function Models for Real-World Situations

  • Solving Word Problems Using Functions

Problem Solving Strategies

  • Developing Problem-Solving Skills Through Mathematical Practices

  • Analyzing Word Problems and Identifying Mathematical Models

  • Using Multiple Representations (Algebraic, Graphical, Numerical)

  • Strategies for Checking Solutions and Estimating Results

  • Applying Math Concepts to Real-Life Contexts

Mathematical Reasoning

  • The Role of Logic in Mathematics: Deductive vs. Inductive Reasoning

  • Building Mathematical Proofs: Statements, Postulates, and Theorems

  • Understanding and Applying Properties of Numbers and Operations

  • Recognizing Patterns and Sequences in Mathematics

  • The Importance of Communication in Mathematics: Explaining Solutions Clearly

Connections to Other Mathematical Disciplines

  • How Algebra and Geometry Interact

  • Connections Between Linear Functions and Geometry

  • Relating Data Analysis to Algebraic and Geometric Concepts

  • Using Trigonometry in Different Mathematical Contexts

  • Mathematical Modelling in Real-Life Applications

Technology in Math

  • Using Graphing Calculators and Software Tools for Problem Solving

  • Introduction to Spreadsheet Software for Data Analysis

  • Modeling Real-World Scenarios Using Technology

  • The Role of Technology in Visualizing Geometric and Algebraic Concepts

Assessment & Practice

  • Regular Quizzes and Tests on Key Topics

  • Midterm and Final Exams: Cumulative Review and Application of Concepts

  • Group Projects and Presentations on Math Applications

  • Homework Assignments for Reinforcement and Practice

  • Opportunities for Extra Credit and Peer Tutoring

Preparation for Integrated Math II

  • Reviewing Key Concepts to Prepare for Advanced Topics

  • Transitioning from Algebra and Geometry to Higher-Level Math

  • Exploring the Next Steps in Mathematical Reasoning and Applications