• ## Course 3, Module 4: Expanding Number Systems

In this module, students connect number, equations, and geometry. They will explore the properties that define the number systems that they are familiar with and then learn about a new system. Students will develop an understanding of the Pythagorean Theorem and its converse and then apply those theorems to solve real-world problems.

Topic 1: The Real Number System

• In this topic, students build onto their knowledge of number systems to include the set of irrational numbers. After recalling what they already know about rational numbers, they'll begin formalizing the properties of each set and learning about irrational numbers.
• MATHia Workspaces (3)
• Introduction to Irrational Numbers
• Graphing Real Numbers on a Number Line
• Ordering Rational and Irrational Numbers

Topic 2: Pythagorean Theorem

• In this topic, students explore the Pythagorean Theorem and its converse. Students will apply the Pythagorean Theorem to real-world and mathematical problems, including determining the length of diagonals of two- and three-dimensional geometric figures.
• MATHia Workspaces (4)
• Exploring the Pythagorean Theorem
• Applying the Pythagorean Theorem
• Problem Solving Using the Pythagorean Theorem
• Calculating Distances on the Coordinate Plane