Unit 5
INVESTIGATING RATIONAL AND IRRATIONAL NUMBERS

UNIT DESCRIPTION

In grade 8, students use decimal expansion to distinguish between rational and irrational numbers and rational approximations of irrational numbers. They use square root and cube root symbols to represent solutions to equations. In this unit, students will extend their understanding using numerical reasoning to explore the differences between rational and irrational numbers. They will rewrite radical expressions consisting of both algebraic and numerical expressions. They use the operations of addition, subtraction, and multiplication, with radicals within expressions limited to square roots and cube roots, to explain the result of a sum or product of combinations of rational and irrational numbers. This unit provides specific preparation and scaffolding for work with quadratic functions in the subsequent unit.

LEARNING TARGETS

•   I can simplify radical expressions.
• I can perform operations on radical expressions.
• I can distinguish between rational and irrational numbers.
• ​I can determine a rational or irrational solution after performing operations on radical numbers.

TEXTBOOK CONNECTION

Module 8 
Lesson 5- Simplifying Radical Expression: Simplify radical expressions.  
Lesson 6- Operations with Radical Expressions: Students perform operations with radical expressions. 
 
Module 1  
Lesson 3- Properties of Real Number: Students apply the properties of real numbers to simplify expressions. 

IXL 

Radicals:
Simplify- FF.1
Operations- FF.5 (Add/Subtract), FF.4 (Multiply), FF.6 (Multiply)

Rational and Irrational Numbers:
Distinguish- A.8, A.9
Determine- A.10