The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.

Students Can (Evidence Outcomes):

HS.N-RN.A. The Real Number System: Extend the properties of exponents to rational exponents. 

• Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. (CCSS: HS.N-RN.A.1)

• Rewrite expressions involving radicals and rational exponents using the properties of exponents. (CCSS: HS.N-RN.A.2)

HS.A-REI.A. Reasoning with Equations & Inequalities: Understand solving equations as a process of reasoning and explain the reasoning.

• Solve simple radical equations in one variable, and give examples showing how extraneous solutions may arise. (CCSS: HS.A-REI.A.2)

HS.F-IF.C. Interpreting Functions: Analyze functions using different representations. 

• Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.⭑ (CCSS: HS.F-IF.C.7)

  • Graph square root, cube root functions. (CCSS: HS.F-IF.C.7.b)

HS.F-BF.B. Building Functions: Build new functions from existing functions. 

• Find inverse functions. (CCSS: HS.F-BF.B.4)

  • Solve an equation in the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2x3 or f(x) = (x + 1)/(x – 1) for x ≠ 1. (CCSS: HS.F-BF.B.4.a)

A star symbol (⭑) represents grade level expectations and evidence outcomes that make up a mathematical modeling standards category.

Assessments:

• Chapter 5 Assessment (PDF)

• SAT Suite Educator Question Bank (Content Domain: Advanced Math)

• Additional Assessment Tasks

Instructional Resources & Notes:

• Big Ideas Algebra 2 Chapter 5 (skip Lessons 5.5, 5.6)

• Supplemental Lesson Resources for Chapter 5

• Additional Modeling Tasks

  • Swing Time (References: Completing the Modeling Cycle, Advice on Modeling)

• Notes: 

  • Lesson 5.1 (nth Roots and Rational Exponents) assumes students are familiar with rational exponents from Algebra 1. Teachers may choose to pull examples and exercises from Lesson 6.2 (Radicals and Rational Exponents) in Algebra 1 before starting Chapter 5.

    • Big Ideas Algebra 1 Lesson 6.2 - Radicals and Rational Exponents (Teaching Edition)