Big Ideas Algebra 2 Chapter 5
November – December (5 weeks); 1st Semester
Embedded Files
Chapter Title(s):
Rational Exponents and Radical Functions (Chapter 5)
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
Standard(s):
1. Number and Quantity
2. Algebra and Functions
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.
Additional Colorado Academic Standards Resources:
Please visit the complete 2020 Colorado Academic Standards for High School Mathematics to view the following:
Colorado Essential Skills and Mathematical Practices connections
Inquiry Questions
Coherence Connections
Prior Knowledge Connections:
Properties of integer exponents (Grade 8)
Academic Vocabulary & Language Expectations:
nth root of a, index of the radical, simplest form, like radicals, radical function, radical equation, extraneous solutions, inverse functions
Assessments:
SAT Suite Educator Question Bank (Content Domain: Advanced Math)
Instructional Resources & Notes:
Big Ideas Algebra 2 Chapter 5 (skip Lessons 5.5, 5.6)
Additional Modeling Tasks
Swing Time (References: Completing the Modeling Cycle, Advice on Modeling)
Honors Algebra 2:
Honors Algebra 2 students can extend their learning beyond the Colorado Academic Standards with the following concepts and lessons:
Lesson 5.5: Performing Function Operations
Lesson 5.6: Composition of Functions
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