Big Ideas Algebra 1 Chapter 6
January – February (5 weeks); 2nd Semester
Big Ideas Algebra 1 Chapter 6
January – February (5 weeks); 2nd Semester
Chapter Title(s):
Exponential Functions and Sequences (Chapter 6)
Prepared Graduates:
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP4. Model with mathematics.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning.
Standard(s):
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):
Big Ideas Algebra 1 Chapter 6 focuses on the family of exponential functions. Consult Algebra 1 Families of Functions for additional evidence outcomes that apply to exponential functions.
HS.F-IF.A. Interpreting Functions: Understand the concept of a function and use function notation.
Demonstrate that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n − 1) for n ≥ 1. (CCSS: HS.F-IF.A.3)
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 exponential functions, showing intercepts and end behavior. (CCSS: HS.F-IF.C.7.e)
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (CCSS: HS.F-IF.C.8)
Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. (CCSS: HS.F-IF.C.8.b)
HS.F-BF.A. Building Functions: Build a function that models a relationship between two quantities.
Write geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.⭑ (CCSS: HS.F-BF.A.2)
HS.F-LE.A. Linear, Quadratic & Exponential Models: Construct and compare linear, quadratic, and exponential models and solve problems.⭑
Distinguish between situations that can be modeled with linear functions and with exponential functions. (CCSS: HS.F-LE.A.1)
Prove that exponential functions grow by equal factors over equal intervals. (CCSS: HS.F-LE.A.1.a)
Identify situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. (CCSS: HS.F-LE.A.1.c)
Construct exponential functions, including geometric sequences, given a description of a relationship. (CCSS: HS.F-LE.A.2)
HS.F-LE.B. Linear, Quadratic, & Exponential Models: Interpret expressions for functions in terms of the situation they model.⭑
Interpret the parameters in an exponential function in terms of a context. (CCSS: HS.F-LE.B.5)
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:
Exponential function, asymptote, exponential growth, exponential growth function, exponential decay, exponential decay function, compound interest, geometric sequence, common ratio, explicit rule, recursive rule
Assessments:
SAT Suite Educator Question Bank (Content Domains: Advanced Math, Problem-Solving and Data Analysis)
Instructional Resources & Notes:
Big Ideas Algebra 1 Chapter 6 (skip Lessons 6.2, 6.5)
Additional Modeling Tasks
Notes:
Lesson 6.2 (Radicals and Rational Exponents) and Lesson 6.5 (Solving Exponential Equations) address evidence outcomes in Algebra 2. Lesson 6.2 and Lesson 6.5 should be skipped.
Accelerated Algebra 1:
Accelerated Algebra 1 students can extend their learning beyond the Colorado Academic Standards with the following concepts and lessons:
Lesson 6.5: Solving Exponential Equations