Algebra 1B — Functions, Exponential and Quadratic Models is the second semester of a full-year Algebra I course built on the California Common Core State Standards for Mathematics and the Standards for Mathematical Practice.
Four units: Functions, Introduction to Exponential Functions, Introduction to Quadratic Functions and Quadratic Equations. Students model tiered utility rates with piecewise and inverse functions, study exponential growth and decay, launch and model real projectiles, derive the quadratic formula and defend a design problem solved with it.
Sources: the unit sequence and task design are adapted from an openly licensed high-school Algebra 1 curriculum (CC BY 4.0), with original lessons written for this course; OpenStax Elementary Algebra 2e and Intermediate Algebra 2e (CC BY-NC-SA 4.0; referenced, not reproduced) are reference texts; PhET Interactive Simulations (CC BY 4.0) and free graphing tools support the investigations.
Curriculum
- 4 Sections
- 20 Lessons
- Lifetime
- Unit 1: Functions5
- 1.1One Input, One Output: What Makes a Function50 mins
- 1.2Reading Graphs and Tables: Features and Average Rate of Change50 mins
- 1.3Pieces, Steps and Corners: Piecewise and Absolute Value Functions50 mins
- 1.4Working Backward: Tiered Rates and Inverse Functions100 mins
- 1.5Performance Task — Decode a Utility Bill150 mins
- Unit 2: Introduction to Exponential Functions5
- 2.1Adding or Multiplying? Linear and Exponential Change50 mins
- 2.2Sequences and Exponent Rules, Including Rational Exponents50 mins
- 2.3Reading the Rate: Interpreting and Rewriting Exponential Expressions50 mins
- 2.4Building and Graphing Exponential Models100 mins
- 2.5Performance Task — Exponential or Not?150 mins
- Unit 3: Introduction to Quadratic Functions5
- 3.1A New Pattern: Area, Second Differences and Quadratic Growth50 mins
- 3.2Polynomial Arithmetic: Adding, Subtracting and Multiplying50 mins
- 3.3Three Forms, One Parabola: Vertex Form and Transformations50 mins
- 3.4Falling Objects and Revenue: Quadratic Models in Context100 mins
- 3.5Performance Task — Launch Lab150 mins
- Unit 4: Quadratic Equations5
Instructor
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