Year 1 of Implementation

Pre-Calculus

Year 1 of Implementation

East High School

72 Minute Blocks

Unit / CCSSM Content Standards / CCSSM Practice Standards / Investigations/Additional Work / Big Ideas of the Unit / Essential Questions / Time Frame (classes)
Unit 1
Functions: Polynomial and Rational / A.SSE.1
A.SSE.2
A.APR.1
A.APR.2
A.APR.3
A.APR.6
A.APR.7
A.CED.2
F.IF.1
F.IF.2
F.IF.4
F.IF.5
F.IF.7
F.IF.8
F.BF.1
N.CN.1
N.CN.2
N.CN.7
A.SSE.1
A.SSE.3
A.REI.1
A.REI.4
A.REI.a0 G.GPE.1
Connected to
A.CED.1
F.IF.5
F.BF.3
G.MG.3
G.SRT.5
G.SRT.6
S.ID.6
N.CN.4
N.CN.9
N.VM.8
F.IF.7 / Opportunities to engage in the standards for mathematics practice / Core-Plus Mathematics
CORE 3
Unit 5 Polynomial and Rational Functions
Lesson 1: Polynomial Expressions and Functions
Lesson 2: Review of Solving Quadratics with complex roots
Lesson 3: Investigations 1, 2: Rational Functions / Model problems using polynomial or rational functions
Identify patterns relating rules and graphs of polynomial functions
Review operations with polynomial expressions
Find zeroes of polynomial functions and write rules give the zeroes
Analyze graphs of rational functions and asymptotes / How can problem situations be modeled and analyzed using polynomial or rational functions?
How can multiple representation be used to analyze polynomial or rational functions? / 15
Unit 2: Circular Motion and Periodic Functions / G.SRT.6
G.SRT.7
G.SRT.8
F.BF.3
F.TF.1
F.TF.2
F.TF.3
F.TF.5
G.C.O.6
G.MG.1
G.MG.3N
Coneected to
NQ.3
NQ,1
N.VM.11
N.VM.12
F.IF.7
F.IF.8 / Opportunities to engage in the standards for mathematics practice / Core-Plus 2
Unit 7: Circular Motion
Lesson 1: Investigation 1
Connecting angle measures and linear measures
Include the connection questions p.477: 9-13 to extend beyond the first quadrant
Core-Plus 3
Unit 6: Lesson 2
Circular Motion and Periodic Functions / Determine values of sine, cosine and tangent of an angle in standard position in the coordinate plane using (x,y,r)
Determine the sine, cosine, tangent of an acute angle in a right triangle and determine the angle if given one of the trig values
Analyze linear and angular velocity
Understand what a radian is and how it can be used
Define sine and cosine as functions of real numbers and analyze the resulting periodic graphs
Use sine and cosine functions to model periodic patterns of change / How are angular and linear measure related?
How can sine, cosine and tangent be defined in terms of x, y and r?
How can symmetry and the coordinate grid be used to justify properties of trig functions?
How are angular and linear velocity related?
What is radian measure and why is it important?
How can sine and cosine be used to model periodic patterns of change in physical phenomena? / 10
Unit 3: Inverse Functions / F.IF.1
F.IF.4
F.IF.5
F.IF.7
F.IF.8
F.BF.1
F.BF.4
F.BF.5
F.LE.4
F.TF.5
F.TF.6
F.TF.7
A.CED.1
A.REI.1
Connected to
N.VM.8
A.REI.10
A.REI.11
F.IF.7
S.ID.6
A.CED.1
A.SSE.1
A.SSE.3
A.CED.2 / Opportunities to engage in the standards for mathematics practice / Students may need some short introductory log work from CORE 2 Unit 5 Lesson 2 before beginning this
Core Plus 3
Unit 8:
Lesson 1: What is an Inverse Function?
Lesson 2: Common Logarithms and Their Properties
Lesson 3: Inverse Trigonometric Functions / Understand inverse functions
Solve problems with direct and indirect variation
Use multiple representation to make sense of functions
Define and evaluate common logarithms
Use logarithms to solve exponential equations
Develop and use the properties of logarithmic functions
Define and use the inverse trig functions
Express the general solution of a trig equation
Use trig equation and their solutions to answer questions about periodic phenomena / What is the inverse of a functions and how is it used?
How can common logarithms be used to solve exponential equations?
How can the properties of logarithms be used to express relationships? / 14
Unit 4: Families of Functions / F.IF.1
F.IF.3
F.IF.4
F.IF.5
F.IF.7
F.IF.8
F.IF.9
F.BF.2
F.LE.5
Connected to
A.CED.1
A.CED.2
F.IF.2
F.BF.1
F.LE.4
F.TF.5
G.GMD.3
G.MG.2 / Opportunities to engage in the standards for mathematics practice / Core Plus 4
Unit 1; Families of Functions
Lesson 1 Function Models Revisited
Lesson 2: Customizing Models by Translation and Reflection
Lesson 3: Customizing Models by Stretching and Compressing
Lesson 4: Combining Functions / Multiple Representation
Families of Functions
Patterns of Change
Transformations of Functions
Combining Functions—arithmetic and composition / How can multiple representation be used to analyze families of functions?
How can transformations be used to modify functions and how do the affect the properties of the functions?
How can functions be combined and what does it mean? / 24
Unit 5: Trigonometric Functions and Equations / A.SSE.1
A.SSE.2
A.SSE.3
F.IF.4
F.IF.7
F.IF.8
F.TF.3
F.TF.4
F.TF.5
F.TF.6
F.TF.7
F.TF.8
F.TF.9
G.SRT.8
N.CN.2
N.CN.3
N.CN.4
N.CN.5
N.CN.9
G.CO.2
Connected to
A.REI.1
A.REI.4
A.REI.10
A.REI.11
A.CED.2
F.BF.1
F.BF.3
G.SRT.10
G.SRT.11
N.VM.4
N.VM.5 / Opportunities to engage in the standards for mathematics practice / CORE Plus 4
Unit 4: Trigonometric Functions and Equations
Lesson 1: Reasoning with Trigonometric Functions (don’t emphasize proving identities) The second investigation can become tedious. Students should be aware that there are other identities but it is not necessary to prove these.
Lesson 2: Solving Trigonometric Equations
Lesson 3: The Geometry of Complex Numbers / Know and be able to use the definitions of the six trigonometric functions
Use the fundamental trigonometric identities
Solve trigonometric equations
Represent complex numbers geometrically and interpret multiplication and division of these numbers geometrically
Use DeMoivre”s Theorem to find roots and powers of complex numbers / How can trigonometric identities be used to transform relationships?
How can trigonometric equations be solve symbolically?
How can complex numbers be represented geometrically?
How can calculations with complex numbers be represented geometrically? / 20
Unit 6: Exponential Functions and Logarithms / A.SSE.1
A.SSE.2
F.IF.4
F.IF.7
F.IF.8
F.BF.5
F.LE.5
Connected to
A.REI.1
F.IF.3 / Opportunities to engage in the standards for mathematics practice / CORE Plus 4
Unit 5: Lesson 1
Exponential Functions and Natural Logs / Understand e as a limit
Use exponential functions with a base of e to solve growth and decay problems
Rewrite exponential equations with a base of e and logarithms with a base of 10 or e
Use properties of exponents and logarithms to solve problems / What is e and how is it used in mathematics?
How care exponential and logarithmic equations related?
How can exponents and logarithms be used to solve problems? / 7

Optional Units: Recursion and Iteration: CORE 3: Unit 7 Lesson 1 and 2 (Using recursion for problem solving; series and sequences)

Vectors: and Motion: CORE 4: Unit 2

Mathematics Outreach Division

Center for Professional Development and Education Reform

Warner Graduate School of Education and Human Development

University of Rochester • PO Box 270425 • Rochester, NY 14627 • 585-275-2616