Major MatheMatICal theMeS In eaCh Grade Band | 9the signifiCanCe of funCtions
Functions are the central objects in most fields of modern mathematics. They are also
one of the fundamental tools that scientists use to model physical phenomena. A function is a
correspondence between two sets in which each input element of the first set corresponds to
one and only one output element of the second set. This definition generalizes the notion of
proportional and linear relationships that students studied in middle school. In those grades,
these relationships were represented by equations in which there was an independent
variable (usually denoted by x) and a dependent variable (usually denoted by y). In high school,
a linear relationship is represented as a function f from the set of real numbers to the set of
real numbers by fx()=+mx b (where m is the rate of change and b is the initial value). It is then
generalized to exponential, polynomial, rational, trigonometric, and logarithmic functions
throughout high school.
Figure 2.3 Grades 9–12 Year-Long Curriculum Map: A Story of FunctionsGrade 9 – Algebra IGrade 10 – GeometryGrade 11 – Algebra IIM1:
Relationships Between
Quantities and Reasoning
with Equations and
Their Graphs
(40 days)M1:
Congruence, Proof, and
Constructions
(45 days)M1:
Polynomial, Rational, and
Radical Relationships
(45 days)M2:
Tr igonometric Functions
(20 days)M3: Extending to Three
Dimensions (15 days)M3: Exponential and
Logarithmic Functions
(45 days)M4: Connecting Algebra
and Geometry through
Coordinates (20 days)
M4:
Inferences and
Conclusions from Data
(40 days)M4:
Polynomial and
Quadratic Expressions,
Equations, and Functions
(30 days)
M5:
Circles with and Without
Coordinates
(25 days)M5:
A Synthesis of Modeling
with Equations and
Functions (20 days)Grade 12 – PrecalculusM1:
Complex Numbers and
Tr ansformations
(41 days)M2:
Vectors and Matrices
(36 days)M3:
Rational and Exponential
Functions
(26 days)M4: Tr igonometry
(21 days)M5:
Probability and Statistics
(26 days)M2:
Descriptive Statistics
(25 days)30 days allotted for
review and examinations**30 days allotted for
review and examinations**30 days allotted for
review and examinations**30 days allotted for
review and examinations**M2:
Similarity, Proof, and
Tr igonometry
(45 days)
M3:
Linear and Exponential
Functions (35 days)1st TRIMESTER2nd TRIMESTER3rd TRIMESTER1st QUARTER2nd QUARTER3rd QUARTER4th QUARTERKey: Number and Quantityand Modeling Geometry andModeling Algebra andModeling Statistics and Probabilityand Modeling Functions andModeling*The columns indicating trimesters and quarters are provided to give you a rough guideline. Please use your own pacing considerations based
on the specific dates of your academic calender.
**Note that each high school grade accounts for 150 instructional days, allowing 30 days fo r teachers to address concerns and administer end of
course exams.