Major MatheMatICal theMeS In eaCh Grade Band | 11course. A Story of Functions was specifically designed to prepare high school students to take
Calculus in their senior year or as a first-year college course. In particular, the functions and
mathematical definitions used throughout A Story of Functions are the same as those used in
the most popular calculus textbooks—every effort was made to prepare students for a smooth
transition to Calculus and other advanced mathematics courses in college.
how A Story of functionS aLigns with the instruCtionaL shifts
A Story of Functions is structured around the essential Instructional Shifts needed to
implement the new college- and career-ready standards. These principles, articulated as three
shifts (focus, coherence, and rigor), help educators understand what is required to implement
the necessary changes. Rigor involves fluency, conceptual understanding, and application—
and all three are achieved with a dual-intensity emphasis on practicing and understanding.
shift 1: foCus
“f ocus deeply on the major work of each grade so that students can gain strong
foundations.”^1
The Publishers’ Criteria states: “Focus in high school is important in order to prepare
students for college and careers.”^2 Evidence of focus is seen in A Story of Functions through
the integral use of the Partnership for Assessment of Readiness for College and Careers
(PARCC) Content Emphases to focus on the major work of the course. Each module contains
Focus Standards clearly stating the clusters of standards that are emphasized in the material.
As noted in the Publishers’ Criteria, “a college-ready curriculum... should devote the
majority of students’ time to building the particular knowledge and skills that are most
important as prerequisites for a wide range of college majors, postsecondary programs, and
careers.”^3 Assessments concentrate on the work of the course and do not test students on
content from prior courses or grade levels.
Foundational Standards are identified in each module so that teachers are empowered
to assess and address gaps in prerequisite understanding as they begin the module. These
standards are clearly distinguished from the major work of the course so that there is no
question for teachers and students what their specific responsibilities are for the current year.
Student Outcomes are provided at the start of each lesson. These outcomes clarify
expectations and are clearly shaped by the standards. Lessons allow students to work
extensively with problems and exercises that are course appropriate.
shift 2: CoherenCe
“Learning is carefully connected across grades so that students can build new
understanding onto foundations built in previous years.”^4
A Story of Functions is not a random collection of topics. Rather, the modules and topics
in the curriculum are woven through the progressions of the standards. A Story of Functions
carefully prioritizes and sequences the standards with a deliberate emphasis on mastery of
major cluster standards. Modules connect supporting content to the major work of the