Major MatheMatICal theMeS In eaCh Grade Band | 13between the current lesson and their previous learning, in addition to listening to and
debating their peers’ perspectives. The goal is to interweave the learning of new concepts
with reflection time into students’ everyday math experience.
At the module level, sequence is everything. Standards within the module and modules
throughout the year carefully build to ensure that students have the requisite understanding
to fully access new learning goals and integrate them into their developing schemas of
understanding. The very deliberate progression of the material follows the critical
instructional areas outlined in the introduction of the standards for each course.
Procedural Skill and Fluency
“the standards call for speed and accuracy in calculation. students are given
opportunities to practice core functions... so that they have access to more complex
concepts and procedures.”^7
A Story of Functions provides students with ample opportunities to practice procedural
skills, but teaching procedures without a rich context is ineffective. Students can too easily
forget procedures and will fail if they do not have deeper, more concrete knowledge from
which they can draw. A Story of Functions weaves the mathematical concepts, applications,
and fluency of the high school story together by relating everything students do back to the
theme of studying functions. Problem sets integrated into lessons for use in class and at home
assist students on their path to fluency.
Application
“the standards call for students to use math flexibly for applications in
problem-solving contexts.”^8
A Story of Functions is designed to help students understand how to choose and apply
mathematics concepts to solve problems. To achieve this, the modules include diagrams that
aid problem solving, interesting problems that encourage students to think quantitatively and
creatively, and opportunities to model situations using mathematics. The goal is for students
to come to see mathematics as connected to their environment, to other disciplines, and to
the mathematics itself. Ranges of problems are presented within modules, topics, and lessons
that serve multiple purposes:
● (^) One-step word problems that help students understand the meaning of a particular
concept.
● (^) Multi-step word problems that support and develop instructional concepts and allow
for the incorporation of multiple concepts into a single problem.
● (^) Exploratory tasks designed to break potential habits of “rigid thinking.”
Problems are designed so that there is a healthy mix of PARCC Type I, II, and III tasks.
The three types of tasks outlined in PARCC are as follows:
Type I: Such tasks include computational problems, fluency exercises, conceptual problems,
and applications, including one-step and multi-step word problems.
Type II: These tasks require students to demonstrate reasoning skills, justify their arguments,
and critique the reasoning of their peers.