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28 | eureka Math algebra I StuDy guIDe
○ (^) Focus Standards are the major standards that the module targets.
○ (^) Foundational Standards comprise prerequisite knowledge and support the Focus
Standards. These include standards addressed prior to the module that are essential
for student learning and understanding. This section can be helpful in preparing for
teaching lessons and for addressing any gaps that might crop up, especially during
the first couple of years of implementation.
○ (^) Focus Standards for Mathematical Practice act as a guide to create a well-rounded,
standards-aligned classroom environment. This module element highlights which of
the eight Standards for Mathematical Practice are a focus of the module and explains
how each is addressed in the module.
○ (^) Terminology consists of both new and recently introduced terms and familiar terms
and symbols. Definitions of the terms are included in this section.
○ (^) Suggested Tools and Representations provides teachers with a list of the models,
manipulatives, diagrams, and so forth that are recommended to teach the content of
the module.
○ (^) The Assessment Summary gives key information about the assessments of the module,
including where in the module they are given and what standards are addressed.
● (^) Each Topic Overview lists the Focus Standards as well as the lessons associated with the
topic. Each also provides a narrative similar to that found in the Module Overview but
with information regarding specific lessons within the topic.
● (^) Lessons and assessments are the remaining primary parts of the module. The sections
that follow detail these module components.
ApproAch to leSSon Structure
Fluency, concept development, and application, all components of instructional rigor, are
demanded by the new standards and should be layered into daily lessons to help guide
students through the mathematics. Lessons must be structured to incorporate the
development of conceptual understanding, procedural skills, and problem solving. The time
spent on each component of rigor in a daily lesson should vary between lessons and is guided
by the rigor emphasized in the standard(s) the lesson is addressing. Ideally, these components
are taught through the deliberate progression of material. During the early grades, this
progression typically moves from concrete to pictorial to abstract. As students progress
through the grades and into middle and high school, the emphasis remains on moving from
simple to complex, although the dependency on concrete and pictorial representations
diminishes.
All stages of instruction ought to be designed to help students reach higher and
higher levels of understanding. The lesson design in A Story of Functions reflects this
ideal and is an exemplary model of how to achieve the demands that the standards
necessitate. Through a balanced approach to lesson design, A Story of Functions supports
the development of an increasingly complex understanding of the mathematical concepts
and topics within the standards. This type of balanced approach to lesson design naturally
reveals patterns and connections among concepts, tools, strategies, and real-world
applications.