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12 | eureka Math alGeBra II Study GuIde
course in meaningful ways that enhance coherence. This meticulous sequencing enables
students to transfer their mathematical knowledge and understanding to new, increasingly
challenging concepts.
In each module, the Table of Contents shows how topics are aligned with standards to
create an instructional sequence that is organized precisely to build on previous learning and
to support future learning.
The Module Overview and Topic Overview narratives outline the instructional path, as
do the Student Outcomes listed at the beginning of each lesson. The sequence of problems
in the material is structured to help teachers analyze the mathematics for themselves and
to help them differentiate instruction: As students advance from simple concepts to more
complex, the different problems provide opportunities for teachers to either (1) break
problems down for students struggling with a next step or (2) stretch problems out for those
hungry for greater challenges. Modules include problems and exercises that connect two or
more clusters in a domain or two or more domains in a course in meaningful ways, further
developing coherence.
Foundational Standards assist teachers and students in relating course concepts
explicitly to prior knowledge from previous courses or grades. New learning is built on an
existing foundation of common knowledge shared by students, allowing connections to be
made between new and previously learned content.
shift 3: rigor
“i n major topics pursue: conceptual understanding, procedural skill and fluency,
and application with equal intensity.”^5
The three-pronged nature of rigor undergirds a main theme of the Publishers’ Criteria.
Each of the three components of rigor—fluency, deep understanding, and application—must
drive instruction with equal intensity for students to meet the standards’ rigorous
expectations.
Lessons provide problems designed to develop deep conceptual understanding, connect
the content with mathematical and real-world problems, and cultivate fluency of newly
developed skills. The distribution of tasks in each of the rigor categories is not prescribed
but is driven by the content itself.
Conceptual Understanding
“s tudents must be able to access concepts from a number of perspectives in order
to see math as more than a set of mnemonics or discrete procedures.”^6
Conceptual understanding requires far more than performing discrete and often
disjointed procedures to determine an answer. Students must not only learn mathematical
content but also be able to access that knowledge from numerous vantage points and
communicate about the process. In A Story of Functions, students use writing and speaking
to solve mathematical problems, reflect on their learning, and analyze their thinking. The
lessons and problem sets frequently require students to write solutions to word problems.
Thus students learn to express their understanding of concepts and articulate their thought
processes through writing. Similarly, students learn to verbalize the patterns and connections