Index | 139relationship between two quantities, 72, 74, 85;
transformations of, 10, 72, 78–79; use function
notation and understand concept of a, 71–72.
See also Quadratic functionsGeometry: constructing viable arguments and
critique reasoning of others,’ 15; definition and
uses of, 10; making sense and use of pattern or
structure, 18; modeling with mathematics, 16;
precision used in, 17; reasoning abstractly and
quantitatively, 15; regularity in repeated
reasoning, 18; strategic use of appropriate
tools, 16–17; terminology of, 107–109
Graphing stories, 50, 55–56
Graphs: analyzing a, 100; cubic, square root, and
cube root functions, 93; exploring symmetry in
quadratic functions, 89; Focus Standards on, 52;
functions and, 56, 77–79; interpreting quadratic
functions from, 90; modeling a context from a,
101; problem solving using functions and, 80–81;
of quadratic functions from factored form, 89;
quadratic functions from the Standard Form, 92;
quadratic functions from the Vertex Form, 92;
represent and solve equations and inequalities
using, 75, 83; stretching and shrinking functions,
93; transformations of functions into, 10, 72,
78–79; water usage during school day, 56
Great Minds: coherent curriculum approach of,
2–3; teaching philosophy and support by, 1–2
Inequalities: applications of systems of equations
and, 60; represent and solve equations and
inequalities graphically, 83; solution sets to
two-variable, 60; solving equations and, 58–60;
solving one variable, 52–53, 74, 85
Instructional Days: Module 1: Relationships
Between Quantities and Reasoning with
Equations and Their Graphs, 9fig, 56, 57, 58, 61;
Module 2: Descriptive Statistics, 9fig, 66, 67, 68,
69; Module 3: Linear and Exponential Functions,
9 fig, 76, 77, 79, 80; Module 4: Polynomial and
Quadratic Expressions, Equations, and Functions,
9 fig, 88, 91, 93; Module 5: A Synthesis of Modeling
with Equations and Functions, 9fig, 100, 101
Instructional Shifts: 1: focus, 11; 2: coherence, 11–12;
3: rigor, 12–14; evidenced during debriefing, 1;
requiring equal intensity of lesson rigor, 30; A
Story of Functions alignment with, 11–14
Integer exponents: linear and exponential
sequences, 70, 75–77; work with radicals and,
54, 73, 85
Invasive Species Population modeling, 80
Irrational numbers properties, 82Lesson 14 (Grade 9 Module 3): classwork examples
of problem sets, 31fig–32fig, 33fig–36fig;
comparing growth rates of linear and exponential
models, 31fig–40fig; discussion of, 33; Exit Ticket
and solutions, 36fig–38; introduction to, 30;
problem set sample solutions, 38fig–40fig;
scaffolding used during, 33, 35; Student
Outcomes of, 31
Lesson structure components: Foundational
Standards, 12; Module Overview, 12; Table of
Contents, 12; Topic Overview, 12
Lesson types: Exploration, 29; Modeling Cycle, 29;
Problem Set, 29, 30–40fig; Socratic, 29
Lessons: approach to the structure of, 28–30;
debriefing built into the, 1; four icons indicating
type of, 29fig; Instructional Shifts requiring
equal intensity of rigor in, 30; narratives used
in, 30; sample Lesson 14 (Grade 9 Module 3),
30–40fig; structural components of, 12. See also
Modeling Cycle lessons
Linear functions: analyze and solve equations, 54;
piecewise, 56, 78–79, 81
Linear models: construct and compare quadratic,
exponential, and, 73, 80; interpreting, 63; linear
and exponential sequences, 70, 75–77; sample
Lesson 14 (Grade 9 Module 3) comparing
exponential and, 30–40fig
Linear problems: making sense and solving, 14;
solving linear equations, 54Major Emphasis Clusters, 20
Mathematic tools: strategic use of, 16–17;
Suggested Tools and Representations in each
module, 28
Mid-Module Assessment Task, 42, 44
Modeling Cycle lessons: analyzing a data set,
100; analyzing a graph, 100; analyzing a verbal
description, 100; build function modeling
relationship between two quantities, 72, 74, 85;
creating equations to solve problems, 50, 60–62;
description and activities of, 29; diagram of basic
modeling cycle, 60–61; Double and Add 5 Game,
61, 62; exponential decay, 77; federal income tax,
62; icon indicating a, 29fig; Invasive Species
Population, 80; modeling a context from a graph,
101; modeling a context from data, 102; modeling
from a sequence, 102; modeling cycle used as
organizing structure in, 94–95. See also Lessons