140 | Index
Modeling with mathematics: completing the
modeling cycle, 95, 100–102; diagram of basic
modeling cycle, 60–61; elements of, 95, 99–100;
modules for development of, 16; Suggested
Tools and Representations for, 28
Module 1 (Relationships Between Quantities and
Reasoning with Equations and Their Graphs):
aligned with the standards, 22; Focus Standards,
51–52, 56, 57, 58, 61; Focus Standards for
Mathematical Practice, 54–55; Foundational
Standards, 52–54; Instructional Days for, 9fig,
56, 57, 58, 61; Module Topic Summaries, 55–62;
overview of the, 50; rational for sequence of,
20–21; terminology of, 103–104
Module 1 topic summaries: Topic A: Introduction to
Functions Studied This Year––Graphing Stories,
50, 55–56; Topic B: The Structure of Expressions,
50, 56–58; Topic C: Solving Equations and
Inequalities, 50, 58–60; topic D: Creating
Equations to Solve Problems, 50, 60–62
Module 2 (Descriptive Statistics): aligned with the
standards, 23; Focus Standards, 63, 66, 67, 68,
69; Focus Standards for Mathematical Practice,
65; Foundational Standards, 64–65;
Instructional Days for the, 9fig, 66, 67, 68, 69;
Module Topic Summaries, 65–70; overview of
the, 62–63; rational for sequence of, 21;
terminology of, 104–105
Module 2 topic summaries: Topic A: Shapes and
Centers of Distributions, 65–66; Topic B:
Describing and Comparing Distributions, 67–68;
Topic C: Categorical Data on Two Variables, 68;
Topic D: Numerical Data on Two Variables, 68–70
Module 3 (Linear and Exponential Functions):
aligned with the standards, 23–24; Focus
Standards, 71–73, 76, 77, 79, 80; Focus Standards
for Mathematical Practice, 75; Foundational
Standards, 73–75; Instructional Days for the,
9 fig, 76, 77, 79, 80; Module Topic Summaries,
75–81; overview of the, 70–71; rational for
sequence of, 21; sample Lesson 14 in, 30–40fig;
terminology of, 105
Module 3 topic summaries: Topic A: Linear and
Exponential Sequences, 70, 75–77; Topic B:
Functions and Their Graphs, 70, 77–78; Topic C:
Transformations of Functions, 71, 78–79; Topic
D: Using Functions and Graphs to Solve
Problems, 71, 80–81
Module 4 (Polynomial and Quadratic Expressions,
Equations, and Functions): aligned with the
standards, 25–26; Focus Standards, 82–84, 88,
90–91, 93; Focus Standards for Mathematical
Practice, 85–87; Foundational Standards, 84–85;
Instructional Days for the, 9fig, 88, 91, 93;
Module Topic summaries, 87–94; overview of
the, 81–82; rational for sequence of, 21;
terminology of, 105–106
Module 4 topic summaries: Topic A: Quadratic
Expressions, Equations, Functions, and Their
Connection to Rectangles, 81, 87–90; Topic B:
Using Different Forms for Quadratic Functions,
81–82, 90–92; Topic C: Function
Transformations and Modeling, 82, 92–94
Module 5 (A Synthesis of Modeling with Equations
and Functions): aligned with the standards,
26; Focus Standards, 96, 99–100, 101; Focus
Standards for Mathematical Practice, 97–98;
Foundational Standards, 97; Instructional Days
for the, 9fig, 100, 101; Module Topic Summaries,
99–102; overview of the, 94–95; rational for
sequence of, 21; terminology of, 106
Module 5 topic summaries: Topic A: Elements of
Modeling, 95, 99–100; Topic B: Completing the
Modeling Cycle, 95, 100–102
Module Overview: coherence supported by the,
12; description and function of, 27; lesson
structure component of, 12
Multiplying polynomials, 58, 88–89Narratives in lessons, 30
New York State Education Department, 2
Newton’s Law of Cooling, 80
Numbers: create equations that describe
relationships or, 83, 85; extending
understanding of rational, 52; know that not all
are rational and approximate them by rational,
84; use properties of rational and irrational, 82;
write equations that describe relationships or,
51, 71, 74One-variable equations and inequalities:
representing and interpreting one-variable
data, 63; solving, 52–53, 75, 83, 85; zero product
property lesson on, 89PARCC (Partnership for Assessment of Readiness
for College and Careers): on importance of
focus, 11; Problem Sets Types I, II, III tasks, 13–14
Patterns. See Structure in expressions
Pictorial models, 12
Piecewise functions, 56, 78–79, 81
Polynomials: adding and subtracting, 58; Focus
Standards on arithmetic operations on, 51;
multiplying, 58; perform arithmetic operations