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Scope and Sequence Algebra and Functions Geometry and Trigonometry Statistics and Probability Discrete Mathematics
ISBN: 978-0-07-892135-3MHID: 0-07-892135-X
www.glencoe.com
Visit us at www.glencoe.com
Christian R. Hirsch • James T. Fey • Eric W. Hart Harold L. Schoen • Ann E. Watkins
with
Beth E. Ritsema • Rebecca K. Walker • Sabrina Keller Robin Marcus • Arthur F. Coxford • Gail Burrill
Scope and Sequence
ii CPMP • Scope and Sequence
Copyright © 2009 by the McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher.
This material is based upon work supported, in part, by the National Science Foundation under grant no. ESI 0137718. Opinions expressed are those of the authors and not necessarily those of the Foundation.
Send all inquires to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 978-0-07-892135-3 Core-Plus MathematicsMHID: 0-07-892135-X Contemporary Mathematics in Context
Scope and Sequence
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CPMP • Scope & Sequence iii
About the Core-Plus Mathematics Project
The Core-Plus Mathematics Project (CPMP) was funded by the National Science Foundation to
develop student and teacher materials for a comprehensive Standards-based high school mathematics
curriculum. Courses 1–3 comprise a core program appropriate for all students. Course 4 continues the
preparation of students for college mathematics and statistics.
Senior Curriculum Developers
Christian R. Hirsch (Director)Western Michigan University
James T. FeyUniversity of Maryland
Eric W. HartMaharishi University of Management
Harold L. SchoenUniversity of Iowa
Ann E. WatkinsCalifornia State University,
Northridge
Contributing Curriculum
Developers
Beth E. RitsemaWestern Michigan University
Rebecca K. WalkerGrand Valley State University
Sabrina KellerMichigan State University
Robin MarcusUniversity of Maryland
Arthur F. Coxford (deceased)University of Michigan
Gail BurrillMichigan State University
(First edition only)
Principal Evaluator
Steven W. ZiebarthWestern Michigan University
Advisory Board
Diane BriarsPittsburgh Public Schools
Jeremy KilpatrickUniversity of Georgia
Robert E. MegginsonUniversity of Michigan
Kenneth RuthvenUniversity of Cambridge
David A. SmithDuke University
Mathematical Consultants
Deborah Hughes-HallettUniversity of Arizona /
Harvard University
Stephen B. MaurerSwarthmore College
William McCallumUniversity of Arizona
Doris SchattschneiderMoravian College
Richard ScheafferUniversity of Florida
Evaluation Consultant
Norman L. WebbUniversity of Wisconsin-Madison
Collaborating Teachers
Mary Jo MessengerHoward Country Public Schools,
Maryland
Jacqueline StewartOkemos, Michigan
Technical Coordinator
James LaserWestern Michigan University
Production and Support Staff
Angie Reiter
Matt Tuley
Teri ZiebarthWestern Michigan University
Graduate Assistants
Allison BrckaLorenz
Christopher HlasUniversity of Iowa
Madeline Ahearn
Geoffrey Birky
Kyle Cochran
Michael Conklin
Brandon Cunningham
Tim Fukawa-Connelly
Ming TomaykoUniversity of Maryland
Karen Fonkert
Dana Grosser
Anna Kruizenga
Nicole Lanie
Diane MooreWestern Michigan University
Undergraduate Assistants
Cassie DurginUniversity of Maryland
Rachael Kaluzny
Megan O’Connor
Jessica Tucker
Ashley WiersmaWestern Michigan University
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iv CPMP • Scope and Sequence
Core-Plus Mathematics 2Field-Test Sites
Core-Plus Mathematics 2 builds on the strengths of the 1st edition which was shaped by multi-year fi eld
tests in 36 high schools in Alaska, California, Colorado, Georgia, Idaho, Iowa, Kentucky, Michigan,
Ohio, South Carolina, and Texas. Each revised text is the product of a three-year cycle of research and
development, pilot testing and refi nement, and fi eld testing and further refi nement. Special thanks are
extended to the following teachers and their students who participated in the testing and evaluation of
the 2nd Edition materials.
Hickman High SchoolColumbia, Missouri
Peter Doll
Melissa Hundley
Stephanie Krawczyk
Cheryl Lightner
Amy McCann
Tiffany McCracken
Ryan Pingrey
Michael Westcott
Holland Christian High SchoolHolland, Michigan
Jeff Goorhouse
Tim Laverell
Brian Lemmen
Betsi Roelofs
John Timmer
Mike Verkaik
Jefferson Junior High SchoolColumbia, Missouri
Marla Clowe
Lori Kilfoil
Martha McCabe
Paul Rahmoeller
Evan Schilling
Malcolm Price Lab SchoolCedar Falls, Iowa
Megan Balong
Dennis Kettner
James Maltas
North Shore Middle SchoolHolland, Michigan
Sheila Schippers
Brenda Katerberg
Oakland Junior High SchoolColumbia, Missouri
Teresa Barry
Erin Little
Christine Sedgwick
Dana Sleeth
Riverside University High SchoolMilwaukee, Wisconsin
Cheryl Brenner
Dave Cusma
Alice Lanphier
Ela Kiblawi
Ulices Sepulveda
Rock Bridge High SchoolColumbia, Missouri
Nancy Hanson
Emily Hawn
Lisa Holt
Betsy Launder
Linda Shumate
Sauk Prairie High SchoolPrairie du Sac, Wisconsin
Joel Amidon
Shane Been
Kent Jensen
Joan Quenan
Scott Schutt
Dan Tess
Mary Walz
Sauk Prairie Middle SchoolSauk City, Wisconsin
Julie Dahlman
Janine Jorgensen
South Shore Middle SchoolHolland, Michigan
Lynn Schipper
Washington High SchoolMilwaukee, Wisconsin
Anthony Amoroso
Debbie French
West Junior High SchoolColumbia, Missouri
Katie Bihr
Josephus Johnson
Rachel Lowery
Mike Rowson
Amanda Schoenfeld
Patrick Troup
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CPMP • Scope and Sequence 1
A Balanced and Unifi ed Curriculum
Core-Plus Mathematics is a four-year unifi ed curriculum that replaces the Algebra-Geometry-Advanced
Algebra/Trigonometry-Precalculus sequence. Each course features interwoven strands of algebra
and functions, geometry and trigonometry, statistics and probability, and discrete mathematics.
Each of these strands is developed within coherent focused units connected by fundamental ideas
such as symmetry, functions, matrices, and data analysis and curve-fi tting. By actively investigating
mathematics and its applications every year from an increasingly more mathematically sophisticated
point of view, students’ understanding of the mathematics in each strand deepens across the four-
year curriculum. Mathematical connections between strands and ways of thinking mathematically
that are common across strands are emphasized. These mathematical habits of mind include visual
thinking, recursive thinking, searching for and explaining patterns, making and checking conjectures,
reasoning with multiple representations, and providing convincing arguments and proofs.
Algebra and Functions
The Algebra and Functions strand develops student ability to recognize,
represent, and solve problems involving relations among quantitative
variables. Central to the development is the use of functions as
mathematical models. The key algebraic models in the curriculum
are linear, exponential, power, polynomial, logarithmic, rational, and
trigonometric functions. Modeling with systems of equations, both
linear and nonlinear, is developed. Attention is also given to symbolic
reasoning and manipulation.
Geometry and Trigonometry
The primary goal of the Geometry and Trigonometry strand is to
develop visual thinking and ability to construct, reason with, interpret,
and apply mathematical models of patterns in visual and physical
contexts. The focus is on describing patterns in shape, size, and
location; representing patterns with drawings, coordinates, or vectors;
predicting changes and invariants in shapes under transformations;
and organizing geometric facts and relationships through deductive
reasoning.
Statistics and Probability
The primary role of the Statistics and Probability strand is to develop
student ability to analyze data intelligently, to recognize and measure
variation, and to understand the patterns that underlie probabilistic
situations. The ultimate goal is for students to understand how
inferences can be made about a population by looking at a random
sample from that population. Graphical methods of data analysis,
simulations, sampling, and experience with the collection and
interpretation of real data are featured.
Discrete Mathematics
The Discrete Mathematics strand develops student ability to solve problems
using vertex-edge graphs, recursion, matrices, systematic counting methods
(combinatorics), and mathematical methods for democratic decision
making and information processing. Key themes are discrete mathematical
modeling, optimization, and algorithmic problem solving.
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2 CPMP • Scope and Sequence
Organization of the Curriculum
The fi rst three courses in the Core-Plus Mathematics series provide a signifi cant core of broadly
useful mathematics for all students. They were developed to prepare students for success in
college, in careers, and in daily life in contemporary society. Course 4: Preparation for Calculus
formalizes and extends the core program, with a focus on the mathematics needed to be successful
in undergraduate programs requiring calculus. Unit titles for the four courses are given in the
following table. Focus and content of these units are described on pages 3–7.
Course 1
1 Patterns of Change
2 Patterns in Data
3 Linear Functions
4 Vertex-Edge Graphs
5 Exponential Functions
6 Patterns in Shape
7 Quadratic Functions
8 Patterns in Chance
Course 2
1 Functions, Equations, and Systems
2 Matrix Methods
3 Coordinate Methods
4 Regression and Correlation
5 Nonlinear Functions and Equations
6 Network Optimization
7 Trigonometric Methods
8 Probability Distributions
Course 3
1 Reasoning and Proof
2 Inequalities and Linear Programming
3 Similarity and Congruence
4 Samples and Variation
5 Polynomial and Rational Functions
6 Circles and Circular Functions
7 Recursion and Iteration
8 Inverse Functions
Course 4: Preparation for Calculus
1 Families of Functions
2 Vectors and Motion
3 Algebraic Functions and Equations
4 Trigonometric Functions and Equations
5 Exponential Functions, Logarithms, and
Data Modeling
6 Surfaces and Cross Sections
7 Concepts of Calculus
8 Counting Methods and Induction
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CPMP • Scope and Sequence 3
Core-Plus Mathematics 2nd Edition
Course 1 Units
Unit 1 Patterns of Change develops student ability to recognize and describe important patterns that relate
quantitative variables, to use data tables, graphs, words, and symbols to represent the relationships, and
to use reasoning and calculating tools to answer questions and solve problems.
Topics include variables and functions, algebraic expressions and recurrence relations, coordinate graphs,
data tables and spreadsheets, and equations and inequalities.
Unit 2 Patterns in Data develops student ability to make sense of real-world data through use of graphical
displays, measures of center, and measures of variability.
Topics include distributions of data and their shapes, as displayed in dot plots, histograms, and box plots;
measures of center including mean and median, and their properties; measures of variability including
interquartile range and standard deviation, and their properties; and percentiles and outliers.
Unit 3 Linear Functions develops student ability to recognize and represent linear relationships between variables
and to use tables, graphs, and algebraic expressions for linear functions to solve problems in situations that
involve constant rate of change or slope.
Topics include linear functions, slope of a line, rate of change, modeling linear data patterns, solving linear
equations and inequalities, equivalent linear expressions.
Unit 4 Vertex-Edge Graphs develops student understanding of vertex-edge graphs and ability to use these graphs
to represent and solve problems involving paths, networks, and relationships among a fi nite number of
elements, including fi nding effi cient routes and avoiding confl icts.
Topics include vertex-edge graphs, mathematical modeling, optimization, algorithmic problem solving,
Euler circuits and paths, matrix representation of graphs, vertex coloring and chromatic number.
Unit 5 Exponential Functions develops student ability to recognize and represent exponential growth and decay
patterns, to express those patterns in symbolic forms, to solve problems that involve exponential change,
and to use properties of exponents to write expressions in equivalent forms.
Topics include exponential growth and decay functions, data modeling, growth and decay rates, half-life
and doubling time, compound interest, and properties of exponents.
Unit 6 Patterns in Shape develops student ability to visualize and describe two- and three-dimensional shapes,
to represent them with drawings, to examine shape properties through both experimentation and careful
reasoning, and to use those properties to solve problems.
Topics include Triangle Inequality, congruence conditions for triangles, special quadrilaterals and
quadrilateral linkages, Pythagorean Theorem, properties of polygons, tilings of the plane, properties of
polyhedra, and the Platonic solids.
Unit 7 Quadratic Functions develops student ability to recognize and represent quadratic relations between
variables using data tables, graphs, and symbolic formulas, to solve problems involving quadratic functions,
and to express quadratic polynomials in equivalent factored and expanded forms.
Topics include quadratic functions and their graphs, applications to projectile motion and economic
problems, expanding and factoring quadratic expressions, and solving quadratic equations by the quadratic
formula and calculator approximation.
Unit 8 Patterns in Chance develops student ability to solve problems involving chance by constructing sample
spaces of equally-likely outcomes or geometric models and to approximate solutions to more complex
probability problems by using simulation.
Topics include sample spaces, equally-likely outcomes, probability distributions, mutually exclusive
(disjoint) events, Addition Rule, simulation, random digits, discrete and continuous random variables,
Law of Large Numbers, and geometric probability.
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4 CPMP • Scope and Sequence
Course 2 Units
Unit 1 Functions, Equations, and Systems reviews and extends student ability to recognize, describe, and use
functional relationships among quantitative variables, with special emphasis on relationships that involve
two or more independent variables.
Topics include direct and inverse variation and joint variation; power functions; linear equations in
standard form; and systems of two linear equations with two variables, including solution by graphing,
substitution, and elimination.
Unit 2 Matrix Methods develops student understanding of matrices and ability to use matrices to represent and
solve problems in a variety of real-world and mathematical settings.
Topics include constructing and interpreting matrices, row and column sums, matrix addition, scalar
multiplication, matrix multiplication, powers of matrices, inverse matrices, properties of matrices, and
using matrices to solve systems of linear equations.
Unit 3 Coordinate Methods develops student understanding of coordinate methods for representing and analyzing
properties of geometric shapes, for describing geometric change, and for producing animations.
Topics include representing two-dimensional fi gures and modeling situations with coordinates, including
computer-generated graphics; distance in the coordinate plane, midpoint of a segment, and slope;
coordinate and matrix models of rigid transformations (translations, rotations, and line refl ections), of size
transformations, and of similarity transformations; animation effects.
Unit 4 Regression and Correlation develops student understanding of the characteristics and interpretation of
the least squares regression equation and of the use of correlation to measure the strength of the linear
association between two variables.
Topics include interpreting scatterplots; least squares regression, residuals and errors in prediction, sum
of squared errors, infl uential points; Pearson’s correlation coeffi cient and its properties, lurking variables,
and cause and effect.
Unit 5 Nonlinear Functions and Equations introduces function notation, reviews and extends student ability
to construct and reason with functions that model parabolic shapes and other quadratic relationships in
science and economics, with special emphasis on formal symbolic reasoning methods, and introduces
common logarithms and algebraic methods for solving exponential equations.
Topics include formalization of function concept, notation, domain and range; factoring and expanding
quadratic expressions, solving quadratic equations by factoring and the quadratic formula, applications
to supply and demand, break-even analysis; common logarithms and solving exponential equations using
base 10 logarithms.
Unit 6 Network Optimization develops student understanding of vertex-edge graphs and ability to use these
graphs to solve network optimization problems.
Topics include optimization, mathematical modeling, algorithmic problem solving, digraphs, trees,
minimum spanning trees, distance matrices, Hamilton circuits and paths, the Traveling Salesperson
Problem, critical paths, and the PERT technique.
Unit 7 Trigonometric Methods develops student understanding of trigonometric functions and the ability to use
trigonometric methods to solve triangulation and indirect measurement problems.
Topics include sine, cosine, and tangent functions of measures of angles in standard position in a coordinate
plane and in a right triangle; indirect measurement; analysis of variable-sided triangle mechanisms; Law
of Sines and Law of Cosines.
Unit 8 Probability Distributions further develops student ability to understand and visualize situations involving
chance by using simulation and mathematical analysis to construct probability distributions.
Topics include Multiplication Rule, independent and dependent events, conditional probability, probability
distributions and their graphs, waiting-time (or geometric) distributions, expected value, and rare events.
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CPMP • Scope and Sequence 5
Course 3 Units
Unit 1 Reasoning and Proof develops student understanding of formal reasoning in geometric, algebraic, and
statistical contexts and of basic principles that underlie those reasoning strategies.
Topics include inductive and deductive reasoning strategies; principles of logical reasoning—Affi rming
the Hypothesis and Chaining Implications; relation among angles formed by two intersecting lines or by
two parallel lines and a transversal; rules for transforming algebraic expressions and equations; design
of experiments including the role of randomization, control groups, and blinding; sampling distribution,
randomization test, and statistical signifi cance.
Unit 2 Inequalities and Linear Programming develops student ability to reason both algebraically and graphically
to solve inequalities in one and two variables, introduces systems of inequalities in two variables, and
develops a strategy for optimizing a linear function in two variables within a system of linear constraints
on those variables.
Topics include inequalities in one and two variables (including absolute value and quadratic inequalities),
number line graphs, interval notation, systems of linear inequalities, and linear programming.
Unit 3 Similarity and Congruence extends student understanding of similarity and congruence and their ability
to use those relations to solve problems and to prove geometric assertions with and without the use of
coordinates.
Topics include connections between Law of Cosines, Law of Sines, and suffi cient conditions for similarity
and congruence of triangles, centers of triangles, applications of similarity and congruence in real-world
contexts, necessary and suffi cient conditions for parallelograms, suffi cient conditions for congruence of
parallelograms, and midpoint connector theorems.
Unit 4 Samples and Variation extends student understanding of the measurement of variability, develops
student ability to use the normal distribution as a model of variation, introduces students to the binomial
distribution and its use in decision making, and introduces students to the probability and statistical
inference involved in control charts used in industry for statistical process control.
Topics include normal distribution, standardized scores, binomial distributions (shape, expected value,
standard deviation), normal approximation to a binomial distribution, odds, statistical process control,
control charts, and the Central Limit Theorem.
Unit 5 Polynomial and Rational Functions extends student ability to represent and draw inferences about
polynomial and rational functions using symbolic expressions and manipulations.
Topics include defi nition and properties of polynomials, operations on polynomials; completing the
square, proof of the quadratic formula, solving quadratic equations (including complex number solutions),
vertex form of quadratic functions; defi nition and properties of rational functions, operations on rational
expressions.
Unit 6 Circles and Circular Functions develops student understanding of relationships among special lines,
segments, and angles in circles and the ability to use properties of circles to solve problems; develops
student understanding of circular functions and the ability to use these functions to model periodic change;
and extends student ability to reason deductively in geometric settings.
Topics include properties of chords, tangent lines, and central and inscribed angles of circles; linear and
angular velocity; radian measure of angles; and circular functions as models of periodic change.
Unit 7 Recursion and Iteration extends student ability to represent, analyze, and solve problems in situations
involving sequential and recursive change.
Topics include iteration and recursion as tools to model and analyze sequential change in real-world
contexts, including compound interest and population growth; arithmetic, geometric, and other sequences;
arithmetic and geometric series; fi nite differences; linear and nonlinear recurrence relations; and function
iteration, including graphical iteration and fi xed points.
Unit 8 Inverse Functions develops student understanding of inverses of functions with a focus on logarithmic
functions and their use in modeling and analyzing problem situations and data patterns.
Topics include inverses of functions; logarithmic functions and their relation to exponential functions,
properties of logarithms, equation solving with logarithms; and inverse trigonometric functions and their
applications to solving trigonometric equations.
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6 CPMP • Scope and Sequence
Course 4 Units: Preparation for Calculus
Unit 1 Families of Functions extends student understanding of linear, exponential, quadratic, power, and
trigonometric functions to model data patterns whose graphs are transformations of basic patterns; and
develops understanding of operations on functions useful in representing and reasoning about quantitative
relationships.
Topics include linear, exponential, quadratic, power, and trigonometric functions; data modeling;
translation, refl ection, and stretching of graphs; and addition, subtraction, multiplication, division, and
composition of functions.
Unit 2 Vectors and Motion develops student understanding of two-dimensional vectors and their use in modeling
linear, circular, and other nonlinear motion.
Topics include concept of vector as a mathematical object used to model situations defi ned by magnitude
and direction; equality of vectors, scalar multiples, opposite vectors, sum and difference vectors, dot
product of two vectors, position vectors and coordinates; and parametric equations for motion along a line
and for motion of projectiles and objects in circular and elliptical orbits.
Unit 3 Algebraic Functions and Equations reviews and extends student understanding of properties of polynomial
and rational functions and skills in manipulating algebraic expressions and solving polynomial and rational
equations, and develops student understanding of complex number representations and operations.
Topics include polynomials, polynomial division, factor and remainder theorems, operations on complex
numbers, representation of complex numbers as vectors, solution of polynomial equations, rational function
graphs and asymptotes, and solution of rational equations and equations involving radical expressions.
Unit 4 Trigonometric Functions and Equations extends student understanding of, and ability to reason with,
trigonometric functions to prove or disprove two trigonometric expressions are identical and to solve
trigonometric equations; to geometrically represent complex numbers and complex number operations
and to fi nd roots of complex numbers.
Topics include the tangent, cotangent, secant, and cosecant functions; fundamental trigonometric identities,
sum and difference identities, double-angle identities; solving trigonometric equations and expression of
periodic solutions; rectangular and polar representations of complex numbers, absolute value, DeMoivre’s
Theorem, and the roots of complex numbers.
Unit 5 Exponential Functions, Logarithms, and Data Modeling extends student understanding of exponential
and logarithmic functions to the case of natural exponential and logarithmic functions, solution of exponential
growth and decay problems, and use of logarithms for linearization and modeling of data patterns.
Topics include exponential functions with rules in the form f(x) = Aekx, natural logarithm function,
linearizing bivariate data and fi tting models using log and log-log transformations.
Unit 6 Surfaces and Cross Sections extends student ability to visualize and represent three-dimensional shapes
using contours, cross sections, and reliefs, and to visualize and represent surfaces and conic sections
defi ned by algebraic equations.
Topics include using contours to represent three-dimensional surfaces and developing contour maps from
data; sketching surfaces from sets of cross sections; conics as planar sections of right circular cones and
as locus of points in a plane; three-dimensional rectangular coordinate system; sketching surfaces using
traces, intercepts and cross sections derived from algebraically-defi ned surfaces; and surfaces of revolution
and cylindrical surfaces.
Unit 7 Concepts of Calculus develops student understanding of fundamental calculus ideas through explorations
in a variety of applied problem contexts and their representations in function tables and graphs.
Topics include instantaneous rates of change, linear approximation, area under a curve, and applications
to problems in physics, business, and other disciplines.
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CPMP • Scope and Sequence 7
Unit 8 Counting Methods and Induction extends student ability to count systematically and solve enumeration
problems, and develops understanding of, and ability to do, proof by mathematical induction.
Topics include systematic listing and counting, counting trees, the Multiplication Principle of Counting,
Addition Principle of Counting, combinations, permutations, selections with repetition; the binomial
theorem, Pascal’s triangle, combinatorial reasoning; the general multiplication rule for probability; the
Principle of Mathematical Induction; and the Least Number Principle.
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8 CPMP • Scope and Sequence
Mathematics Content
Elaborated
The mathematical content of the four courses of Core-Plus Mathematics
are elaborated in the remainder of this booklet. Pages 9–21 provide strand
charts and pages 22–26 provide an alignment with the Common Core State
Standards Mathematical Practices.
Strand Charts The following charts provide an overview of the mathematical content and
fl ow of Courses 1–4 in the Core-Plus Mathematics curriculum. The charts
are organized by mathematical strand: algebra and functions, geometry
and trigonometry, statistics and probability, and discrete mathematics. Each
of the four strands has been divided into major content categories, and
under each of these categories you will fi nd the key mathematical topics
developed in the curriculum.
Many cells in the grid have either a “F” or a “C” to indicate the units in
which each topic is treated. The “F” indicates focus; this means that the
topic is initially developed or is extended beyond its initial development
or use. The “C” indicates connections, which means that a conceptual
basis for the topic is developed, the topic is informally introduced, or the
topic is revisited and used without further development.
To help build and maintain profi ciency with key topics in the charts,
Review tasks in each lesson of each unit provide students distributed
practice with related concepts and skills. These practice opportunities
are not referenced in the following strand charts.
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CPMP • Scope and Sequence 9
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and
inte
rcep
tsC
FC
CC
CSo
lvin
g eq
uatio
ns a
nd in
equa
litie
sC
FF
CC
FRat
es o
f ch
ange
CF
CA
sym
ptot
esC
CSo
lvin
g eq
uatio
ns u
sing
loga
rith
ms
FF
F
0ii_028_SS_892135.indd Page 9 12/23/10 7:41:23 PM u-082 /Volumes/106/GO00220_r1/work/indd/
10 CPMP • Scope and Sequence
ALG
EB
RA
AN
D F
UN
CTI
ON
S
F : Fo
cus
C : C
onne
ctio
nsCours
e 1
Cours
e 2
Cours
e 3
Cours
e 4
12
34
56
78
12
34
56
78
12
34
56
78
12
34
56
78
Pow
er E
xpre
ssio
ns
and R
elat
ions
Sym
bolic
for
ms
and
effe
cts
of p
aram
eter
sC
FF
CC
CC
CC
Gra
phs,
inte
rcep
ts, a
nd z
eroe
sC
FF
CC
CC
CFr
actio
nal a
nd n
egat
ive
expo
nent
sF
CC
Law
s of
exp
onen
tsF
CC
CM
odel
ing
situ
atio
nsF
CC
CF
Inve
rse
variat
ion
CF
CC
CC
CA
sym
ptot
es (in
vers
e va
riat
ion)
CF
CSo
lvin
g eq
uatio
ns a
nd in
equa
litie
sF
CC
CC
Roo
ts a
nd r
adic
als
CF
CC
CC
CC
FRat
es o
f ch
ange
FC
CC
CC
CF
Quad
rati
c Exp
ress
ions
and R
elat
ions
Mod
elin
g si
tuat
ions
CC
FC
CC
CC
FC
CF
Sym
bolic
for
ms
and
effe
cts
of p
aram
eter
sC
C
FC
CF
FF
CC
CC
CG
raph
s, in
terc
epts
, and
zer
oes
CF
FF
FC
Rat
es o
f ch
ange
CC
CC
CSo
lvin
g eq
uatio
ns a
nd in
equa
litie
s by
gra
phic
and
num
eric
app
roxi
mat
ion
CF
CC
CC
Num
ber
of s
olut
ions
FF
FC
CSo
lvin
g in
equa
litie
sF
Solv
ing
equa
tions
by
fact
orin
gC
FC
FC
Solv
ing
equa
tions
by
usin
g th
e qu
adra
tic for
mul
aF
FC
CF
CPa
ram
etric
equa
tions
for
pro
ject
ile m
otio
nF
Para
met
ric
equa
tions
for
circu
lar
mot
ion
CF
Para
met
ric
equa
tions
for
elli
ptic
al m
otio
nF
Con
ic s
ectio
nsC
CC
CC
F
Poly
nom
ial Exp
ress
ions
and R
elat
ions
Mod
elin
g si
tuat
ions
CC
CF
CF
Sym
bolic
for
ms
and
effe
cts
of p
aram
eter
sC
CC
FC
FC
Gra
phs,
inte
rcep
ts, a
nd z
eroe
sC
CC
FC
FRat
es o
f ch
ange
CC
End
beha
vior
CF
Solv
ing
equa
tions
and
ineq
ualit
ies
CC
CC
CN
umbe
r of
sol
utio
nsC
CC
FF
0ii_028_SS_892135.indd Page 10 12/23/10 7:41:24 PM u-082 /Volumes/106/GO00220_r1/work/indd/
CPMP • Scope and Sequence 11
ALG
EB
RA
AN
D F
UN
CTI
ON
S
F : Fo
cus
C : C
onne
ctio
nsCours
e 1
Cours
e 2
Cours
e 3
Cours
e 4
12
34
56
78
12
34
56
78
12
34
56
78
12
34
56
78
Rat
ional
Exp
ress
ions
and R
elat
ions
Prop
ortio
nsC
CC
CC
Sym
bolic
for
ms
and
effe
cts
of p
aram
eter
sC
CF
CF
Gra
phs,
inte
rcep
ts, a
nd z
eroe
sC
CF
FRat
es o
f ch
ange
CC
CM
odel
ing
situ
atio
nsC
CF
FSo
lvin
g eq
uatio
ns a
nd in
equa
litie
sC
CC
FA
sym
ptot
esF
CSi
mpl
ifyin
g: a
ddin
g su
btra
ctin
g, m
ultip
lyin
g, a
ndF
F
Per
iodic
Rel
atio
ns
Mod
elin
g si
tuat
ions
CF
CSy
mbo
lic for
ms
and
effe
cts
of p
aram
eter
sC
FC
Gra
phs,
inte
rcep
ts, a
nd z
eroe
sC
CC
Rat
es o
f ch
ange
CIn
vers
e tr
igon
omet
ric
func
tions
CC
FC
Solv
ing
trig
onom
etric
equa
tions
CC
FF
Trig
onom
etric
iden
titie
sC
CF
Logar
ithm
ic E
xpre
ssio
ns
and R
elat
ions
Defi
niti
on a
nd n
otat
ion
FF
FCom
mon
loga
rith
ms
FF
CM
odel
ing
situ
atio
nsF
FF
Gra
phs
and
inte
rcep
tsC
FSy
mbo
lic for
ms
and
effe
cts
of p
aram
eter
sF
Prop
ertie
s of
loga
rith
ms
FC
Solv
ing
loga
rith
mic
equ
atio
ns a
nd in
equa
litie
sC
CEv
alua
ting
loga
rith
mic
exp
ress
ions
CF
CN
atur
al lo
garith
ms
FCha
nge
of b
ase
for
loga
rith
ms
CC
0ii_028_SS_892135.indd Page 11 12/23/10 7:41:26 PM u-082 /Volumes/106/GO00220_r1/work/indd/
12 CPMP • Scope and Sequence
ALG
EB
RA
AN
D F
UN
CTI
ON
S
F : Fo
cus
C : C
onne
ctio
nsCours
e 1
Cours
e 2
Cours
e 3
Cours
e 4
12
34
56
78
12
34
56
78
12
34
56
78
12
34
56
78
Mult
ivar
iable
Exp
ress
ions
and R
elat
ions
Form
ulas
CC
CC
CC
CC
CC
CC
CC
CF
Pyth
agor
ean
Theo
rem
CF
FC
CC
CC
Law
of Si
nes
and
Law
of Cos
ines
FC
FC
Mod
elin
g us
ing
sym
bolic
equ
atio
ns a
nd in
equa
litie
sF
FC
FF
CSo
lvin
g fo
r on
e va
riab
le in
ter
ms
of o
ther
sF
CC
CC
CEf
fect
of ch
ange
am
ong
variab
les
FC
CC
C
Sys
tem
s of
Rel
atio
ns
Gra
phin
g sy
stem
sF
FC
FC
FSo
lvin
g lin
ear
syst
ems
by g
raph
ical
and
num
eric
met
hods
FF
CF
CC
Solv
ing
linea
r sy
stem
s by
sub
stitu
tion
CF
CF
CC
CC
Solv
ing
linea
r sy
stem
s by
mat
rix
met
hods
FC
CC
CC
Solv
ing
linea
r sy
stem
s by
line
ar c
ombi
natio
nsF
CC
CSo
lvin
g sy
stem
s of
line
ar in
equa
litie
sF
Line
ar p
rogr
amm
ing
FLi
near
-qua
drat
ic s
yste
ms
FC
Line
ar-inv
erse
sys
tem
sF
Syst
ems
of p
aram
etric
equa
tions
CC
Funct
ions
Defi
niti
on a
nd n
otat
ion
CF
CC
CC
CC
CD
omai
n an
d ra
nge
CC
FC
CF
CC
CC
Rat
es o
f ch
ange
CF
CC
CC
CF
Tran
sfor
mat
ions
of gr
aphs
CC
CC
CC
CC
FC
Com
posi
tion
of fun
ctio
nsC
CF
FZ
eroe
s of
fun
ctio
nsC
CC
CF
CC
FSe
quen
ces
and
series
CF
CIn
vers
es o
f fu
nctio
nsC
CF
Cof
tw
o or
mor
e va
riab
les
FF
F
0ii_028_SS_892135.indd Page 12 12/23/10 7:41:27 PM u-082 /Volumes/106/GO00220_r1/work/indd/
CPMP • Scope and Sequence 13
ALG
EB
RA
AN
D F
UN
CTI
ON
S
F : Fo
cus
C : C
onne
ctio
nsCours
e 1
Cours
e 2
Cours
e 3
Cours
e 4
12
34
56
78
12
34
56
78
12
34
56
78
12
34
56
78
Alg
ebra
ic R
easo
nin
gEq
uiva
lent
exp
ress
ions
FF
FC
FF
FF
CD
istr
ibut
ive
prop
erty
CC
CC
CC
CC
Com
mut
ativ
e pr
oper
ties
CC
FC
CC
CC
Prop
ertie
s of
exp
onen
tsF
CC
CC
CC
Ass
ocia
tive
prop
ertie
sC
CC
CC
CC
Prop
ertie
s of
equ
atio
nsC
CF
CC
Add
itive
inve
rse
CC
CC
Mul
tiplic
ativ
e in
vers
eC
FC
Clo
sure
pro
pert
yC
CF
CRad
ical
s an
d op
erat
ions
FC
CC
FA
lgeb
raic
pro
ofC
FC
CC
CC
CC
CC
Poly
nom
ials
and
bin
ary
oper
atio
nsF
FC
Fact
orin
g, e
xpan
ding
, and
sim
plify
ing
FF
CC
FC
CB
inom
ial t
heor
emF
Pasc
al’s
trian
gle
FCom
plet
ing
the
squa
reF
CSu
bstit
utio
n of
var
iabl
eC
CF
CC
CC
CPr
oof by
mat
hem
atic
al in
duct
ion
FD
e M
oivr
e’s
Theo
rem
F
Alg
ebra
ic S
yste
ms
Rea
l num
bers
and
the
ir p
rope
rtie
sC
CF
CC
CF
Mat
rice
s an
d th
eir
prop
ertie
sF
CTr
ansf
orm
atio
ns a
nd t
heir p
rope
rtie
sF
FF
FC
FV
ecto
rs a
nd t
heir p
rope
rtie
sF
Com
plex
num
bers
and
the
ir p
rope
rtie
sC
F
Cal
culu
s U
nder
pin
nin
gs
Rat
es o
f ch
ange
CF
FC
CC
CF
Max
ima
and
min
ima
CC
FF
CF
CF
FLi
mits
CC
CC
CC
Sequ
ence
s an
d se
ries
CC
FC
Loca
l lin
earity
FD
eriv
ativ
e fu
nctio
nsF
Acc
umul
atio
n of
cha
nge
FA
rea
unde
r a
curv
eC
CF
FD
efi n
ite in
tegr
alF
0ii_028_SS_892135.indd Page 13 12/23/10 7:41:28 PM u-082 /Volumes/106/GO00220_r1/work/indd/
14 CPMP • Scope and Sequence
GEO
METR
Y A
ND
TRIG
ON
OM
ETR
Y
F : Fo
cus
C : C
onne
ctio
nsCours
e 1
Cours
e 2
Cours
e 3
Cours
e 4
12
34
56
78
12
34
56
78
12
34
56
78
12
34
56
78
Two-d
imen
sional
Fig
ure
sA
ngle
rel
atio
ns for
tw
o in
ters
ectin
g lin
esC
FC
Para
llel l
ines
and
ang
le r
elat
ions
FC
CTr
iang
les
and
thei
r pr
oper
ties
FF
CF
CC
CQ
uadr
ilate
rals
and
the
ir p
rope
rtie
sF
CC
FPa
ralle
logr
ams
and
thei
r pr
oper
ties
FF
CF
CTr
iang
ular
and
qua
drila
tera
l lin
kage
sF
FC
Poly
gons
and
the
ir p
rope
rtie
sC
FF
CC
CG
eom
etric
cons
truc
tions
CF
FC
Circl
es a
nd t
heir p
rope
rtie
sC
FC
FC
CCon
ic s
ectio
ns a
nd t
heir p
rope
rtie
sC
CC
FB
ilate
ral a
nd r
otat
iona
l sym
met
ryF
CC
FTe
ssel
latio
nsF
Tran
slat
iona
l sym
met
ryF
CC
FFr
acta
lsC
CC
Con
grue
nce
FF
CF
FCon
grue
nce
cond
ition
s fo
r tr
iang
les
FC
CC
FC
Sim
ilarity
CF
CF
CSi
mila
rity
con
ditio
ns for
trian
gles
CC
FC
C
Thre
e-d
imen
sional
Fig
ure
sRig
ht p
olyg
onal
prism
s an
d py
ram
ids
FC
Con
es, c
ylin
ders
, and
sph
eres
FC
CC
CC
Sket
chin
g sh
apes
FRig
idity
FB
ilate
ral a
nd r
otat
iona
l sym
met
ryF
Reg
ular
(Pl
aton
ic) so
lids
CF
CC
Cro
ss s
ectio
nsC
FCon
tour
dia
gram
sF
Surf
aces
FSu
rfac
es o
f re
volu
tion
FF
Cyl
indr
ical
sur
face
sC
F
0ii_028_SS_892135.indd Page 14 12/23/10 7:41:29 PM u-082 /Volumes/106/GO00220_r1/work/indd/
CPMP • Scope and Sequence 15
GEO
METR
Y A
ND
TRIG
ON
OM
ETR
YF
: Fo
cus
C : C
onne
ctio
nsCours
e 1
Cours
e 2
Cours
e 3
Cours
e 4
12
34
56
78
12
34
56
78
12
34
56
78
12
34
56
78
Mea
sure
men
tPe
rim
eter
CF
CC
CA
rea
CF
CC
CC
CPy
thag
orea
n Th
eore
mC
FC
CC
CC
Surf
ace
area
FC
CV
olum
eF
CRad
ian
and
degr
ee m
easu
reC
CF
FC
Ang
ular
vel
ocity
FF
Line
ar v
eloc
ityF
F
Coord
inat
e M
odel
sCoo
rdin
ate
repr
esen
tatio
n of
fi gu
res
FC
CC
CD
ista
nce
and
mid
poin
t fo
rmul
asF
CC
CC
Slop
e of
a li
neF
CC
CC
CF
Equa
tions
of lin
esF
FF
FC
CC
Slop
es o
f pa
ralle
l and
per
pend
icul
ar li
nes
CC
FC
CEq
uatio
ns o
f ci
rcle
sF
CC
CC
CCoo
rdin
ate
repr
esen
tatio
n of
tra
nsfo
rmat
ions
FC
Con
grue
nce
and
sim
ilarity
FF
CC
CM
atrix
repr
esen
tatio
n of
pol
ygon
sC
FCoo
rdin
ate
proo
fF
CC
CV
ecto
rsF
CPo
lar
coor
dina
tes
CF
3-d
imen
sion
al c
oord
inat
e gr
aphs
FSk
etch
ing
surf
aces
in 3
-dim
ensi
onal
spa
ceC
FEq
uatio
ns o
f su
rfac
esF
Equa
tions
of pl
anes
FEq
uatio
ns o
f co
nic
sect
ions
CC
CF
Trac
es o
f su
rfac
esF
Tran
sform
atio
ns
Rig
id t
rans
form
atio
ns (is
omet
ries
)C
FC
CC
CSi
ze t
rans
form
atio
ns (di
latio
ns)
FC
CC
CCom
posi
tion
of t
rans
form
atio
nsF
CSi
mila
rity
tra
nsfo
rmat
ions
FC
CC
Mat
rix
repr
esen
tatio
n of
tra
nsfo
rmat
ions
FC
CC
Ani
mat
ion
FTr
ansf
orm
atio
ns o
f gr
aphs
and
fun
ctio
n ru
les
CC
FC
CCom
plex
num
ber
oper
atio
ns a
nd t
rans
form
atio
nsF
0ii_028_SS_892135.indd Page 15 12/27/10 3:38:07 PM s-74user /Volumes/106/GO00220_r1/work/indd/
16 CPMP • Scope and Sequence
GEO
METR
Y A
ND
TRIG
ON
OM
ETR
Y
F : Fo
cus
C : C
onne
ctio
nsCours
e 1
Cours
e 2
Cours
e 3
Cours
e 4
12
34
56
78
12
34
56
78
12
34
56
78
12
34
56
78
Trig
onom
etry
Trig
onom
etric
ratio
s an
d fu
nctio
ns(s
ine,
cos
ine,
and
tan
gent
)F
CF
CF
F
Law
of Si
nes
FC
FC
Law
of Cos
ines
FC
FC
Rad
ian
and
degr
ee m
easu
reC
CF
CC
CC
Trig
onom
etric
grap
hsC
FF
FPe
riod
CF
FF
FA
mpl
itude
CF
FF
Period
ic m
odel
sC
FF
FIn
vers
e tr
igon
omet
ric
func
tions
CC
FF
Trig
onom
etric
iden
titie
sC
CF
Trig
onom
etric
ratio
s an
d fu
nctio
ns(s
ecan
t, co
seca
nt, a
nd c
otan
gent
)F
Circu
lar
and
period
ic m
otio
nC
FF
Com
pone
nt a
naly
sis
of v
ecto
rsF
Indi
rect
mea
sure
men
t (a
ngle
s an
d le
ngth
s)F
CC
Tria
ngul
ar li
nkag
es w
ith o
ne v
aria
ble
side
F
Rea
sonin
g a
nd P
roof
Indu
ctiv
e re
ason
ing
CC
CC
CC
CC
CC
CC
CC
CF
CC
CC
CC
CC
CC
CC
CC
CCou
nter
exam
ples
CC
CC
CF
CC
CD
educ
tive
reas
onin
gC
CC
FC
CF
FF
CC
CF
FD
esig
ning
and
just
ifyin
g al
gorith
ms
CC
CC
CC
Coo
rdin
ate
and
anal
ytic
al p
roof
FC
CC
CC
Synt
hetic
pro
ofC
FF
FC
CA
ssum
ptio
ns in
pro
ofC
CF
CC
FPr
inci
ples
of lo
gic
FC
Con
vers
eC
CF
CC
Vec
tor
proo
fF
0ii_028_SS_892135.indd Page 16 12/23/10 7:41:31 PM u-082 /Volumes/106/GO00220_r1/work/indd/
CPMP • Scope and Sequence 17
STA
TISTI
CS A
ND
PRO
BA
BIL
ITY
F : Fo
cus
C : C
onne
ctio
nsCours
e 1
Cours
e 2
Cours
e 3
Cours
e 4
12
34
56
78
12
34
56
78
12
34
56
78
12
34
56
78
Univ
aria
te D
ata
Num
ber
line
(dot
) pl
ots
FM
easu
res
of c
ente
r an
d th
eir
prop
ertie
s: m
ean,
med
ian
FC
CC
CB
asic
sha
pes
of d
istr
ibut
ions
FC
CC
Skew
ness
and
sym
met
ryF
CC
CH
isto
gram
sF
FF
FClu
ster
s, g
aps,
and
out
liers
FC
FB
ox p
lots
FC
Line
ar t
rans
form
atio
ns o
f da
taF
CC
FSt
em-a
nd-lea
f pl
ots
FRan
ge a
nd in
terq
uart
ile r
ange
(IQ
R)
FM
ean
abso
lute
dev
iatio
n (M
AD
)C
Perc
entil
es a
nd q
uart
iles
FC
CSt
anda
rd d
evia
tion
and
its p
rope
rtie
sF
CC
FC
Freq
uenc
y ta
bles
FF
FF
FSt
anda
rdiz
ed o
r z-
scor
esF
Con
cept
of di
stribu
tion
FF
FF
F
Biv
aria
te D
ata
Scat
terp
lots
and
ass
ocia
tion
FF
CC
FF
Plot
s an
d tr
ends
ove
r tim
eF
CC
FC
CSu
m o
f sq
uare
d di
ffere
nces
FF
Cen
troi
dF
Leas
t sq
uare
s re
gres
sion
line
CF
FEr
rors
of pr
edic
tion
and
resi
dual
sF
FN
onlin
ear
regr
essi
onC
CIn
fl uen
tial p
oint
sF
Spea
rman
’s r
ank
corr
elat
ion
FPe
arso
n’s
corr
elat
ion
rF
FEx
plan
ator
y an
d re
spon
se v
aria
bles
CF
FLu
rkin
g va
riab
les
CF
FCau
se-a
nd-e
ffect
rel
atio
nshi
psF
FF
Log
and
log-
log
tran
sfor
mat
ions
F
0ii_028_SS_892135.indd Page 17 12/23/10 7:41:32 PM u-082 /Volumes/106/GO00220_r1/work/indd/
18 CPMP • Scope and Sequence
STA
TISTI
CS A
ND
PRO
BA
BIL
ITY
F : Fo
cus
C : C
onne
ctio
nsCours
e 1
Cours
e 2
Cours
e 3
Cours
e 4
12
34
56
78
12
34
56
78
12
34
56
78
12
34
56
78
Pro
bab
ility
Nor
mal
dis
trib
utio
nF
FSi
mul
atio
nF
CC
CRan
dom
dig
it ta
bles
and
ran
dom
num
ber
gene
rato
rsF
CLa
w o
f La
rge
Num
bers
FEm
pirica
l (ex
perim
enta
l) an
d th
eore
tical
pro
babi
litie
sF
FC
Inde
pend
ent
even
tsF
CB
inom
ial d
istr
ibut
ion
CF
CW
aitin
g-tim
e (g
eom
etric)
dis
trib
utio
nC
FC
Mul
tiplic
atio
n Rul
e fo
r in
depe
nden
t ev
ents
FC
CG
eom
etric
(are
a) m
odel
sF
CCon
ditio
nal p
roba
bilit
yF
CEx
pect
ed v
alue
FC
CRar
e ev
ents
CF
Sam
plin
g di
stribu
tions
FM
utua
lly e
xclu
sive
eve
nts
FC
Add
ition
Rul
e fo
r m
utua
lly e
xclu
sive
eve
nts
FC
Ven
n D
iagr
amF
CC
CCen
tral
Lim
it Th
eore
mF
Prob
abili
ty d
istr
ibut
ion
FF
FG
ener
al m
ultip
licat
ion
rule
FF
Bin
omia
l pro
babi
lity
form
ula
CN
orm
al a
ppro
xim
atio
n to
a b
inom
ial
F
Infe
rential
Sta
tist
ics
Popu
latio
n vs
. sam
ple
FC
FCon
trol
(ru
n) c
hart
sF
Test
s of
sig
nifi c
ance
incl
udin
g Ty
pe I
and
Type
II e
rror
sF
CSt
atis
tical
sig
nifi c
ance
FC
Gen
eral
izab
ility
of re
sults
FF
F
0ii_028_SS_892135.indd Page 18 12/23/10 7:41:33 PM u-082 /Volumes/106/GO00220_r1/work/indd/
CPMP • Scope and Sequence 19
STA
TISTI
CS A
ND
PRO
BA
BIL
ITY
F : Fo
cus
C : C
onne
ctio
nsCours
e 1
Cours
e 2
Cours
e 3
Cours
e 4
12
34
56
78
12
34
56
78
12
34
56
78
12
34
56
78
Surv
eys
Sta
tist
ical
Stu
die
sSa
mpl
e su
rvey
FEx
perim
ent
FSa
mpl
e si
zeC
Sim
ple
rand
om s
ampl
eC
Obs
erva
tiona
l stu
dyF
Exp
erim
ents
Cha
ract
eris
tics
of a
wel
l-de
sign
ed e
xper
imen
ts:
trea
tmen
ts, c
ontr
ol g
roup
s, r
ando
m a
ssig
nmen
t, an
d re
plic
atio
nC
F
Sour
ce o
f bi
as a
nd c
onfo
undi
ng, i
nclu
ding
pla
cebo
ef
fect
and
blin
ding
F
Ran
dom
izat
ion
test
F
0ii_028_SS_892135.indd Page 19 12/23/10 7:41:34 PM u-082 /Volumes/106/GO00220_r1/work/indd/
20 CPMP • Scope and Sequence
DIS
CRETE
MATH
EM
ATI
CS
F : Fo
cus
C : C
onne
ctio
nsCours
e 1
Cours
e 2
Cours
e 3
Cours
e 4
12
34
56
78
12
34
56
78
12
34
56
78
12
34
56
78
Ver
tex-
Edge
Gra
phs
Ver
tex-
edge
gra
ph m
odel
sF
CC
CF
CD
igra
phs
CC
FA
djac
ency
mat
rice
s fo
r ve
rtex
-edg
e gr
aphs
FF
Eule
r pa
ths
and
circ
uits
FC
Gra
ph c
olor
ing
FC
Critic
al p
ath
anal
ysis
and
PER
T ch
arts
FC
Tree
s an
d m
inim
um s
pann
ing
tree
sF
CC
Ham
ilton
pat
hs a
nd c
ircu
its (in
clud
ing
TSP)
F
Rec
urs
ion a
nd Ite
rati
on
Info
rmal
rep
rese
ntat
ion
with
wor
ds li
ke N
OW
and
NEX
TF
CF
CF
CC
Rec
ursi
ve r
epre
sent
atio
n of
line
ar fun
ctio
nsF
CF
Rec
ursi
ve r
epre
sent
atio
n of
exp
onen
tial f
unct
ions
FF
FRec
ursi
ve r
epre
sent
atio
n of
pol
ynom
ial f
unct
ions
FRec
urre
nce
rela
tions
FC
Sequ
ence
s an
d se
ries
CF
CFi
nite
diff
eren
ces
CF
Func
tion
itera
tion
FFi
xed
poin
tsF
Gra
phic
al it
erat
ion
FC
Frac
tals
CC
CC
Mat
rice
sM
atrix
mod
els
CF
CC
CRow
and
col
umn
sum
sC
FM
atrix
addi
tion
FSc
alar
mul
tiplic
atio
nF
CM
atrix
mul
tiplic
atio
nF
CC
CId
entit
y m
atrice
sF
Inve
rse
mat
rice
sF
CPr
oper
ties
of m
atrice
sF
Mat
rix
solu
tions
of lin
ear
syst
ems
FC
CA
djac
ency
mat
rice
s fo
r ve
rtex
-edg
e gr
aphs
FF
Tran
sfor
mat
ion
mat
rice
sF
CC
CSc
atte
rplo
t m
atrice
sF
0ii_028_SS_892135.indd Page 20 12/23/10 7:41:34 PM u-082 /Volumes/106/GO00220_r1/work/indd/
CPMP • Scope and Sequence 21
DIS
CRETE
MATH
EM
ATI
CS
F : Fo
cus
C : C
onne
ctio
nsCours
e 1
Cours
e 2
Cours
e 3
Cours
e 4
12
34
56
78
12
34
56
78
12
34
56
78
12
34
56
78
Alg
ori
thm
sA
lgor
ithm
ic p
robl
em s
olvi
ngF
FC
Des
igni
ng a
lgor
ithm
sF
FC
Ana
lyzi
ng a
nd c
ompa
ring
alg
orith
ms
CF
Prog
ram
min
g al
gorith
ms
CC
Sys
tem
atic
Counti
ng M
ethods
Cou
ntin
g tr
ees
FF
Mul
tiplic
atio
n Pr
inci
ple
of c
ount
ing
CC
FF
Add
ition
Princ
iple
of co
untin
gF
FPi
geon
hole
princ
iple
CPe
rmut
atio
nsC
FCom
bina
tions
FSe
lect
ions
with
rep
etiti
onC
FPa
scal
’s t
rian
gle
FB
inom
ial t
heor
emF
Com
bina
torial
rea
soni
ngF
FC
F
0ii_028_SS_892135.indd Page 21 12/23/10 7:41:36 PM u-082 /Volumes/106/GO00220_r1/work/indd/
22 CPMP • Scope and Sequence
Com
mon C
ore
Sta
te S
tandar
ds
for
Mat
hem
atic
s Corr
elat
ed t
o
Core
-Plu
s M
athem
atic
s:
Cours
e 1, Cours
e 2
, Cours
e 3, an
d C
ours
e 4: Pre
par
atio
n f
or
Cal
culu
s
The C
ore
-Plu
s M
ath
emati
cs c
urr
iculu
m,
by d
esi
gn,
inco
rpora
tes
the C
om
mon C
ore
Sta
te S
tandard
s (C
CSS)
Math
em
ati
cal Pra
ctic
es
into
each
less
on.
Desc
ripti
ons
of
the M
ath
em
ati
cal Pra
ctic
es
alo
ng w
ith s
ele
cted e
xam
ple
s of
these
pra
ctic
es
in e
ach
Core
-Plu
s M
ath
em
ati
cs t
ext
are
pro
vid
ed in t
he f
ollow
ing t
able
. A
com
ple
te c
orr
ela
tion t
hat
incl
udes
the c
onte
nt
standard
s is
available
fro
m y
our
Gle
nco
e s
ale
s re
pre
senta
tive o
r
at
ww
w.w
mic
h.e
du/c
pm
p.
Sta
ndar
ds
for
Mat
hem
atic
al P
ract
ice
Stu
den
t Editio
n L
esso
ns
Cours
e 1
Cours
e 2
Cours
e 3
Cours
e 4:
Pre
par
atio
n
for
Cal
culu
s
The
Stan
dard
s fo
r M
athe
mat
ical
Pra
ctic
e de
scribe
var
ietie
s of
exp
ertis
e th
at m
athe
mat
ics
educ
ator
s at
all
leve
ls s
houl
d se
ek t
o de
velo
p in
the
ir s
tude
nts.
The
se p
ract
ices
res
t on
impo
rtan
t “p
roce
sses
and
pro
fi cie
ncie
s” w
ith lo
ngst
andi
ng im
port
ance
in m
athe
mat
ics
educ
atio
n. T
he fi
rst
of t
hese
are
the
NCTM
pro
cess
sta
ndar
ds o
f pr
oble
m s
olvi
ng,
reas
onin
g an
d pr
oof,
com
mun
icat
ion,
rep
rese
ntat
ion,
and
con
nect
ions
. The
sec
ond
are
the
stra
nds
of m
athe
mat
ical
pro
fi cie
ncy
spec
ifi ed
in t
he N
atio
nal R
esea
rch
Cou
ncil’
s re
port
A
ddin
g It
Up:
ada
ptiv
e re
ason
ing,
str
ateg
ic c
ompe
tenc
e, c
once
ptua
l und
erst
andi
ng (co
mpr
ehen
sion
of m
athe
mat
ical
con
cept
s, o
pera
tions
and
rel
atio
ns),
proc
edur
al fl
uenc
y (s
kill
in c
arry
ing
out
proc
edur
es fl
exib
ly, a
ccur
atel
y, e
ffi ci
ently
and
app
ropr
iate
ly),
and
prod
uctiv
e di
spos
ition
(ha
bitu
al in
clin
atio
n to
see
mat
hem
atic
s as
sen
sibl
e, u
sefu
l, an
d w
orth
whi
le, c
oupl
ed w
ith a
bel
ief in
dili
genc
e an
d on
e’s
own
effi c
acy)
.
1.
Mak
e se
nse
of
pro
ble
ms
and p
erse
vere
in s
olv
ing t
hem
.
Mat
hem
atic
ally
pro
fi cie
nt s
tude
nts
star
t by
exp
lain
ing
to t
hem
selv
es t
he m
eani
ng o
f a
prob
lem
and
look
ing
for
entr
y po
ints
to
its s
olut
ion.
The
y an
alyz
e gi
vens
, con
stra
ints
, re
latio
nshi
ps, a
nd g
oals
. The
y m
ake
conj
ectu
res
abou
t th
e fo
rm a
nd m
eani
ng o
f th
e so
lutio
n an
d pl
an a
sol
utio
n pa
thw
ay r
athe
r th
an s
impl
y ju
mpi
ng in
to a
sol
utio
n at
tem
pt. T
hey
cons
ider
ana
logo
us p
robl
ems,
and
try
spe
cial
cas
es a
nd s
impl
er
form
s of
the
origi
nal p
robl
em in
ord
er t
o ga
in in
sigh
t in
to it
s so
lutio
n. T
hey
mon
itor
and
eval
uate
the
ir p
rogr
ess
and
chan
ge c
ours
e if
nece
ssar
y. O
lder
stu
dent
s m
ight
, de
pend
ing
on t
he c
onte
xt o
f th
e pr
oble
m, t
rans
form
alg
ebra
ic e
xpre
ssio
ns o
r ch
ange
th
e vi
ewin
g w
indo
w o
n th
eir
grap
hing
cal
cula
tor
to g
et t
he in
form
atio
n th
ey n
eed.
M
athe
mat
ical
ly p
rofi c
ient
stu
dent
s ca
n ex
plai
n co
rres
pond
ence
s be
twee
n eq
uatio
ns,
verb
al d
escr
iptio
ns, t
able
s, a
nd g
raph
s or
dra
w d
iagr
ams
of im
port
ant
feat
ures
and
re
latio
nshi
ps, g
raph
dat
a, a
nd s
earc
h fo
r re
gula
rity
or
tren
ds. Y
oung
er s
tude
nts
mig
ht r
ely
on u
sing
con
cret
e ob
ject
s or
pic
ture
s to
hel
p co
ncep
tual
ize
and
solv
e a
prob
lem
. Mat
hem
atic
ally
pro
fi cie
nt s
tude
nts
chec
k th
eir
answ
ers
to p
robl
ems
usin
g a
diffe
rent
met
hod,
and
the
y co
ntin
ually
ask
the
mse
lves
, “D
oes
this
mak
e se
nse?
” Th
ey
can
unde
rsta
nd t
he a
ppro
ache
s of
oth
ers
to s
olvi
ng c
ompl
ex p
robl
ems
and
iden
tify
corr
espo
nden
ces
betw
een
diffe
rent
app
roac
hes.
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 8–1
0,
56
–58
, 61
#1
1,
93
#8
, 11
1, 1
31,
15
9, 2
39
–24
2,
29
7 S
TM, 4
13
#
3, 4
20
–42
1
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 61–6
4, 1
21
#7, 1
24 #
11,
141 C
heck
You
r Und
erst
andi
ng
(CYU
) 280–2
85,
314 #
13,
364–3
67,
372 #
17,
474 #
2, #
3
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 32–3
3, 1
49 #
14,
233 #
7, 3
60
#15, 4
32 C
YU,
435 #
7, 4
40
#8, 4
50 #
33,
459–4
61, 4
70
#4, 5
54 #
22
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 71 #
22,
178–1
80, 2
31
CYU
, 288 #
7,
300–3
01,
318–3
21,
394–3
98,
470–4
73,
496–5
01,
591–5
95,
611–6
14
0ii_028_SS_892135.indd Page 22 12/23/10 7:41:36 PM u-082 /Volumes/106/GO00220_r1/work/indd/
CPMP • Scope and Sequence 23
Com
mon C
ore
Sta
te S
tandar
ds
for
Mat
hem
atic
s Corr
elat
ed t
o
Core
-Plu
s M
athem
atic
s:
Cours
e 1, Cours
e 2
, Cours
e 3, an
d C
ours
e 4: Pre
par
atio
n f
or
Cal
culu
s
Sta
ndar
ds
for
Mat
hem
atic
al P
ract
ice
Stu
den
t Editio
n L
esso
ns
Cours
e 1
Cours
e 2
Cours
e 3
Cours
e 4:
Pre
par
atio
n
for
Cal
culu
s
2.
Rea
son a
bst
ract
ly a
nd q
uan
tita
tive
ly.
Mat
hem
atic
ally
pro
fi cie
nt s
tude
nts
mak
e se
nse
of q
uant
ities
and
the
ir r
elat
ions
hips
in
pro
blem
situ
atio
ns. T
hey
brin
g tw
o co
mpl
emen
tary
abi
litie
s to
bea
r on
pro
blem
s in
volv
ing
quan
titat
ive
rela
tions
hips
: the
abi
lity
to d
econ
text
ualiz
e—to
abs
trac
t a
give
n si
tuat
ion
and
repr
esen
t it
sym
bolic
ally
and
man
ipul
ate
the
repr
esen
ting
sym
bols
as
if th
ey h
ave
a lif
e of
the
ir o
wn,
with
out
nece
ssar
ily a
tten
ding
to
thei
r re
fere
nts—
and
the
abili
ty t
o co
ntex
tual
ize,
to
paus
e as
nee
ded
during
the
m
anip
ulat
ion
proc
ess
in o
rder
to
prob
e in
to t
he r
efer
ents
for
the
sym
bols
invo
lved
. Q
uant
itativ
e re
ason
ing
enta
ils h
abits
of cr
eatin
g a
cohe
rent
rep
rese
ntat
ion
of t
he
prob
lem
at
hand
; con
side
ring
the
uni
ts in
volv
ed; a
tten
ding
to
the
mea
ning
of
quan
titie
s, n
ot ju
st h
ow t
o co
mpu
te t
hem
; and
kno
win
g an
d fl e
xibl
y us
ing
diffe
rent
pr
oper
ties
of o
pera
tions
and
obj
ects
.
Thro
ugho
ut
Uni
ts 1
–3, 5
, 8
Exam
ples
: 2
7–3
1,
11
6–1
23
, 1
94
–19
7,
25
0–2
54
, 3
07
–31
1, 3
69
CYU
, 46
9–4
72
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 70–7
1,
104–1
17,
145 #
2, 2
23
#15, 3
31,
349–3
50 #
17,
472 #
4,
489–4
97,
552–5
53
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 118 #
1, #
2,
145–1
50, 2
20
#18, 3
38–3
39,
353 #
1, 5
62
CYU
, 468–4
71
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 68 #
10,
146 #
3,1
57–1
61,
239–2
42,
305–3
06,
364–3
67,
399–4
04,
439–4
42,
490–4
95
3.
Const
ruct
via
ble
arg
um
ents
and c
ritique
the
reas
onin
g o
f oth
ers.
Mat
hem
atic
ally
pro
fi cie
nt s
tude
nts
unde
rsta
nd a
nd u
se s
tate
d as
sum
ptio
ns,
defi n
ition
s, a
nd p
revi
ousl
y es
tabl
ishe
d re
sults
in c
onst
ruct
ing
argu
men
ts. T
hey
mak
e co
njec
ture
s an
d bu
ild a
logi
cal p
rogr
essi
on o
f st
atem
ents
to
expl
ore
the
trut
h of
the
ir
conj
ectu
res.
The
y ar
e ab
le t
o an
alyz
e si
tuat
ions
by
brea
king
the
m in
to c
ases
, and
ca
n re
cogn
ize
and
use
coun
tere
xam
ples
. The
y ju
stify
the
ir c
oncl
usio
ns, c
omm
unic
ate
them
to
othe
rs, a
nd r
espo
nd t
o th
e ar
gum
ents
of ot
hers
. The
y re
ason
indu
ctiv
ely
abou
t da
ta, m
akin
g pl
ausi
ble
argu
men
ts t
hat
take
into
acc
ount
the
con
text
fro
m
whi
ch t
he d
ata
aros
e. M
athe
mat
ical
ly p
rofi c
ient
stu
dent
s ar
e al
so a
ble
to c
ompa
re
the
effe
ctiv
enes
s of
tw
o pl
ausi
ble
argu
men
ts, d
istin
guis
h co
rrec
t lo
gic
or r
easo
ning
fr
om t
hat
whi
ch is
fl aw
ed, a
nd—
if th
ere
is a
fl aw
in a
n ar
gum
ent—
expl
ain
wha
t it
is. E
lem
enta
ry s
tude
nts
can
cons
truc
t ar
gum
ents
usi
ng c
oncr
ete
refe
rent
s su
ch a
s ob
ject
s, d
raw
ings
, dia
gram
s, a
nd a
ctio
ns. S
uch
argu
men
ts c
an m
ake
sens
e an
d be
co
rrec
t, ev
en t
houg
h th
ey a
re n
ot g
ener
aliz
ed o
r m
ade
form
al u
ntil
late
r gr
ades
. La
ter, s
tude
nts
lear
n to
det
erm
ine
dom
ains
to
whi
ch a
n ar
gum
ent
appl
ies.
Stu
dent
s at
all
grad
es c
an li
sten
or
read
the
arg
umen
ts o
f ot
hers
, dec
ide
whe
ther
the
y m
ake
sens
e, a
nd a
sk u
sefu
l que
stio
ns t
o cl
arify
or
impr
ove
the
argu
men
ts.
Thro
ugho
ut
Uni
ts 1
–7
Exam
ples
: 18
0
#3
0, 1
94
#4
, 3
35
–33
7, 3
48
#
29
, 37
4–3
77
, 3
87
, 49
3 #
2,
50
4 #
13
, 51
7
CYU
b
Thro
ugho
ut
Uni
ts 1
–7
Exam
ples
: 22
#14, 5
4–5
5,
111#
7, 1
23
#10, 1
68 #
9,
170–1
80, 1
79
#8, 2
07 #
3, #
4,
490–4
91
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 2–1
5,
166 #
5, 1
71
#5, 2
04–2
08,
233 #
7, 3
52 #
9,
405–4
06, 4
87
#11, 5
66–5
67
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 124
#19, 2
87–2
94,
315 #
5, 3
16 #
10,
326 #
22, 4
34 #
6,
472 #
8, 5
94–5
95,
598 #
8, 6
04–6
14
0ii_028_SS_892135.indd Page 23 12/23/10 7:41:37 PM u-082 /Volumes/106/GO00220_r1/work/indd/
24 CPMP • Scope and Sequence
Com
mon C
ore
Sta
te S
tandar
ds
for
Mat
hem
atic
s Corr
elat
ed t
o
Core
-Plu
s M
athem
atic
s:
Cours
e 1, Cours
e 2
, Cours
e 3, an
d C
ours
e 4: Pre
par
atio
n f
or
Cal
culu
s
Sta
ndar
ds
for
Mat
hem
atic
al P
ract
ice
Stu
den
t Editio
n L
esso
ns
Cours
e 1
Cours
e 2
Cours
e 3
Cours
e 4:
Pre
par
atio
n
for
Cal
culu
s
4.
Model
with m
athem
atic
s.
Mat
hem
atic
ally
pro
fi cie
nt s
tude
nts
can
appl
y th
e m
athe
mat
ics
they
kno
w t
o so
lve
prob
lem
s ar
isin
g in
eve
ryda
y lif
e, s
ocie
ty, a
nd t
he w
orkp
lace
. In
early
grad
es, t
his
mig
ht b
e as
sim
ple
as w
ritin
g an
add
ition
equ
atio
n to
des
crib
e a
situ
atio
n. In
mid
dle
grad
es, a
stu
dent
mig
ht a
pply
pro
port
iona
l rea
soni
ng t
o pl
an a
sch
ool e
vent
or
anal
yze
a pr
oble
m in
the
com
mun
ity. B
y hi
gh s
choo
l, a
stud
ent
mig
ht u
se g
eom
etry
to
sol
ve a
des
ign
prob
lem
or
use
a fu
nctio
n to
des
crib
e ho
w o
ne q
uant
ity o
f in
tere
st
depe
nds
on a
noth
er. M
athe
mat
ical
ly p
rofi c
ient
stu
dent
s w
ho c
an a
pply
wha
t th
ey k
now
ar
e co
mfo
rtab
le m
akin
g as
sum
ptio
ns a
nd a
ppro
xim
atio
ns t
o si
mpl
ify a
com
plic
ated
si
tuat
ion,
rea
lizin
g th
at t
hese
may
nee
d re
visi
on la
ter.
They
are
abl
e to
iden
tify
impo
rtan
t qu
antit
ies
in a
pra
ctic
al s
ituat
ion
and
map
the
ir r
elat
ions
hips
usi
ng s
uch
tool
s as
dia
gram
s, t
wo-
way
tab
les,
gra
phs,
fl ow
char
ts a
nd for
mul
as. T
hey
can
anal
yze
thos
e re
latio
nshi
ps m
athe
mat
ical
ly t
o dr
aw c
oncl
usio
ns. T
hey
rout
inel
y in
terp
ret
thei
r m
athe
mat
ical
res
ults
in t
he c
onte
xt o
f th
e si
tuat
ion
and
refl e
ct o
n w
heth
er t
he r
esul
ts
mak
e se
nse,
pos
sibl
y im
prov
ing
the
mod
el if
it h
as n
ot s
erve
d its
pur
pose
.
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 1
61
–16
7, 2
80
#
10
, 32
3–3
32
, 3
63
–36
9, 3
83
, 4
63
–46
8,
55
1–5
61
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 158–1
60,
232–2
42,
260–2
68,
439–4
42,
518–5
19,
522–5
31,
569 C
YU,
573–5
76
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 81–8
8,
132–1
43, 2
18
#12, 2
31 #
5,
242–2
47, 3
60
#14, 4
35–4
37,
495–5
06
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 126 #
23,
157–1
61,
182–1
87,
425–4
29, 4
36
#9, 4
64–4
70,
482 #
26, 5
01,
512–5
16
5.
Use
appro
pri
ate
tools
str
ateg
ical
ly.
Mat
hem
atic
ally
pro
fi cie
nt s
tude
nts
cons
ider
the
ava
ilabl
e to
ols
whe
n so
lvin
g a
mat
hem
atic
al p
robl
em. T
hese
too
ls m
ight
incl
ude
penc
il an
d pa
per, c
oncr
ete
mod
els,
a r
uler
, a p
rotr
acto
r, a
cal
cula
tor, a
spr
eads
heet
, a c
ompu
ter
alge
bra
syst
em, a
sta
tistic
al p
acka
ge, o
r dy
nam
ic g
eom
etry
sof
twar
e. P
rofi c
ient
stu
dent
s ar
e su
ffi ci
ently
fam
iliar
with
too
ls a
ppro
pria
te for
the
ir g
rade
or
cour
se t
o m
ake
soun
d de
cisi
ons
abou
t w
hen
each
of th
ese
tool
s m
ight
be
help
ful,
reco
gniz
ing
both
the
in
sigh
t to
be
gain
ed a
nd t
heir li
mita
tions
. For
exa
mpl
e, m
athe
mat
ical
ly p
rofi c
ient
hi
gh s
choo
l stu
dent
s an
alyz
e gr
aphs
of fu
nctio
ns a
nd s
olut
ions
gen
erat
ed u
sing
a
grap
hing
cal
cula
tor. T
hey
dete
ct p
ossi
ble
erro
rs b
y st
rate
gica
lly u
sing
est
imat
ion
and
othe
r m
athe
mat
ical
kno
wle
dge.
Whe
n m
akin
g m
athe
mat
ical
mod
els,
the
y kn
ow
that
tec
hnol
ogy
can
enab
le t
hem
to
visu
aliz
e th
e re
sults
of va
ryin
g as
sum
ptio
ns,
expl
ore
cons
eque
nces
, and
com
pare
pre
dict
ions
with
dat
a. M
athe
mat
ical
ly p
rofi c
ient
st
uden
ts a
t va
riou
s gr
ade
leve
ls a
re a
ble
to id
entif
y re
leva
nt e
xter
nal m
athe
mat
ical
re
sour
ces,
suc
h as
dig
ital c
onte
nt lo
cate
d on
a w
ebsi
te, a
nd u
se t
hem
to
pose
or
solv
e pr
oble
ms.
The
y ar
e ab
le t
o us
e te
chno
logi
cal t
ools
to
expl
ore
and
deep
en t
heir
unde
rsta
ndin
g of
con
cept
s.
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 5
2–5
6, 1
37
#
16
, 16
1–1
67
, 2
81
#1
3, 2
97
, 4
80
–48
2,
56
8–5
70
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 49–5
7, 9
7
#18, 2
80–2
98,
385, 4
05 #
12,
498–5
01, 5
07
#11, 5
81
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 93–9
5,
220 #
19, 2
54
#13, 2
60–2
65,
462–4
67, 4
75
#11, 5
19–5
22
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 138–1
44, 4
51
#31, 4
68–4
70,
483 #
28,
505–5
07, 5
18
#20, 5
36–5
37,
591–5
95
0ii_028_SS_892135.indd Page 24 12/23/10 7:41:37 PM u-082 /Volumes/106/GO00220_r1/work/indd/
CPMP • Scope and Sequence 25
Com
mon C
ore
Sta
te S
tandar
ds
for
Mat
hem
atic
s Corr
elat
ed t
o
Core
-Plu
s M
athem
atic
s:
Cours
e 1, Cours
e 2
, Cours
e 3, an
d C
ours
e 4: Pre
par
atio
n f
or
Cal
culu
s
Sta
ndar
ds
for
Mat
hem
atic
al P
ract
ice
Stu
den
t Editio
n L
esso
ns
Cours
e 1
Cours
e 2
Cours
e 3
Cours
e 4:
Pre
par
atio
n
for
Cal
culu
s
6.
Att
end t
o p
reci
sion.
Mat
hem
atic
ally
pro
fi cie
nt s
tude
nts
try
to c
omm
unic
ate
prec
isel
y to
oth
ers.
The
y tr
y to
us
e cl
ear
defi n
ition
s in
dis
cuss
ion
with
oth
ers
and
in t
heir o
wn
reas
onin
g. T
hey
stat
e th
e m
eani
ng o
f th
e sy
mbo
ls t
hey
choo
se, i
nclu
ding
usi
ng t
he e
qual
sig
n co
nsis
tent
ly
and
appr
opriat
ely.
The
y ar
e ca
refu
l abo
ut s
peci
fyin
g un
its o
f m
easu
re, a
nd la
belin
g ax
es t
o cl
arify
the
cor
resp
onde
nce
with
qua
ntiti
es in
a p
robl
em. T
hey
calc
ulat
e ac
cura
tely
and
effi
cien
tly, e
xpre
ss n
umer
ical
ans
wer
s w
ith a
deg
ree
of p
reci
sion
ap
prop
riat
e fo
r th
e pr
oble
m c
onte
xt. I
n th
e el
emen
tary
gra
des,
stu
dent
s gi
ve
care
fully
for
mul
ated
exp
lana
tions
to
each
oth
er. B
y th
e tim
e th
ey r
each
hig
h sc
hool
th
ey h
ave
lear
ned
to e
xam
ine
clai
ms
and
mak
e ex
plic
it us
e of
defi
niti
ons.
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 20
–21
#
15
, 17
5 #
17
, 3
74
–37
7, 3
87
#
10
, 39
0 #
17
, 3
91
#1
9, 4
66
#
5, 4
82
#9
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 32–3
3,
92 #
7, 1
72 #
6,
261 #
3, 3
82–
383, 4
67–4
77,
531
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 123
#16, 1
65–1
68,
245–2
47,
283–2
96,
321–3
23,
581–5
83
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 66 #
7,
110 #
4, 2
39 #
10,
366, 4
93–4
95,
517 #
15, 5
35
#3c,
576 #
11
7.
Look
for
and m
ake
use
of
stru
cture
.
Mat
hem
atic
ally
pro
fi cie
nt s
tude
nts
look
clo
sely
to
disc
ern
a pa
tter
n or
str
uctu
re.
Youn
g st
uden
ts, f
or e
xam
ple,
mig
ht n
otic
e th
at t
hree
and
sev
en m
ore
is t
he s
ame
amou
nt a
s se
ven
and
thre
e m
ore,
or
they
may
sor
t a
colle
ctio
n of
sha
pes
acco
rdin
g to
how
man
y si
des
the
shap
es h
ave.
Lat
er, s
tude
nts
will
see
7 ×
8 e
qual
s th
e w
ell
rem
embe
red
7 ×
5 +
7 ×
3, i
n pr
epar
atio
n fo
r le
arni
ng a
bout
the
dis
trib
utiv
e pr
oper
ty. I
n th
e ex
pres
sion
x2 +
9x
+ 1
4, o
lder
stu
dent
s ca
n se
e th
e 1
4 a
s 2 ×
7 a
nd t
he 9
as
2 +
7. T
hey
reco
gniz
e th
e si
gnifi
canc
e of
an
exis
ting
line
in a
ge
omet
ric
fi gur
e an
d ca
n us
e th
e st
rate
gy o
f dr
awin
g an
aux
iliar
y lin
e fo
r so
lvin
g pr
oble
ms.
The
y al
so c
an s
tep
back
for
an
over
view
and
shi
ft p
ersp
ectiv
e. T
hey
can
see
com
plic
ated
thi
ngs,
suc
h as
som
e al
gebr
aic
expr
essi
ons,
as
sing
le o
bjec
ts o
r as
bei
ng c
ompo
sed
of s
ever
al o
bjec
ts. F
or e
xam
ple,
the
y ca
n se
e 5
– 3
(x –
y)2
as
5
min
us a
pos
itive
num
ber
times
a s
quar
e an
d us
e th
at t
o re
aliz
e th
at it
s va
lue
cann
ot
be m
ore
than
5 for
any
rea
l num
bers
x a
nd y
.
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 17
8
#2
4, 1
95
, 2
39
–24
7,
29
1–2
97
, 30
3
STM
, 32
8 S
TM,
46
8, 4
78
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 26–2
9,
42 #
21, 6
0
STM
d, 9
6 C
YU,
178 #
6,
332–3
40, 3
51
#22, 4
81 #
20
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 60 #
5,
62–7
1, 1
12–1
17,
334, 3
48–3
52,
387 #
28,
489–4
95, 5
06
#19, 5
97 #
29
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 59–6
4,
141–1
44,
188–1
93, 2
02
#14, 2
50–2
56,
260 #
14, 2
62
#24, 3
69–3
72,
391–3
93,
464–4
70
0ii_028_SS_892135.indd Page 25 12/23/10 7:41:37 PM u-082 /Volumes/106/GO00220_r1/work/indd/
26 CPMP • Scope and Sequence
Com
mon C
ore
Sta
te S
tandar
ds
for
Mat
hem
atic
s Corr
elat
ed t
o
Core
-Plu
s M
athem
atic
s:
Cours
e 1, Cours
e 2
, Cours
e 3, an
d C
ours
e 4: Pre
par
atio
n f
or
Cal
culu
s
Sta
ndar
ds
for
Mat
hem
atic
al P
ract
ice
Stu
den
t Editio
n L
esso
ns
Cours
e 1
Cours
e 2
Cours
e 3
Cours
e 4:
Pre
par
atio
n
for
Cal
culu
s
8. L
ook
for
and e
xpre
ss r
egula
rity
in r
epea
ted r
easo
nin
g.
Mat
hem
atic
ally
pro
fi cie
nt s
tude
nts
notic
e if
calc
ulat
ions
are
rep
eate
d, a
nd lo
ok
both
for
gen
eral
met
hods
and
for
sho
rtcu
ts. U
pper
ele
men
tary
stu
dent
s m
ight
no
tice
whe
n di
vidi
ng 2
5 b
y 1
1 t
hat
they
are
rep
eatin
g th
e sa
me
calc
ulat
ions
ove
r an
d ov
er a
gain
, and
con
clud
e th
ey h
ave
a re
peat
ing
deci
mal
. By
payi
ng a
tten
tion
to t
he c
alcu
latio
n of
slo
pe a
s th
ey r
epea
tedl
y ch
eck
whe
ther
poi
nts
are
on t
he
line
thro
ugh
(1, 2
) w
ith s
lope
3, m
iddl
e sc
hool
stu
dent
s m
ight
abs
trac
t th
e eq
uatio
n (y
– 2
)/(x
– 1
) =
3. N
otic
ing
the
regu
larity
in t
he w
ay t
erm
s ca
ncel
whe
n ex
pand
ing
(x –
1)(x
+ 1
), (x
– 1
)(x2 +
x +
1),
and
(x –
1)(x
3 +
x2 +
x +
1) m
ight
lead
the
m t
o th
e ge
nera
l for
mul
a fo
r th
e su
m o
f a
geom
etric
series
. As
they
wor
k to
sol
ve a
pr
oble
m, m
athe
mat
ical
ly p
rofi c
ient
stu
dent
s m
aint
ain
over
sigh
t of
the
pro
cess
, w
hile
att
endi
ng t
o th
e de
tails
. The
y co
ntin
ually
eva
luat
e th
e re
ason
able
ness
of th
eir
inte
rmed
iate
res
ults
.
Thro
ugho
ut
Uni
ts 1
–7
Exam
ples
: 2
7–3
5, 1
52
#
1e,
33
2–3
34
, 4
04
–40
6,
43
7–4
38
#
6, 4
73
–47
8,
49
7 #
5
Thro
ugho
ut
Uni
ts 1
–7
Exam
ples
: 23
#20, 4
0 #
15,
210–2
16, 3
71
#13, 5
70–5
72,
578 #
14
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 62
#4, #
5, 1
03 #
3,
329–3
31, 3
41
#12, 4
82–4
89,
507, 5
39–5
42
Thro
ugho
ut
Uni
ts 1
–8
Exam
ples
: 107 #
7,
165–1
68, 2
05
#28, 2
45 #
26,
318–3
21, 3
61 #
7,
499 1
0, 5
01–5
04,
535 #
3, 5
91–5
95
0ii_028_SS_892135.indd Page 26 12/23/10 7:41:38 PM u-082 /Volumes/106/GO00220_r1/work/indd/
Scope and Sequence Algebra and Functions Geometry and Trigonometry Statistics and Probability Discrete Mathematics
ISBN: 978-0-07-892135-3MHID: 0-07-892135-X
www.glencoe.com
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