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For use withGlencoe Algebra 1Glencoe Algebra 2
Guide to DailyIntervention
Glencoe/McGraw-Hill
abc
Copyright © by The McGraw-Hill Companies, Inc. All right reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without char; and be used solely in conjunction with Glencoe Algebra or Glencoe Algebra 2. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027 ISBN: 0-07-827742-6 Guide to Daily Intervention 1 2 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04 03 02
Contents Teacher’s Guide to Using the Guide to Daily Intervention ............................................... iv Daily Intervention in the Student Edition ........................................................................... 1 Daily Intervention in the Teacher Wraparound Edition...................................................... 2 Daily Intervention in the Teacher Classroom Resources .................................................... 3 Daily Intervention on the Internet ....................................................................................... 4 Daily Intervention with other Resources............................................................................. 5 Student Remediation Plan ................................................................................................... 6 Correlation of Glencoe Algebra 1 to Daily Intervention Resources ................................... 8 Correlation of Glencoe Algebra 2 to Daily Intervention Resources ................................. 36
©Glencoe/McGraw-Hill iii Glencoe Algebra 1 and 2
Teacher’s Guide to Using the Guide to Daily Intervention
Today it is vital that students understand the mathematics that they are learning. Using computers on the job, making good consumer choices, evaluating information, and other life skills depend upon good mathematics skills. Since no two students are exactly the same, in every classroom there will be students of various abilities and skill levels. This booklet focuses on ways that teachers can intervene to assist the struggling student to improve his or her performance. Helping all students succeed in mathematics and develop their mathematical reasoning skills is an ambitious and worthwhile goal. In order to ensure students’ success, teachers can follow a three-step process of daily intervention. 1. Assessment of individual student needs Teachers need to evaluate
the needs of students in order to meet those needs. 2. Ongoing evaluation of student progress Monitoring students’
progress and understanding on a daily basis allows a teacher to head off trouble.
3. Monitoring instructional activities to strengthen students’ weaknesses Providing opportunities for students to immediately address any weaknesses ensures students’ continued success.
The Glencoe Algebra program includes tools for daily intervention in the Student Edition, the Teacher Wraparound Edition, the Teacher Classroom Resources, the Internet, and other products. Using these tools can help you help your students realize mathematical success. The following pages detail each resource available and the correlation shows how they are used in each lesson of Glencoe Algebra 1 and Glencoe Algebra 2.
©Glencoe/McGraw-Hill iv Glencoe Algebra 1 and 2
Daily Intervention in the Student Edition • In the Getting Started section at the beginning of each
chapter in the Student Edition, the Prerequisite Skills check students’ preparedness for the chapter. You can check prior knowledge by reviewing prerequisite topics and explaining how these prerequisite topics are related to the current concept.
• Additional practice of Prerequisite Skills is provided at the end of each lesson with page references to help students review the concepts. These exercises review concepts and skills that will be applied in the next lesson. The Prerequisite Skills section in the Student
Handbook the back of the Student Edition provides explanation and practice of skills that are needed for success in algebra.
Algebra 1 Student Edition, p. 5
Mini of Algebra 1 SE p. 5
• You can use the Check for Understanding exercises in class to ensure that all students understand the concepts.
Mini of Algebra 1 SE p. 13
• Concept Check Students communicate their understanding of the concepts just taught by defining, describing, and explaining mathematical concepts.
• Guided Practice These exercises present a representative sample of the exercises in the Practice and Apply section. A key is provided in the Teacher Wraparound Edition that correlates the exercises to the corresponding examples. Find the Error exercises help students identify and address common errors before they occur.
Algebra 1 Student Edition, p. 13 • Application Students have the opportunity to solve a real-world or mathematical connection problem as a check for understanding.
• Extra Practice, located in the back of the Student
Edition, provides additional, immediate practice with the skills and concepts from each lesson.
Mini of Algebra 1 SE p. 829
• Mixed Problem Solving, also in the back of the Student Edition, includes numerous verbal problems for students to reinforce their problem-solving skills.
Algebra 1 Student Edition, p. 829 ©Glencoe/McGraw-Hill 1 Glencoe Algebra 1 and 2
Daily Intervention in the Teacher Wraparound Edition
• Daily Intervention features provide suggestions for addressing various learning styles and helping students who are having difficulty.
Mini of Algebra 1 TWE p. 85
• The Differentiated Instruction suggestions are keyed to eight commonly-accepted learning styles.
• Unlocking Misconceptions suggestions help you analyze where students make common errors so you can point these trouble spots out to them.
Algebra 1 Teacher Wraparound Edition, p. 85
• Each lesson ends with Open-Ended Assessment strategies for closing the lesson and ensuring that students understand and can apply the concepts. These strategies for bringing closure to the lesson are addressed through writing, modeling, and speaking.
Algebra 1 Teacher Wraparound Edition, p. 72
Mini of Algebra 1 TWE p. 72
Mini of Algebra 1 TWE p. 99
• Teacher to Teacher features contain teaching suggestions from teachers who are successfully teaching Algebra 1 or Algebra 2 in their classrooms. Suggestions include content tips, techniques, and activities that can be used in intervention.
Algebra 1 Teacher Wraparound Edition, p. 99
©Glencoe/McGraw-Hill 2 Glencoe Algebra 1 and 2
Daily Intervention in the Teacher Classroom Resources
• The Study Guide and Intervention masters found
in the Chapter Resource Masters summarize key concepts for each objective and provide practice exercises. These masters are also available as a consumable Study Guide and Intervention Workbook in English and Spanish. You may wish to use these masters for additional instruction and practice with individual students, in cooperative groups, or in peer tutoring situations.
Show Study Guide and Intervention master (Chapter 1 Resource Masters, p. 15)
Algebra 1 Chapter 1 Resource Masters, p. 15
• 5-Minute Check Transparencies with Standardized Test Practice For each lesson, there is a full-size transparency with questions covering the previous lesson or chapter. Also included on each transparency is a Standardized Test Practice question. These provide an excellent ongoing opportunity for checking students’ understanding of the mathematics they are learning.
Show a 5-Minute Check Transparency
Algebra 1 5-Minute Check Transparency 5-1
Algebra 1 Parent and Student Study Guide Workbook, p. 11
Show Parent and Student Study Guide Workbook p. 11
• Parents or guardians may need specific advice for helping students make improvements. It may help to engage in frequent correspondence, encourage parental monitoring of homework, and provide parents with a schedule of students’ assignments. The Parent and Student Study Guide Workbook contains a one-page worksheet for each lesson in the Student Edition and a one-page review for each chapter. This workbook offers an excellent opportunity for students and parents to work together to strengthen weaknesses and develop mathematical understanding.
©Glencoe/McGraw-Hill 3 Glencoe Algebra 1 and 2
Daily Intervention on the Internet • Online Study Tools These comprehensive review and intervention tools are
available anytime, anyplace, simply by logging on to: www.algebra1.com or www.algebra2.com
• Self-Check Quizzes are available for every
lesson. Immediate feedback lets the student know whether the answers are correct and references specific pages and examples in the Student Edition for review. Access the Self-Check Quizzes directly at:
Show a screen-capture of a self-check quiz (pick up from Alg 1 SE front matter, p. 1)
www.algebra1.com/self_check_quiz or
www.algebra2.com/self_check_quiz
• Extra Examples that mimic the ones in the Student Edition are completely worked out and available for students to review at:
www.algebra1.com/extra_examples or
www.algebra2.com/extra_examples You may wish to use these examples in reteaching or to have students review areas of weakness.
Show a screen-capture of an extra example
Show a screen-capture of a vocab review
• Vocabulary Review lets you and your
students check their understanding of the terms and definitions used in each chapter. Access this game-style review at:
www.algebra1.com/vocabulary_review or
www.algebra2.com/vocabulary_review
©Glencoe/McGraw-Hill 4 Glencoe Algebra 1 and 2
Daily Intervention with Other Resources
Show Prerequisite Skills Workbook p. 75
• The Prerequisite Skills Workbook provides extra practice on basic skills that are needed for success in Algebra 1. You may use these pages to give students an opportunity to review and refresh their skills. Topics addressed include: • Operations with Whole Numbers • Operations with Decimals • Operations with Fractions • Measures in the Metric and Customary Systems • Line Graphs • Histograms • Probability Prerequisite Skills Workbook, p. 75
Show a screen-capture of AlgePASS
• The AlgePASS: Tutorial Plus and Alge2PASS: Tutorial Plus CD-ROMs provide an interactive, self-paced tutorial for an Algebra 1 or Algebra 2 curriculum. The lessons are correlated directly to Glencoe Algebra 1 and Glencoe Algebra 2. Each lesson, or concept, includes a pretest, tutorial, guided practice, and post test. Students’ answers to the pretests automatically determine whether the tutorial is needed for that concept – without taking teacher time to grade it. This software is designed to identify and address student weaknesses.
• Hot Words, Hot Topics is Glencoe’s mathematical handbook for students. The Hot Words section includes a glossary of terms while the Hot Topics section consists of explanations of key mathematical concepts. An exercise set is included to check students’ understanding of the concepts. This valuable resource can be used as a reference in the classroom or for home study.
Show cover of Hot Words
©Glencoe/McGraw-Hill 5 Glencoe Algebra 1 and 2
Student Remediation Plan Teacher Instructions You can use the Student Remediation Plan template that follows to plan for students who are in need of intervention/remediation. It can be used for high stakes tests, if there is no formal remediation plan required by your school or district. It can also be used for mid-semester reviews or project-based work. Purpose • To identify students’ specific problem areas and link them to steps that
can produce attainable results. • To provide a template to easily record remediation plans and use them
to communicate with students and/or parents. Suggested Uses • Involve Students in their Remediation Plans.
Hold a teacher-student conference to go over the details of the remediation plan. Make certain they understand what they are to do, and have them sign a copy of their plan as a sign of good faith.
• Involve Parents As Much As Possible. You may also wish to involve parents in the remediation plan, if the situation is appropriate. Like your students, make sure the parents understand the steps their child should take to improve their performance in your class.
• Identify common steps and resources that can be used for different levels of remedial study. Try to identify several sets of steps and resources for at least two different levels of student need. For example, you might identify a course of action for students who need a small amount of extra work, and one for those that need a great deal of extra study in the identified academic area. Then, as you identify students in need of intervention, you can choose their level and the appropriate remediation plan. While you will probably want to customize the plan per student, you will at least have a defined set of steps with which to begin. After the semester ends, you can then evaluate each plan's success rate and determine what can be revised to improve each set of actions or resources.
©Glencoe/McGraw-Hill 6 Glencoe Algebra 1 and 2
Student Remediation Plan Student _________________________ Teacher____________________________ Course __________________________ Date_______________________________ Topic/Project/Exam_____________________________
Problem Area Solution Steps to Be Taken Resources Needed
©Glencoe/McGraw-Hill 7 Glencoe Algebra 1 and 2
Cha
pter
1
The
Lan
guag
e of
Alg
ebra
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
1-1
Va
riabl
es a
nd
Expr
essi
ons
• W
rite
mat
hem
atic
al
expr
essi
ons
for v
er-
bal e
xpre
ssio
ns.
• W
rite
verb
al
expr
essi
ons
for
mat
hem
atic
al
expr
essi
ons.
DI,
Verb
al/
Lin
guis
tic, 7
1,
2
1-1
1 9,
10
1-1
6.
1, 6
.3
1-2
O
rder
of
Ope
ratio
ns
• Ev
alua
te n
umer
ical
ex
pres
sion
s by
us
ing
the
orde
r of
oper
atio
ns.
• Ev
alua
te a
lgeb
raic
ex
pres
sion
s by
us
ing
the
orde
r of
oper
atio
ns.
Find
the
Erro
r, 13
U
nloc
king
M
isco
ncep
tions
, 1
3 D
I, Lo
gica
l/ M
athe
mat
ical
, 1
5
7, 8
1-
2 2
5-12
, 21-
24
1-2
1 1.
3, 6
.2
1-3
O
pen
Sent
ence
s
• So
lve
open
sen
-te
nce
equa
tions
. •
Solv
e op
en s
en-
tenc
e in
equa
litie
s.
DI,
Nat
ural
ist,
17
13
, 14
1-3
3 1,
2, 5
-12,
25
, 26,
47-
50, 5
5-58
, 61
, 62
1-3
2.4,
6.4
,6.
6
1-4
Id
entit
y an
d Eq
ualit
y Pr
oper
ties
• R
ecog
nize
the
prop
ertie
s of
iden
tity
and
equa
lity.
•
Use
the
prop
ertie
s of
iden
tity
and
equa
lity.
DI,
Intra
pers
onal
, 2
2
19, 2
0 1-
4 4
5-8,
11,
12,
21
, 22,
25,
26
, 55,
56
1-4
1.
2,6.
3
1-5
Th
e D
istri
butiv
e Pr
oper
ty
• U
se th
e D
istri
butiv
e Pr
oper
ty to
eva
luat
e ex
pres
sion
s.
• U
se th
e D
istri
butiv
e Pr
oper
ty to
sim
plify
ex
pres
sion
s.
Tips
for N
ew
Tea
cher
s, 2
7 D
I, Ki
nest
hetic
,
29
Find
the
Erro
r, 29
25, 2
6 1-
5 5
49, 5
0, 5
5,
56, 7
7, 7
8 1-
5
1.2,
7.5
1-6
C
omm
utat
ive
and
Asso
ciat
ive
Prop
ertie
s
• R
ecog
nize
the
Com
mut
ativ
e an
d As
soci
ativ
e Pr
oper
ties.
•
Use
the
Com
mut
a-tiv
e an
d As
soci
ativ
e Pr
oper
ties
to s
im-
plify
exp
ress
ions
.
DI,
Visu
al/
Spa
tial,
33
31, 3
2 1-
6 6
49, 5
0, 7
7,
78
1-6
2
1.2,
6.3
1-7
Lo
gica
l R
easo
ning
• Id
entif
y th
e hy
po-
thes
is a
nd c
oncl
u-si
on in
a c
ondi
tiona
l st
atem
ent.
• U
se a
cou
nter
ex-
ampl
e to
sho
w th
at
an a
sser
tion
is fa
lse.
DI,
Inte
rper
sona
l, 3
8 37
, 38
1-7
7
1-7
2.
8, 5
.1,
5.2
1-8
G
raph
s an
d Fu
nctio
ns
• In
terp
ret g
raph
s of
fu
nctio
ns.
• D
raw
gra
phs
of
func
tions
.
DI,
Audi
tory
/
Mus
ical
, 45
43, 4
4 1-
8 8
95, 9
6 1-
8
4.2,
6.7
1-9
St
atis
tics:
An
alyz
ing
Dat
a by
Usi
ng T
able
s an
d G
raph
s
• An
alyz
e da
ta g
iven
in
tabl
es a
nd g
raph
s (b
ar, l
ine,
and
ci
rcle
). •
Det
erm
ine
whe
ther
gr
aphs
are
m
isle
adin
g.
Unl
ocki
ng
Mis
conc
eptio
ns,
51
DI,
Visu
al/
Spa
tial,
52
49, 5
0 1-
9 9
1-
9
4.2,
4.3
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
2
Rea
l Num
bers
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
2-1
R
atio
nal
Num
bers
on
the
Num
ber L
ine
• G
raph
ratio
nal
num
bers
on
a nu
mbe
r lin
e.
• Fi
nd a
bsol
ute
valu
es o
f rat
iona
l nu
mbe
rs.
Unl
ocki
ng
Mis
conc
eptio
ns,
70
DI,
Verb
al/
Lin
guis
tic, 7
2
75, 7
6 2-
1 11
1-
4, 1
5, 1
6,
19, 2
0, 4
5,
46, 5
5, 5
6,
63-6
6, 7
5, 7
6
2-1
1.5,
2.2
,2.
3, 2
.5
2-2
Ad
ding
and
Su
btra
ctin
g R
atio
nal
Num
bers
• Ad
d in
tege
rs a
nd
ratio
nal n
umbe
rs.
• Su
btra
ct in
tege
rs
and
ratio
nal
num
bers
.
DI,
Visu
al/
Spa
tial,
75
Find
the
Erro
r, 76
81, 8
2 2-
2 12
15
, 16,
19-
24, 3
9, 4
0,
55-6
0, 6
5,
66, 7
5, 7
6
2-2
1.5,
2.3
,2.
4, 2
.6
2-3
M
ultip
lyin
g R
atio
nal
Num
bers
• M
ultip
ly in
tege
rs.
• M
ultip
ly ra
tiona
l nu
mbe
rs.
DI,
Logi
cal,
81
87, 8
8 2-
3 13
15
, 16,
19,
20
, 25-
28,
39, 4
0, 4
7-50
, 65,
66,
75
, 76
2-3
1.5,
2.4
,2.
6
2-4
D
ivid
ing
Rat
iona
l N
umbe
rs
• D
ivid
e in
tege
rs.
• D
ivid
e ra
tiona
l nu
mbe
rs.
DI,
Kine
sthe
tic,
85
93, 9
4 2-
4 14
15
, 16,
19,
20
, 29-
32,
39, 4
0, 4
7,
48, 5
1-54
, 63
-66,
75,
76
2-4
31.
5, 2
.4,
2.6,
4.4
2-5
St
atis
tics:
D
ispl
ayin
g an
d An
alyz
ing
Dat
a
• In
terp
ret a
nd
crea
te li
ne p
lots
an
d st
em-a
nd-le
af
plot
s.
• An
alyz
e da
ta
usin
g m
ean,
m
edia
n, a
nd
mod
e.
DI,
Visu
al/
Spa
tial,
90
Unl
ocki
ng
Mis
conc
eptio
ns,
91
99, 1
00
2-5
15
15, 1
6, 6
1,
62, 7
5, 7
6 2-
5
2.
1, 4
.2,
4.3,
4.4
2-6
Pr
obab
ility:
Si
mpl
e Pr
obab
ility
and
Odd
s
• Fi
nd th
e pr
obab
ility
of a
si
mpl
e ev
ent.
• Fi
nd th
e od
ds o
f a
sim
ple
even
t.
Unl
ocki
ng
Mis
conc
eptio
ns,
97
DI,
Inte
rper
sona
l, 9
8 Fi
nd th
e Er
ror,
99
105,
106
2-
6 16
17
, 18,
37,
38
, 67-
70,
99, 1
00
2-6
3.4,
4.5
,4.
6
2-7
Sq
uare
Roo
ts
and
Rea
l N
umbe
rs
• Fi
nd s
quar
e ro
ots.
•
Cla
ssify
and
ord
er
real
num
bers
.
DI,
Intra
pers
onal
, 1
07
111,
112
2-
7 17
75
, 76
2-7
3.
2
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
3
Sol
ving
Lin
ear
Equ
atio
ns
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
3-1
W
ritin
g Eq
uatio
ns
• Tr
ansl
ate
verb
al
sent
ence
s in
to
equa
tions
. •
Tran
slat
e eq
uatio
ns in
to
verb
al s
ente
nces
.
DI,
Verb
al/
Lin
guis
tic, 1
21
137,
138
3-
1 19
3-1
2.
3, 2
.5,
6.1
3-2
So
lvin
g Eq
uatio
ns b
y U
sing
Add
ition
an
d Su
btra
ctio
n
• So
lve
equa
tions
by
usi
ng a
dditi
on.
• So
lve
equa
tions
by
usi
ng
subt
ract
ion.
Unl
ocki
ng
Mis
conc
eptio
ns,
129
D
I, Vi
sual
/ S
patia
l, 13
0
143,
144
3-
2 20
21
, 22,
59,
60
3-
2
2.
4, 2
.6,
6.4
3-3
So
lvin
g Eq
uatio
ns b
y U
sing
M
ultip
licat
ion
and
Div
isio
n
• So
lve
equa
tions
by
usi
ng
mul
tiplic
atio
n.
• So
lve
equa
tions
by
usi
ng d
ivis
ion.
Tips
for N
ew
Tea
cher
s, 1
36
DI,
Audi
tory
/ M
usic
al, 1
37
Find
the
Erro
r,
138
149,
150
3-
3 21
9-
12, 5
1, 5
2 3-
3
1.3,
6.4
3-4
So
lvin
g M
ulti-
Step
Equ
atio
ns
• So
lve
prob
lem
s by
w
orki
ng
back
war
d.
• So
lve
equa
tions
in
volv
ing
mor
e th
an o
ne
oper
atio
n.
DI,
Logi
cal,
144
15
5, 1
56
3-4
22
77, 7
8 3-
4 4
6.2,
6.4
3-5
So
lvin
g Eq
uatio
ns w
ith
the
Varia
ble
on
Each
Sid
e
• So
lve
equa
tions
w
ith th
e va
riabl
e on
eac
h si
de.
• So
lve
equa
tions
in
volv
ing
grou
ping
sy
mbo
ls.
DI,
Kine
sthe
tic,
150
16
1, 1
62
3-5
23
23, 2
4 3-
5 5
2.1,
6.4
3-6
R
atio
s an
d Pr
opor
tions
• D
eter
min
e w
heth
er tw
o ra
tios
form
a p
ropo
rtion
. •
Solv
e pr
opor
tions
.
DI,
Inte
rper
sona
l L
earn
ers,
157
167,
168
3-
6 24
27
, 28,
67-
74
3-6
6 2.
8, 6
.5
3-7
Pe
rcen
t of
Cha
nge
• Fi
nd p
erce
nts
of
incr
ease
and
de
crea
se.
• So
lve
prob
lem
s in
volv
ing
perc
ents
of
cha
nge.
DI,
Nat
ural
ist,
1
61
Find
the
Erro
r,
162
173,
174
3-
7 25
17
, 18,
41-
44, 7
1, 7
2,
77, 7
8
3-7
2.8,
6.4
,6.
5
3-8
So
lvin
g Eq
uatio
ns a
nd
Form
ulas
• So
lve
equa
tions
fo
r giv
en
varia
bles
. •
Use
form
ulas
to
solv
e re
al-w
orld
pr
oble
ms.
DI,
Intra
pers
onal
, 1
68
179,
180
3-
8 26
81
, 82
3-8
7, 8
6.
2, 6
.4
3-9
W
eigh
ted
Aver
ages
• So
lve
mix
ture
pr
oble
ms.
•
Solv
e un
iform
m
otio
n pr
oble
ms.
DI,
Logi
cal,
173
185,
186
3-
9 27
3-9
6.
4, 6
.5
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
4
Gra
phin
g R
elat
ions
and
Fun
ctio
ns
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
4-1
Th
e C
oord
inat
e Pl
ane
• Lo
cate
poi
nts
on
the
coor
dina
te
plan
e.
• G
raph
poi
nts
on a
co
ordi
nate
pla
ne.
DI,
Verb
al/
Lin
guis
tic, 1
96
213,
214
4-
1 29
4-1
6.
2, 6
.7
4-2
Tr
ansf
orm
atio
ns
on th
e C
oord
inat
e Pl
ane
• Tr
ansf
orm
figu
res
by u
sing
re
flect
ions
, tra
nsla
tions
, dila
-tio
ns, a
nd
rota
tions
. •
Tran
sfor
m fi
gure
s on
a c
oord
inat
e pl
ane
by u
sing
re-
flect
ions
, tra
nsla
-tio
ns, d
ilatio
ns,
and
rota
tions
.
Unl
ocki
ng
Mis
conc
eptio
ns,
198
D
I, Vi
sual
/ S
patia
l, 19
9
219,
220
4-
2 30
4-2
6.
7, 7
.3
4-3
R
elat
ions
•
Rep
rese
nt
rela
tions
as
sets
of
ord
ered
pai
rs,
tabl
es, m
appi
ngs,
an
d gr
aphs
. •
Find
the
inve
rse
of
a re
latio
n.
DI,
Audi
tory
/ M
usic
al, 2
06
225,
226
4-
3 31
4-3
6.
7
4-4
Eq
uatio
ns a
s R
elat
ions
• U
se a
n eq
uatio
n to
det
erm
ine
the
rang
e fo
r a g
iven
do
mai
n.
• G
raph
the
solu
tion
set f
or a
giv
en
dom
ain.
DI,
Verb
al/
Lin
guis
tic, 2
13
Find
the
Erro
r,
215
231,
232
4-
4 32
4-4
6.
4, 6
.7
4-5
G
raph
ing
Line
ar
Equa
tions
• D
eter
min
e w
heth
er a
n eq
uatio
n is
line
ar.
• G
raph
line
ar
equa
tions
.
Unl
ocki
ng
Mis
conc
eptio
ns,
219
Ti
ps fo
r New
T
each
ers,
220
D
I, Ki
nest
hetic
, 2
20
237,
238
4-
5 33
4-5
9 6.
2, 6
.7
4-6
Fu
nctio
ns
• D
eter
min
e w
heth
er a
rela
tion
is a
func
tion.
•
Find
func
tion
valu
es.
DI,
Inte
rper
sona
l, 2
27
243,
244
4-
6 34
4-6
10
1.5,
2.3
, 6.
7
4-7
Ar
ithm
etic
Se
quen
ces
• R
ecog
nize
ar
ithm
etic
se
quen
ces.
•
Exte
nd a
nd w
rite
form
ulas
for
arith
m??
etic
se
quen
ces.
DI,
Nat
ural
ist,
2
35
Find
the
Erro
r,
236
249,
250
4-
7 35
5-
8 4-
7
6.7
4-8
W
ritin
g Eq
uatio
ns fr
om
Patte
rns
• Lo
ok fo
r a p
atte
rn.
• W
rite
an e
quat
ion
give
n so
me
of th
e so
lutio
ns.
DI,
Intra
pers
onal
, 2
42
255,
256
4-
8 36
4-8
6.
1
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
5
Sol
ving
Sys
tem
s of L
inea
r E
quat
ions
and
Ineq
ualit
ies
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
5-1
Sl
ope
• Fi
nd th
e sl
ope
of a
lin
e.
• U
se ra
te o
f ch
ange
to s
olve
pr
oble
ms.
Unl
ocki
ng
Mis
conc
eptio
ns,
257
Fi
nd th
e Er
ror,
2
59
DI,
Kine
sthe
tic,
260
Ti
ps fo
r New
T
each
ers,
262
281,
282
5-
1 38
39
, 40,
63,
64
5-
1
2.4,
6.8
5-2
Sl
ope
and
Dire
ct V
aria
tion
• W
rite
and
grap
h di
rect
var
iatio
n eq
uatio
ns.
• So
lve
prob
lem
s in
volv
ing
dire
ct
varia
tion.
DI,
Inte
rper
sona
l, 2
66
287,
288
5-
2 39
29
, 30
5-2
6.
4, 6
.8
5-3
Sl
ope-
Inte
rcep
t Fo
rm
• W
rite
and
grap
h lin
ear e
quat
ions
in
slop
e-in
terc
ept
form
. •
Mod
el re
al-w
orld
da
ta w
ith a
n eq
uatio
n in
slo
pe-
inte
rcep
t for
m.
DI,
Visu
al/
Spa
tial,
274
293,
294
5-
3 40
5-3
6.
7, 6
.8
5-4
W
ritin
g Eq
uatio
ns in
Sl
ope-
Inte
rcep
t Fo
rm
• W
rite
an e
quat
ion
of a
line
giv
en th
e sl
ope
and
one
poin
t on
a lin
e.
• W
rite
an e
quat
ion
of a
line
giv
en tw
o po
ints
on
the
line.
DI,
Logi
cal,
282
299,
300
5-
4 41
5-4
11
1.5,
6.8
5-5
W
ritin
g Eq
uatio
ns in
Po
int-S
lope
Fo
rm
• W
rite
the
equa
tion
of a
line
in p
oint
-sl
ope
form
. •
Writ
e lin
ear
equa
tions
in
diffe
rent
form
s.
DI,
Verb
al/
Lin
guis
tic, 2
88
Find
the
Erro
r,
289
305,
306
5-
5 42
5-5
12
6.8
5-6
G
eom
etry
: Pa
ralle
l and
Pe
rpen
dicu
lar
Line
s
• W
rite
an e
quat
ion
of th
e lin
e th
at
pass
es th
roug
h a
give
n po
int,
para
llel t
o a
give
n lin
e.
• W
rite
an e
quat
ion
of th
e lin
e th
at
pass
es th
roug
h a
give
n po
int,
perp
endi
cula
r to
a gi
ven
line.
DI,
Nat
ural
ist,
2
94
311,
312
5-
6 43
5-6
13
6.8
5-7
St
atis
tics:
Sc
atte
r Plo
ts
and
Line
s of
Fit
• In
terp
ret p
oint
s on
a
scat
ter p
lot.
• W
rite
equa
tions
fo
r lin
es o
f fit.
DI,
Intra
pers
onal
, 3
04
317,
318
5-
7 44
5-7
4.
3
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
6
Sol
ving
Lin
ear
Ineq
ualit
ies
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
6-1
So
lvin
g In
equa
litie
s by
Ad
ditio
n an
d Su
btra
ctio
n
• So
lve
linea
r ine
-qu
aliti
es b
y us
ing
addi
tion.
•
Solv
e lin
ear
ineq
ualit
ies
by
usin
g su
btra
ctio
n.
DI,
Verb
al/
Lin
guis
tic, 3
20
Unl
ocki
ng
Mis
conc
eptio
ns,
321
Ti
ps fo
r New
T
each
ers,
323
343,
344
6-
1 46
6-1
6.
4, 6
.6
6-2
So
lvin
g In
equa
litie
s by
M
ultip
licat
ion
and
Div
isio
n
• So
lve
linea
r in
equa
litie
s by
us
ing
mul
tiplic
atio
n.
• So
lve
linea
r in
equa
litie
s by
us
ing
divi
sion
.
DI,
Kine
sthe
tic,
327
Fi
nd th
e Er
ror,
3
29
349,
350
6-
2 47
6-2
6.
4, 6
.6
6-3
So
lvin
g
Mul
ti-St
ep
Ineq
ualit
ies
• So
lve
linea
r in
equa
litie
s in
volv
ing
mor
e th
an o
ne
oper
atio
n.
• So
lve
linea
r in
equa
litie
s in
volv
ing
the
Dis
tribu
tive
Prop
erty
.
Tips
for N
ew
Tea
cher
s, 3
34
Unl
ocki
ng
Mis
conc
eptio
ns,
334
D
I, In
terp
erso
nal,
335
355,
356
6-
3 48
6-3
14
6.6
6-4
So
lvin
g C
ompo
und
Ineq
ualit
ies
• So
lve
com
poun
d in
equa
litie
s co
ntai
ning
the
wor
d an
d an
d gr
aph
thei
r so
lutio
n se
ts.
• So
lve
com
poun
d in
equa
litie
s co
ntai
ning
the
wor
d or
and
gra
ph
thei
r sol
utio
n se
ts.
DI,
Visu
al/
Spa
tial,
340
361,
362
6-
4 49
6-4
15
6.6
6-5
So
lvin
g O
pen
Sent
ence
s In
volv
ing
Abso
lute
Val
ue
• So
lve
abso
lute
va
lue
equa
tions
. •
Solv
e ab
solu
te
valu
e in
equa
litie
s.
DI,
Logi
cal,
346
Find
the
Erro
r,
348
367,
368
6-
5 50
79
, 80,
83,
84
6-
5
6.
4
6-6
G
raph
ing
Ineq
ualit
ies
in
Two
Varia
bles
• G
raph
ineq
ualit
ies
on th
e co
ordi
nate
pl
ane.
•
Solv
e re
al-w
orld
pr
oble
ms
invo
lvin
g lin
ear
ineq
ualit
ies.
DI,
Intra
pers
onal
, 3
53
373,
374
6-
6 51
6-6
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
7
Sol
ving
Sys
tem
s of L
inea
r E
quat
ions
and
Ineq
ualit
ies
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
7-1
G
raph
ing
Syst
ems
of
Equa
tions
• D
eter
min
e w
heth
er a
sys
tem
of
line
ar e
quat
ions
ha
s 0,
1, o
r in
finite
ly m
any
solu
tions
. •
Solv
e sy
stem
s of
eq
uatio
ns b
y gr
aphi
ng.
DI,
Logi
cal,
370
Unl
ocki
ng
Mis
conc
eptio
ns,
372
403,
404
7-
1 53
7-1
6.
4
7-2
Su
bstit
utio
n •
Solv
e sy
stem
s of
eq
uatio
ns b
y us
ing
subs
titut
ion.
•
Solv
e re
al-w
orld
pr
oble
ms
invo
lvin
g sy
stem
s of
equ
atio
ns.
DI,
Intra
pers
onal
, 3
78
409,
410
7-
2 54
27
, 28
7-2
16
6.2
7-3
El
imin
atio
n U
sing
Add
ition
an
d Su
btra
ctio
n
• So
lve
syst
ems
of
equa
tions
by
usin
g el
imin
atio
n w
ith a
dditi
on.
• So
lve
syst
ems
of
equa
tions
by
usin
g el
imin
atio
n w
ith s
ubtra
ctio
n.
DI,
Kine
sthe
tic,
383
Ti
ps fo
r New
T
each
ers,
384
Fi
nd th
e Er
ror,
3
84
415,
416
7-
3 55
7-3
6.
2
7-4
El
imin
atio
n U
sing
M
ultip
licat
ion
• So
lve
syst
ems
of
equa
tions
by
usin
g el
imin
atio
n w
ith m
ultip
licat
ion.
•
Det
erm
ine
the
best
met
hod
for
solv
ing
syst
ems
of
equa
tions
.
DI,
Verb
al/
Lin
guis
tic, 3
89
421,
422
7-
4 56
7-4
6.
6
7-5
G
raph
ing
Syst
ems
of
Ineq
ualit
ies
• So
lve
syst
ems
of
ineq
ualit
ies
by
grap
hing
. •
Solv
e re
al-w
orld
pr
oble
ms
invo
lvin
g sy
stem
s of
ineq
ualit
ies.
Find
the
Erro
r,
396
D
I, In
terp
erso
nal,
396
427,
428
7-
5 57
7-5
17
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
8
Pol
ynom
ials
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
8-1
M
ultip
lyin
g M
onom
ials
• M
ultip
ly
mon
omia
ls.
• Si
mpl
ify
expr
essi
ons
invo
lvin
g po
wer
s of
mon
omia
ls.
DI,
Logi
cal,
412
Find
the
Erro
r,
413
455,
456
8-
1 59
8-1
18
2.1
8-2
D
ivid
ing
Mon
omia
ls
• Si
mpl
ify
expr
essi
ons
invo
lvin
g th
e qu
otie
nt o
f m
onom
ials
. •
Sim
plify
ex
pres
sion
s co
ntai
ning
ne
gativ
e ex
pone
nts.
DI,
Nat
ural
ist,
4
19
Unl
ocki
ng
Mis
conc
eptio
ns,
421
Fi
nd th
e Er
ror,
4
21
461,
462
8-
2 60
8-2
19
3.4
8-3
Sc
ient
ific
Not
atio
n
• Ex
pres
s nu
mbe
rs
in s
cien
tific
no
tatio
n an
d st
anda
rd n
otat
ion.
•
Find
pro
duct
s an
d qu
otie
nts
of
num
bers
ex
pres
sed
in
scie
ntifi
c no
tatio
n.
Tips
for N
ew
Tea
cher
s, 4
26
DI,
Kine
sthe
tic,
426
467,
468
8-
3 61
33
-36
8-3
20
3.3,
6.3
8-4
Po
lyno
mia
ls
• Fi
nd th
e de
gree
of
a po
lyno
mia
l. •
Arra
nge
the
term
s of
a p
olyn
omia
l in
asce
ndin
g or
de
scen
ding
ord
er.
Unl
ocki
ng
Mis
conc
eptio
ns,
433
D
I, Au
dito
ry/
Mus
ical
, 434
473,
474
8-
4 62
8-4
6.
2
8-5
Ad
ding
and
Su
btra
ctin
g Po
lyno
mia
ls
• Ad
d po
lyno
mia
ls.
• Su
btra
ct
poly
nom
ials
.
DI,
Inte
rper
sona
l, 4
41
Find
the
Erro
r,
441
479,
480
8-
5 63
8-5
6.
2
8-6
M
ultip
lyin
g a
Poly
nom
ial b
y a
Mon
omia
l
• Fi
nd th
e pr
oduc
t of
a m
onom
ial a
nd
a po
lyno
mia
l. •
Solv
e eq
uatio
ns
invo
lvin
g po
lyno
mia
ls.
DI,
Visu
al/
Spa
tial,
445
485,
486
8-
6 64
8-6
21
6.2
8-7
M
ultip
lyin
g Po
lyno
mia
ls
• M
ultip
ly tw
o bi
nom
ials
by
usin
g th
e FO
IL m
etho
d.
• M
ultip
ly tw
o po
lyno
mia
ls b
y us
ing
the
Dis
tribu
tive
Prop
erty
.
DI,
Audi
tory
/ M
usic
al, 4
53
491,
492
8-
7 65
8-7
22
3.2,
3.4
8-8
Sp
ecia
l Pr
oduc
ts
• Fi
nd s
quar
es o
f su
ms
and
diffe
renc
es.
• Fi
nd th
e pr
oduc
t of
a s
um a
nd a
di
ffere
nce.
Tips
for N
ew
Tea
cher
s, 4
59
DI,
Verb
al/
Lin
guis
tic, 4
60
497,
498
8-
8 66
8-8
23
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
9
Fac
tori
ng
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
9-1
Fa
ctor
s an
d G
reat
est
Com
mon
Fa
ctor
s
• Fi
nd p
rime
fact
oriz
atio
ns o
f in
tege
rs a
nd
mon
omia
ls.
• Fi
nd th
e gr
eate
st
com
mon
fact
ors
of
inte
gers
and
m
onom
ials
.
DI,
Verb
al/
Lin
guis
tic, 4
75
523,
524
9-
1 68
13
, 14
9-1
6.
2
9-2
Fa
ctor
ing
Usi
ng
the
Dis
tribu
tive
Prop
erty
• Fa
ctor
po
lyno
mia
ls b
y us
ing
the
Dis
tribu
tive
Prop
erty
. •
Solv
e qu
adra
tic
equa
tions
of t
he
form
ax2 +
bx
= 0.
DI,
Visu
al/
Spa
tial,
483
529,
530
9-
2 69
13
, 14
9-2
9-3
Fa
ctor
ing
Trin
omia
ls:
x2 + b
x +
c
• Fa
ctor
trin
omia
ls
of th
e fo
rm x
2 + b
x +
c.
• So
lve
equa
tions
of
the
form
x2 +
bx
+ c
= 0.
DI,
Kine
sthe
tic,
490
Fi
nd th
e Er
ror,
4
92
535,
536
9-
3 70
9-3
24, 2
5
9-4
Fa
ctor
ing
Trin
omia
ls:
ax2 +
bx
+ c
• Fa
ctor
trin
omia
ls
of th
e fo
rm a
x2 +
bx +
c.
• So
lve
equa
tions
of
the
form
ax2 +
bx
+ c
= 0.
DI,
Inte
rper
sona
l, 4
96
Unl
ocki
ng
Mis
conc
eptio
ns,
497
Fi
nd th
e Er
ror,
4
98
541,
542
9-
4 71
13
, 14
9-4
26
3.2
9-5
Fa
ctor
ing
Diff
eren
ces
of
Squa
res
• Fa
ctor
bin
omia
ls
that
are
the
diffe
renc
es o
f sq
uare
s.
• So
lve
equa
tions
in
volv
ing
the
diffe
renc
es o
f sq
uare
s.
Find
the
Erro
r,
504
D
I, In
trape
rson
al,
504
547,
548
9-
5 72
13
, 14
9-5
9-6
Pe
rfect
Squ
ares
an
d Fa
ctor
ing
• Fa
ctor
per
fect
sq
uare
trin
omia
ls.
• So
lve
equa
tions
in
volv
ing
perfe
ct
squa
res.
DI,
Logi
cal,
510
553,
554
9-
6 73
9-6
27
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
10
Q
uadr
atic
and
Exp
onen
tial F
unct
ions
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
10-1
G
raph
ing
Qua
drat
ic
Func
tions
• G
raph
qua
drat
ic
func
tions
. •
Find
the
equa
tion
of th
e ax
is o
f sy
mm
etry
and
the
coor
dina
tes
of th
e ve
rtex
of a
pa
rabo
la.
DI,
Inte
rper
sona
l, 5
26
579,
580
10
-1
75
10
-1
28
6.8
10-2
So
lvin
g Q
uadr
atic
Eq
uatio
ns b
y G
raph
ing
• So
lve
quad
ratic
eq
uatio
ns b
y gr
aphi
ng.
• Es
timat
e so
lutio
ns
of q
uadr
atic
equ
a-tio
ns b
y gr
aphi
ng.
Unl
ocki
ng
Mis
conc
eptio
ns,
534
D
I, Lo
gica
l, 53
5
585,
586
10
-2
76
10
-2
10-3
So
lvin
g Q
uadr
atic
Eq
uatio
ns b
y G
raph
ing
• So
lve
quad
ratic
eq
uatio
ns b
y fin
ding
the
squa
re
root
. •
Solv
e qu
adra
tic
equa
tions
by
com
plet
ing
the
squa
re.
Unl
ocki
ng
Mis
conc
eptio
ns,
540
D
I, Vi
sual
/ S
patia
l, 54
1
591,
592
10
-3
77
10
-3
29
6.3
10-4
So
lvin
g Q
uadr
atic
Eq
uatio
ns b
y U
sing
the
Qua
drat
ic
Form
ula
• So
lve
quad
ratic
eq
uatio
ns b
y us
ing
the
Qua
drat
ic
Form
ula.
•
Use
the
disc
rimin
ant t
o de
term
ine
the
num
ber o
f so
lutio
ns fo
r a
quad
ratic
eq
uatio
n.
DI,
Verb
al/
Lin
guis
tic, 5
47
Find
the
Erro
r,
550
597,
598
10
-4
78
10
-4
30, 3
1 6.
3
10-5
Ex
pone
ntia
l Fu
nctio
ns
• G
raph
exp
onen
tial
func
tions
. •
Iden
tify
data
that
di
spla
ys
expo
nent
ial
beha
vior
.
DI,
Audi
tory
/ M
usic
al, 5
57
Find
the
Erro
r,
558
603,
604
10
-5
79
10
-5
6.
3
10-6
G
row
th a
nd
Dec
ay
• So
lve
prob
lem
s in
volv
ing
expo
nent
ial
grow
th.
• So
lve
prob
lem
s in
volv
ing
expo
nent
ial
deca
y.
DI,
Kine
sthe
tic,
562
60
9, 6
10
10-6
80
10-6
10-7
G
eom
etric
Se
quen
ces
• R
ecog
nize
and
ex
tend
geo
met
ric
sequ
ence
s.
• Fi
nd g
eom
etric
m
eans
.
DI,
Logi
cal,
568
615,
616
10
-7
81
9-12
, 47,
48
10-7
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
11
R
adic
al E
xpre
ssio
ns a
nd T
rian
gles
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
11-1
Si
mpl
ifyin
g R
adic
al
Expr
essi
ons
• Si
mpl
ify ra
dica
l ex
pres
sion
s us
ing
the
Prod
uct
Prop
erty
of
Squa
re R
oots
. •
Sim
plify
radi
cal
expr
essi
ons
usin
g th
e Q
uotie
nt
Prop
erty
of
Squa
re R
oots
.
Tips
for N
ew
Tea
cher
s, 5
87
DI,
Logi
cal,
588
643,
644
11
-1
83
11
-1
3.
2
11-2
O
pera
tions
with
R
adic
al
Expr
essi
ons
• Ad
d an
d su
btra
ct
radi
cal
expr
essi
ons.
•
Mul
tiply
radi
cal
expr
essi
ons.
DI,
Visu
al/
Spa
tial,
594
649,
650
11
-2
84
37, 3
8 11
-2
3.
2
11-3
R
adic
al
Equa
tions
• So
lve
radi
cal
equa
tions
. •
Solv
e ra
dica
l eq
uatio
ns w
ith
extra
neou
s so
lutio
ns.
DI,
Verb
al/
Lin
guis
tic, 5
99
Find
the
Erro
r,
600
655,
656
11
-3
85
11
-3
11-4
Th
e Py
thag
orea
n Th
eore
m
• So
lve
prob
lem
s by
us
ing
the
Pyth
agor
ean
Theo
rem
. •
Det
erm
ine
whe
ther
a tr
iang
le
is a
righ
t tria
ngle
.
DI,
Kine
sthe
tic,
607
66
1, 6
62
11-4
86
11-4
32
7.
9
11-5
Th
e D
ista
nce
Form
ula
• Fi
nd th
e di
stan
ce
betw
een
two
poin
ts o
n th
e co
ordi
nate
pla
ne.
• Fi
nd a
poi
nt th
at is
a
give
n di
stan
ce
from
a s
econ
d po
int i
n a
plan
e.
Unl
ocki
ng
Mis
conc
eptio
ns,
612
D
I, In
terp
erso
nal,
613
667,
668
11
-5
87
11
-5
11-6
Si
mila
r Tr
iang
les
• D
eter
min
e w
heth
er tw
o tri
angl
es a
re
sim
ilar.
• Fi
nd th
e un
know
n m
easu
res
of s
ides
of
two
sim
ilar
trian
gles
.
Find
the
Erro
r,
618
D
I, N
atur
alis
t,
618
673,
674
11
-6
88
61, 6
2 11
-6
8.
6
11-7
Tr
igon
omet
ric
Rat
ios
• D
efin
e th
e si
ne,
cosi
ne, a
nd
tang
ent r
atio
s.
• U
se tr
igon
omet
ric
ratio
s to
sol
ve
right
tria
ngle
s.
DI,
Audi
tory
/ M
usic
al, 6
24
679,
680
11
-7
89
11
-7
7.
10
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
12
R
atio
nal E
xpre
ssio
ns a
nd E
quat
ions
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
12-1
In
vers
e Va
riatio
n
• G
raph
inve
rse
varia
tions
. •
Solv
e pr
oble
ms
invo
lvin
g in
vers
e va
riatio
n.
DI,
Kine
sthe
tic,
644
70
5, 7
06
12-1
91
12-1
1.4
12-2
R
atio
nal
Expr
essi
ons
• Id
entif
y va
lues
ex
clud
ed fr
om th
e do
mai
n of
a
ratio
nal
expr
essi
on.
• Si
mpl
ify ra
tiona
l ex
pres
sion
s.
Unl
ocki
ng
Mis
conc
eptio
ns,
649
D
I, In
terp
erso
nal,
650
711,
712
12
-2
92
12
-2
33
8.2
12-3
M
ultip
lyin
g R
atio
nal
Expr
essi
ons
• M
ultip
ly ra
tiona
l ex
pres
sion
s.
• U
se d
imen
sion
al
anal
ysis
with
m
ultip
licat
ion.
DI,
Logi
cal,
656
Find
the
Erro
r,
657
717,
718
12
-3
93
12
-3
12-4
D
ivid
ing
Rat
iona
l Ex
pres
sion
s
• D
ivid
e ra
tiona
l ex
pres
sion
s.
• U
se d
imen
sion
al
anal
ysis
with
di
visi
on.
DI,
Visu
al/
Spa
tial,
661
723,
724
12
-4
94
12
-4
12-5
D
ivid
ing
Poly
nom
ials
• D
ivid
e a
poly
nom
ial b
y a
mon
omia
l. •
Div
ide
a po
lyno
mia
l by
a bi
nom
ial.
DI,
Intra
pers
onal
, 6
68
729,
730
12
-5
95
12
-5
12-6
R
atio
nal
Expr
essi
ons
with
Lik
e D
enom
inat
ors
• Ad
d ra
tiona
l ex
pres
sion
s w
ith
like
deno
min
ator
s.
• Su
btra
ct ra
tiona
l ex
pres
sion
s w
ith
like
deno
min
ator
s.
Find
the
Erro
r,
674
D
I, Ve
rbal
/ L
ingu
istic
, 674
735,
736
12
-6
96
12
-6
1.
4
12-7
R
atio
nal
Expr
essi
ons
with
Unl
ike
Den
omin
ator
s
• Ad
d ra
tiona
l ex
pres
sion
s w
ith
unlik
e de
nom
inat
ors.
•
Subt
ract
ratio
nal
expr
essi
ons
with
un
like
deno
min
ator
s.
DI,
Visu
al/
Spa
tial,
681
741,
742
12
-7
97
17, 1
8 12
-7
12-8
M
ixed
Ex
pres
sion
s an
d C
ompl
ex
Frac
tions
• Si
mpl
ify m
ixed
ex
pres
sion
s.
• Si
mpl
ify c
ompl
ex
fract
ions
.
DI,
Audi
tory
/ M
usic
al, 6
85
Find
the
Erro
r,
686
747,
748
12
-8
98
12
-8
6.
4
12-9
So
lvin
g R
atio
nal
Equa
tions
• So
lve
ratio
nal
equa
tions
. •
Elim
inat
e ex
trane
ous
solu
tions
.
DI,
Kine
sthe
tic,
6
92
Unl
ocki
ng
Mis
conc
eptio
ns,
693
753,
754
12
-9
99
12
-9
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
13
St
atis
tics
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
13-1
Sa
mpl
ing
and
Bias
• Id
entif
y va
rious
sa
mpl
ing
tech
niqu
es.
• R
ecog
nize
a
bias
ed s
ampl
e.
DI,
Visu
al/
Spa
tial,
710
781,
782
13
-1
101
13
-1
2.
6, 4
.1
13-2
In
trodu
ctio
n to
M
atric
es
• O
rgan
ize
data
in
mat
rices
•
Solv
e pr
oble
ms
by
addi
ng o
r su
btra
ctin
g m
atric
es o
r by
mul
tiply
ing
by a
sc
alar
.
Find
the
Erro
r,
717
D
I, Ve
rbal
/ L
ingu
istic
, 720
787,
788
13
-2
102
13
-2
4.
2
13-3
H
isto
gram
s •
Inte
rpre
t dat
a di
spla
yed
in
hist
ogra
ms.
•
Dis
play
dat
a in
hi
stog
ram
s.
DI,
Kine
sthe
tic,
724
U
nloc
king
M
isco
ncep
tions
, 7
25
793,
794
13
-3
103
97, 9
8 13
-3
4.
2, 4
.4
13-4
M
easu
res
of
Varia
tion
• Fi
nd th
e ra
nge
of
a se
t of d
ata.
•
Find
the
quar
tiles
an
d in
terq
uarti
le
rang
e of
a s
et o
f da
ta.
Unl
ocki
ng
Mis
conc
eptio
ns,
732
D
I, Au
dito
ry/
Mus
ical
, 733
Fi
nd th
e Er
ror,
7
33
799,
800
13
-4
104
1, 2
, 19,
20
13-4
4.2,
4.3
13-5
Bo
x-an
d-W
hisk
er P
lots
• O
rgan
ize
and
use
data
in b
ox-a
nd-
whi
sker
plo
ts.
• O
rgan
ize
and
use
data
in p
aral
lel
box-
and-
whi
sker
pl
ots.
Unl
ocki
ng
Mis
conc
eptio
ns,
738
D
I, In
terp
erso
nal,
739
805,
806
13
-5
105
13
-5
34
4.2
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
14
Pr
obab
ility
Stud
ent E
ditio
n (le
sson
num
ber
and
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Pare
nt a
nd
Stud
ent
Stud
y G
uide
W
orkb
ook
(pag
e)
Prer
equi
site
Sk
ills
Wor
kboo
k (p
ages
)
Onl
ine
Stud
y To
ols
(less
on)
Alge
PASS
: Tu
toria
l Pl
us
(less
on)
Hot
W
ords
, H
ot
Topi
cs
(less
on)
14-1
C
ount
ing
Out
com
es
• C
ount
out
com
es
usin
g a
tree
diag
ram
. •
Cou
nt o
utco
mes
us
ing
the
Fund
amen
tal
Cou
ntin
g Pr
inci
ple.
DI,
Logi
cal,
755
831,
832
14
-1
107
14
-1
4.
5, 4
.6
14-2
Pe
rmut
atio
ns
and
Com
bina
tions
• D
eter
min
e pr
obab
ilitie
s us
ing
perm
utat
ions
. •
Det
erm
ine
prob
abilit
ies
usin
g co
mbi
natio
ns.
DI,
Visu
al/
Spa
tial,
761
Find
the
Erro
r,
764
837,
838
14
-2
108
14
-2
2.
3, 2
.4,
4.5
14-3
Pr
obab
ility
of
Com
poun
d Ev
ents
• Fi
nd th
e pr
obab
ility
of tw
o in
depe
nden
t ev
ents
or
depe
nden
t eve
nts.
•
Find
the
prob
abilit
y of
two
mut
ually
exc
lusi
ve
or in
clus
ive
even
ts.
DI,
Nat
ural
ist,
7
70
Find
the
Erro
r,
773
843,
844
14
-3
109
47, 4
8, 5
5,
56, 6
7-70
, 99
, 100
14-3
35
2.9,
4.6
14-4
Pr
obab
ility
Dis
tribu
tions
• U
se ra
ndom
va
riabl
es to
co
mpu
te
prob
abilit
y.
• U
se p
roba
bilit
y di
strib
utio
ns to
so
lve
real
-wor
ld
prob
lem
s.
DI,
Inte
rper
sona
l, 7
78
849,
850
14
-4
110
14
-4
2.
1, 4
.6
14-5
Pr
obab
ility
Sim
ulat
ions
• U
se th
eore
tical
an
d ex
perim
enta
l pr
obab
ility
to
repr
esen
t and
so
lve
prob
lem
s in
volv
ing
unce
rtain
ty.
• Pe
rform
pr
obab
ility
sim
ulat
ions
to
mod
el re
al-w
orld
si
tuat
ions
in
volv
ing
unce
rtain
ty.
DI,
Kine
sthe
tic,
784
85
5, 8
56
14-5
11
1
14-5
4.6
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
1
Sol
ving
Equ
atio
ns a
nd In
equa
litie
s
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
1-1
Ex
pres
sion
s an
d Fo
rmul
as
• U
se th
e or
der o
f ope
ratio
ns to
ev
alua
te e
xpre
ssio
ns.
• U
se fo
rmul
as.
DI,
Visu
al/S
patia
l,
8
Tips
for N
ew
Tea
cher
s, 1
0
1, 2
1-
1 1-
1
1-2
Pr
oper
ties
of R
eal
Num
bers
• C
lass
ify re
al n
umbe
rs.
• U
se th
e pr
oper
ties
of re
al n
umbe
rs
to e
valu
ate
expr
essi
ons.
DI,
Kine
sthe
tic, 1
4 U
nloc
king
M
isco
ncep
tions
, 1
5 U
nloc
king
M
isco
ncep
tions
, 1
8
7, 8
1-
2 1-
2
1-3
So
lvin
g Eq
uatio
ns
• Tr
ansl
ate
verb
al e
xpre
ssio
ns in
to
alge
brai
c ex
pres
sion
s an
d eq
uatio
ns, a
nd v
ice
vers
a.
• So
lve
equa
tions
usi
ng th
e pr
oper
ties
of e
qual
ity.
Unl
ocki
ng
Mis
conc
eptio
ns,
22
Find
the
Erro
r, 24
D
I, In
terp
erso
nal,
2
4 Ti
ps fo
r New
T
each
ers,
27
13, 1
4 1-
3 1-
3
1-4
So
lvin
g Ab
solu
te
Valu
e Eq
uatio
ns
• Ev
alua
te e
xpre
ssio
ns in
volv
ing
abso
lute
val
ues.
•
Solv
e ab
solu
te v
alue
equ
atio
ns.
DI,
Verb
al/
Lin
guis
tic, 2
9 19
, 20
1-4
1-4
1
1-5
So
lvin
g In
equa
litie
s •
Solv
e in
equa
litie
s.
• So
lve
real
-wor
ld p
robl
ems
invo
lvin
g in
equa
litie
s.
DI,
Intra
pers
onal
, 3
5 25
, 26
1-5
1-5
2
1-6
So
lvin
g C
ompo
und
and
Abso
lute
Val
ue
Ineq
ualit
ies
• So
lve
com
poun
d in
equa
litie
s.
• So
lve
abso
lute
val
ue in
equa
litie
s.
DI,
Kine
sthe
tic, 4
2 Fi
nd th
e Er
ror,
44
31, 3
2 1-
6 1-
6
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
NO
TES
Cha
pter
2
Lin
ear
Rel
atio
ns a
nd F
unct
ions
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
2-1
R
elat
ions
and
Fu
nctio
ns
• An
alyz
e an
d gr
aph
rela
tions
. •
Find
func
tiona
l val
ues.
U
nloc
king
M
isco
ncep
tions
, 5
8 D
I, Au
dito
ry/
Mus
ical
, 59
Find
the
Erro
r, 60
Ti
ps fo
r New
T
each
ers,
62
57, 5
8 2-
1 2-
1
2-2
Li
near
Equ
atio
ns
• Id
entif
y lin
ear e
quat
ions
and
fu
nctio
ns.
• W
rite
linea
r equ
atio
ns in
sta
ndar
d fo
rm a
nd g
raph
them
.
DI,
Visu
al/S
patia
l,
65
63, 6
4 2-
2 2-
2 3
2-3
Sl
ope
• Fi
nd a
nd u
se th
e sl
ope
of a
line
. •
Gra
ph p
aral
lel a
nd p
erpe
ndic
ular
lin
es.
DI,
Nat
ural
ist,
71
Find
the
Erro
r, 71
Ti
ps fo
r New
T
each
ers,
74
69, 7
0 2-
3 2-
3
2-4
W
ritin
g Li
near
Eq
uatio
ns
• W
rite
an e
quat
ion
of a
line
giv
en
the
slop
e an
d a
poin
t on
the
line.
•
Writ
e an
equ
atio
n of
a li
ne p
aral
lel
or p
erpe
ndic
ular
to a
giv
en li
ne.
DI,
Intra
pers
onal
, 7
8 75
, 76
2-4
2-4
2-5
M
odel
ing
Rea
l-W
orld
Dat
a: U
sing
Sc
atte
r Plo
ts
• D
raw
sca
tter p
lots
. •
Find
and
use
pre
dict
ion
equa
tions
.D
I, N
atur
alis
t, 82
81
, 82
2-5
2-5
2-6
Sp
ecia
l Fun
ctio
ns
• Id
entif
y an
d gr
aph
step
, con
stan
t, an
d id
entit
y fu
nctio
ns.
• Id
entif
y an
d gr
aph
abso
lute
val
ue
and
piec
ewis
e fu
nctio
ns.
Tips
for N
ew
Tea
cher
s, 9
0 D
I, Ve
rbal
/ L
ingu
istic
, 92
87, 8
8 2-
6 2-
6
2-7
G
raph
ing
Ineq
ualit
ies
• G
raph
line
ar in
equa
litie
s.
• G
raph
abs
olut
e va
lue
ineq
ualit
ies.
D
I, In
terp
erso
nal,
9
7 93
, 94
2-7
2-7
4
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
NO
TES
Cha
pter
3
Sys
tem
s of E
quat
ions
and
Ineq
ualit
ies
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
3-1
So
lvin
g Sy
stem
s of
Eq
uatio
ns b
y G
raph
ing
• So
lve
syst
ems
of li
near
equ
atio
ns
by g
raph
ing.
•
Det
erm
ine
whe
ther
a s
yste
m o
f lin
ear e
quat
ions
is c
onsi
sten
t and
in
depe
nden
t, co
nsis
tent
and
de
pend
ent,
or in
cons
iste
nt.
DI,
Inte
rper
sona
l,
111
11
9, 1
20
3-1
3-1
3-2
So
lvin
g Sy
stem
s of
Eq
uatio
ns
Alge
brai
cally
• So
lve
syst
ems
of li
near
equ
atio
ns
by u
sing
sub
stitu
tion.
•
Solv
e sy
stem
s of
line
ar e
quat
ions
by
usi
ng e
limin
atio
n.
DI,
Logi
cal,
119
125,
126
3-
2 3-
2 5
3-3
So
lvin
g Sy
stem
s of
In
equa
litie
s by
G
raph
ing
• So
lve
syst
ems
of in
equa
litie
s by
gr
aphi
ng.
• D
eter
min
e th
e co
ordi
nate
s of
the
verti
ces
of a
regi
on fo
rmed
by
the
grap
h of
a s
yste
m o
f ine
qual
ities
.
DI,
Verb
al/
Lin
guis
tic, 1
25
131,
132
3-
3 3-
3
3-4
Li
near
Pro
gram
min
g •
Find
the
max
imum
and
min
imum
va
lues
of a
func
tion
over
a re
gion
. •
Solv
e re
al-w
orld
pro
blem
s us
ing
linea
r pro
gram
min
g.
DI,
Visu
al/S
patia
l,
131
13
7, 1
38
3-4
3-4
3-5
So
lvin
g Sy
stem
s of
Eq
uatio
ns in
Thr
ee
Varia
bles
• So
lve
syst
ems
of li
near
equ
atio
ns
in th
ree
varia
bles
. •
Solv
e re
al-w
orld
pro
blem
s us
ing
syst
ems
of li
near
equ
atio
ns in
th
ree
varia
bles
.
Unl
ocki
ng
Mis
conc
eptio
ns,
140
D
I, Ve
rbal
/ L
ingu
istic
, 141
Fi
nd th
e Er
ror,
1
42
Tips
for N
ew
Tea
cher
s, 1
44
143,
144
3-
5 3-
5
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
NO
TES
Cha
pter
4
Mat
rice
s
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
4-1
In
trodu
ctio
n to
M
atric
es
• O
rgan
ize
data
in m
atric
es.
• So
lve
equa
tions
invo
lvin
g m
atric
es.
DI,
Kine
sthe
tic,
155
Ti
ps fo
r New
T
each
ers,
159
169,
170
4-
1 4-
1
4-2
O
pera
tions
with
M
atric
es
• Ad
d an
d su
btra
ct m
atric
es.
• M
ultip
ly b
y a
mat
rix s
cala
r. U
nloc
king
M
isco
ncep
tions
, 1
61
DI,
Verb
al/
Lin
guis
tic, 1
62
Tips
for N
ew
Tea
cher
s, 1
66
175,
176
4-
2 4-
2 6
4-3
M
ultip
lyin
g M
atric
es
• M
ultip
ly m
atric
es.
• U
se th
e pr
oper
ties
of m
atrix
m
ultip
licat
ion.
DI,
Audi
tory
/ M
usic
al, 1
70
181,
182
4-
3 4-
3
4-4
Tr
ansf
orm
atio
ns
with
Mat
rices
• U
se m
atric
es to
det
erm
ine
the
coor
dina
tes
of a
tran
slat
ed o
r di
late
d fig
ure.
•
Use
mat
rix m
ultip
licat
ion
to fi
nd
the
coor
dina
tes
of a
refle
cted
or
rota
ted
figur
e.
DI,
Visu
al/S
patia
l,
177
18
7, 1
88
4-4
4-4
4-5
D
eter
min
ants
•
Eval
uate
the
dete
rmin
ant o
f a 2
×
2 m
atrix
. •
Eval
uate
the
dete
rmin
ant o
f a 3
×
3 m
atrix
.
Unl
ocki
ng
Mis
conc
eptio
ns,
183
D
I, In
terp
erso
nal,
1
84
193,
194
4-
5 4-
5
4-6
C
ram
er’s
Rul
e •
Solv
e sy
stem
s of
two
linea
r eq
uatio
ns b
y us
ing
Cra
mer
’s R
ule.
•
Solv
e sy
stem
s of
thre
e lin
ear
equa
tions
by
usin
g C
ram
er’s
Rul
e.
DI,
Intra
pers
onal
, 1
91
199,
200
4-
6 4-
6 7
4-7
Id
entit
y an
d In
vers
e M
atric
es
• D
eter
min
e w
heth
er tw
o m
atric
es
are
inve
rses
. •
Find
the
inve
rse
of a
2 ×
2 m
atrix
.
DI,
Logi
cal,
198
205,
206
4-
7 4-
7
4-8
U
sing
Mat
rices
to
Solv
e Sy
stem
s of
Eq
uatio
ns
• W
rite
mat
rix e
quat
ions
for s
yste
ms
of e
quat
ions
. •
Solv
e sy
stem
s of
equ
atio
ns u
sing
m
atrix
equ
atio
ns.
DI,
Logi
cal,
204
211,
212
4-
8 4-
8
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
5
Pol
ynom
ial a
nd R
adic
al E
quat
ions
and
Ineq
ualit
ies
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
5-1
M
onom
ials
•
Mul
tiply
and
div
ide
mon
omia
ls.
• U
se e
xpre
ssio
ns w
ritte
n in
sc
ient
ific
nota
tion.
Unl
ocki
ng
Mis
conc
eptio
ns,
223
D
I, In
terp
erso
nal,
2
25
Find
the
Erro
r,
226
Ti
ps fo
r New
T
each
ers,
228
239,
240
5-
1 5-
1
5-2
Po
lyno
mia
ls
• Ad
d an
d su
btra
ct p
olyn
omia
ls.
• M
ultip
ly p
olyn
omia
ls.
DI,
Logi
cal,
232
24
5, 2
46
5-2
5-2
5-3
D
ivid
ing
Poly
nom
ials
• D
ivid
e po
lyno
mia
ls u
sing
long
di
visi
on.
• D
ivid
e po
lyno
mia
ls u
sing
syn
thet
ic
divi
sion
.
Unl
ocki
ng
Mis
conc
eptio
ns,
235
Fi
nd th
e Er
ror,
2
36
DI,
Inte
rper
sona
l,
236
Ti
ps fo
r New
T
each
ers,
238
251,
252
5-
3 5-
3
5-4
Fa
ctor
ing
Poly
nom
ials
• Fa
ctor
pol
ynom
ials
. •
Sim
plify
pol
ynom
ial q
uotie
nts
by
fact
orin
g.
DI,
Audi
tory
/ M
usic
al, 2
42
Tips
for N
ew
Tea
cher
s, 2
44
Unl
ocki
ng
Mis
conc
eptio
ns,
244
257,
258
5-
4 5-
4 8
5-5
R
oots
of R
eal
Num
bers
• Si
mpl
ify ra
dica
ls.
• U
se a
cal
cula
tor t
o ap
prox
imat
e ra
dica
ls.
Unl
ocki
ng
Mis
conc
eptio
ns,
246
D
I, Vi
sual
/Spa
tial,
2
47
263,
264
5-
5 5-
5
5-
6
Rad
ical
Exp
ress
ions
•
Sim
plify
radi
cal e
xpre
ssio
ns.
• Ad
d, s
ubtra
ct, m
ultip
ly, a
nd d
ivid
e ra
dica
l exp
ress
ions
.
DI,
Intra
pers
onal
, 2
51
Unl
ocki
ng
Mis
conc
eptio
ns,
253
Ti
ps fo
r New
T
each
ers,
256
269,
270
5-
6 5-
6
5-7
R
atio
nal E
xpon
ents
•
Writ
e ex
pres
sion
s w
ith ra
tiona
l ex
pone
nts
in ra
dica
l for
m, a
nd v
ice
vers
a.
• Si
mpl
ify e
xpre
ssio
ns in
ex
pone
ntia
l or r
adic
al fo
rm.
Unl
ocki
ng
Mis
conc
eptio
ns,
258
D
I, Au
dito
ry/
Mus
ical
, 259
Ti
ps fo
r New
T
each
ers,
262
275,
276
5-
7 5-
7
5-8
R
adic
al E
quat
ions
an
d In
equa
litie
s
• So
lve
equa
tions
con
tain
ing
radi
cals
. •
Solv
e in
equa
litie
s co
ntai
ning
ra
dica
ls.
DI,
Logi
cal,
265
Tips
for N
ew
Tea
cher
s, 2
67
281,
282
5-
8 5-
8 9
5-9
C
ompl
ex N
umbe
rs
• Ad
d an
d su
btra
ct c
ompl
ex
num
bers
. •
Mul
tiply
and
div
ide
com
plex
nu
mbe
rs.
DI,
Verb
al/
Lin
guis
tic, 2
71
Tips
for N
ew
Tea
cher
s, 2
75
287,
288
5-
9 5-
9
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
6
Qua
drat
ic F
unct
ions
and
Ineq
ualit
ies
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
6-1
G
raph
ing
Qua
drat
ic
Func
tions
• G
raph
qua
drat
ic fu
nctio
ns.
• Fi
nd a
nd in
terp
ret t
he m
axim
um
and
min
imum
val
ues
of a
qu
adra
tic fu
nctio
n.
Tips
for N
ew
Tea
cher
s, 2
88
Unl
ocki
ng
Mis
conc
eptio
ns,
288
D
I, Au
dito
ry/
Mus
ical
, 289
313,
314
6-
1 6-
1 10
6-2
So
lvin
g Q
uadr
atic
Eq
uatio
ns b
y G
raph
ing
• So
lve
quad
ratic
equ
atio
ns b
y gr
aphi
ng.
• Es
timat
e so
lutio
ns o
f qua
drat
ic
equa
tions
by
grap
hing
.
Unl
ocki
ng
Mis
conc
eptio
ns,
295
D
I, Ve
rbal
/ L
ingu
istic
, 296
319,
320
6-
2 6-
2
6-3
So
lvin
g Q
uadr
atic
Eq
uatio
ns b
y Fa
ctor
ing
• So
lve
quad
ratic
equ
atio
ns b
y fa
ctor
ing.
•
Writ
e a
quad
ratic
equ
atio
n w
ith
give
n ro
ots.
DI,
Visu
al/S
patia
l,
303
Fi
nd th
e Er
ror,
3
03
Tips
for N
ew
Tea
cher
s, 3
05
325,
326
6-
3 6-
3
6-4
C
ompl
etin
g th
e Sq
uare
• So
lve
quad
ratic
equ
atio
ns b
y us
ing
the
Squa
re R
oot P
rope
rty.
• So
lve
quad
ratic
equ
atio
ns b
y co
mpl
etin
g th
e sq
uare
.
DI,
Kine
sthe
tic,
309
Fi
nd th
e Er
ror,
3
10
Tips
for N
ew
Tea
cher
s, 3
12
331,
332
6-
4 6-
4
6-5
Th
e Q
uadr
atic
Fo
rmul
a an
d th
e D
iscr
imin
ant
• So
lve
quad
ratic
equ
atio
ns b
y us
ing
the
Qua
drat
ic F
orm
ula.
•
Use
the
disc
rimin
ant t
o de
term
ine
the
num
ber a
nd ty
pe o
f roo
ts o
f a
quad
ratic
equ
atio
n.
DI,
Logi
cal,
316
337,
338
6-
5 6-
5 11
, 12
6-6
An
alyz
ing
Gra
phs
of
Qua
drat
ic F
unct
ions
• An
alyz
e qu
adra
tic fu
nctio
ns o
f the
fo
rm y
= a
(x –
h)2
+ k.
•
Writ
e a
quad
ratic
func
tion
in th
e fo
rm y
= a
(x –
h)2
+ k.
Tips
for N
ew
Tea
cher
s, 3
23
DI,
Nat
ural
ist,
324
Find
the
Erro
r,
343,
344
6-
6 6-
6
325
6-
7
Gra
phin
g an
d So
lvin
g Q
uadr
atic
In
equa
litie
s
• G
raph
qua
drat
ic in
equa
litie
s in
two
varia
bles
. •
Solv
e qu
adra
tic in
equa
litie
s in
one
va
riabl
e.
DI,
Intra
pers
onal
, 3
31
349,
350
6-
7 6-
7
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
7
Pol
ynom
ial F
unct
ions
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
7-1
Po
lyno
mia
l Fu
nctio
ns
• Ev
alua
te p
olyn
omia
l fun
ctio
ns.
• Id
entif
y ge
nera
l sha
pes
of g
raph
s of
pol
ynom
ial f
unct
ions
.
DI,
Inte
rper
sona
l,
349
37
5, 3
76
7-1
7-1
7-2
G
raph
ing
Poly
nom
ial
Func
tions
• G
raph
pol
ynom
ial f
unct
ions
and
lo
cate
thei
r rea
l zer
os.
• Fi
nd th
e m
axim
a an
d m
inim
a of
po
lyno
mia
l fun
ctio
ns.
Unl
ocki
ng
Mis
conc
eptio
ns,
354
D
I, Ve
rbal
/ L
ingu
istic
, 356
381,
382
7-
2 7-
2
7-3
So
lvin
g Eq
uatio
ns
Usi
ng Q
uadr
atic
Te
chni
ques
• W
rite
expr
essi
ons
in q
uadr
atic
fo
rm.
• U
se q
uadr
atic
tech
niqu
es to
sol
ve
equa
tions
.
Unl
ocki
ng
Mis
conc
eptio
ns,
361
D
I, Vi
sual
/Spa
tial,
3
62
387,
388
7-
3 7-
3 13
7-4
Th
e R
emai
nder
and
Fa
ctor
The
orem
s
• Ev
alua
te fu
nctio
ns u
sing
syn
thet
ic
subs
titut
ion.
•
Det
erm
ine
whe
ther
a b
inom
ial i
s a
fact
or o
f a p
olyn
omia
l by
usin
g sy
nthe
tic s
ubst
itutio
n.
DI,
Intra
pers
onal
, 3
67
393,
394
7-
4 7-
4
7-5
R
oots
and
Zer
os
• D
eter
min
e th
e nu
mbe
r and
type
of
root
s fo
r a p
olyn
omia
l equ
atio
n.
• Fi
nd th
e ze
ros
of a
pol
ynom
ial
func
tion.
DI,
Kine
sthe
tic,
373
U
nloc
king
M
isco
ncep
tions
, 3
75
399,
400
7-
5 7-
5 14
7-6
R
atio
nal Z
ero
Theo
rem
• Id
entif
y th
e po
ssib
le ra
tiona
l zer
os
of a
pol
ynom
ial f
unct
ion.
•
Find
all
the
ratio
nal z
eros
of a
po
lyno
mia
l fun
ctio
n.
DI,
Logi
cal,
379
Find
the
Erro
r,
380
405,
406
7-
6 7-
6
7-7
O
pera
tions
on
Func
tions
• Fi
nd th
e su
m, d
iffer
ence
, pro
duct
, an
d qu
otie
nt o
f fun
ctio
ns.
• Fi
nd th
e co
mpo
sitio
n of
func
tions
.
Tips
for N
ew
Tea
cher
s, 3
84
DI,
Nat
ural
ist,
385
Find
the
Erro
r,
386
411,
412
7-
7 7-
7
7-
8
Inve
rse
Func
tions
an
d R
elat
ions
• Fi
nd th
e in
vers
e of
a fu
nctio
n or
re
latio
n.
• D
eter
min
e w
heth
er tw
o fu
nctio
ns
or re
latio
ns a
re in
vers
es.
DI,
Logi
cal,
391
417,
418
7-
8 7-
8
7-9
Sq
uare
Roo
t Fu
nctio
ns a
nd
Ineq
ualit
ies
• G
raph
and
ana
lyze
squ
are
root
fu
nctio
ns.
• G
raph
squ
are
root
ineq
ualit
ies.
DI,
Audi
tory
/ M
usic
al, 3
97
423,
424
7-
9 7-
9
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
8
Con
ic S
ectio
ns
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
8-1
M
idpo
int a
nd
Dis
tanc
e Fo
rmul
as
• Fi
nd th
e m
idpo
int o
f a s
egm
ent o
n th
e co
ordi
nate
pla
ne.
• Fi
nd th
e di
stan
ce b
etw
een
two
poin
ts o
n th
e co
ordi
nate
pla
ne.
DI,
Visu
al/S
patia
l L
earn
ers,
414
Ti
ps fo
r New
T
each
ers,
416
455,
456
8-
1 8-
1
8-2
Pa
rabo
las
• W
rite
equa
tions
of p
arab
olas
in
stan
dard
form
. •
Gra
ph p
arab
olas
.
Unl
ocki
ng
Mis
conc
eptio
ns,
420
D
I, Ki
nest
hetic
, 4
22
Find
the
Erro
r,
423
461,
462
8-
2 8-
2
8-3
C
ircle
s •
Writ
e eq
uatio
ns o
f circ
les.
•
Gra
ph c
ircle
s.
DI,
Nat
ural
ist,
428
Find
the
Erro
r,
429
467,
468
8-
3 8-
3 15
8-4
El
lipse
s •
Writ
e eq
uatio
ns o
f ellip
ses.
•
Gra
ph e
llipse
s.
DI,
Audi
tory
/ M
usic
al, 4
34
Unl
ocki
ng
Mis
conc
eptio
ns,
435
Ti
ps fo
r New
T
each
ers,
440
473,
474
8-
4 8-
4
8-5
H
yper
bola
s •
Writ
e eq
uatio
ns o
f hyp
erbo
las.
•
Gra
ph h
yper
bola
s.
Unl
ocki
ng
Mis
conc
eptio
ns,
442
D
I, Lo
gica
l, 44
3 Ti
ps fo
r New
T
each
ers,
448
479,
480
8-
5 8-
5 16
8-6
C
onic
Sec
tions
•
Writ
e eq
uatio
ns o
f con
ic s
ectio
ns
in s
tand
ard
form
. •
Iden
tify
coni
c se
ctio
ns fr
om th
eir
equa
tions
.
DI,
Intra
pers
onal
, 4
50
485,
486
8-
6 8-
6
8-
7
Solv
ing
Qua
drat
ic
Syst
ems
• So
lve
syst
ems
of q
uadr
atic
eq
uatio
ns a
lgeb
raic
ally
and
gr
aphi
cally
. •
Solv
e sy
stem
s of
qua
drat
ic
ineq
ualit
ies
grap
hica
lly.
DI,
Logi
cal,
456
491,
492
8-
7 8-
7
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
9
Rat
iona
l Exp
ress
ions
and
Equ
atio
ns
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
9-1
M
ultip
lyin
g an
d D
ivid
ing
Rat
iona
l Ex
pres
sion
s
• Si
mpl
ify ra
tiona
l exp
ress
ions
. •
Sim
plify
com
plex
frac
tions
. U
nloc
king
M
isco
ncep
tions
, 4
74
DI,
Intra
pers
onal
, 4
76
Tips
for N
ew
Tea
cher
s, 4
78
517,
518
9-
1 9-
1 17
9-2
Ad
ding
and
Su
btra
ctin
g R
atio
nal
Expr
essi
ons
• D
eter
min
e th
e LC
M o
f po
lyno
mia
ls.
• Ad
d an
d su
btra
ct ra
tiona
l ex
pres
sion
s.
DI,
Inte
rper
sona
l,
481
Fi
nd th
e Er
ror,
4
81
Tips
for N
ew
Tea
cher
s, 4
84
523,
524
9-
2 9-
2 18
9-3
G
raph
ing
Rat
iona
l Fu
nctio
ns
• D
eter
min
e th
e ve
rtica
l asy
mpt
otes
an
d th
e po
int d
isco
ntin
uity
for t
he
grap
hs o
f rat
iona
l fun
ctio
ns.
• G
raph
ratio
nal f
unct
ions
.
Unl
ocki
ng
Mis
conc
eptio
ns,
486
Ti
ps fo
r New
T
each
ers,
487
D
I, Vi
sual
/Spa
tial,
4
88
529,
530
9-
3 9-
3
9-4
D
irect
, Joi
nt, a
nd
Inve
rse
Varia
tion
• R
ecog
nize
and
sol
ve d
irect
and
jo
int v
aria
tion
prob
lem
s.
• R
ecog
nize
and
sol
ve in
vers
e va
riatio
n pr
oble
ms.
Unl
ocki
ng
Mis
conc
eptio
ns,
494
D
I, Au
dito
ry/
Mus
ical
, 495
Ti
ps fo
r New
T
each
ers,
498
535,
536
9-
4 9-
4
9-5
C
lass
es o
f Fu
nctio
ns
• Id
entif
y gr
aphs
as
diffe
rent
type
s of
func
tions
. •
Iden
tify
equa
tions
as
diffe
rent
ty
pes
of fu
nctio
ns.
DI,
Inte
rper
sona
l,
501
Ti
ps fo
r New
T
each
ers,
504
541,
542
9-
5 9-
5
9-
6
Solv
ing
Rat
iona
l Eq
uatio
ns a
nd
Ineq
ualit
ies
• So
lve
ratio
nal e
quat
ions
. •
Solv
e ra
tiona
l ine
qual
ities
. D
I, Lo
gica
l, 50
9 Fi
nd th
e Er
ror,
5
09
Tips
for N
ew
Tea
cher
s, 5
11
547,
548
9-
6 9-
6
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
10
E
xpon
entia
l and
Log
arith
mic
Rel
atio
ns
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
10-1
Ex
pone
ntia
l Fu
nctio
ns
• G
raph
exp
onen
tial f
unct
ions
. •
Solv
e ex
pone
ntia
l equ
atio
ns a
nd
ineq
ualit
ies.
DI,
Audi
tory
/ M
usic
al, 5
27
573,
574
10
-1
10-1
10-2
Lo
garit
hms
and
Loga
rithm
ic
Func
tions
• Ev
alua
te lo
garit
hmic
exp
ress
ions
. •
Solv
e lo
garit
hmic
equ
atio
ns a
nd
ineq
ualit
ies.
Tips
for N
ew
Tea
cher
s, 5
34
DI,
Visu
al/S
patia
l,
534
Fi
nd th
e Er
ror,
5
35
579,
580
10
-2
10-2
10-3
Pr
oper
ties
of
Loga
rithm
s
• Si
mpl
ify a
nd e
valu
ate
expr
essi
ons
usin
g th
e pr
oper
ties
of lo
garit
hms.
•
Solv
e lo
garit
hmic
equ
atio
ns u
sing
th
e pr
oper
ties
of lo
garit
hms.
Unl
ocki
ng
Mis
conc
eptio
ns,
542
D
I, In
terp
erso
nal,
5
43
Find
the
Erro
r,
544
585,
586
10
-3
10-3
10-4
C
omm
on
Loga
rithm
s
• So
lve
expo
nent
ial e
quat
ions
and
in
equa
litie
s us
ing
com
mon
lo
garit
hms.
•
Eval
uate
loga
rithm
ic e
xpre
ssio
ns
usin
g th
e C
hang
e of
Bas
e Fo
rmul
a.
Unl
ocki
ng
Mis
conc
eptio
ns,
548
D
I, N
atur
alis
t, 54
9
591,
592
10
-4
10-4
10-5
Ba
se e
and
Nat
ural
Lo
garit
hms
• Ev
alua
te e
xpre
ssio
ns in
volv
ing
the
natu
ral b
ase
and
natu
ral
loga
rithm
s.
• So
lve
expo
nent
ial e
quat
ions
and
in
equa
litie
s us
ing
natu
ral
loga
rithm
s.
DI,
Kine
sthe
tic,
556
Fi
nd th
e Er
ror,
5
57
597,
598
10
-5
10-5
19
10
-6
Expo
nent
ial G
row
th
and
Dec
ay
• U
se lo
garit
hms
to s
olve
pro
blem
s in
volv
ing
expo
nent
ial d
ecay
. •
Use
loga
rithm
s to
sol
ve p
robl
ems
invo
lvin
g ex
pone
ntia
l gro
wth
.
DI,
Logi
cal,
561
60
3, 6
04
10-6
10
-6
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
11
Se
quen
ces a
nd S
erie
s
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
11-1
Ar
ithm
etic
Se
quen
ces
• U
se a
rithm
etic
seq
uenc
es.
• Fi
nd a
rithm
etic
mea
ns.
Unl
ocki
ng
Mis
conc
eptio
ns,
579
Ti
ps fo
r New
T
each
ers,
582
D
I, Ki
nest
hetic
, 5
82
631,
632
11
-1
11-1
20
11-2
Ar
ithm
etic
Ser
ies
• Fi
nd s
ums
of a
rithm
etic
ser
ies.
•
Use
sig
ma
nota
tion.
D
I, Au
dito
ry/
Mus
ical
, 587
Ti
ps fo
r New
T
each
ers,
587
637,
638
11
-2
11-2
11-3
G
eom
etric
Se
quen
ces
• U
se g
eom
etric
seq
uenc
es.
• Fi
nd g
eom
etric
mea
ns.
Find
the
Erro
r,
590
D
I, In
terp
erso
nal,
5
90
Tips
for N
ew
Tea
cher
s, 5
92
643,
644
11
-3
11-3
11-4
G
eom
etric
Ser
ies
• Fi
nd s
ums
of g
eom
etric
ser
ies.
•
Find
spe
cific
term
s of
geo
met
ric
serie
s.
DI,
Nat
ural
ist,
596
Tips
for N
ew
Tea
cher
s, 5
98
649,
650
11
-4
11-4
21
11-5
In
finite
Geo
met
ric
Serie
s
• Fi
nd th
e su
m o
f an
infin
ite
geom
etric
ser
ies.
•
Writ
e re
peat
ing
deci
mal
s as
fra
ctio
ns.
Unl
ocki
ng
Mis
conc
eptio
ns,
600
D
I, Lo
gica
l, 60
1 Fi
nd th
e Er
ror,
6
02
Tips
for N
ew
Tea
cher
s, 6
04
655,
656
11
-5
11-5
11-6
R
ecur
sion
and
Sp
ecia
l Seq
uenc
es
• R
ecog
nize
and
use
spe
cial
se
quen
ces.
•
Itera
te fu
nctio
ns.
DI,
Kine
sthe
tic,
608
Ti
ps fo
r New
T
each
ers,
610
661,
662
11
-6
11-6
11
-7
The
Bino
mia
l Th
eore
m
• U
se P
asca
l’s tr
iang
le to
exp
and
pow
ers
of b
inom
ials
. •
Use
the
Bino
mia
l The
orem
to
expa
nd p
ower
s of
bin
omia
ls.
DI,
Verb
al/
Lin
guis
tic, 6
15
Tips
for N
ew
Tea
cher
s, 6
17
667,
668
11
-7
11-7
11-8
Pr
oof a
nd
Mat
hem
atic
al
Indu
ctio
n
• Pr
ove
stat
emen
ts b
y us
ing
mat
hem
atic
al in
duct
ion.
•
Dis
prov
e st
atem
ents
by
findi
ng a
co
unte
rexa
mpl
e.
DI,
Visu
al/S
patia
l,
619
Ti
ps fo
r New
T
each
ers,
620
673,
674
11
-8
11-8
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
12
Pr
obab
ility
and
Sta
tistic
s
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
12-1
Th
e C
ount
ing
Prin
cipl
e
• So
lve
prob
lem
s in
volv
ing
inde
pend
ent e
vent
s.
• So
lve
prob
lem
s in
volv
ing
depe
nden
t eve
nts.
DI,
Inte
rper
sona
l,
634
69
9, 7
00
12-1
12
-1
12-2
Pe
rmut
atio
ns a
nd
Com
bina
tions
• So
lve
prob
lem
s in
volv
ing
linea
r pe
rmut
atio
ns.
• So
lve
prob
lem
s in
volv
ing
com
bina
tions
.
Unl
ocki
ng
Mis
conc
eptio
ns,
639
D
I, Vi
sual
/Spa
tial,
6
40
705,
706
12
-2
12-2
22
12-3
Pr
obab
ility
• Fi
nd th
e pr
obab
ility
and
odds
of
even
ts.
• C
reat
e an
d us
e gr
aphs
of
prob
abilit
y di
strib
utio
ns.
DI,
Nat
ural
ist,
646
Tips
for N
ew
Tea
cher
s, 6
48
711,
712
12
-3
12-3
12-4
M
ultip
lyin
g Pr
obab
ilitie
s
• Fi
nd th
e pr
obab
ility
of tw
o in
depe
nden
t eve
nts.
•
Find
the
prob
abilit
y of
two
depe
nden
t eve
nts.
Find
the
Erro
r,
654
D
I, N
atur
alis
t, 65
4
717,
718
12
-4
12-4
23
12-5
Ad
ding
Pro
babi
litie
s •
Find
the
prob
abilit
y of
mut
ually
ex
clus
ive
even
ts.
• Fi
nd th
e pr
obab
ility
of in
clus
ive
even
ts.
Find
the
Erro
r,
660
D
I, In
trape
rson
al,
660
723,
724
12
-5
12-5
12-6
St
atis
tical
Mea
sure
s •
Use
mea
sure
s of
cen
tral t
ende
ncy
to re
pres
ent a
set
of d
ata.
•
Find
mea
sure
s of
var
iatio
n fo
r a
set o
f dat
a.
DI,
Inte
rper
sona
l,
667
Ti
ps fo
r New
T
each
ers,
668
729,
730
12
-6
12-6
12-7
Th
e N
orm
al
Dis
tribu
tion
• D
eter
min
e w
heth
er a
set
of d
ata
appe
ars
to b
e no
rmal
ly d
istri
bute
d or
ske
wed
. •
Solv
e pr
oble
ms
invo
lvin
g no
rmal
ly
dist
ribut
ed d
ata.
DI,
Kine
sthe
tic,
672
73
5, 7
36
12-7
12
-7
12
-8
Bino
mia
l Ex
perim
ents
• U
se b
inom
ial e
xpan
sion
s to
find
pr
obab
ilitie
s.
• Fi
nd p
roba
bilit
ies
for b
inom
ial
expe
rimen
ts.
DI,
Kine
sthe
tic,
677
74
1, 7
42
12-8
12
-8
12-9
Sa
mpl
ing
and
Erro
r •
Det
erm
ine
whe
ther
a s
ampl
e is
un
bias
ed.
• Fi
nd m
argi
ns o
f sam
plin
g er
ror.
DI,
Verb
al/
Lin
guis
tic, 6
83
747,
748
12
-9
12-9
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
13
T
rigo
nom
etri
c Fu
nctio
ns
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
13-1
R
ight
Tria
ngle
Tr
igon
omet
ry
• Fi
nd v
alue
s of
trig
onom
etric
fu
nctio
ns fo
r acu
te a
ngle
s.
• So
lve
prob
lem
s in
volv
ing
right
tri
angl
es.
Tips
for N
ew
Tea
cher
s, 7
03
DI,
Visu
al/S
patia
l,
704
775,
776
13
-1
13-1
13-2
An
gles
and
Ang
le
Mea
sure
• C
hang
e ra
dian
mea
sure
to d
egre
e m
easu
re a
nd v
ice
vers
a.
• Id
entif
y co
term
inal
ang
les.
Tips
for N
ew
Tea
cher
s, 7
11
DI,
Kine
sthe
tic,
712
781,
782
13
-2
13-2
13-3
Tr
igon
omet
ric
Func
tions
of
Gen
eral
Ang
les
• Fi
nd v
alue
s of
trig
onom
etric
fu
nctio
ns fo
r gen
eral
ang
les.
•
Use
refe
renc
e an
gles
to fi
nd
valu
es o
f trig
onom
etric
func
tions
.
Unl
ocki
ng
Mis
conc
eptio
ns,
718
D
I, Au
dito
ry/
Mus
ical
, 720
787,
788
13
-3
13-3
24
, 25
13-4
La
w o
f Sin
es
• So
lve
prob
lem
s by
usi
ng th
e La
w
of S
ines
. •
Det
erm
ine
whe
ther
a tr
iang
le h
as
one,
two,
or n
o so
lutio
ns.
Unl
ocki
ng
Mis
conc
eptio
ns,
726
D
I, In
trape
rson
al,
728
Fi
nd th
e Er
ror,
7
30
793,
794
13
-4
13-4
13-5
La
w o
f Cos
ines
•
Solv
e pr
oble
ms
by u
sing
the
Law
of
Cos
ines
. •
Det
erm
ine
whe
ther
a tr
iang
le c
an
be s
olve
d by
firs
t usi
ng th
e La
w o
f Si
nes
or th
e La
w o
f Cos
ines
.
DI,
Verb
al/
Lin
guis
tic, 7
35
Find
the
Erro
r,
735
799,
800
13
-5
13-5
26
13-6
C
ircul
ar F
unct
ions
•
Def
ine
and
use
the
trigo
nom
etric
fu
nctio
ns b
ased
on
the
unit
circ
le.
• Fi
nd th
e ex
act v
alue
s of
tri
gono
met
ric fu
nctio
ns o
f ang
les.
DI,
Nat
ural
ist,
742
805,
806
13
-6
13-6
13
-7
Inve
rse
Trig
onom
etric
Fu
nctio
ns
• So
lve
equa
tions
by
usin
g in
vers
e tri
gono
met
ric fu
nctio
ns.
• Fi
nd v
alue
s of
exp
ress
ions
in
volv
ing
trigo
nom
etric
func
tions
.
DI,
Visu
al/S
patia
l,
748
81
1, 8
12
13-7
13
-7
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
Cha
pter
14
T
rigo
nom
etri
c G
raph
s and
Iden
titie
s
Stud
ent E
ditio
n (le
sson
num
ber a
nd
title
) Le
sson
Obj
ectiv
es
Teac
her
Wra
paro
und
Editi
on
(topi
c, p
age)
Stud
y G
uide
an
d In
terv
entio
n,
CR
M
(pag
es)
5-M
inut
e C
heck
Tr
ansp
ar-
enci
es
(less
on)
Onl
ine
Stud
y To
ols
(less
on)
Alge
2PAS
S:
Tuto
rial P
lus
(less
on)
14-1
G
raph
ing
Trig
onom
etric
Fu
nctio
ns
• G
raph
trig
onom
etric
func
tions
. •
Find
the
ampl
itude
and
per
iod
of
varia
tion
of th
e si
ne, c
osin
e, a
nd
tang
ent f
unct
ions
.
DI,
Visu
al/S
patia
l,
763
Fi
nd th
e Er
ror,
7
66
837,
838
14
-1
14-1
14-2
Tr
ansl
atio
ns o
f Tr
igon
omet
ric
Gra
phs
• G
raph
hor
izon
tal t
rans
latio
ns o
f tri
gono
met
ric g
raph
s an
d fin
d ph
ase
shift
s.
• G
raph
ver
tical
tran
slat
ions
of
trigo
nom
etric
gra
phs.
DI,
Kine
sthe
tic,
773
84
3, 8
44
14-2
14
-2
27
14-3
Tr
igon
omet
ric
Iden
titie
s
• U
se id
entit
ies
to fi
nd tr
igon
omet
ric
valu
es.
• U
se tr
igon
omet
ric id
entit
ies
to
sim
plify
exp
ress
ions
.
DI,
Logi
cal,
778
849,
850
14
-3
14-3
14-4
Ve
rifyi
ng
Trig
onom
etric
Id
entit
ies
• Ve
rify
trigo
nom
etric
iden
titie
s by
tra
nsfo
rmin
g on
e si
de o
f an
equa
tion
into
the
form
of t
he o
ther
si
de.
• Ve
rify
trigo
nom
etric
iden
titie
s by
tra
nsfo
rmin
g ea
ch s
ide
of th
e eq
uatio
n in
to th
e sa
me
form
.
DI,
Inte
rper
sona
l,
784
85
5, 8
56
14-4
14
-4
28
14-5
Su
m a
nd D
iffer
ence
of
Ang
les
Form
ulas
• Fi
nd v
alue
s of
sin
e an
d co
sine
in
volv
ing
sum
and
diff
eren
ce
form
ulas
. •
Verif
y id
entit
ies
by u
sing
sum
and
di
ffere
nce
form
ulas
.
DI,
Nat
ural
ist,
787
861,
862
14
-5
14-5
14-6
D
oubl
e-An
gle
and
Hal
f-Ang
le F
orm
ulas
• Fi
nd v
alue
s of
sin
e an
d co
sine
in
volv
ing
doub
le-a
ngle
form
ulas
. •
Find
val
ues
of s
ine
and
cosi
ne
invo
lvin
g ha
lf-an
gle
form
ulas
.
DI,
Audi
tory
/ M
usic
al, 7
93
867,
868
14
-6
14-6
14
-7
Solv
ing
Trig
onom
etric
Eq
uatio
ns
• So
lve
trigo
nom
etric
equ
atio
ns.
• U
se tr
igon
omet
ric e
quat
ions
to
solv
e re
al-w
orld
pro
blem
s.
DI,
Inte
rper
sona
l,
801
87
3, 8
74
14-7
14
-7
DI =
Diff
eren
tiate
d In
stru
ctio
n, C
RM
= C
hapt
er R
esou
rce
Mas
ters
