el monte union high school district

El Monte Union High School District

Course Outline 12/19/16

High School District-Wide

Title: Math Lab

Transitional*_______(Eng. Dept.

Only)

Sheltered (SDAIE)*___Bilingual*___

AP** Honors**

Department:___Mathematics____

Grade Level (s): 9/10

Semester Year X

Year of State Framework

Adoption _______

This course meets

graduation requirements:

( ) English

( ) Fine Arts

( ) Foreign Language

( ) Health & Safety

( ) Math

( ) Physical Education

( ) Science

( ) Social Science

(X) Elective

Department/Cluster Approval Date

________________ ___________

*Instructional materials appropriate for English language learners are required.

**For AP/Honors course attach a page describing how this course is above and beyond a regular course. Also,

explain why this course is the equivalent of a college level class.

1. Prerequisite(s):

9th or 10th grade student

AND

Concurrent enrollment in Integrated Math 1

AND

D- (60%) or Below in 8th Grade Common Core Math or Integrated Math 1

AND

Math Inventory (MI) Quantile Score of 800 or below for students tested in the 8th grade and 865 or below

for students tested in the 9th grade

OR

Math SBAC scale score of 2483 or below for 7th grade results or 2503 or below for 8th grade results.

2. Short description of course, which may also be used in the registration manual:

This course is designed to assist students who need additional support to achieve at least a “C” in Integrated

Math 1. Along with supporting the Integrated Math 1 curriculum, this course will incorporate a blended

learning environment, which allows for students to have access to technology, teacher led instruction, as well

as collaborative group instruction. The Math Lab course will utilize an adaptive computer-based program to

help target the needs of individual students. Students will review and reinforce the Common Core Standards

addressed in Integrated Math 1 as well as the 8 Standards for Mathematical Practice. The Math Lab course

will also emphasize note-taking, clarifying concepts, review of basic math skills, and exploration. Students

will only receive elective credits for this course.

3. Describe how this course integrates the school’s SLOs (School-wide Learning Outcomes):

(Site SLOs may replace those listed below)

All schools have SLOs that refer to students as academic achievers, critical thinkers, and effective

communicators. The following shows how this course addresses these components:

Academic Achievers – Students will further develop and refine their skills in reading, writing, and

math.

Critical Thinkers – Students will be using their critical thinking skills to solve various types of math

problems including real-world related problems.

Effective Communicators – Students will be working in collaborative groups to share their thought

processes in order to promote teamwork and peer tutoring.

Technology – Students will be utilizing an online computer based math program that is adaptive to

their needs.

4. Describe the additional efforts/teaching techniques/methodology to be used to meet the needs of English

language learners:

Oral and academic language development will be utilized.

Study skills and Cornell notes will be emphasized.

Research based strategies and activities such as SIOP, AVID, metacognitive strategies, Marzano

strategies, Kinsella strategies will assist student learning.

Prior knowledge will be used to build connections and support new learning.

Vocabulary and content development will be highlighted.

Graphic organizers, visuals, relia, audio, and technology software will be utilized during instruction in

order to support multiple learning modalities and Universal Design for Learning.

Engagement routines such as think-write-pair-share, text mark-up, and group/pair work.

Writing support scaffolds such as sentence-framing and paragraph-framing will be utilized.

Reasoning and justifying answers will be highly encouraged.

Flexible instructional organization for whole-class, group, paired and individualized learning will be

implemented.

5. Describe the interdepartmental articulation process for this course:

There is more intradepartmental articulation than interdepartmental, as this course is designed to support the

existing Integrated Math 1 course. The mathematics concepts reinforced in this class help support all other

disciplines in developing the following: understanding of logical reasoning; interpretation of graphs; analysis

of the reasonability of results; and basic skills in applying percents, ratios, and fractions.

6. Describe how this course will integrate academic and vocational concepts, possibly through connecting

activities. Describe how this course will address work-based learning/school to career concepts:

This course will provide students with a plethora of real-world and career-related applications problems to

solve. Students will be given opportunities to apply their reasoning, communicating, problem solving, data

analysis, and modeling skills throughout the course with various activities and performance tasks.

7. Materials of Instruction (Note that materials of instruction for English language learners are required

and should be listed below.)

a. Textbook(s) and Core Reading(s): Integrated Mathematics 1. Kanold, T.D., Burger, E.B., Dixon, J.K.,

Larson, M.R., Leinwand, S.J. Houghton Mifflin Harcourt Publishing Company 2015.

b. Supplemental Materials and Resources:

HMH Integrated Math 1 California Student Workbooks

HMH Integrated Math 1 California Response to Intervention Teacher Resources

HMH Integrated Math 1 California Online Teacher Resource Management Center

o https://my.hrw.com (Personal Math Trainer)

Khan Academy

o https://www.khanacademy.org

8.

a. Objectives of Course

The primary objective of the Math Lab course is to strengthen the knowledge and foundation

presented by the Integrated Math 1 course along with the following:

o Clarify additional questions that arise after homework has been attempted

o Provide additional practice and feedback to ensure in-depth learning

o Utilize an adaptive online program to allow for remediation of basic skills and skills needed

to support understanding of current math topics based on each individual student’s need

o Provide students with an opportunity to explore mathematics in a non-traditional manner

b. Unit detail including projects and activities including duration of units (pacing plan):

A third of each class period will be devoted to clarifying questions about the primary instruction.

Teachers will present/reteach concepts from the Integrated Math 1 primary instruction utilizing the

Integrated Mathematics 1 Response to Intervention Resources in order to clarify and strengthen

student understanding. Another third of the class will be spent reviewing basic skills that are weak

(utilizing an adaptive math program such as Khan Academy or Personal Math Trainer from HMH)

and/or additional practice for current material. The final third of the class will be spent exploring

math through performance tasks, activities, manipulatives and or games.

Additionally, the amount of support and intervention required by students will be based on each

student’s individual needs and will be provided with either a Tier 1, Tier 2, or Tier 3 Intervention

support (See attached Response to Intervention matrix).

https://my.hrw.com/

https://www.khanacademy.org/

c. Indicate references to state framework(s)/standards (If state standard is not applicable, then

national standard should be used.)

The Math Lab course will be in line with the Integrated Math 1 course and will generally follow the

pacing structure and Common Core Standards set forth by Integrated Math 1. (See attachment for

Integrated Math 1 CCSS standards)

d. Student performance standard

Students will be assessed in the Math Lab course based on the scale of

90% - 100% A

80% – 89% B

70% - 79%C

60% - 69%D

59% and lower is failing

e. Evaluation/assessment/rubrics

Students will be assessed in the lab class with quizzes, tests, and class participation as well as

homework completion and notebooks. Students will be taking the district math benchmarks in their

primary Integrated Math 1 classes.

Additionally, teachers utilizing an adaptive math program will grade students in accordance to hours

spent on using the program as well as number of skills mastered. (See attachment for sample

grading rubric)

f. Include minimal attainment for student to pass course

Students will receive elective credit for passing the Math Lab class with a grade of “D” or better

(60% or above).

Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

xi

Response to Intervention UNIT 1 QUANTITIES AND MODELING Student Edition Lessons

Tier 1 Skills

Pre-Tests Tier 2 Skills Strategic Intervention

Post- Tests

Tier 3 Skills Intensive Intervention

Module 1 Quantitative Reasoning

Building Block (Tier 3) worksheets are available online for students who need additional support on prerequisite skills. See the teacher page of each Tier 2 Skill lesson for a list of Building Block skills.

1.1 Solving Equations Reteach 1-1 Module 1 13 One-Step Equations 17 Scale Factor and Scale

Drawings 19 Significant Digits 24 Writing Linear Equations

Skill 13 Skill 17 Skill 19 Skill 24

1.2 Modeling Quantities Reteach 1-2

1.3 Reporting with Precision and Accuracy

Reteach 1-3

Module 2 Algebraic Models

2.1 Modeling with Expressions

Reteach 2-1 Module 2 2 Algebraic Expressions 13 One-Step Equations 14 One-Step Inequalities 21 Two-Step Equations 22 Two-Step Inequalities

Skill 2 Skill 13 Skill 14 Skill 21 Skill 22

2.2 Creating and Solving Equations

Reteach 2-2

2.3 Solving for a Variable Reteach 2-3

2.4 Creating and Solving Inequalities

Reteach 2-4

2.5 Creating and Solving Compound Inequalities

Reteach 2-5

UNIT 2 UNDERSTANDING FUNCTIONS Student Edition Lessons

Tier 1 Skills


Post- Tests


Module 3 Functions and Models


3.1 Graphing Relationships

Reteach 3-1 Module 3 6 Graphing Linear Nonproportional Relationships

7 Graphing Linear Proportional Relationships

10 Linear Functions

Skill 6 Skill 7 Skill 10

3.2 Understanding Relations and Functions

Reteach 3-2

3.3 Modeling with Functions

Reteach 3-3

3.4 Graphing Functions Reteach 3-4

Module 4 Patterns and Sequences

4.1 Identifying and Graphing Sequences

Reteach 4-1 Module 4 1 Add and Subtract Integers 2 Algebraic Expressions 12 Multiply and Divide

Integers

Skill 1 Skill 2 Skill 12 4.2 Constructing Arithmetic

Sequences Reteach 4-2

4.3 Modeling with Arithmetic Sequences

Reteach 4-3

ADDITIONAL ONLINE INTERVENTION RESOURCES

Tier 1, Tier 2, Tier 3 Skills Personal Math Trainer will automatically create a standards-based, personalized intervention assignment for your students, targeting each student’s individual needs!

Tier 2 Skills Students scan QR codes with their smart phones to watch Math on the Spot tutorial videos for every Tier 2 skill.


xii

Response to Intervention UNIT 3 LINEAR FUNCTIONS, EQUATIONS, AND INEQUALITIES Student Edition Lessons

Tier 1 Skills


Post- Tests


Module 5 Linear Functions


5.1 Understanding Linear Functions

Reteach 5-1 Module 5 4 Constant Rate of Change 7 Graphing Linear

Proportional Relationships 8 Interpreting the Unit Rate

as Slope 11 Multi-Step Equations 20 Slope 23 Unit Rates



5.2 Using Intercepts Reteach 5-2 5.3 Interpreting Rate of

Change and Slope

Reteach 5-3

Module 6 Forms of Linear Equations

6.1 Slope-Intercept Form Reteach 6-1 Module 6 4 Constant Rate of Change 7 Graphing Linear

Proportional Relationships 10 Linear Functions 20 Slope 21 Two-Step Equations 23 Unit Rates

Skill 4 Skill 7 Skill 10 Skill 20 Skill 21 Skill 23

6.2 Point-Slope Form Reteach 6-2

6.3 Standard Form Reteach 6-3 6.4 Transforming Linear

Functions 6.5 Comparing Properties

of Linear Functions

Reteach 6-4 Reteach 6-5

Module 7 Linear Equations and Inequalities

7.1 Modeling Linear Relationships

7.2 Using Functions to Solve One-Variable Linear Equations

7.3 Linear Inequalities in Two Variables

Reteach 7-1 Reteach 7-2 Reteach 7-3

Module 7 2 Algebraic Expressions 7 Graphing Linear

Proportional Relationships 10 Linear Functions 24 Writing Linear Equations


UNIT 4 STATISTICAL MODELS Student Edition Lessons

Tier 1 Skills


Post- Tests


Module 8 Multi-Variable Categorical Data


8.1 Two-Way Frequency Tables

Reteach 8-1 Module 8 15 Percents 25 Two-Way Frequency

Tables 26 Two-Way Relative

Frequency Tables


8.2 Relative Frequency Reteach 8-2

Module 9 One-Variable Data Distributions 9.1 Measures of Center

and Spread Reteach 9-1 Module 9 28 Measures of Center

29 Box Plots 30 Histograms


9.2 Data Distributions and Outliers

Reteach 9-2

9.3 Histograms and Box Plots

9.4 Normal Distributions


Module 10 Linear Modeling and Regression 10.1 Scatter Plots and

Trend Lines 10.2 Fitting a Linear Model

to Data


Module 10 9 Linear Associations 10 Linear Functions 18 Scatter Plots 24 Writing Linear Equations



xiii

Response to Intervention

UNIT 5 LINEAR SYSTEMS AND PIECE-WISE DEFINED FUNCTIONS Student Edition Lessons

Tier 1 Skills


Post- Tests


Module 11 Solving Systems of Linear Equations


11.1 Solving Linear Systems by Graphing

Reteach 11-1 Module 11 2 Algebraic Expressions 6 Graphing Linear

Nonproportional Relationships

7 Graphing Linear Proportional Relationships

10 Linear Functions


Skill 10

11.2 Solving Linear Systems by Substitution

Reteach 11-2

11.3 Solving Linear Systems by Adding or Subtracting

Reteach 11-3

11.4 Solving Linear Systems by Multiplying First

Reteach 11-4

Module 12 Modeling with Linear Systems

12.1 Creating Systems of Linear Equations

Reteach 12-1 Module 12 2 Algebraic Expressions 10 Linear Functions 14 One-Step Inequalities 21 Two-Step Equations 22 Two Step Inequalities


12.2 Graphing Systems of Linear Inequalities

Reteach 12-2

12.3 Modeling with Linear Systems

Reteach 12-3

Module 13 Piecewise-Defined Functions

13.1 Understanding Piecewise-Defined Functions

Reteach 13-1 Module 13 10 Linear Functions 11 Multi-Step Equations 22 Two-Step Inequalities 27 Absolute Value


13.2 Absolute Value Functions and Transformations

Reteach 13-2

13.3 Solving Absolute Value Equations

Reteach 13-3

13.4 Solving Absolute Value Inequalities

Reteach 13-4





xiv

Response to Intervention UNIT 6 EXPONENTIAL RELATIONSHIPS Student Edition Lessons

Tier 1 Skills


Post- Tests


Module 14 Geometric Sequences and Exponential Functions


14.1 Understanding Geometric Sequences

Reteach 14-1 Module 14 2 Algebraic Expressions 5 Exponents 11 Multi-Step Equations

Skill 2 Skill 5 Skill 11 14.2 Constructing

Geometric Sequences Reteach 14-2

14.3 Constructing Exponential Functions

14.4 Graphing Exponential Functions

14.5 Transforming Exponential Functions


Module 15 Exponential Equations and Models

15.1 Using Graphs and Properties to Solve Equations with Exponents

15.2 Modeling Exponential Growth and Decay

15.3 Using Exponential Regression Models

15.4 Comparing Linear and Exponential Models

Reteach 15-1 Reteach 15-2 Reteach 15-3 Reteach 15-4

Module 15 4 Constant Rate of Change 5 Exponents 15 Percent 18 Scatter Plots


UNIT 7 TRANSFORMATIONS AND CONGRUENCE Student Edition Lessons

Tier 1 Skills


Post- Tests


Module 16 Tools of Geometry


16.1 Segment Length and Midpoints

Reteach 16-1 Module 16 33 More Algebraic Representations of Transformations

34 Angle Relationships 38 Distance and Midpoint

Formulas

Skill 33

Skill 34 Skill 38

16.2 Angle Measure and Angle Bisectors

Reteach 16-2

16.3 Representing and Describing Transformations

16.4 Reasoning and Proof

Reteach 16-3

Reteach 16-4

Module 17 Transformations and Symmetry

17.1 Translations Reteach 17-1 Module 17 42 Properties of Reflections 43 Properties of Rotations 44 Properties of Translations


17.2 Reflections Reteach 17-2

17.3 Rotations Reteach 17-3

17.4 Investigating Symmetry

Reteach 17-4

Module 18 Congruent Figures

18.1 Sequences of Transformations

18.2 Proving Figures are Congruent Using Rigid Motions

18.3 Corresponding Parts of Congruent Figures Are Congruent


Reteach 18-3

Module 18 37 Congruent Figures 42 Properties of Reflections 43 Properties of Rotations 44 Properties of Translations



xv

Response to Intervention UNIT 8 LINES, ANGLES, AND TRIANGLES Student Edition Lessons

Tier 1 Skills


Post- Tests


Module 19 Lines and Angles


19.1 Angles Formed by Intersecting Lines

Reteach 19-1 Module 19 34 Angle Relationships 40 Parallel Lines Cut by a

Transversal 42 Properties of Reflections 47 Writing Equations of

Parallel, Perpendicular, Vertical, and Horizontal Lines


19.2 Transversals and Parallel Lines

Reteach 19-2

19.3 Proving Lines Are Parallel

19.4 Perpendicular Lines

19.5 Equations of Parallel and Perpendicular Lines


Reteach 19-5

Module 20 Triangle Congruence Criteria

20.1 Exploring What Makes Triangles Congruent

Reteach 20-1 Module 20 37 Congruent Figures 40 Parallel Lines Cut by a

Transversal 42 Properties of Reflection 43 Properties of Rotations 44 Properties of Translations


20.2 ASA Triangle Congruence

Reteach 20-2

20.3 SAS Triangle Congruence

Reteach 20-3

20.4 SSS Triangle Congruence

Reteach 20-4

Module 21 Applications of Triangle Congruence

21.1 Justifying Constructions

21.2 AAS Triangle Congruence

21.3 HL Triangle Congruence


Module 21 35 Angle Theorems for Triangles

37 Congruent Figures 40 Parallel Lines Cut by a

Transversal

Skill 35

Skill 37 Skill 40

Module 22 Properties of Triangles

22.1 Interior and Exterior Angles

22.2 Isosceles and Equilateral Triangles

22.3 Triangle Inequalities


Module 22 34 Angle Relationships 35 Angle Theorems for

Triangles 38 Distance and Midpoint

Formulas


Module 23 Special Segments in Triangles

23.1 Perpendicular Bisectors of Triangles

23.2 Angle Bisectors of Triangles

23.3 Medians and Altitudes of Triangles

23.4 Midsegments of Triangles

Reteach 23-1 Reteach 23-2 Reteach 23-3 Reteach 23-4

Module 23 35 Angle Theorems for Triangles

38 Distance and Midpoint Formulas

39 Geometric Drawings






xvi

Response to Intervention UNIT 9 QUADRILATERALS AND COORDINATE PROOF Student Edition Lessons

Tier 1 Skills


Post- Tests


Module 24 Properties of Quadrilaterals


24.1 Properties of Parallelograms

Reteach 24-1 Module 24 37 Congruent Figures 41 Parallelograms

Skill 37 Skill 41

24.2 Conditions for Parallelograms

Reteach 24-2

24.3 Properties of Rectangles, Rhombuses, and Squares

24.4 Conditions for Rectangles, Rhombuses, and Squares

24.5 Properties and Conditions for Kites and Trapezoids


Reteach 24-5

Module 25 Coordinate Proof Using Slope and Distance

25.1 Slope and Parallel Lines

Reteach 25-1 Module 25 36 Area of Composite Figures

38 Distance and Midpoint Formulas

45 Rate of Change and Slope 46 Using Slope and y-

intercept 47 Writing Equations of

Parallel, Perpendicular, Vertical, and Horizontal Lines

Skill 36

Skill 38

Skill 45 Skill 46

Skill 47

25.2 Slope and Perpendicular Lines

Reteach 25-2

25.3 Coordinate Proof Using Distance with Segments and Triangles

Reteach 25-3

25.4 Coordinate Proof Using Distance with Quadrilaterals

25.5 Perimeter and Area on the Coordinate Plane

Reteach 25-4

Reteach 25-5


xvii

Using HMH Integrated Math 1 Response to Intervention

Print

Resources Online

Resources

TIER 1 TIER 2 STRATEGIC INTERVENTION

TIER 1, TIER 2, AND TIER 3

Reteach worksheet (one worksheet per lesson) • Use to provide additional

support for students who are having difficulty mastering the concepts taught in Integrated Math 1.

Skill Intervention worksheets (one set per skill) • Use for students who

require intervention with prerequisite skills taught in Middle School.

Skill Intervention Teacher Guides (one guide per skill) • Use to provide

systematic and explicit instruction, and alternate strategies to help students acquire mastery with prerequisite skills.

T1, T2, and T3 skills • Assign the Personal

Math Trainer, which will create standards-based practice for all students and customized intervention when necessary.

Progress Monitoring • Use the Personal Math

Trainer to assess a student’s mastery of skills.

Progress Monitoring • Use Student Edition

Ready to Go On? Quizzes to assess mastery of skills taught in the Modules. Use for all students.

• Use Assessment Resources Module Quizzes to assess mastery of skills taught in the Modules. For students who are considerably below level, use Modified Quizzes. For all other students, use Level B.

Progress Monitoring • Use Response to

Intervention Module Pre-Tests or the Student Edition Are You Ready? Quizzes to assess whether a student has the necessary prerequisite skills for success in each Module.

• Use Response to Intervention Skill Post-Tests to assess mastery of prerequisite skills.

T2 skills

• Use Math on the Spot tutorial videos to help students review skills taught in Middle School.

T3 skills

• Use Building Block Skills worksheets for struggling students who require additional intervention.


xviii

Recommendations for Intervention

Tier 1 For students who require small group instruction to review lesson skills taught in Integrated Math 1.

Tiers 2–3 For students who require strategic or intensive intervention with prerequisite skills needed for success in Integrated Math 1.

Tiers 1–3 Intervention materials and the Personal Math Trainer are designed to accommodate the diverse skill levels of students at all levels of intervention.

DIAGNOSIS

Tier 2 Module Pre-Tests (RTI ancillary) Tier 2 Are You Ready? Quizzes (Student Edition) Tier 1 Ready to Go On? Quizzes (Student Edition)

�

INTERVENE

Use Tier 1 Reteach and/or Tier 2 Skill Worksheets (RTI ancillary). • Uncluttered with minimum words to help all students, regardless of English acquisition • Vocabulary presented in context to help English learners and struggling readers • Multiple instructional examples for students to practice thinking-aloud their solutions

Use Tier 2 Skill Teacher Guides (RTI ancillary). • Explicit instruction and key teaching points • Alternate strategies to address the different types of learners • Common misconceptions to develop understanding of skills • Visual representations to make concept connections • Checks to fine-tune instruction and opportunities for immediate feedback

MONITOR PROGRESS

Tier 2: Skill Post-Tests (RTI ancillary) Tier 1–2: Assessment Readiness (Student Edition) Tier 1–3: Leveled Module Quizzes (Assessment Resources online)

Use Tiers 1–3 online additional intervention, practice, and review materials.

• Personal Math Trainer • Math on the Spot videos • Building Block Skills worksheets with

Teacher Guides

• Differentiated Instruction with leveled Practice, Reading Strategies, and Success for English Learners worksheets

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s a si

ngle

ent

ity.

SE:

45–5

4

Wri

te e

xpre

ssio

ns in

equ

ival

ent f

orm

s to

solv

e pr

oble

ms

A-S

SE.A

.3

Cho

ose

and

prod

uce

an e

quiv

alen

t for

m o

f an

expr

essi

on to

re

veal

and

exp

lain

pro

perti

es o

f the

qua

ntity

repr

esen

ted

by

the

expr

essi

on.

SE:

655–

666

A-S

SE.A

.3c

Use

the

prop

ertie

s of e

xpon

ents

to tr

ansf

orm

exp

ress

ions

for

expo

nent

ial f

unct

ions

.

SE:

655–

666

Hou

ghto

n M

ifflin

Har

cour

t Int

egra

ted

Mat

h I ©

2015

cor

rela

ted

to th

e C

omm

on C

ore

Stat

e St

anda

rds f

or M

athe

mat

ics,

Mat

hem

atic

s I!

3 !

Stan

dard

s D

escr

ipto

r C

itatio

ns

A-C

ED

Cre

atin

g Eq

uatio

ns

Cre

ate

equa

tions

that

des

crib

e nu

mbe

rs o

f rel

atio

nshi

ps

A-C

ED.A

.1

Cre

ate

equa

tions

and

ineq

ualit

ies i

n on

e va

riabl

e an

d us

e th

em

to so

lve

prob

lem

s. In

clud

e eq

uatio

ns a

risi

ng fr

om li

near

and

qu

adra

tic fu

nctio

ns, a

nd si

mpl

e ra

tiona

l and

exp

onen

tial

func

tions

.

SE:

55–6

6, 7

3–80

, 81–

92, 7

09–7

20

A-C

ED.A

.2

Cre

ate

equa

tions

in tw

o or

mor

e va

riabl

es to

repr

esen

t re

latio

nshi

ps b

etw

een

quan

titie

s; g

raph

equ

atio

ns o

n co

ordi

nate

axe

s with

labe

ls a

nd sc

ales

.

SE:

127–

136,

239

–248

, 249

–260

, 261

–268

, 735

–748

A-C

ED.A

.3

Rep

rese

nt c

onst

rain

ts b

y eq

uatio

ns o

r ine

qual

ities

, and

by

syst

ems o

f equ

atio

ns a

nd/o

r ine

qual

ities

, and

inte

rpre

t so

lutio

ns a

s via

ble

or n

onvi

able

opt

ions

in a

mod

elin

g co

ntex

t.

SE:

55–6

6, 7

3–80

, 301

–308

, 323

–334

, 533

–546

, 547

–55

6, 5

57–5

70

A-C

ED.A

.4

Rea

rran

ge fo

rmul

as to

hig

hlig

ht a

qua

ntity

of i

nter

est,

usin

g th

e sa

me

reas

onin

g as

in so

lvin

g eq

uatio

ns.

SE:

67–7

2

A-R

EI

Rea

soni

ng w

ith E

quat

ions

and

Ineq

ualit

ies

Und

erst

and

solv

ing

equa

tions

as a

pro

cess

of r

easo

ning

and

exp

lain

the

reas

onin

g.

A-R

EI.A

.1

Expl

ain

each

step

in so

lvin

g a

sim

ple

equa

tion

as fo

llow

ing

from

the

equa

lity

of n

umbe

rs a

sser

ted

at th

e pr

evio

us st

ep,

star

ting

from

the

assu

mpt

ion

that

the

orig

inal

equ

atio

n ha

s a

solu

tion.

Con

stru

ct a

via

ble

argu

men

t to

just

ify a

solu

tion

met

hod.

SE:

5–14

, 815

–826

Solv

e eq

uatio

ns a

nd in

equa

litie

s in

one

vari

able

A

-REI

.B.3

So

lve

linea

r equ

atio

ns a

nd in

equa

litie

s in

one

varia

ble,

in

clud

ing

equa

tions

with

coe

ffic

ient

s rep

rese

nted

by

lette

rs.

SE:

55–6

6, 6

7–72

, 73–

80, 8

1–92

Hou

ghto

n M

ifflin

Har

cour

t Int

egra

ted

Mat

h I ©

2015

cor

rela

ted

to th

e C

omm

on C

ore

Stat

e St

anda

rds f

or M

athe

mat

ics,

Mat

hem

atic

s I!

4 !

Stan

dard

s D

escr

ipto

r C

itatio

ns

Solv

e sy

stem

s of e

quat

ions

. A

-REI

.C.5

Pr

ove

that

, giv

en a

syst

em o

f tw

o eq

uatio

ns in

two

varia

bles

, re

plac

ing

one

equa

tion

by th

e su

m o

f tha

t equ

atio

n an

d a

mul

tiple

of t

he o

ther

pro

duce

s a sy

stem

with

the

sam

e so

lutio

ns.

SE:

515–

526

A-R

EI.C

.6

Solv

e sy

stem

s of l

inea

r equ

atio

ns e

xact

ly a

nd a

ppro

xim

atel

y (e

.g.,

with

gra

phs)

, foc

usin

g on

pai

rs o

f lin

ear e

quat

ions

in

two

varia

bles

.

SE:

479–

490,

491

–502

, 503

–514

, 515

–526

Rep

rese

nt a

nd so

lve

equa

tions

and

ineq

ualit

ies g

raph

ical

ly.

A-R

EI.D

.10

Und

erst

and

that

the

grap

h of

an

equa

tion

in tw

o va

riabl

es is

th

e se

t of a

ll its

solu

tions

plo

tted

in th

e co

ordi

nate

pla

ne, o

ften

form

ing

a cu

rve

(whi

ch c

ould

be

a lin

e).

SE:

199–

210,

239

–248

, 249

–260

, 261

–268

A-R

EI.D

.11

Expl

ain

why

the

x-co

ordi

nate

s of t

he p

oint

s whe

re th

e gr

aphs

of

the

equa

tions

y =

f(x)

and

y =

g(x

) int

erse

ct a

re th

e so

lutio

ns

of th

e eq

uatio

n f(x

) = g

(x);

find

the

solu

tions

app

roxi

mat

ely,

e.

g., u

sing

tech

nolo

gy to

gra

ph th

e fu

nctio

ns, m

ake

tabl

es o

f va

lues

, or f

ind

succ

essi

ve a

ppro

xim

atio

ns. I

nclu

de c

ases

w

here

f(x)

and

/or g

(x) a

re li

near

, pol

ynom

ial,

ratio

nal,

abso

lute

val

ue, e

xpon

entia

l, an

d lo

garit

hmic

func

tions

.★

SE:

309–

322,

709

–720

, 735

–748

A-R

EI.D

.12

Gra

ph th

e so

lutio

ns to

a li

near

ineq

ualit

y in

two

varia

bles

as a

ha

lf-pl

ane

(exc

ludi

ng th

e bo

unda

ry in

the

case

of a

stric

t in

equa

lity)

, and

gra

ph th

e so

lutio

n se

t to

a sy

stem

of l

inea

r in

equa

litie

s in

two

varia

bles

as t

he in

ters

ectio

n of

the

corr

espo

ndin

g ha

lf-pl

anes

.

SE:

323–

334,

547

–556

Hou

ghto

n M

ifflin

Har

cour

t Int

egra

ted

Mat

h I ©

2015

cor

rela

ted

to th

e C

omm

on C

ore

Stat

e St

anda

rds f

or M

athe

mat

ics,

Mat

hem

atic

s I!

5 !

Stan

dard

s D

escr

ipto

r C

itatio

ns

F-IF

In

terp

retin

g Fu

nctio

ns

Und

erst

and

the

conc

ept o

f a fu

nctio

n an

d us

e fu

nctio

n no

tatio

n.

F-IF

.A.1

U

nder

stan

d th

at a

func

tion

from

one

set (

calle

d th

e do

mai

n) to

an

othe

r set

(cal

led

the

rang

e) a

ssig

ns to

eac

h el

emen

t of t

he

dom

ain

exac

tly o

ne e

lem

ent o

f the

rang

e. If

f is

a fu

nctio

n an

d x

is a

n el

emen

t of i

ts d

omai

n, th

en f(

x) d

enot

es th

e ou

tput

of f

co

rres

pond

ing

to th

e in

put x

. The

gra

ph o

f f is

the

grap

h of

the

equa

tion

y =

f(x).

SE:

115–

126,

127

–136

, 137

–148

F-IF

.A.2

U

se fu

nctio

n no

tatio

n, e

valu

ate

func

tions

for i

nput

s in

thei

r do

mai

ns, a

nd in

terp

ret s

tate

men

ts th

at u

se fu

nctio

n no

tatio

n in

te

rms o

f a c

onte

xt.

SE:

127–

136,

137

–148

, 663

–676

F-IF

.A.3

R

ecog

nize

that

sequ

ence

s are

func

tions

, som

etim

es d

efin

ed

recu

rsiv

ely,

who

se d

omai

n is

a su

bset

of t

he in

tege

rs.

SE:

155–

164,

165

–174

, 175

–186

Inte

rpre

t fun

ctio

ns th

at a

rise

in a

pplic

atio

ns in

term

s of t

he c

onte

xt.

F-IF

.B.4

Fo

r a fu

nctio

n th

at m

odel

s a re

latio

nshi

p be

twee

n tw

o qu

antit

ies,

inte

rpre

t key

feat

ures

of g

raph

s and

tabl

es in

term

s of

the

quan

titie

s, an

d sk

etch

gra

phs s

how

ing

key

feat

ures

gi

ven

a ve

rbal

des

crip

tion

of th

e re

latio

nshi

p. K

ey fe

atur

es

incl

ude:

inte

rcep

ts; i

nter

vals

whe

re th

e fu

nctio

n is

incr

easi

ng,

decr

easi

ng, p

ositi

ve, o

r neg

ativ

e; re

lativ

e m

axim

ums a

nd

min

imum

s; sy

mm

etri

es; e

nd b

ehav

ior;

and

per

iodi

city

. ★

SE:

105–

114,

211

–220

F-IF

.B.5

R

elat

e th

e do

mai

n of

a fu

nctio

n to

its g

raph

and

, whe

re

appl

icab

le, t

o th

e qu

antit

ativ

e re

latio

nshi

p it

desc

ribes

.★

SE:

721–

734

F-IF

.B.6

C

alcu

late

and

inte

rpre

t the

ave

rage

rate

of c

hang

e of

a

func

tion

(pre

sent

ed sy

mbo

lical

ly o

r as a

tabl

e) o

ver a

spec

ified

in

terv

al. E

stim

ate

the

rate

of c

hang

e fr

om a

gra

ph. ★

SE:

221–

232

Hou

ghto

n M

ifflin

Har

cour

t Int

egra

ted

Mat

h I ©

2015

cor

rela

ted

to th

e C

omm

on C

ore

Stat

e St

anda

rds f

or M

athe

mat

ics,

Mat

hem

atic

s I!

6 !

Stan

dard

s D

escr

ipto

r C

itatio

ns

Ana

lyze

func

tions

usin

g di

ffere

nt r

epre

sent

atio

ns.

F-IF

.C.7

G

raph

func

tions

exp

ress

ed sy

mbo

lical

ly a

nd sh

ow k

ey

feat

ures

of t

he g

raph

, by

hand

in si

mpl

e ca

ses a

nd u

sing

te

chno

logy

for m

ore

com

plic

ated

cas

es.

SE:

199–

210,

211

–220

, 281

–294

, 239

–248

, 609

–622

, 623

–63

6, 6

37–6

48, 6

67–6

80

F-IF

.C.7

a G

raph

line

ar a

nd q

uadr

atic

func

tions

and

show

inte

rcep

ts,

max

ima,

and

min

ima.

SE

: 19

9–21

0, 2

11–2

20, 2

39–2

48

F-IF

.C.7

e G

raph

exp

onen

tial a

nd lo

garit

hmic

func

tions

, sho

win

g in

terc

epts

and

end

beh

avio

r, an

d tri

gono

met

ric fu

nctio

ns,

show

ing

perio

d, m

idlin

e, a

nd a

mpl

itude

.

SE:

663–

676,

677

–690

, 721

–734

F-IF

.C.9

C

ompa

re p

rope

rties

of t

wo

func

tions

eac

h re

pres

ente

d in

a

diff

eren

t way

(alg

ebra

ical

ly, g

raph

ical

ly, n

umer

ical

ly in

ta

bles

, or b

y ve

rbal

des

crip

tions

).

SE:

281–

294,

691

–702

F-BF

Bu

ildin

g Fu

nctio

ns

Build

a fu

nctio

n th

at m

odel

s a r

elat

ions

hip

betw

een

two

quan

titie

s. F-

BF.

A.1

W

rite

a fu

nctio

n th

at d

escr

ibes

a re

latio

nshi

p be

twee

n tw

o qu

antit

ies.

SE:

165–

174,

175

–186

, 649

–662

, 691

–702

, 709

–720

, 721

–73

4

F-B

F.A

.1a

Det

erm

ine

an e

xplic

it ex

pres

sion

, a re

curs

ive

proc

ess,

or st

eps

for c

alcu

latio

n fr

om a

con

text

.

SE:

165–

174,

175

–186

, 649

–662

, 721

–734

F-B

F.A

.1b

Com

bine

stan

dard

func

tion

type

s usi

ng a

rithm

etic

ope

ratio

ns.

SE:

691–

702

F-B

F.A

.2

Writ

e ar

ithm

etic

and

geo

met

ric se

quen

ces b

oth

recu

rsiv

ely

and

with

an

expl

icit

form

ula,

use

them

to m

odel

situ

atio

ns,

and

trans

late

bet

wee

n th

e tw

o fo

rms.★

SE:

155–

164,

165

–174

, 649

–662

Hou

ghto

n M

ifflin

Har

cour

t Int

egra

ted

Mat

h I ©

2015

cor

rela

ted

to th

e C

omm

on C

ore

Stat

e St

anda

rds f

or M

athe

mat

ics,

Mat

hem

atic

s I!

7 !

Stan

dard

s D

escr

ipto

r C

itatio

ns

Build

new

func

tions

from

exi

stin

g fu

nctio

ns.

F-B

F.B

.3

Iden

tify

the

effe

ct o

n th

e gr

aph

of re

plac

ing f(x

) by f(x

) + k

, kf

(x), f(kx)

, and

f(x

+ k)

for s

peci

fic v

alue

s of k

(bot

h po

sitiv

e an

d ne

gativ

e); f

ind

the

valu

e of

k g

iven

the

grap

hs.

Expe

rimen

t with

cas

es a

nd il

lust

rate

an

expl

anat

ion

of th

e ef

fect

s on

the

grap

h us

ing

tech

nolo

gy.

SE:

269–

280,

691

–702

F-LE

Li

near

, Qua

drat

ic, a

nd E

xpon

entia

l Mod

els

Con

stru

ct a

nd c

ompa

re li

near

, qua

drat

ic, a

nd e

xpon

entia

l mod

els a

nd so

lve

prob

lem

s. F-

LE.A

.1

Dis

tingu

ish

betw

een

situ

atio

ns th

at c

an b

e m

odel

ed w

ith li

near

fu

nctio

ns a

nd w

ith e

xpon

entia

l fun

ctio

ns.

SE:

199–

210,

721

–734

, 735

–748

, 749

–762

F-LE

.A.1

a Pr

ove

that

line

ar fu

nctio

ns g

row

by

equa

l diff

eren

ces o

ver

equa

l int

erva

ls, a

nd th

at e

xpon

entia

l fun

ctio

ns g

row

by

equa

l fa

ctor

s ove

r equ

al in

terv

als.

SE:

199–

210,

749

–762

F-LE

.A.1

b R

ecog

nize

situ

atio

ns in

whi

ch o

ne q

uant

ity c

hang

es a

t a

cons

tant

rate

per

uni

t int

erva

l rel

ativ

e to

ano

ther

.

SE:

199–

210,

695

–708

F-LE

.A.1

c R

ecog

nize

situ

atio

ns in

whi

ch a

qua

ntity

gro

ws o

r dec

ays b

y a

cons

tant

per

cent

rate

per

uni

t int

erva

l rel

ativ

e to

ano

ther

.

SE:

721–

734,

735

–748

, 749

–762

F-LE

.A.2

C

onst

ruct

line

ar a

nd e

xpon

entia

l fun

ctio

ns, i

nclu

ding

ar

ithm

etic

and

geo

met

ric se

quen

ces,

give

n a

grap

h, a

de

scrip

tion

of a

rela

tions

hip,

or t

wo

inpu

t-out

put p

airs

(in

clud

e re

adin

g th

ese

from

a ta

ble)

.

SE:

155–

164,

165

–174

, 175

–186

, 199

–210

, 637

–648

, 649

–66

2, 6

63–6

76, 7

09–7

20, 7

21–7

34

F-LE

.A.3

O

bser

ve u

sing

gra

phs a

nd ta

bles

that

a q

uant

ity in

crea

sing

ex

pone

ntia

lly e

vent

ually

exc

eeds

a q

uant

ity in

crea

sing

lin

early

, qua

drat

ical

ly, o

r (m

ore

gene

rally

) as a

pol

ynom

ial

func

tion.

SE:

637–

648,

749

–762

Inte

rpre

t exp

ress

ions

for

func

tions

in te

rms o

f the

situ

atio

n th

ey m

odel

F-

LE.B

.5

Inte

rpre

t the

par

amet

ers i

n a

linea

r or e

xpon

entia

l fun

ctio

n in

te

rms o

f a c

onte

xt.

SE:

211–

220,

221

–232

, 269

–280

, 435

–450

, 451

–466

, 533

–54

6

Hou

ghto

n M

ifflin

Har

cour

t Int

egra

ted

Mat

h I ©

2015

cor

rela

ted

to th

e C

omm

on C

ore

Stat

e St

anda

rds f

or M

athe

mat

ics,

Mat

hem

atic

s I!

8

Stan

dard

s D

escr

ipto

r C

itatio

ns

G-C

O

Con

grue

nce

Expe

rim

ent w

ith tr

ansf

orm

atio

ns in

the

plan

e.

G-C

O.A

.1

Kno

w p

reci

se d

efin

ition

s of a

ngle

, circ

le, p

erpe

ndic

ular

line

, pa

ralle

l lin

e, a

nd li

ne se

gmen

t, ba

sed

on th

e un

defin

ed n

otio

ns

of p

oint

, lin

e, d

ista

nce

alon

g a

line,

and

dis

tanc

e ar

ound

a

circ

ular

arc

.

SE:

775–

788,

789

–800

, 833

–842

, 843

–856

G-C

O.A

.2

Rep

rese

nt tr

ansf

orm

atio

ns in

the

plan

e us

ing,

e.g

., tra

nspa

renc

ies a

nd g

eom

etry

softw

are;

des

crib

e tra

nsfo

rmat

ions

as f

unct

ions

that

take

poi

nts i

n th

e pl

ane

as

inpu

ts a

nd g

ive

othe

r poi

nts a

s out

puts

. Com

pare

tra

nsfo

rmat

ions

that

pre

serv

e di

stan

ce a

nd a

ngle

to th

ose

that

do

not

(e.g

., tra

nsla

tion

vers

us h

oriz

onta

l stre

tch)

.

SE:

801–

814,

833

–842

, 843

–856

, 857

–870

, 885

–896

G-C

O.A

.3

Giv

en a

rect

angl

e, p

aral

lelo

gram

, tra

pezo

id, o

r reg

ular

po

lygo

n, d

escr

ibe

the

rota

tions

and

refle

ctio

ns th

at c

arry

it

onto

itse

lf.

SE:

871–

878

G-C

O.A

.4

Dev

elop

def

initi

ons o

f rot

atio

ns, r

efle

ctio

ns, a

nd tr

ansl

atio

ns

in te

rms o

f ang

les,

circ

les,

perp

endi

cula

r lin

es, p

aral

lel l

ines

, an

d lin

e se

gmen

ts.

SE:

833–

842,

843

–856

, 857

–870

G-C

O.A

.5

Giv

en a

geo

met

ric fi

gure

and

a ro

tatio

n, re

flect

ion,

or

trans

latio

n, d

raw

the

trans

form

ed fi

gure

usi

ng, e

.g.,

grap

h pa

per,

traci

ng p

aper

, or g

eom

etry

softw

are.

Spe

cify

a

sequ

ence

of t

rans

form

atio

ns th

at w

ill c

arry

a g

iven

figu

re o

nto

anot

her.

SE:

801–

814,

833

–842

, 843

–856

, 857

–870

, 885

–896

, 897

–90

8

Hou

ghto

n M

ifflin

Har

cour

t Int

egra

ted

Mat

h I ©

2015

cor

rela

ted

to th

e C

omm

on C

ore

Stat

e St

anda

rds f

or M

athe

mat

ics,

Mat

hem

atic

s I!

9 !

Stan

dard

s D

escr

ipto

r C

itatio

ns

Und

erst

and

cong

ruen

ce in

term

s of r

igid

mot

ions

. G

-CO

.B.6

U

se g

eom

etric

des

crip

tions

of r

igid

mot

ions

to tr

ansf

orm

fig

ures

and

to p

redi

ct th

e ef

fect

of a

giv

en ri

gid

mot

ion

on a

gi

ven

figur

e; g

iven

two

figur

es, u

se th

e de

finiti

on o

f co

ngru

ence

in te

rms o

f rig

id m

otio

ns to

dec

ide

if th

ey a

re

cong

ruen

t.

SE:

833–

842,

843

–856

, 857

–870

, 885

–896

, 897

–908

G-C

O.B

.7

Use

the

defin

ition

of c

ongr

uenc

e in

term

s of r

igid

mot

ions

to

show

that

two

trian

gles

are

con

grue

nt if

and

onl

y if

corr

espo

ndin

g pa

irs o

f sid

es a

nd c

orre

spon

ding

pai

rs o

f ang

les

are

cong

ruen

t.

SE:

909–

920,

989

–100

0, 1

001–

1014

, 101

5–10

24, 1

025–

1036

G-C

O.B

.8

Expl

ain

how

the

crite

ria fo

r tria

ngle

con

grue

nce

(ASA

, SA

S,

and

SSS)

follo

w fr

om th

e de

finiti

on o

f con

grue

nce

in te

rms o

f rig

id m

otio

ns.

SE:

1001

–101

4, 1

015–

1024

, 102

5–10

36

Prov

e ge

omet

ric

theo

rem

s. G

-CO

.C.9

Pr

ove

theo

rem

s abo

ut li

nes a

nd a

ngle

s.

SE:

815–

826,

933

–944

, 945

–954

, 955

–964

, 965

–974

, 11

41–1

150

G-C

O.C

.10

Prov

e th

eore

ms a

bout

tria

ngle

s.

SE

: 10

01–1

014,

101

5–10

24, 1

025–

1036

, 108

3–10

96,

1097

–111

0, 1

111–

1122

, 112

9–11

40, 1

141–

1150

, 11

51–1

164,

116

5–11

74, 1

203–

1216

, 129

1–13

06

G

-CO

.C.1

1 Pr

ove

theo

rem

s abo

ut p

aral

lelo

gram

s.

SE:

1189

–120

2, 1

203–

1216

, 121

7–12

28, 1

229–

1240

, 13

07–1

318

Mak

e ge

omet

ric

cons

truc

tions

. G

-CO

.C.1

2 M

ake

form

al g

eom

etric

con

stru

ctio

ns w

ith a

var

iety

of t

ools

an

d m

etho

ds (c

ompa

ss a

nd st

raig

hted

ge, s

tring

, ref

lect

ive

devi

ces,

pape

r fol

ding

, dyn

amic

geo

met

ric so

ftwar

e, e

tc.).

SE:

775–

788,

789

–800

, 843

–856

, 955

–964

, 965

–974

, 10

43–1

052,

111

1–11

22, 1

129–

1140

, 114

1–11

50,

1151

–116

4, 1

165–

1174

G-C

O.C

.13

Con

stru

ct a

n eq

uila

tera

l tria

ngle

, a sq

uare

, and

a re

gula

r he

xago

n in

scrib

ed in

a c

ircle

.

SE:

1043

–105

2

Hou

ghto

n M

ifflin

Har

cour

t Int

egra

ted

Mat

h I ©

2015

cor

rela

ted

to th

e C

omm

on C

ore

Stat

e St

anda

rds f

or M

athe

mat

ics,

Mat

hem

atic

s I!

10 !

Stan

dard

s D

escr

ipto

r C

itatio

ns

G-G

PE

Expr

essin

g G

eom

etri

c Pr

oper

ties w

ith E

quat

ions

U

se c

oord

inat

es to

pro

ve si

mpl

e ge

omet

ric

theo

rem

s alg

ebra

ical

ly

G-G

PE.B

.4

Use

coo

rdin

ates

to p

rove

sim

ple

geom

etric

theo

rem

s al

gebr

aica

lly

SE:

775–

778,

112

9–11

40, 1

151–

1164

, 116

5–11

74, 1

265–

1278

, 127

9–12

90, 1

291–

1306

, 130

7–13

18

G-G

PE.B

.5

Prov

e th

e sl

ope

crite

ria fo

r par

alle

l and

per

pend

icul

ar li

nes

and

use

them

to so

lve

geom

etric

pro

blem

s (e.

g., f

ind

the

equa

tion

of a

line

par

alle

l or p

erpe

ndic

ular

to a

giv

en li

ne th

at

pass

es th

roug

h a

give

n po

int).

SE:

975–

982,

112

9–11

40, 1

151–

1164

, 116

5–11

74, 1

265–

1278

, 127

9–12

90, 1

291–

1306

, 130

7–13

18

G-G

PE.B

.7

Use

coo

rdin

ates

to c

ompu

te p

erim

eter

s of p

olyg

ons a

nd a

reas

of

tria

ngle

s and

rect

angl

es, e

.g.,

usin

g th

e di

stan

ce fo

rmul

a.

SE:

1291

–130

6, 1

319–

1334

S-ID

In

terp

retin

g C

ateg

oric

al a

nd Q

uant

itativ

e D

ata

Sum

mar

ize,

rep

rese

nt, a

nd in

terp

ret d

ata

on a

sing

le c

ount

or

mea

sure

men

t var

iabl

e. S-

ID.A

.1

Rep

rese

nt d

ata

with

plo

ts o

n th

e re

al n

umbe

r lin

e (d

ot p

lots

, hi

stog

ram

s, an

d bo

x pl

ots)

.

SE:

389–

400,

401

–416

, 417

–428

S-ID

.A.2

U

se st

atis

tics a

ppro

pria

te to

the

shap

e of

the

data

dis

tribu

tion

to c

ompa

re c

ente

r (m

edia

n, m

ean)

and

spre

ad (i

nter

quar

tile

rang

e, st

anda

rd d

evia

tion)

of t

wo

or m

ore

diff

eren

t dat

a se

ts.

SE:

377–

388,

389

–400

, 401

–416

, 417

–428

S-ID

.A.3

In

terp

ret d

iffer

ence

s in

shap

e, c

ente

r, an

d sp

read

in th

e co

ntex

t of

the

data

sets

, acc

ount

ing

for p

ossi

ble

effe

cts o

f ext

rem

e da

ta p

oint

s (ou

tlier

s).

SE:

389–

400

Hou

ghto

n M

ifflin

Har

cour

t Int

egra

ted

Mat

h I ©

2015

cor

rela

ted

to th

e C

omm

on C

ore

Stat

e St

anda

rds f

or M

athe

mat

ics,

Mat

hem

atic

s I!

11 !

Stan

dard

s D

escr

ipto

r C

itatio

ns

Sum

mar

ize,

rep

rese

nt, a

nd in

terp

ret d

ata

on tw

o ca

tego

rica

l and

qua

ntita

tive

vari

able

s. S-

ID.B

.5

Sum

mar

ize

cate

goric

al d

ata

for t

wo

cate

gorie

s in

two-

way

fr

eque

ncy

tabl

es. I

nter

pret

rela

tive

freq

uenc

ies i

n th

e co

ntex

t of

the

data

(inc

ludi

ng jo

int,

mar

gina

l, an

d co

nditi

onal

rela

tive

freq

uenc

ies)

. Rec

ogni

ze p

ossi

ble

asso

ciat

ions

and

tren

ds in

th

e da

ta.

SE:

347–

358,

359

–370

S-ID

.B.6

R

epre

sent

dat

a on

two

quan

titat

ive

varia

bles

on

a sc

atte

r plo

t, an

d de

scrib

e ho

w th

e va

riabl

es a

re re

late

d.

SE:

435–

450,

451

–466

, 735

–748

S-ID

.B.6

a Fi

t a fu

nctio

n to

the

data

; use

func

tions

fitte

d to

dat

a to

solv

e pr

oble

ms i

n th

e co

ntex

t of t

he d

ata.

Use

giv

en fu

nctio

ns o

r ch

oose

a fu

nctio

n su

gges

ted

by th

e co

ntex

t. Em

phas

ize

linea

r, qu

adra

tic, a

nd e

xpon

entia

l mod

els.

SE:

435–

450,

735

–748

S-ID

.B.6

b In

form

ally

ass

ess t

he fi

t of a

func

tion

by p

lotti

ng a

nd

anal

yzin

g re

sidu

als.

SE:

451–

466,

735

–748

S-ID

.B.6

c Fi

t a li

near

func

tion

for a

scat

ter p

lot t

hat s

ugge

sts a

line

ar

asso

ciat

ion.

SE:

435–

450,

451

–466

Inte

rpre

t lin

ear

mod

els.

S-ID

.C.7

In

terp

ret t

he sl

ope

(rat

e of

cha

nge)

and

the

inte

rcep

t (co

nsta

nt

term

) of a

line

ar m

odel

in th

e co

ntex

t of t

he d

ata.

SE:

301–

308,

435

–450

S-ID

.C.8

C

ompu

te (u

sing

tech

nolo

gy) a

nd in

terp

ret t

he c

orre

latio

n co

effic

ient

of a

line

ar fi

t.

SE:

451–

466

S-ID

.C.9

D

istin

guis

h be

twee

n co

rrel

atio

n an

d ca

usat

ion.

SE:

435–

450

!

el monte union high school district

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