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What Core Curriculum Should School Districts be Using?

NYS Mathematics CoreCurriculum(Revised March 2005)PDF/ Microsoft Word / HTML

Mathematics Resource Guide with CoreCurriculum(1999)

The PreK-8 portion of thiscore iseffective September 2005.

The Commencement-level portion of thiscoreremains in effect until the October NYS Board ofRegents meeting. Please visit this site the weekof October 10, 2005.

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New York State Learning Standard for Mathematics Page 2Revised by NYS Board of Regents March 15, 2005

Acknowledgment

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Sherri Blais

Teacher of Mathematics

Monticello School District

Carlos X. Leal

Elementary Math Lead Teacher

Rochester School District

Judith Blood

Elementary Teacher

Ithaca School District

Jennifer Lorio

Elementary Teacher

Yonkers School District

James Boswell

Alternative Education Teacher

Capital Region BOCES

Gwen McKinnon

Middle School Principal

Syracuse School DistrictWilliam Brosnan

Superintendent of Schools

Northport-East Northport School District

Theresa McSweeney


Marcellus School District

Jacqueline Bull

Coordinator of Mathematics, K-8Clarence School District

Brenda Myers

Deputy SuperintendentBroome-Tioga BOCES

Melba Campbell

Teacher of MathematicsSamuel Gompers High School (NYC)

Miguelina Ortiz

Elementary TeacherBaldwin School District

William Caroscio

Teacher of MathematicsElmira School District

Alfred Posamentier

Dean, School of Education, City CollegeProfessor of Mathematics

Vincent Cullen

Certified Public Accountant

Long Island

Roderick Sherman


Plattsburgh School District

Andrew Giordano

Construction Engineer

Albany

Susan Solomonik

Math coach/Teacher

IS 119 (NYC)

Carolyn Goldberg

Professor of MathematicsNiagara County Community College

Debra Sykes

Director of MathematicsBuffalo School District

Robert GylesProfessor of Mathematics EducationCUNY Hunter (NYC)

Thomas TuckerProfessor of MathematicsColgate University, Hamilton

Daniel Jaye

Assistant Principal/Math TeacherStuyvesant High School (NYC)

Stephen West

Professor of MathematicsSUNY Geneseo

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Introduction

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Proposed Mathematics Standard, Content Strands, Process Strands, Bands within the Content

Strands, and Grade-By-Grade Performance Indicators

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The Five Content Strands

Number Sense and Operations Strand

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Algebra Strand

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Geometry Strand

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Measurement Strand

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Statistics and Probability Strand

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The Five Process Strands

Problem Solving Strand

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Reasoning and Proof Strand

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Communication Strand

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Connections Strand

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Representation Strand

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Bands Within the Content Strands

Number Sense and Operations

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Algebra

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Students will build new mathematical knowledge through problem solving.

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Students will solve problems that arise in mathematics and in other contexts.

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Students will apply and adapt a variety of appropriate strategies to solve problems.

5KQ50Q? B*& (2S,-'#/ ),.2$(27 *$-#$&7(&* $, S(23 *,/.$(,2*

5KQ50Qf A^M&-(&2)& $)%&-83(-&)$&3 ].&*$(,2(27 M-,)&** $, .23&-*$#23M-,T/&'*

5KQ50Qg +,'M#-& #23 3(*).** (3* S,- *,/=(27 # M-,T/&' P($% $)%&-#23O,- *$.3&2$* $, e.*$(SR $%&(- $%(26(27

5KQ50Qc B*& '#2(M./#$(=&* &Q7QV $(/&*V T/,)6*a $, ',3&/ $%& #)$(,2 (2M-,T/&'*

5KQ50Qh B*& 3-#P(27*OM()$.-&* $, ',3&/ $%& #)$(,2 (2 M-,T/&'*

Students will monitor and reflect on the process of mathematical problem solving.

5KQ50Q:> A^M/#(2 $, ,$%&-* %,P # M-,T/&' P#* *,/=&3V 7(=(27 *$-#$&7(&*

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Students willrecognize reasoning and proof as fundamental aspects of mathematics.

5KQ

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5KQ+CQ: a

5KQCQ; +,.2$ ,.$ `M-,3.)&a # ),//&)$(,2 ,S # *M&)(S(&3 *(\& : $, :>

5KQCQ4 E&-T#//R ),.2$ TR :X* $, :>

5KQCQ_ A^M/,-& $%& 3(SS&-&2$ -&M-&*&2$#$(,2* ,S # 7-,.M ,S ,Te&)$*

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5KQCQ? L-#P M()$.-&* ,- ,$%&- (2S,-'#/ *R'T,/* $, -&M-&*&2$ # *M,6&22.'T&- .M $, ?

5KQCQf L-#P M()$.-&* ,- ,$%&- (2S,-'#/ *R'T,/* $, -&M-&*&2$ %,P '#2R(2 # ),//&)$(,2 .M $, ?

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Students will collect, organize, display, and analyze data.

Organization and 5KQ0Q: 0,-$ #23 ,-7#2(\& ,Te&)$* TR ,2& #$$-(T.$& `&Q7QV ),/,-V *(\&V ,-Display ofData *%#M&a

5KQ0Q; B*& M%R*()#/ ,Te&)$* $, '#6& 7-#M%*

Analysis of Data 5KQ0Q4 +,.2$ #23 ),'M#-& 7-,.M* S,-'&3 `].#2$(SR 7-,.M* S,-'&3a

5KQ0Q_ L&*)-(T& $%& #$$-(T.$&* ,S ,Te&)$*



KQ50Q: A^M/,-&V &^#'(2&V #23 '#6& ,T*&-=#$(,2* #T,.$ # *,)(#/ M-,T/&',- '#$%&'#$()#/ *($.#$(,2

KQ50Q; D2$&-M-&$ (2S,-'#$(,2 ),--&)$/RV (3&2$(SR $%& M-,T/&'V #237&2&-#$& M,**(T/& *,/.$(,2*


KQ50Q4 I)$ ,.$ ,- ',3&/ P($% '#2(M./#$(=&* #)$(=($(&* (2=,/=(27'#$%&'#$()#/ ),2$&2$ S-,' /($&-#$.-& #23O,- *$,-R $&//(27

KQ50Q_ H,-'./#$& M-,T/&'* #23 *,/.$(,2* S-,' &=&-R3#R *($.#$(,2*`&Q7QV ),.2$(27 $%& 2.'T&- ,S )%(/3-&2 (2 $%& )/#**V .*(27 $%&)#/&23#- $, $)% ),.2$(27aQ


KQ50Q? B*& (2S,-'#/ ),.2$(27 *$-#$&7(&* $, S(23 *,/.$(,2*

KQ50Qf A^M&-(&2)& $)%&-83(-&)$&3 ].&*$(,2(27 M-,)&** $, .23&-*$#23

Kindergarten

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M-,T/&'*

KQ50Qg +,'M#-& #23 3(*).** (3* S,- *,/=(27 # M-,T/&' P($% $)%&-#23O,- *$.3&2$* $, e.*$(SR $%&(- $%(26(27

KQ50Qc B*& '#2(M./#$(=&* `&Q7QV $(/&*V T/,)6*a $, ',3&/ $%& #)$(,2 (2M-,T/&'*

KQ50Qh B*& 3-#P(27*OM()$.-&* $, ',3&/ $%& #)$(,2 (2 M-,T/&'*


KQ50Q:> A^M/#(2 $, ,$%&-* %,P # M-,T/&' P#* *,/=&3V 7(=(27 *$-#$&7(&*



KQ

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Students will analyze and evaluate the mathematical thinking and strategies of others.

KQ+"Q4 W(*$&2 $, *,/.$(,2* *%#-&3 TR ,$%&- *$.3&2$*

KQ+"Q_ H,-'./#$& '#$%&'#$()#//R -&/&=#2$ ].&*$(,2* P($% $)%&-7.(3#2)&

Students will use the language of mathematics to express mathematical ideas precisely.

KQ+"Q? B*& #MM-,M-(#$& '#$%&'#$()#/ $&-'*V =,)#T./#-RV #23 /#27.#7&

Connections Strand

Students will recognize and apply mathematics in contexts outside of mathematics.

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=#/.& .*(27 S(27&-* ,2 R,.- %#23)


Students will understand numbers, multiple ways of representing numbers, relationships

among numbers, and number systems.

Number Systems KQCQ: +,.2$ $%& ($&'* (2 # ),//&)$(,2 #23 62,P $%& /#*$ ),.2$(27 P,-3$&//* %,P '#2R ($&'* #-& (2 $%& ),//&)$(,2 `: $, :>a

KQCQ; +,.2$ ,.$ `M-,3.)&a # ),//&)$(,2 ,S # *M&)(S(&3 *(\& : $, :>

KQCQ4 C.'&-()#//R /#T&/ # 3#$# *&$ ,S : $, ?

KQCQ_ E&-T#//R ),.2$ TR :X* $, ;>

KQCQ? E&-T#//R ),.2$ T#)6P#-3* S-,' :>

KQCQf

KQCQg L-#P M()$.-&* ,- ,$%&- (2S,-'#/ *R'T,/* $, -&M-&*&2$ # *M,6&22.'T&- .M $, :>

KQCQc L-#P M()$.-&* ,- ,$%&- (2S,-'#/ *R'T,/* $, -&M-&*&2$ %,P '#2R (2# ),//&)$(,2 .M $, :>

KQCQh J-($& 2.'T&-* :8:> $, -&M-&*&2$ # ),//&)$(,2

KQCQ:> E(*.#//R 3&$&-'(2& %,P '#2R ',-& ,- /&**V #23 $%&2 .*(27 $%&=&-T#/ ),.2$(27 *&].&2)&V '#$)% #23 ),.2$ :8:>

KQCQ:: B*& #23 .23&-*$#23 =&-T#/ ,-3(2#/ $&-'*V S(-*$ $, $&2$%

Students will understand meanings of operations and procedures, and how they relate to one

another.

Operations KQCQ:; 0,/=& #23 )-$& #33($(,2 #23 *.T$-#)$(,2 =&-T#/ P,-3 M-,T/&'*`.*& ),.2$(278T#*&3 *$-#$&7(&*V *.)% #* ),.2$(27 ,2 #23 $, $&2a

KQCQ:4 L&$&-'(2& *.'* #23 3(SS&-&2)&* TR =#-(,.* '*

Algebra Strand

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Students will recognize, use, and represent algebraically patterns, relations, and functions.

Patterns, Relations, KQIQ: B*& # =#-(&$R ,S '#2(M./#$(=&* $, )-$& M#$$&-2* .*(27 #$$-(T.$&* ,Sand Functions ),/,-V *(\&V ,- *%#M&

KQIQ;

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KQ"Q4 V P%&-& ,2&Display of Data M()$.-& -&M-&*&2$* :

KQ0Q4 0,-$ #23 ,-7#2(\& ,Te&)$* TR $P, #$$-(T.$&* &Q7QV ),/,-V *(\&V ,-*%#M&a

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:Q50Q_ H,-'./#$& M-,T/&'* #23 *,/.$(,2* S-,' &=&-R3#R *($.#$(,2*`&Q7QV ),.2$(27 $%& 2.'T&- ,S )%(/3-&2 (2 $%& )/#** ,- .*(27 $%&)#/&23#- $, $)% ),.2$(27a


:Q50Q? B*& (2S,-'#/ ),.2$(27 *$-#$&7(&* $, S(23 *,/.$(,2*

:Q50Qf A^M&-(&2)& $)%&-83(-&)$&3 ].&*$(,2(27 M-,)&** $, .23&-*$#23M-,T/&'*

:Q50Qg +,'M#-& #23 3(*).** (3* S,- *,/=(27 # M-,T/&' P($% $)%&-#23O,- *$.3&2$* $, e.*$(SR $%&(- $%(26(27

:Q50Qc B*& '#2(M./#$(=&* &Q7QV $(/&*V T/,)6*a $, ',3&/ $%& #)$(,2 (2M-,T/&'*

:Q50Qh B*& 3-#P(27*OM()$.-&* $, ',3&/ $%& #)$(,2 (2 M-,T/&'*


:Q50Q:> A^M/#(2 $, ,$%&-* %,P # M-,T/&' P#* *,/=&3V 7(=(27 *$-#$&7(&*#23 e.*$(S()#$(,2*



:Q

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:Q

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produce a coherent whole.

:Q+CQ_ B23&-*$#23 %,P ',3&/* ,S *($.#$(,2* (2=,/=(27 ,Te&)$*V M()$.-&*V#23 *R'T,/* -&/#$& $, '#$%&'#$()#/ (3*

:Q+CQ? B23&-*$#23 '(27* ,S ,M&-#$(,2* #23 %,P $%&R -&/#$& $, ,2,$%&-

:Q+CQf B23&-*$#23 %,P '#$%&'#$()#/ ',3&/* -&M-&*&2$ ].#2$($#$(=&-&/#$(,2*%(M*


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`&Q7QV ),.2$ #23 -&M-&*&2$ *%#-(27 ),,6(&* T&$P&&2 S-(&23*a

:Q>a

:QCQ; +,.2$ ,.$ `M-,3.)&a # ),//&)$(,2 ,S # *M&)(S(&3 *(\& `:> $, :>>($&'*aV .*(27 7-,.M* ,S $&2

:QCQ4 i.()6/R *&& #23 /#T&/ P($% # 2.'T&-V ),//&)$(,2* ,S : $, :>

:QCQ_ +,.2$ TR :X* $, :>>

:QCQ? 06(M ),.2$ TR :>X* $, :>>

:QCQf 06(M ),.2$ TR ?X* $, ?>

:QCQg 06(M ),.2$ TR ;X* $, ;>

:QCQc E&-T#//R ),.2$ S-,' # 2.'T&- ,$%&- $%#2 ,2& TR :X*

:QCQh +,.2$ T#)6P#-3* S-,' ;> TR :X*

:QCQ:> L-#P M()$.-&* ,- ,$%&- (2S,-'#/ *R'T,/* $, -&M-&*&2$ # *M,6&22.'T&- .M $, ;>

:QCQ::D3&2$(SR $%#$ *M#)(27 ,S $%& *#'& 2.'T&- ,S ,Te&)$* 3,&* 2,$ #SS&)$$%& ].#2$($R `),2*&-=#$(,2a

:QCQ:; I--#27& ,Te&)$* (2 *(\& ,-3&- `(2)-*(27 #23 3&)-*(27a

:QCQ:4 J-($& 2.'T&-* $, :>>

:QCQ:_

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:QCQ:f +,'M#-& #23 ,-3&- P%,/& 2.'T&-* .M $, :>>

:QCQ:g L&=&/,M #2 (2($(#/ .23&-*$#23(27 ,S $%& T#*& $&2 *R*$&'N:> ,2&* j : $&2:> $&2* j : %.23-&3

:QCQ:c B*& # =#-(&$R ,S *$-#$&7(&* $, ),'M,*& #23 3&),'M,*& ,2&83(7($2.'T&-*

:QCQ:h B23&-*$#23 $%& ),''.$#$(=& M-,M&-$R ,S #33($(,2

:QCQ;> C#'& $%& 2.'T&- T&S,-& #23 $%& 2.'T&- #S$&- # 7(=&2 2.'T&-V #232#'& $%& 2.'T&-`*a T&$P&&2 $P, 7(=&2 2.'T&-* .M $, :>> `P($%#23 P($%,.$ $%& .*& ,S # 2.'T&- /(2& ,- # %.23-&3* )%#-$a

:QCQ;: B*& T&S,-&V #S$&-V ,- T&$P&&2 $, ,-3&- 2.'T&-* $, :>> `P($% ,-P($%,.$ $%& .*& ,S # 2.'T&- /(2&a

:QCQ;; B*& $%& P,-3* %(7%&-V /,P&-V 7-$&-V #23 /&** $, ),'M#-& $P,2.'T&-*

:QCQ;4 B*& #23 .23&-*$#23 =&-T#/ ,-3(2#/ $&-'*V S(-*$ $, $P&2$(&$%


another.

Operations :QCQ;_ L&=&/,M #23 .*& *$-#$&7(&* $, *,/=& #33($(,2 #23 *.T$-#)$(,2 P,-3M-,T/&'*

:QCQ;? A*$('#$& $%& 2.'T&- (2 # ),//&)$(,2 $, ?> #23 $%&2 ),'M#-& TR),.2$(27 $%& #)$.#/ ($&'* (2 $%& ),//&)$(,2

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Algebra Strand


Patterns, Relations, :QIQ: L&$&-'(2& #23 3(*).** M#$$&-2* (2 #-($%'&$() P%#$ ),'&* 2&^$ (2 #and Functions -&M$(27 M#$$&-2V .*(27 2.'T&-* ,- ,Te&)$*a

Geometry Strand

Students will use visualization and spatial reasoning to analyze characteristics and properties

of geometric shapes.

Shapes :Q9Q: "#$)% *%#M&* #23 M#-$* ,S *%#M&* $, e.*$(SR ),27-.&2)R

:Q9Q;

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Students will use units to give meaning to measurements.

Units :Q"Q_ K2,P =,)#T./#-R #23 -&),72(\& ),(2* `M&22RV 2()6&/V 3('&V].#-$&-a

:Q"Q?

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Students will make predictions that are based upon data analysis.

Predictions from :Q0Qc L(*).** ),2)/.*(,2* #23 '#6& M-&3()$(,2* (2 $&-'* ,S $%& P,-3*Data /(6&/R #23 .2/(6&/R

:Q0Qh +,2*$-.)$ # ].&*$(,2 $%#$ )#2 T& #2*P&-&3 TR .*(27 (2S,-'#$(,2S-,' # 7-#M%



;Q50Q: A^M/,-&V &^#'(2&V #23 '#6& ,T*&-=#$(,2* #T,.$ # *,)(#/ M-,T/&',- '#$%&'#$()#/ *($.#$(,2

;Q50Q; D2$&-M-&$ (2S,-'#$(,2 ),--&)$/RV (3&2$(SR $%& M-,T/&'V #237&2&-#$& M,**(T/& *,/.$(,2*


;Q50Q4 I)$ ,.$ ,- ',3&/ P($% '#2(M./#$(=&* #)$(=($(&* (2=,/=(27'#$%&'#$()#/ ),2$&2$ S-,' /($&-#$.-& #23O,- *$,-R $&//(27

;Q50Q_ H,-'./#$& M-,T/&'* #23 *,/.$(,2* S-,' &=&-R3#R *($.#$(,2*`&Q7QV ),.2$(27 $%& 2.'T&- ,S )%(/3-&2 (2 $%& )/#**V .*(27 $%&)#/&23#- $, $)% ),.2$(27aQ


;Q50Q? B*& (2S,-'#/ ),.2$(27 *$-#$&7(&* $, S(23 *,/.$(,2*

;Q50Qf A^M&-(&2)& $)%&-83(-&)$&3 ].&*$(,2(27 M-,)&** $, .23&-*$#23M-,T/&'*

;Q50Qg +,'M#-& #23 3(*).** (3* S,- *,/=(27 # M-,T/&' P($% $)%&-#23O,- *$.3&2$* $, e.*$(SR $%&(- $%(26(27

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;Q50Qc B*& '#2(M./#$(=&* &Q7QV $(/&*V T/,)6*a $, ',3&/ $%& #)$(,2 (2M-,T/&'*

;Q50Qh B*& 3-#P(27*OM()$.-&* $, ',3&/ $%& #)$(,2 (2 M-,T/&'*


;Q50Q:> A^M/#(2 $, ,$%&-* %,P # M-,T/&' P#* *,/=&3V 7(=(27 *$-#$&7(&*#23 e.*$(S()#$(,2*



;Q

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;Q+"Q; E&-T#//R *.MM,-$ $%&(- -*,2(27 #23 #2*P&-

Students will communicate their mathematical thinking coherently and clearly to peers,

teachers, and others.

;Q+"Q4 0%#-& '#$%&'#$()#/ (3* $%-,.7% $%& '#2(M./#$(,2 ,S ,Te&)$*V3-#P(27*V M()$.-&*V )%#-$*V #23 *R'T,/* (2 T,$% P-($$&2 #23 =&-T#/&^M/#2#$(,2*


;Q+"Q_ W(*$&2 $, *,/.$(,2* *%#-&3 TR ,$%&- *$.3&2$*

;Q+"Q? H,-'./#$& '#$%&'#$()#//R -&/&=#2$ ].&*$(,2*


;Q+"Qf B*& #MM-,M-(#$& '#$%&'#$()#/ $&-'*V =,)#T./#-RV #23 /#27.#7&

Connections Strand

Students will recognize and use connections among mathematical ideas.

;Q+CQ:

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;Q+CQg

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Number Systems ;QCQ: 06(M ),.2$ $, :>> TR ;X*V ?X*V :>X*

;QCQ; +,.2$ T#)6 S-,' :>> TR :X*V ?X*V :>X* .*(27 # 2.'T&- )%#-$

;QCQ4 06(M ),.2$ TR 4X* $, 4f S,- './$(M/()#$(,2 -(2&**

;QCQ_ 06(M ),.2$ TR _X* $, _c S,- './$(M/()#$(,2 -(2&**

;QCQ? +,'M#-& #23 ,-3&- 2.'T&-* $, :>>

;QCQf L&=&/,M #2 .23&-*$#23(27 ,S $%& T#*& $&2 *R*$&'N:> ,2&* j : $&2:> $&2* j : %.23-&3:> %.23-&3* j : $%,.*#23

;QCQg B*& # =#-(&$R ,S *$-#$&7(&* $, ),'M,*& #23 3&),'M,*& $P,83(7($2.'T&-*

;QCQc B23&-*$#23 #23 .*& $%& ),''.$#$(=& M-,M&-$R ,S #33($(,2

;QCQh C#'& $%& 2.'T&- T&S,-& #23 $%& 2.'T&- #S$&- # 7(=&2 2.'T&-V #232#'& $%& 2.'T&-`*a T&$P&&2 $P, 7(=&2 2.'T&-* .M $, :>> `P($%#23 P($%,.$ $%& .*& ,S # 2.'T&- /(2& ,- # %.23-&3* )%#-$a

;CQ:> B*& #23 .23&-*$#23 =&-T#/ ,-3(2#/ $&-'*

;QCQ::

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;QCQ:g L&',2*$-#$& S/.&2)R #23 #MM/R #33($(,2 #23 *.T$-#)$(,2 S#)$* .M $,#23 (2)/.3(27 :c

;QCQ:c B*& 3,.T/(27 $, #33 ;83(7($ 2.'T&-*

;QCQ:h B*& ),'M&2*#$(,2 $, #33 ;83(7($ 2.'T&-*

;QCQ;> L&=&/,M -(2&** S,- './$(M/()#$(,2 TR.*(27 -&M$&3 #33($(,2

;QCQ;: L&=&/,M -(2&** S,- 3(=(*(,2 TR .*(27 -&M$&3 *.T$-#)$(,2V3(=(3(27 ,Te&)$* (2$, 7-,.M* `S#(- *%#-&a

Students will compute accurately and make reasonable estimates.

Estimation ;QCQ;; A*$('#$& $%& 2.'T&- (2 # ),//&)$(,2 $, :>> #23 $%&2 ),'M#-& TR),.2$(27 $%& #)$.#/ ($&'* (2 $%& ),//&)$(,2

Algebra Strand

Students will perform algebraic procedures accurately.

Equations and ;QIQ: B*& $%& *R'T,/* lV mV j `P($% #23 P($%,.$ $%& .*& ,S # 2.'T&-Inequalities /(2&a $, ),'M#-& P%,/& 2.'T&-* .M $, :>>


Patterns, Relations, ;QIQ; L&*)-(T& #23 &^$&23 (2)-*(27 ,- 3&)-*(27 `nV8a *&].&2)&* #23and Functions M#$$&-2* `2.'T&-* ,- ,Te&)$* .M $, :>>a

Geometry Strand



Shapes ;Q9Q: A^M&-('&2$ P($% */(3&*V S/(M*V #23 $.-2* $, ),'M#-& $P,83('&2*(,2#/ *%#M&*

;Q9Q; D3&2$(SR #23 #MM-,M-(#$&/R 2#'& $P,83('&2*(,2#/ *%#M&*N )(-)/&V*].#-&V -&)$#27/&V #23 $-(#27/& `T,$% -&7./#- #23 (--&7./#-a

;Q9Q4 +,'M,*& `M.$ $,7&$%&-a #23 3&),'M,*& `T- #M#-$a $P,83('&2*(,2#/ *%#M&*

Students will identify and justify geometric relationships, formally and informally.

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Geometric ;Q9Q_ 9-,.M ,Te&)$* TR /(6& M-,M&-$(&*Relationships

Students will apply transformations and symmetry to analyze problem solving situations.

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;Q9Qf A^M/,-& /(2& *R''&$-R

Measurement Strand

Students will determine what can be measured and how, using appropriate methods and

formulas.

Units of ;Q"Q: B*& 2,28*$#23#-3 #23 *$#23#-3 .2($* $, '*.-& T,$% =&-$()#/ #23Measurement %,-(\,2$#/ /&27$%*

;Q"Q; B*& # -./&- $, '*.-& *$#23#-3 .2($* `(2)/.3(27 P%,/& (2)%&* #23P%,/& S&&$a

;Q"Q4 +,'M#-& #23 ,-3&- ,Te&)$* #)),-3(27 $, $%& #$$-(T.$& ,S /&27$%

;Q"Q_

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Collection of Data ;Q0Q: H,-'./#$& ].&*$(,2* #T,.$ $%&'*&/=&* #23 $%&(- *.--,.23(27*

;Q0Q; +,//&)$ #23 -&),-3 3#$# `.*(27 $#//(&*a -&/#$&3 $, $%& ].&*$(,2

Organization and ;Q0Q4 L(*M/#R 3#$# (2 M()$,7-#M%* #23 T#- 7-#M%* .*(27 ),2)-&$& ,Te&)$*Display of Data ,- # -&M-&*&2$#$(,2 ,S $%& ,Te&)$

Analysis of Data ;Q0Q_ +,'M#-& #23 (2$&-M-&$ 3#$# (2 $&-'* ,S 3&*)-(T(27 ].#2$($R`*('(/#-($R ,- 3(SS&-&2)&*a


Predictions from ;Q0Q? L(*).** ),2)/.*(,2* #23 '#6& M-&3()$(,2* S-,' 7-#M%*Data



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4Q50Q; B23&-*$#23 $%#$ *,'& P#R* ,S -&M-&*&2$(27 # M-,T/&' #-& ',-&%&/MS./ $%#2 ,$%&-*

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4Q50Q_ I)$ ,.$ ,- ',3&/ P($% '#2(M./#$(=&* #)$(=($(&* (2=,/=(27'#$%&'#$()#/ ),2$&2$ S-,' /($&-#$.-&

Grade 3

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4Q50Q;4 E&-(SR -&*./$* ,S # M-,T/&'

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4Q

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4Q+"Qg W(*$&2 S,- .23&-*$#23(27 ,S '#$%&'#$()#/ *,/.$(,2* *%#-&3 TR,$%&- *$.3&2$*

4Q+"Qc +,2*(3&- *$-#$&7(&* .*&3 #23 *,/.$(,2* S,.23 (2 -&/#$(,2 $, $%&(-,P2 P,-6


4Q+"Qh D2)-*& $%&(- .*& ,S '#$%&'#$()#/ =,)#T./#-R #23 /#27.#7&P%&2 ),''.2()#$(27 P($% ,$%&-*

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Connections Strand


4Q+CQ:

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Students will understand numbers, multiple ways of representing numbers, relationships

among numbers, and number systems.

Number Systems 4QCQ: 06(M ),.2$ TR ;?X*V ?>X*V :>>X* $, :V>>>

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4QCQ:4 B*& # =#-(&$R ,S *$-#$&7(&* $, *,/=& './$(M/()#$(,2 M-,T/&'* P($%S#)$,-* .M $, :; ^ :;

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M-,=(3& '(27 S,- './$(M/()#$(,2

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Estimation 4QCQ;? A*$('#$& 2.'T&-* .M $, ?>>

4QCQ;f

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Algebra Strand


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Geometry Strand



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Measurement Strand


formulas.

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Students will develop strategies for estimating measurements.

Estimation 4Q"Qh 1&// $('& $, $%& '(2.$&V .*(27 3(7($#/ #23 #2#/,7 )/,)6*

4Q"Q:> 0&/&)$ #23 .*& *$#23#-3 `).*$,'#-Ra #23 2,28*$#23#-3 .2($* $,&*$('#$& '*.-&'&2$*



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4Q0Qf 0$#$& $%& -&/#$(,2*%(M* T&$P&&2 M()$,7-#M%* #23 T#- 7-#M%*

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Analysis of Data 4Q0Qg

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_Q50Q:> B*& M-,)&** ,S &/('(2#$(,2 $, *,/=& M-,T/&'*

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_Q50Q;_

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Students will make and investigate mathematical conjectures.

_Q

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_Q+"Qg

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Representation Strand

Students will create and use representations to organize, record, and communicate

mathematical ideas.

_Q

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_QCQ; V>>>

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Estimation _QCQ;f

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Geometry Strand



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*%#M&*Students will identify and justify geometric relationships, formally and informally.

Geometric _Q9Qf L-#P #23 (3&2$(SR (2$&-*&)$(27V M&-M&23()./#-V #23 M#-#//&/ /(2&*Relationships

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Measurement Strand

Students will determine what can be measured and how, using appropriate methods andformulas.

Units of _Q"Q: 0&/&)$ $,,/* #23 .2($* `).*$,'#-R #23 '&$-()a #MM-,M-(#$& S,- $%&Measurement /&27$% T&(27 '*.-&3

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_Q"Q4 K2,P #23 .23&-*$#23 &].(=#/&2$ *$#23#-3 .2($* ,S /&27$%N

:; (2)%&* j : S,,$4 S&&$ j : R#-3

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_Q"Q? "*.-& '#**V .*(27 7-#'*

_Q"Qf 0&/&)$ $,,/* #23 .2($* #MM-,M-(#$& $, $%& )#M#)($R T&(27 '*.-&3`'(//(/($&-* #23 /($&-*a

_Q"Qg "*.-& )#M#)($RV .*(27 '(//(/($&-* #23 /($&-*Students will use units to give meaning to measurements.

Units _Q"Qc "#6& )%#27&V .*(27 ),'T(2&3 ),(2* #23 3,//#- #',.2$*

_Q"Qh +#/)./#$& &/#M*&3 $('& (2 %,.-* #23 %#/S %,.-*V 2,$ )-,**(27IQ"QO5Q"Q

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Organization and _Q0Q4

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Display of Data

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M-,T/&'

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?Q

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?Q+"Qg

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?Q+CQf

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?QCQ_ +-$& &].(=#/&2$ S-#)$(,2*V 7(=&2 # S-#)$(,2

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cup, etc.

?QCQf B23&-*$#23 $%& ),2)&M$ ,S -#$(,

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?QCQc +,'M#-& 3&)('#/* .*(27 lV mV ,- j

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Number Theory ?QCQ:;

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'./$(M/& ,S $P, 2.'T&-*

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another.

Operations ?QCQ:f B*& # =#-(&$R ,S *$-#$&7(&* $, './$(M/R $%-&&83(7($ TR $%-&&83(7($2.'T&-* Note: Multiplication by anything greater than a three-digit multiplier/ multiplicand should be done using technology.

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$, ('M-,M&- S-#)$(,2*

?QCQ;: B*& # =#-(&$R ,S *$-#$&7(&* $, #33 #23 *.T$-#)$ S-#)$(,2* P($% /(6&3&2,'(2#$,-*

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Estimation ?QCQ;_

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Algebra Strand

Students will represent and analyze algebraically a wide variety of problem solving situations.

Variables and ?QIQ: L&S(2& #23 .*& #MM-,M-(#$& $&-'(2,/,7R P%&2 -&S&--(27 $,Expressions ),2*$#2$*V =#-(#T/&*V #23 #/7&T-#() &^M-&**(,2*

?QIQ; 1-#2*/#$& *('M/& =&-T#/ &^M-&**(,2* (2$, #/7&T-#() &^M-&**(,2*


Variables and ?QIQ4 0.T*$($.$& #**(72&3 =#/.&* (2$, =#-(#T/& &^M-&**(,2* #23 &=#/.#$&Expressions .*(27 ,-3&- ,S ,M&-#$(,2*

Equations and ?QIQ_ 0,/=& *('M/& ,2&8*$&M &].#$(,2* .*(27 T#*() P%,/&82.'T&- S#)$*Inequalities

?QIQ? 0,/=& #23 &^M/#(2 *('M/& ,2&8*$&M &].#$(,2* .*(27 (2=&-*&,M&-#$(,2* (2=,/=(27 P%,/& 2.'T&-*

?QIQf A=#/.#$& $%& M&-('&$&- S,-'./# S,- 7(=&2 (2M.$ =#/.&*


Patterns,Relations, ?QIQg +-$& #23 &^M/#(2 M#$$&-2* #23 #/7&T-#() -&/#$(,2*%(M*

and Functions `&Q7QV;V_VfVcQQQa #/7&T-#()#//RN ;2 `3,.T/(27a

?QIQc +-$& #/7&T-#() ,- 7&,'&$-() M#$$&-2* .*(27 ),2)-&$& ,Te&)$* ,-=(*.#/ 3-#P(27* `&Q7QV -,$#$& #23 *%#3& 7&,'&$-() *%#M&*a

Geometry Strand



Shapes ?Q9Q: +#/)./#$& $%& M&-('&$&- ,S -&7./#- #23 (--&7./#- M,/R7,2*


Geometric ?Q9Q; D3&2$(SR M#(-* ,S *('(/#- $-(#27/&*Relationships

?Q9Q4 D3&2$(SR $%& -#$(, ,S ),--&*M,23(27 *(3&* ,S *('(/#- $-(#27/&*

?Q9Q_ +/#**(SR ].#3-(/#$&-#/* TR M-,M&-$(&* ,S $%&(- #27/&* #23 *(3&*

?Q9Q? K2,P $%#$ $%& *.' ,S $%& (2$&-(,- #27/&* ,S # ].#3-(/#$&-#/ (*

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4f> 3&7-&&*

?Q9Qf +/#**(SR $-(#27/&* TR M-,M&-$(&* ,S $%&(- #27/&* #23 *(3&*

?Q9Qg K2,P $%#$ $%& *.' ,S $%& (2$&-(,- #27/&* ,S # $-(#27/& (*:c> 3&7-&&*

?Q9Qc H(23 # '(**(27 #27/& P%&2 7(=&2 $P, #27/&* ,S # $-(#27/&

?Q9Qh D3&2$(SR M#(-* ,S ),27-.&2$ $-(#27/&*

?Q9Q:> D3&2$(SR ),--&*M,23(27 M#-$* ,S ),27-.&2$ $-(#27/&*


Transformational ?Q9Q:: D3&2$(SR #23 3-#P /(2&* ,S *R''&$-R ,S T#*() 7&,'&$-() *%#M&*Geometry

Students will apply coordinate geometry to analyze problem solving situations.

Coordinate ?Q9Q:; D3&2$(SR #23 M/,$ M,(2$* (2 $%& S(-*$ ].#3-#2$Geometry

?Q9Q:4 5/,$ M,(2$* $, S,-' T#*() 7&,'&$-() *%#M&* `(3&2$(SR #23 )/#**(SRa

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Measurement Strand


formulas.

Units of ?Q"Q: B*& # -./&- $, '*.-& $, $%& 2-&*$ (2)%V V

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Measurement ?Q"Q; D3&2$(SR ).*$,'#-R &].(=#/&2$ .2($* ,S /&27$%

?Q"Q4 "*.-& $, $%& 2-&*$ )&2$('&$&-

?Q"Q_ D3&2$(SR &].(=#/&2$ '&$-() .2($* ,S /&27$%

?Q"Q? +,2=&-$ '*.-&'&2$ P($%(2 # 7(=&2 *R*$&'

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Tools and Methods ?Q"Qf L&$&-'(2& $%& $,,/ #23 $&)%2(].& $, '*.-& P($% #2 #MM-,M-(#$&/&=&/ ,S M-&)(*(,2N /&27$%* #23 #27/&*

Students will use units to give meaning to measurements.

Units ?Q"Qg +#/)./#$& &/#M*&3 $('& (2 %,.-* #23 '(2.$&*

?Q"Qc "*.-& #23 3-#P #27/&* .*(27 # M-,$-#)$,-


Estimation ?Q"Qh L&$&-'(2& M&-*,2#/ -&S&-&2)&* S,- ).*$,'#-R .2($* ,S /&27$%`&Q7QV R,.- M#)& (* #MM-,^('#$&/R 4 S&&$V R,.- %&(7%$ (*#MM-,^('#$&/R ? S&&$V &$)Qa

?Q"Q:> L&$&-'(2& M&-*,2#/ -&S&-&2)&* S,- '&$-() .2($* ,S /&27$%

?Q"Q:: Y.*$(SR $%& -*,2#T/&2&** ,S &*$('#$&*



Collection of Data ?Q0Q: +,//&)$ #23 -&),-3 3#$# S-,' # =#-(&$R ,S *,.-)&* `&Q7QV 2&P*M#M&-*V'#7#\(2&*V M,//*V )%#-$*V #23 *.-=&R*a

Organization and ?Q0Q; L(*M/#R 3#$# (2 # /(2& 7-#M% $, *%,P #2 (2)-*& ,- 3&)-*& ,=&-Display of Data $('&

Analysis of Data ?Q0Q4 +#/)./#$& $%& ' S,- # 7(=&2 *&$ ,S 3#$# #23 .*& $, 3&*)-(T& # *&$,S 3#$#


Predictions from ?Q0Q_ H,-'./#$& ),2)/.*(,2* #23 '#6& M-&3()$(,2* S-,' 7-#M%*Data

Students will understand and apply concepts of probability.

Probability ?Q0Q? W(*$ $%& M,**(T/& ,.$),'&* S,- # *(27/&8&=&2$ &^M&-('&2$

?Q0Qf

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fQ50Q: K2,P $%& 3(SS&-&2)& T&$P&&2 -&/&=#2$ #23 (--&/&=#2$ (2S,-'#$(,2P%&2 *,/=(27 M-,T/&'*

fQ50Q; B23&-*$#23 $%#$ *,'& P#R* ,S -&M-&*&2$(27 # M-,T/&' #-& ',-&&SS()(&2$ $%#2 ,$%&-*

fQ50Q4 D2$&-M-&$ (2S,-'#$(,2 ),--&)$/RV (3&2$(SR $%& M-,T/&'V #23 7&2&-#$&M,**(T/& *$-#$&7(&* #23 *,/.$(,2*


fQ50Q_ I)$ ,.$ ,- ',3&/ P($% '#2(M./#$(=&* #)$(=($(&* (2=,/=(27'#$%&'#$()#/ ),2$&2$ S-,' /($&-#$.-&

fQ50Q? H,-'./#$& M-,T/&'* #23 *,/.$(,2* S-,' &=&-R3#R *($.#$(,2*

fQ50Qf 1-#2*/#$& S-,' # M()$.-&O3(#7-#' $, # 2.'&-() &^M-&**(,2

fQ50Qg

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fQ50Q:4 ",3&/ M-,T/&'* P($% M()$.-&*O3(#7-#'* ,- M%R*()#/ ,Te&)$*

fQ50Q:_ I2#/R\& M-,T/&'* TR ,T*&-=(27 M#$$&-2*

fQ50Q:? "#6& ,-7#2(\&3 /(*$* ,- )%#-$* $, *,/=& 2.'&-()#/ M-,T/&'*


fQ50Q:f L(*).** P($% M&&-* $, .23&-*$#23 # M-,T/&' *($.#$(,2

fQ50Q:g L&$&-'(2& P%#$ (2S,-'#$(,2 (* 2&&3&3 $, *,/=& M-,T/&'

fQ50Q:c L&$&-'(2& $%& &SS()(&2)R ,S 3(SS&-&2$ -&M-&*&2$#$(,2* ,S #

M-,T/&'

fQ50Q:h L(SS&-&2$(#$& T&$P&&2 =#/(3 #23 (2=#/(3 #MM-,#)%&*

fQ50Q;> B23&-*$#23 =#/(3 ),.2$&-&^#'M/&*

fQ50Q;: A^M/#(2 $%& '&$%,3* #23 -*,2(27 T&%(23 $%& M-,T/&' *,/=(27*$-#$&7(&* .*&3

fQ50Q;; L(*).** P%&$%&- # *,/.$(,2 (* -*,2#T/& (2 $%& ),2$&^$ ,S $%&,-(7(2#/ M-,T/&'

fQ50Q;4 E&-(SR -&*./$* ,S # M-,T/&'



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Students will develop and evaluate mathematical arguments and proofs.

fQ

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fQ+"Qc +,2*(3&- *$-#$&7(&* .*&3 #23 *,/.$(,2* S,.23 TR ,$%&-* (2 -&/#$(,2$, $%&(- ,P2 P,-6


fQ+"Qh D2)-*& $%&(- .*& ,S '#$%&'#$()#/ =,)#T./#-R #23 /#27.#7&P%&2 ),''.2()#$(27 P($% ,$%&-*

fQ+"Q:> B*& #MM-,M-(#$& =,)#T./#-R P%&2 3&*)-(T(27 ,Te&)$*V-&/#$(,2*%(M*V '#$%&'#$()#/ *,/.$(,2*V #23 -#$(,2#/&

fQ+"Q:: L&),3& #23 ),'M-&%&23 '#$%&'#$()#/ =(*.#/* #23 *R'T,/* $,),2*$-.)$ '(27

Connections Strand


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fQ+CQ; A^M/,-& #23 &^M/#(2 $%& -&/#$(,2*%(M T&$P&&2 '#$%&'#$()#/ (3*

fQ+CQ4 +,22&)$ #23 #MM/R '#$%&'#$()#/ (2S,-'#$(,2 $, *,/=& M-,T/&'*

Students will understand how mathematical ideas interconnect and build on one another to

produce a coherent whole.

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fQ+CQ? ",3&/ *($.#$(,2* P($% ,Te&)$* #23 -&M-&*&2$#$(,2* #23 T& #T/& $,3-#P ),2)/.*(,2*


fQ+CQf

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fQ+CQh

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Number Systems fQCQ:

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fQCQ:h D3&2$(SR $%& './$(M/()#$(=& (2=&-*& `-&)(M-,)#/a ,S # 2.'T&-

fQCQ;> t$, :>>ta

fQCQ;g Y.*$(SR $%& -*,2#T/&2&** ,S #2*P&-* .*(27 &*$('#$(,2 `(2)/.3(27-,.23(27a

Algebra Strand


Variables and fQIQ: 1-#2*/#$& $P,8*$&M =&-T#/ &^M-&**(,2* (2$, #/7&T-#() &^M-&**(,2*Expressions


Variables and fQIQ; B*& *.T*$($.$(,2 $, &=#/.#$& #/7&T-#() &^M-&**(,2* `'#R (2)/.3&Expressions &^M,2&2$*,S ,2&V $P, #23 $%-&&a

Equations and fQIQ4 1-#2*/#$& $P,8*$&M =&-T#/ *&2$&2)&* (2$, #/7&T-#() &].#$(,2*Inequalities

fQIQ_ 0,/=& #23 &^M/#(2 $P,8*$&M &].#$(,2* (2=,/=(27 P%,/& 2.'T&-*.*(27 (2=&-*& ,M&-#$(,2*

fQIQ? 0,/=& *('M/& M-,M,-$(,2* P($%(2 ),2$&^$

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fQIQf A=#/.#$& S,-'./#* S,- 7(=&2 (2M.$ =#/.&* `)(-).'S&-&2)&V #-V=,/.'&V 3(*$#2)&V $&'M&-#$.-&V (2$&-&*$V &$)Qa

Geometry Strand



Shapes fQ9Q: +#/)./#$& $%& /&27$% ,S ),--&*M,23(27 *(3&* ,S *('(/#- $-(#27/&*V.*(27 M-,M,-$(,2#/ -*,2(27

fQ9Q; L&$&-'(2& $%& #- ,S $-(#27/&* #23 ].#3-(/#$&-#/* `*].#-&*V-&)$#27/&*V -%,'T(V #23 $-#M&\,(3*a #23 3&=&/,M S,-'./#*

fQ9Q4 B*& # =#-(&$R ,S *$-#$&7(&* $, S(23 $%& #- ,S -&7./#- #23 (--&7./#-M,/R7,2*

fQ9Q_ L&$&-'(2& $%& =,/.'& ,S -&)$#27./#- M-(*'* TR ),.2$(27 ).T&* #233&=&/,M $%& S,-'./#

fQ9Q? D3&2$(SR -#3(.*V 3(#'&$&-V )%,-3* #23 )&2$-#/ #27/&* ,S # )(-)/&

fQ9Qf B23&-*$#23 $%& -&/#$(,2*%(M T&$P&&2 $%& 3(#'&$&- #23 -#3(.* ,S #)(-)/&

fQ9Qg L&$&-'(2& $%& #- #23 )(-).'S&-&2)& ,S # )(-)/&V .*(27 $%MM-,M-(#$& S,-'./#

fQ9Qc +#/)./#$& $%& #- ,S # *&)$,- ,S # )(-)/&V 7(=&2 $%& '*.-& ,S #)&2$-#/ #27/& #23 $%& -#3(.* ,S $%& )(-)/&

fQ9Qh B23&-*$#23 $%& -&/#$(,2*%(M T&$P&&2 $%& )(-).'S&-&2)& #23 $%&3(#'&$&- ,S # )(-)/&


Coordinate fQ9Q:> D3&2$(SR #23 M/,$ M,(2$* (2 #// S,.- ].#3-#2$*Geometry

fQ9Q:: +#/)./#$& $%& #- ,S T#*() M,/R7,2* 3-#P2 ,2 # ),,-3(2#$& M/#2&`-&)$#27/&* #23 *%#M&* ),'M,*&3 ,S -&)$#27/&* %#=(27 *(3&* P($%(2$&7&- /&27$%*a

Measurement Strand

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formulas.

Units of fQ"Q: "*.-& )#M#)($R #23 )#/)./#$& =,/.'& ,S # -&)$#27./#- M-(*'Measurement

fQ"Q; D3&2$(SR ).*$,'#-R .2($* ,S )#M#)($R `).M*V M(2$*V ].#-$*V #237#//,2*a

fQ"Q4 D3&2$(SR &].(=#/&2$ ).*$,'#-R .2($* ,S )#M#)($R ).M* $, M(2$*V M(2$*$, ].#-$*V #23 ].#-$* $, 7#//,2*a

fQ"Q_ D3&2$(SR '&$-() .2($* ,S )#M#)($R `/($&- #23 '(//(/($&-a

fQ"Q? D3&2$(SR &].(=#/&2$ '&$-() .2($* ,S )#M#)($R '(//(/($&- $, /($&- #23

/($&- $, '(//(/($&-a

Tools and Methods fQ"Qf L&$&-'(2& $%& $,,/ #23 $&)%2(].& $, '*.-& P($% #2 #MM-,M-(#$&/&=&/ ,S M-&)(*(,2N )#M#)($R


Estimation fQ"Qg A*$('#$& =,/.'&V #-V #23 )(-).'S&-&2)& `*&& S(7.-&* (3&2$(S(&3 (27&,'&$-R *$-#23a

fQ"Qc Y.*$(SR $%& -*,2#T/&2&** ,S &*$('#$&*

fQ"Qh L&$&-'(2& M&-*,2#/ -&S&-&2)&* S,- )#M#)($R



Collection of Data fQ0Q: L&=&/,M $%& ),2)&M$ ,S *#'M/(27 P%&2 ),//&)$(27 3#$# S-,' #M,M./#$(,2 #23 3&)(3& $%& T&*$ '&$%,3 $, ),//&)$ 3#$# S,- # M#-$()./#-].&*$(,2

Organization and fQ0Q;

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fQ0Qf L&$&-'(2& $%& -#27& S,- # 7(=&2 *&$ ,S 3#$#

fQ0Qg L&$&-'(2& $%& M-,T#T(/($R ,S 3&M&23&2$ &=&2$*

fQ0Q:: L&$&-'(2& $%& 2.'T&- ,S M,**(T/& ,.$),'&* S,- # ),'M,.23 &=&2$TR .*(27 $%& S.23#'&2$#/ ),.2$(27 M-(2)(M/& #23 .*& $%(* $,3&$&-'(2& $%& M-,T#T(/($(&* ,S &=&2$* P%&2 $%& ,.$),'&* %#=&&].#/ M-,T#T(/($R



7.50Q: B*& # =#-(&$R ,S *$-#$&7(&* $, .23&-*$#23 2&P'#$%&'#$()#/ ),2$&2$ #23 $, 3&=&/,M ',-& &SS()(&2$ '&$%,3*

gQ50Q; +,2*$-.)$ #MM-,M-(#$& &^$&2*(,2* $, M-,T/&' *($.#$(,2*

gQ50Q4 B23&-*$#23 #23 3&',2*$-#$& %,P P-($$&2 *R'T,/*-&M-&*&2$ '#$%&'#$()#/ (3*


gQ50Q_ GT*&-=& M#$$&-2* #23 S,-'./#$& 7&2&-#/(\#$(,2*

gQ50Q? "#6& ),2e&)$.-&* S-,' 7&2&-#/(\#$(,2*

gQ50Qf

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gQ50Qg B23&-*$#23 $%#$ $%&-& (* 2, ,2& -(7%$ P#R $, *,/=&'#$%&'#$()#/ M-,T/&'* T.$ $%#$ 3(SS&-&2$ '&$%,3* %#==#2$#7&* #23 3(*#3=#2$#7&*

gQ50Qc B23&-*$#23 %,P $, T- # ),'M/&^ M-,T/&' (2$, *('M/&-M#-$* ,- .*& # *('(/#- M-,T/&' $RM& $, *,/=& # M-,T/&'

gQ50Qh J,-6 T#)6P#-3* S-,' # *,/.$(,2

gQ50Q:> B*& M-,M,-$(,2#/($R $, ',3&/ M-,T/&'*

gQ50Q:: J,-6 (2 ),//#T,-#$(,2 P($% ,$%&-* $, *,/=& M-,T/&'*


gQ50Q:; D2$&-M-&$ *,/.$(,2* P($%(2 $%& 7(=&2 ),2*$-#(2$* ,S #M-,T/&'

gQ50Q:4 0&$ &^M&)$#$(,2* #23 /('($* S,- M,**(T/& *,/.$(,2*

gQ50Q:_ L&$&-'(2& (2S,-'#$(,2 -&].(-&3 $, *,/=& $%& M-,T/&'

gQ50Q:? +%,,*& '&$%,3* S,- ,T$#(2(27 -&].(-&3 (2S,-'#$(,2

gQ50Q:f Y.*$(SR *,/.$(,2 '&$%,3* $%-,.7% /,7()#/ #-7.'&2$

gQ50Q:g A=#/.#$& $%& &SS()(&2)R ,S 3(SS&-&2$ -&M-&*&2$#$(,2* ,S #M-,T/&'



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(--&/&=#2$ (2S,-'#$(,2 $, -)% # ),2)/.*(,2 ,- '#6MM-,M-(#$& &*$('#$&*

Students will develop and evaluate mathematical arguments and proofs.

gQ

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gQ+"Qf I2#/R\& '#$%&'#$()#/ *,/.$(,2* *%#-&3 TR ,$%&-*

gQ+"Qg +,'M#-& *$-#$&7(&* .*&3 #23 *,/.$(,2* S,.23 TR ,$%&-* (2 -&/#$(,2$, $%&(- ,P2 P,-6

gQ+"Qc H,-'./#$& '#$%&'#$()#/ ].&*$(,2* $%#$ &/()($V &^$&23V ,- )%#//&27&*$-#$&7(&*V *,/.$(,2*V #23O,- ),2e&)$.-&* ,S ,$%&-*


gQ+"Qh D2)-*& $%&(- .*& ,S '#$%&'#$()#/ =,)#T./#-R #23 /#27.#7& P%&2),''.2()#$(27 P($% ,$%&-*

gQ+"Q:> B*& #MM-,M-(#$& /#27.#7&V -&M-&*&2$#$(,2*V #23 $&-'(2,/,7R

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Connections Strand


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gQ+CQ;

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gQ+CQf

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gQ

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Operations gQCQ:: 0('M/(SR &^M-&**(,2* .*(27 ,-3&- ,S ,M&-#$(,2* Note: Expressionsmay include absolute value and/or integral exponents greater than0.

gQCQ:; I33V *.T$-#)$V './$(M/RV #23 3(=(3& (2$&7&-*

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gQCQ:?

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Equations and gQIQ_ 0,/=& './$(8*$&M &].#$(,2* TR ),'T(2(27 /(6& $&-'*V .*(27 $%&Inequalities 3(*$-(T.$(=& M-,M&-$RV ,- ',=(27 =#-(#T/&* $, ,2& *(3& ,S $%&

&].#$(,2

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gQIQf A=#/.#$& S,-'./#* S,- 7(=&2 (2M.$ =#/.&* `*.-S#)& #-V -#$&V #233&2*($R M-,T/&'*a


Patterns, Relations, gQIQg L-#P $%& 7-#M%() -&M-&*&2$#$(,2 ,S # M#$$&-2 S-,' #2 &].#$(,2and Functions ,- S-,' # $#T/& ,S 3#$#

gQIQc +-$& #/7&T-#() M#$$&-2* .*(27 )%#-$*O$#T/&*V 7-#M%*V &].#$(,2*V#23 &^M-&**(,2*

gQIQh U.(/3 # M#$$&-2 $, 3&=&/,M # -./& S,- 3&$&-'(2(27 $%& *.' ,S $%&(2$&-(,- #27/&* ,S M,/R7,2*

gQIQ:> J-($& #2 &].#$(,2 $, -&M-&*&2$ # S.2)$(,2 S-,' # $#T/& ,S =#/.&*

Geometry Strand



Shapes gQ9Q: +#/)./#$& $%& -#3(.* ,- 3(#'&$&-V 7(=&2 $%& )(-).'S&-&2)& ,- #- ,S# )(-)/&

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Measurement Strand


formulas.

Units of gQ"Q: +#/)./#$& 3(*$#2)& .*(27 # '#M *)#/&Measurement

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Communication StrandStudents will organize and consolidate their mathematical thinking through communication.

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Connections Strand


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Algebra Strand


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cQIQh L(=(3& # M,/R2,'(#/ TR # ',2,'(#/ `(2$&7&- ),&SS()(&2$*a Note:The degree of the denominator is less than or equal to the degree

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Geometry Strand



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Constructions cQ9Q> +,2*$-.)$ $%& S,//,P(27V .*(27 # *$-#(7%$ &37& #23 ),'M#**N0&7'&2$ ),27-.&2$ $, # *&7'&2$I27/& ),27-.&2$ $, #2 #27/&5&-M&23()./#- T(*&)$,-I27/& T(*&)$,-


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cQ9Q:_L&$&-'(2& $%& R8(2$&-)&M$ ,S # /(2& S-,' # 7-#M% #23 T& #T/& $,&^M/#(2 $%& R8(2$&-)&M$

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$%&-&S,-& ('M,-$#2$ $%#$ # )/- #23 ),'',2 3&S(2($(,2 ,S $%&*& $&-'* T& .23&-*$,,3Q 1%& ,-3&-,S $%&*& $&-'* -&S/&)$* 3(SS&-&2$ *$#7&* ,S $%& -*,2(27 M-,)&**Q

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Argument8 0$.3&2$* P(// ),''.2()#$&V (2 =&-T#/ ,- P-($$&2 S,-'V $%& -*,2(27 M-,)&** $%#$/* $, # ),2)/.*(,2Q I =#/(3 #-7.'&2$ (* $%& &23 -&*./$ ,S $%& ),2e&)$.-&O-*,2(27 M-,)&**Q

Justify/Explain8 0$.3&2$* P(// M-,=(3& #2 #-7.'&2$ S,- # '#$%&'#$()#/ ),2e&)$.-&Q D$ '#R T& #2(2$.($(=& #-7.'&2$ ,- # *&$ ,S &^#'M/&* $%#$ *.MM,-$ $%& ),2e&)$.-&Q 1%& #-7.'&2$ '#R (2)/.3&VT.$ (* 2,$ /('($&3 $,V # P-($$&2 M#-#7-#M%V '*.-&'&2$ .*(27 #MM-,M-(#$& $,,/*V $%& .*& ,S3R2#'() *,S$P#-&V ,- # P-($$&2 M-,,SQ

Proof8 0$.3&2$* P(// M-&*&2$ # =#/(3 #-7.'&2$V &^M-&**&3 (2 P-($$&2 S,-'V e.*$(S(&3 TR #^(,'*V3&S(2($(,2*V #23 $%&,-&'*Q

Apply8 0$.3&2$* P(// .*& # $%&,-&' ,- ),2)&M$ $, *,/=& #2 #/7&T-#() ,- 2.'&-()#/ M-,T/&'Q


Students willbuild new mathematical knowledge through problem solving.

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