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This resource provides facilitator notes and timelines for use by professional developers as they help teachers move from being standards-referenced to standards-based. It also includes an extensive array of copy-ready graphic organizers and templates for teacher use in designing and implementing standards-based lessons in their classrooms. Elementary, middle, and high school exemplars of the templates are provided. These tools are perfect for collaborative use in team and department meetings.
Citation preview
S T A N D A R D S - B A S E D C L A S S R O O M
Operator’s Manual
SBE Design Team Centennial BOCES
830 South Lincoln Street • Longmont, CO 80501 Phone 303.772.4420 • Fax 303.776.0504
Standards-Based Classroom Operator’s ManualPublished by Just ASK Publications & Professional Development2214 King StreetAlexandria, Virginia 22301VOICE 703-535-5434FAX 703-535-8502email: [email protected]
Copyright 2002Just ASK Publications & Professional Development and Centennial BOCESAll Rights ReservedPrinted in the United States of AmericaISBN-10: 0-9777796-6-1ISBN-10: 978-0-9777796-6-6
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Table of Contents
INTRODUCTION i
SECTION I. STANDARDSDirections for Standard/Benchmark Analysis 1
Standard/Benchmark Analysis (P1) 4
Example(s) 5
Directions for Assessment & Instruction Pre-Planner 9
Integrating Instruction and Assessment 12
Assessment & Instruction Pre-Planner (P2) 13
Examples(s) 15
SECTION II. ASSESSMENTDirections for Assessment Task(s) Selector 23
Types of Assessment 26
End Products for Performance Assessments 27
Assessment Task(s) Selector (P3) 28
Example(s) 29
Directions for Assessment Scoring Guide Template 33
Phrases for Rubric Design 37
Levels “Cheat Sheet” 38
Assessment Scoring Guide Template (P4) 39
Example(s) 40
Directions for Assessment Accomodations Planner 45
Ensuring That All Means All 47
Requirements for Demonstrating Fair
“Opportunities to Learn” in a High-Stakes System 48
Assessment Accomodations Planner (P5) 49
Example(s) 50
Directions for Assessment Critique Sheet 55
Assessment Quality Rubric 57
Assessment Critique Sheet (P6) 58
Example(s) 59
Directions for Parallel Self and Teacher Evaluation 63
Parallel Self and Teacher Evaluation (P7) 65
Example(s) 66
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SECTION III. CURRICULUMDirections for Curriculum/Course Matrix 71
Curriculum/Course Matrix (P8) 74
Example(s) 75
Directions for Curriculum/Course Map 79
Curriculum/Course Map Rubric 82
Curriculum/Course Map (P9) 83
Example(s) 84
SECTION IV. INSTRUCTIONDirections for Unit Organizer Map 89
Unit Organizer Map Rubric 91
Unit Organizer Map (P10) 92
Example(s) 93
Directions for Critical Questions Unit Organizer 97
Formulating Critical Questions 99
Critical Questions Unit Organizer (P11) 100
Example(s) 101
Directions for Daily Planner for Unit 105
Daily Planner for Unit (P12) 107
Example(s) 109
Directions for Student’s Unit Study Planner 119
Student’s Unit Study Planner (P13) 121
Example(s) 122
SECTION V. EVALUATIONDirections for Group Assessment Results 129
Group Assessment Results (P14) 131
Example(s) 132
Directions for Cause/Effect Analysis and Revision 135
Cause/Effect Analysis and Revision (P15) 137
Example(s) 138
GLOSSARY 142
APPENDICESAppendix A, Colorado Model Content Standards 145
Appendix B, Instruction Verbs for Six Levels of Thinking 150
Appendix C, Differentiating Between Content & Skills 151
Appendix D, Priortizing Content Knowledge 152
Appendix E, Kinds of Achievement Targets 153
Appendix F, Conversions with Critical Friends 154
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INTRODUCTION
Background
Colorado Department of Education staff,school district employees, and communitymembers throughout Colorado begandeveloping content standards in response to abill passed by the Colorado Legislature in 1993.
In 1996 the Centennial BOCES created theStandards-Based Education (SBE) Design Teamto assist educators in envisioning andimplementing standards-based classrooms. Thefollowing energetic and ambitious Coloradoeducators contributed significantly to thedevelopment and refinement of this manual: • Sheila Arredondo• Dennis Bake• Pam Beemer• Dave Benson• Gloria Corbi• Karen Crawford• Pete Denzin• Lois Easton• Judy Gilbert• Linda Gleckler• Dianne Harper• Melanie Isenhour• Bobbi Johnson• Robert Johnson• Nancy Kellogg• Kathy Moore• Amy Nicholl• Linda Schwartz• Jan Silverstein• Mary Smith• Susan Sparks• BJ Stone• Karen Trusler• Debbie Welch
Drive Train Metaphor
This Standards-Based Classroom Operator’s Manual iskeyed to a drive train metaphor of arecommended sequence of eight steps to beused in a standards-based process of designing,delivering, and evaluating instruction. Everyplanner and guide contains a miniature drivetrain indicating to which of the eight steps itrelates:
Each time a teacher sets out to develop astandards-based lesson or unit, thinking must bedriven by the content standards themselves andthe school-level benchmarks detailing themeaning of each standard.
STEP 1 in the standards-driven process is,therefore, a comprehensive analysis of eachrelevant standard and benchmark.
Write ContentStandard
DesignAssessment
Task
EstablishPerformance
Levels DesignCurriculum
PlanInstructionStrategies
ImplementInstructionAssess
Students
Evaluate& RefineWhole
Process
1
2 3
4
5
67
8
Standards-Driven Process
Standards-Based Classroom Operator’s Manual Copyright © 2002, Just ASK Publications & Professional Developmentand Centennial BOCES. All rights reserved. No reproduction without written permission from the publisher. To orderplease call 1-800-940-5434 or visit www.justaskpublications.com
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Consequently, all workshop participantsneed copies of their school or district’sstandards and benchmarks while workingthrough this manual.
STEP 2, the selection of an assessment task,follows the analysis of standards andbenchmarks. At this point the teacher asks,“What is the best way for students todemonstrate what they know and can do?”When selecting an appropriate assessment task itmay be useful to consider how adults use theknowledge and skills implied in the selectedstandard(s) and benchmark(s).
STEP 3 is the development of a scoring guidefor the assessment task. Two questions must beaddressed when designing scoring guidelines forevaluating student work: (1) What criteria shouldbe used to judge the performance? And, (2)how should the performance levels be describedand distinguished from one another? In mostColorado school districts four performancelevels are defined: unsatisfactory, partiallyproficient, proficient, and advanced.
STEP 4 is the design of a curriculum that willassist all students in performing successfully onthe assessment task. The teacher asks, “Whatcontent, unit, or curriculum will help studentsperform well on the assessment task?”
STEP 5 is planning the instructional strategiesthat will help all students learn the curriculum.Here the teacher asks, “What methods andstrategies will best facilitate student learning?”
STEP 6 is the actual delivery of instruction.
STEP 7 involves administering the assessmenttask to the students. Assessment is integral withor immediately follows instruction, and theassessment results data are used in
STEP 8 to evaluate and refine the entire eight-step process.
The Instructional Organizer Comparison guideon page iv further details the differencesbetween traditional lesson planning and theabove eight steps in the standards-basedapproach. Note the shift in focus from what theteacher does to what the student does.
A Map to Planners and Guides for theStandards-Driven Process follows on page v.This index connects each planner to one ormore steps in the standards-driven process. Areview and discussion of this introductoryinformation is beneficial prior to using any ofthe planners.
Use of the Planning ToolsWe suspect that each facilitator may find someplanners to be of value while having no use forothers. We encourage you to select and use theplanners that best meet the needs of yourworkshop’s participants. Page vi of theintroduction, “Figuring Out Which Planners toUse,” is designed to guide facilitators andparticipants to the planning tools that will meettheir needs best.
Knowing the creativity of teachers, we expectthat most will wish to use these planners only asmodels to stimulate thinking, soon designingtheir own forms to meet their unique needs.When modifying the planners, please makesure that all essential elements of theoriginal form are retained.
We recommend that, whenever possible, youcomplete these planning tools with yourcolleagues, since the synergy involved in such aprocess often results in a product of greaterquality than one developed by an individual. Wealso recommend that you share your completedplanners not only with your students and theirparents but with administrators, specialeducators, and other support staff so thateveryone involved in the learning process has a
Standards-Based Classroom Operator’s Manual Copyright © 2002, Just ASK Publications & Professional Developmentand Centennial BOCES. All rights reserved. No reproduction without written permission from the publisher. To orderplease call 1-800-940-5434 or visit www.justaskpublications.com
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clear understanding of your plan to facilitatestudent achievement of the content standards.
Furthermore, understanding and application ofthe planning tools tends to increase whenteachers spend one week during a summerinstitute reviewing and exploring the operator’smanual and then convene regularly throughoutthe academic year to complete and refine thevarious planners. Administrative support andpressure are often necessary to sustain theseongoing professional development experiences.In schools and districts where administratorsparticipate in SBE dialogues, an expectationexists that these tools will be used and discussed.
Organization of This ManualThis manual is divided into six sections:introduction, standards, assessment, curriculum,instruction, and evaluation. The introductioncontinues with a Planning Tools Rubric on pagevii. This rubric should be used by tool authorsand their colleagues to evaluate planning toolwork. Three criteria are assessed: the essentialcomponents of SBE, tool use, and the tooldevelopment process. Please use the five-pointscale and the following performance levels toscore your work: (1) not standards-based, (3) intransition, and (5) standards based.
The five sections following the introductioncorrespond to the major topics contained in thedrive train described previously. These divisionswere made to assist facilitators in quickly locatingplanning tools for specific workshops. Eachsection includes tool directions organized undereleven headings: purpose, overview, before youstart, possible applications, steps for facilitators,steps for participants, dialogue, estimated time,materials, resources, and tips. The directions areintended to serve as a guide for designing andfacilitating use of the respective planning tool.
Finally, each set of directions is followed by itsassociated planning tool as well as two examples.We hope you find this structure useful and theseplanners beneficial.
Good Luck!
Standards-Based Classroom Operator’s Manual Copyright © 2002, Just ASK Publications & Professional Developmentand Centennial BOCES. All rights reserved. No reproduction without written permission from the publisher. To orderplease call 1-800-940-5434 or visit www.justaskpublications.com
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S T A N D A R D S
Sta
nd
ard
/Be
nch
ma
rk A
na
lysi
s (P
1)
12
34 5
67
8St
anda
rd(s
)/Ben
chm
ark(
s):
Kno
wle
dge
– W
hat
mu
st s
tud
ents
kn
ow?
Wh
at s
hou
ld t
hey
rem
emb
er y
ears
fro
m n
ow?
Skill
s –
Wh
at m
ust
stu
den
ts b
e ab
le t
o d
o?
W
hat
sh
ould
th
ey b
e ab
le t
o d
o ye
ars
from
now
?R
elev
ance
– W
hy d
o st
ud
ents
nee
d t
his
kn
owle
dge
an
d
thes
e sk
ills
righ
t n
ow?
H
ow a
re k
now
led
ge a
nd
ski
lls u
sed
by
adu
lts?
Kno
w (n
ouns
):
Und
erst
and
(nou
ns):
Be
able
to (v
erbs
):
Stan
dard
Fou
r: S
tude
nts u
se g
eom
etric
con
cept
s, pr
oper
ties,
and
relat
ions
hips
in p
robl
em-s
olvi
ng si
tuat
ions
and
com
mun
icate
the
reas
onin
g us
ed in
solv
ing
thes
e pr
oblem
s.
Benc
hmar
k 4.
5: S
olve
pro
blem
s inv
olvi
ng p
erim
eter
and
are
a in
tw
o di
men
sions
, and
invo
lvin
g su
rfac
e ar
ea a
nd v
olum
e in
thre
e di
men
sions
.St
uden
ts in
grad
e 6 w
ill k
now
and
be a
ble to
:So
lve p
roble
ms in
volvi
ng p
erime
ter a
nd a
rea of
recta
ngles
, squ
ares,
and
irreg
ular s
hape
s (u
se of
grid
pape
r with
irreg
ular s
hape
s).
• B
asic
geom
etric
term
s and
con
cept
s suc
h as
pol
ygon
,
reg
ular
shap
e, irr
egul
ar sh
ape,
lengt
h, w
idth
, heig
ht,
a
rea,
perim
eter
……
• B
asic
stra
tegi
es fo
r pro
blem
solv
ing
• C
once
pts s
uch
as p
arall
el, c
ongr
uent
, and
righ
t ang
le
• Id
entif
y an
d dr
aw m
ulti-
sided
shap
es (h
exag
on, n
onag
on e
tc)
• U
se to
ols s
uch
as a
ruler
and
grid
pap
er w
ith a
n ac
cept
able
d
egre
e of
acc
urac
y•
Dev
elop
stra
tegi
es fo
r sol
ving
per
imet
er a
nd a
rea
• S
olve
(usin
g a
form
ula)
app
licat
ions
invo
lvin
g pe
rimet
er a
nd
a
rea
• C
omm
unica
te th
e re
ason
ing
used
in so
lvin
g th
e pr
oblem
.
Stud
ents
that
are
com
forta
ble
with
solv
ing
area
and
pe
rimet
er p
robl
ems a
re d
evelo
ping
som
e of
the
basic
sk
ills t
hey
may
use
in h
ighe
r mat
h su
ch a
s Alg
ebra
.
In th
e fu
ture
stud
ents
with
thes
e sk
ills w
ill b
e ab
le to
so
lve
a w
ide
varie
ty o
f pr
oblem
s suc
h as
:•
Pric
ing
carp
et fo
r the
ir ho
use
• F
indi
ng q
uant
ities
of
pain
t nee
ded
to p
aint w
alls
• S
olvi
ng p
robl
ems s
uch
as in
sect
icide
cro
p co
vera
ge•
Dec
idin
g ho
w la
rge
of a
poo
l to
inst
all in
the
back
y
ard
Standards-Based Classroom Operator’s Manual Copyright © 2002, Just ASK Publications & Professional Developmentand Centennial BOCES. All rights reserved. No reproduction without written permission from the publisher. To orderplease call 1-800-940-5434 or visit www.justaskpublications.com
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19
S T A N D A R D S
31
2 4
567
8
Assessment nstr cti n Pre Planner (P )
Author(s):
Course/Grade Level/Unit:
Knowledge – What must students? (May be combined with skills and stated as critical questions)
Skills – What must students be able to do? (May be combined with knowledge and stated as critical questions.)
Relevance –Why do students need this knowledge and these skills right now? How are knowledge and skills used by adults?
Pre-Assessment –How will I determine what students know and can do?
Instruction –What instructional strategies and resources might I use to help students perform well on the assessment(s)?
Mike WilliamsArea and Perimeter 6th Grade Math
Students Should Know:• Basic geometric terms and concepts such as
polygon, regular shape, irregular shape, length,width, area perimeter…
• Basic strategies for problem solvingStudents Should Understand:Concepts such as parallel, congruent, and right angle
Students that are comfortablesolving area and perimeterproblems are developing someof the basic skills they may use inhigher math such as Algebra. In the future, students with theseskills will be able to solve a widevariety of problems such as:• Pricing carpet for their house• Finding quantities of paint
needed to cover walls• Solve problems such as
insecticide crop coverage• Decide how large of a pool to
install in the back yard
Students Should be Able to• Identify and draw multi-sided shapes (hexagon, nonagon etc.) • Use tools such as a ruler and graph paper with an acceptable
degree of accuracy.• Develop strategies for solving area and perimeter• Communicate the reasoning used in solving problems
• Informal assessment such as classroomdiscussions
• Informal assessment such as math journals• Creating a model from tiles and then
explaining how to solve for both area andperimeter
• Creating a model on graph paper andexplaining how to solve for both area andperimeter
• Discuss area and perimeter in theclassroom
• Have students journal area and perimeterand make connections to their everydaylife
• Solve application problems• Have students create models to solve for
area and perimeter using tiles and graphpaper, then explain and defend theiranswers
Standards-Based Classroom Operator’s Manual Copyright © 2002, Just ASK Publications & Professional Developmentand Centennial BOCES. All rights reserved. No reproduction without written permission from the publisher. To orderplease call 1-800-940-5434 or visit www.justaskpublications.com
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S T A N D A R D S
20
Standard(s): Benchmark(s):
Assessment Task(s) –What will students do to demonstrate this knowledge and these skills?
Scoring Criteria –On what traits will student responses be evaluated?
Potential Accommodations –What changes might I make to accommodate my students’ unique learning needs?
Follow-up – What activities might I use for remediation or extension?
Cover Page for Assessment/Unit PacketComplete Assessment Prompt for StudentsTemplate(s)/Organizer(s) for Students’ ResponsesSimplified Scoring Guide for Student ReferenceAnchor Papers for Students &/ or ScorersComplete Instructions for Administering Asmt.List of Potential Instructional StrategiesLesson PlansUnit Study-Planner for StudentsList of Instruction/Assessment AccommodationsExtension Activities for Advanced StudentsList of Instructional Materials and ResourcesStudent Self-Evaluation FormParallel Self and Teacher Evaluation FormScoring Process InstructionsScoring Guide/RubricScoring Folder (Scoring Guide Laminated Inside)Group Summary Report Form
Other:
Products: (Check those I need to create.)
Standard Four: Students use geometricconcepts, properties, and relationships, inproblem-solving situations and communicatethe reasoning used in solving these problems.
4.5: Solve problems involving perimeter and area intwo dimensions, and involving surface area andvolume in three dimensions.Students in grade 6 will know and be able to: Solve problems involving perimeter and area of rectangles, squares, andirregular shapes (use of graph paper with irregular shapes).
• Solve applications involving area andperimeter (appropriate shapes) usingmanipulatives and graph paper
• Communicate the reasoning used insolving the problem
• Design and create a bumper car racetrack that meets a set criteria, then writean explanation that explains thereasoning used to solve for size (areaand perimeter) of their track (this workmay be computer generated)
• Conceptual Understanding – Does thestudent understand the problem?
• Computation and Execution – Is thestudent’s work accurate and complete?
• Strategies – Does the student have alogical plan and show a verifiableprocess?
• Communication – Does the studentexplain their ideas effectively?
.
• Additional time• Assignments and assessment prompt
given in students native language• Modify complexity of the assignment• Directions given orally as well as written• Repeat and clarify directions
• Create a sales brochure• The final assessment is open-ended so that
students may design a ride that matchestheir ability from easy to moderate tocomplex in design
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Standards-Based Classroom Operator’s Manual Copyright © 2002, Just ASK Publications & Professional Developmentand Centennial BOCES. All rights reserved. No reproduction without written permission from the publisher. To orderplease call 1-800-940-5434 or visit www.justaskpublications.com
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A S S E S S M E N T
42
Assessment Sc rin ide (P ) r
12 3 4
567
8
Standard/Benchmark(s) Assessed:
Midwest Amusement Rides
Math Standard 4; Benchmark 4.5: Solve problems involving perimeter and areain two dimensions, and involving surface area and volume in three dimensions.
Students in grade 6 will know and be able to: Solve problems involving perimeterand area of rectangles, squares, and irregular shapes (use of graph paper withirregular shapes).
Criteria/Traits Basic Partially Proficient Proficient Advanced
ConceptualUnderstanding
Does the studentunderstand theproblem?
Mathrepresentations ofthe problem wereincorrect.
Mathrepresentations ofthe problem wereinaccurate.
Mathrepresentations ofthe problem wereappropriate.
Mathrepresentations ofthe problem wereappropriate andclarified.
Computation andExecution
Is the student’swork accurate andcomplete?
Solution wasincorrect.
No evidence ofhow you arrived atyour answer.
Solution wasessentially correct.
Evidence for yoursolution wasinconsistent orunclear.
Solution wascorrect.
Evidence for yoursolution was clearand supported youranswer.
Solution wascorrect.
Evidence for yoursolution was clearand supported youranswer.
You showedevidence ofverifying youranswer.
Strategies
Does the studenthave an appropriatestrategy?
Strategies for theproblem were notappropriate andwould not lead to acorrect solution.
Strategies for theproblem werepartially effectiveand will lead topartially correctsolution.
Strategies for theproblem wereeffective and willlead to completelycorrect solution.
Strategies for theproblem wereinsightful, effectiveand will lead tocompletely correctsolution
Communication
Does the studentexplain their ideaseffectively?
Little or noexplanation, orimpossible tofollow.
Explanation hardto follow andinferences had tobe made in places
Explanation fairlyclear, I understoodwhat you did andwhy.
Explanation wasclear and concise;you gave an in-depth explanationof your reasoning.
Standards-Based Classroom Operator’s Manual Copyright © 2002, Just ASK Publications & Professional Developmentand Centennial BOCES. All rights reserved. No reproduction without written permission from the publisher. To orderplease call 1-800-940-5434 or visit www.justaskpublications.com
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I N S T R U C T I O N
12
34 5
67
8
Uni
t rg
ani
er
ap (P
) or
: M
idw
est
Am
use
men
t R
ides
Pre
viou
s U
nit
: Fr
actio
nsC
urr
ent
Un
it:
Are
a an
d Pe
rimet
er o
f 2D
Sha
pes
Nex
t U
nit
: Neg
ativ
e N
umbe
rs
Stan
dar
d(s
)/B
ench
mar
k(s)
– R
esta
ted
as q
uest
ion,
“Ca
n I …
?”R
elev
ance
– H
ow w
ill I
use
this
know
ledge
and
thes
e sk
ills r
ight
now
? H
ow a
re k
now
ledge
and
skill
s use
d by
adu
lts?
Th
is U
nit
is A
bou
t –
Wha
t is t
he m
ain
conc
ept,
them
e, or
big
idea
?A
sses
smen
t(s)
– H
ow w
ill I
show
my
teac
her I
’ve
met
/exc
eede
d th
ese
stan
dard
s/be
nchm
arks
?
Inst
ruct
ion
– W
hat s
tudy
stra
tegi
es
and
reso
urce
s will
I us
e to
help
me
perf
orm
well
on
the
asse
ssm
ent(s
)?
Can
I dev
elop
stra
tegi
es th
at a
llow
me
to c
orre
ctly
solv
e fo
r are
a an
d pe
rimet
er o
f sim
ple
regu
lar sh
apes
? Ca
n I d
evelo
p st
rate
gies
to c
orre
ctly
solv
e fo
r are
a an
d pe
rimet
er o
f sim
ple
irreg
ular
shap
es?
Afte
r sol
ving
su
ch p
robl
ems c
an I
effe
ctiv
ely c
omm
unica
te m
y re
ason
ing
for s
olvi
ng
the
prob
lem?
Stud
ents
that
are
com
forta
ble
solv
ing
area
and
per
imet
er p
robl
ems a
re d
evelo
p-in
g so
me
of th
e ba
sic sk
ills t
hey
may
use
in h
ighe
r mat
h su
ch a
s Alg
ebra
.In
the
futu
re st
uden
ts w
ith th
ese
skill
s will
be
able
to so
lve
a w
ide
varie
ty o
f pr
oblem
s suc
h as
:•
Prici
ng c
arpe
t for
their
hou
se•
Find
ing
quan
tities
of
pain
t nee
ded
to c
over
wall
s•
Solv
e pr
oblem
s suc
h as
inse
ctici
de c
rop
cove
rage
• D
ecid
e ho
w la
rge
of a
poo
l to
inst
all in
the
back
yar
d
By jo
urna
ling
idea
s ab
out a
rea
and
perim
eter
By c
reat
ing
a m
odel
with
tiles
By c
reat
ing
and
draw
ing
a bu
mpe
r ca
r rid
e
By so
lvin
g ap
plica
tions
By d
efen
ding
and
ex
plain
ing
your
so
lutio
n
• I w
ill c
orre
ctly
solv
e ap
plica
tions
in
volv
ing
area
and
per
imet
er
(app
ropr
iate
shap
es) u
sing
m
anip
ulat
ives
and
gra
ph p
aper
• I w
ill e
ffect
ively
com
mun
icate
the
re
ason
ing
used
in so
lvin
g th
e pr
oblem
•
I will
des
ign
and
crea
te a
bum
per c
ar
ra
cetra
ck th
at m
eets
a se
t crit
eria,
then
writ
e an
exp
lanat
ion
that
com
mun
icate
s
the
reas
onin
g us
ed to
solv
e fo
r the
track
’s siz
e (a
rea
and
perim
eter
). I
un
ders
tand
that
this
work
may
be
co
mpu
ter d
raw
n an
d I n
eed
to ra
te a
t
least
pro
ficien
t on
this
asse
ssm
ent.
• I w
ill p
artic
ipat
e in
clas
sroo
m
d
iscus
sions
of
area
and
per
imet
er
• I w
ill jo
urna
l my
idea
s and
que
stio
ns
a
bout
are
a an
d pe
rimet
er a
nd tr
y to
mak
e co
nnec
tions
to m
y ev
eryd
ay li
fe•
I will
solv
e fo
r are
a an
d pe
rimet
er
u
sing
tiles
and
gra
ph p
aper
and
ver
ify
m
y an
swer
s•
I will
be
able
to o
ffer b
oth
oral
and
w
ritte
n cle
ar e
xplan
atio
ns o
f m
y
reas
onin
g us
ed to
solv
e pr
oblem
s and
be
able
to d
efen
d m
y an
swer
s•
I will
then
pro
ficien
tly c
reat
e an
d
dra
w a
bum
per c
ar ri
de, s
olve
for
a
rea
and
perim
eter
, and
then
cos
t out
the
ride.
Solv
ing
for A
rea
and
Perim
eter
of
2D
shap
es a
nd c
omm
unica
ting
the
reas
onin
g fo
r so
lvin
g th
e pr
oblem
.
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