COMMONWEALTH OF PENNSYLVANIA - rio.edu · COMMONWEALTH OF PENNSYLVANIA Mark Schweiker, Governor ......

COMMONWEALTH OF PENNSYLVANIA Mark Schweiker, Governor DEPARTMENT OF EDUCATION Charles B. Zogby, Secretary OFFICE OF ELEMENTARY AND SECONDARY EDUCATION Thomas P. Carey, Deputy Secretary BUREAU OF CURRICULUM AND ACADEMIC SERVICES Michael J. Kozup, Director DIVISION OF CURRICULUM & INSTRUCTION Nancy Neil, Chief DIVISION OF FEDERAL PROGRAMS Jim M. Sheffer, Chief DIVISION OF EVALUATION & REPORTS Lee Plempel, Chief DIVISION OF SCHOOL BASED IMPROVEMENT Marian Sutter, Chief BUREAU OF SPECIAL EDUCATION Frances James-Warkomski, Director John Tommasini, Assistant Director

PENNSYLVANIA DEPARTMENTOF EDUCATION

333 Market StreetHarrisburg, PA 17126-0333

The Pennsylvania Department of Education (PDE) will not discriminate in its educational programs, activities or employment practices, based on race, color, national origin, sex, sexual orientation, disability, age, religion, ancestry, union membership, or any other legally protected category. Announcement of this policy is in accordance with State law including the Pennsylvania Human Relations Act and with Federal law, including Title VI of the Civil Rights Act of 1964, Title IX of the Education Amendments of 1972, Section 504 of the Rehabilitation Act of 1973, the Age Discrimination in Employment Act of 1967, and the Americans with Disabilities Act of 1990. If you have any questions about this publication, or for additional copies, contact: Bureau of Curriculum and Academic Services, Department of Education, 333 Market Street, Harrisburg, PA 17126-0333, Telephone: 717 787-8913. Any complaint of harassment or discrimination pertaining to education should be directed to the Equal Employment Opportunity Manager, Department of Education, 333 Market Street, Harrisburg, PA 17126-0333, Voice Telephone: 717-787-4417, Text Telephone TTY: 717-783-8445, Fax: 717-783-9348. For further information on accommodations for persons with disabilities, contact the ADA Coordinator, Department of Education at the same address, Voice Telephone: 717-783-9791, Fax: 717-772-2317, at the same Text Telephone TTY.

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Mathematics Instructional Rubrics Mathematics Instructional Rubrics Mathematics Instructional Rubrics Mathematics Instructional Rubrics

This resource was developed through the Pennsylvania Academic Educational Excellence Network (PEEN): A Partnership between the Pennsylvania Department of Education and Pennsylvania Association of Intermediate Units

Primary Development Team

Grace Cisek Berks County Intermediate Unit Janet Lorant Consultant Frank Marburger Pennsylvania Department of Education Sheila Simyak Berks County Intermediate Unit Melody Wilt Berks County Intermediate Unit

Core Team Members

Judy Battista Tulpehocken Area School District Jennifer Cooper South Western School District Lorraine Felker Kutztown Area School District Kris Gushue Wilson School District Becky Kercher Berks County Intermediate Unit Shelley Noel Grove City Area School District Rebecca Shaffer West York Area School District Donna Spatz Antietam School District Deborah White Tulpehocken Area School District Julie Yoder Governor Mifflin School District

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Pilot Team Members

Thomas Baraniak Meyersdale Area School District Karen Baum Spring Grove Area School District Maureen Bilik Mount Pleasant Area School District Jacqueline Burton Philadelphia City School District Blair Caboot Abington Heights School District Alice Coleman Scranton City School District Charlene Collins Philadelphia City School District Pat Crist General McLane School District Susan Dougherty Reading School District Diane Eskin Reading School District Susan Estep Central Cambria School District Heather Godine Central York School District Kathy Hohenadel Northeastern York School District Tracey Karlie Meyersdale Area School District Mike Lacey Baldwin-Whitehall School District Noreen Lynott Scranton City School District Barbara MacDonald North Allegheny School District Susan Mace South Western School District Deborah Matthews Philadelphia City School District Virginia Merkel Reading School District Debra Migden Philadelphia City School District Joyce Minnis Conneaut School District Lou Ann Nudi Monaca School District Christina Pagnotto North Allegheny School District Tom Parker General McLane School District Kristy Paterson Northwest Tri-County IU 5 Virginia Perfetto Scranton City School District Vince Pricci Abington Heights School District Debra Printz Reading School District Juliann Ranieri Beaver Area School District Jill Ruch Philadelphia City School District Debra Schwenk Reading School District Ilene Silverman Philadelphia City School District Marva Stacey Altoona Area School District Darlene Stone Rochester Area School District Patti Trotz Central Cambria School District Anna Walker Philadelphia City School District Robert Weber General McLane School District Deb Wirth Dover Area School District

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TTTTABLE OF ABLE OF ABLE OF ABLE OF CCCCONTENTSONTENTSONTENTSONTENTS Acknowledgements .............................................................................................. i Table of Contents................................................................................................. iii

MATHEMATICS INSTRUCTIONAL RUBRICS

Introduction and Overview................................................................................... 1 Mathematics Instructional Rubrics for all Organizational Levels ......................................................................................... 10

Analytic……………………………………………………………………………......10 24 36

Holistic…………………………………………………………………………….......Combination………………………………………………………………………......

Organizational Level Rubrics, Prompts, and Student Anchor Papers ............................................................................... 40

Communication Analytic…………………………………………………………..... 41 Reasoning Analytic………………………………………………………………...... 56 Representation Analytic…………………………………………………………...... 71 Communication Holistic……………………………………………………………...84 Reasoning Holistic…………………………………………………………………....95 Representation Holistic……………………………………………………………..108 Combination………………………………………………………………………....123

Resources ......................................................................................................... 153

Websites…………………………………………………………………………..... 153 References………………………………………………………………………….. 155 Glossary…………………………………………………………………..…….…... 157

Mathematics Instructional Rubrics – Section One 1

INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION The Mathematics Instructional Rubrics manual contains scoring guides for students to evaluate and improve their mathematical problem solving skills. It also contains many teacher resources to help students learn how to use the rubrics. Pennsylvania educators developed these materials through a project conducted by Partnership for Educational Excellence Network. Every rubric in the manual has two components: the criteria for judging a student performance and descriptions of student performances ranging from a low of a one-point score to a high of a four-point score. Accompanying each rubric are student anchor papers illustrating student work representative of each score point in the rubric, explanations of the score points, teacher suggestions on how to introduce the rubric to a class of students, and a prompt. Purpose The purpose of the Mathematics Instructional Rubrics is to help students increase their proficiency in solving open-ended mathematical problems such as those found on the Pennsylvania System of School Assessment (PSSA). They are designed in conjunction with the Mathematics General Rubric found in the Pennsylvania System of School Assessment Handbook. The rubrics in this document are designed specifically for student use and are written in student appropriate language. The developers of the Mathematics Instructional Rubrics hoped to create tools that would identify and clarify specific performance expectations and provide goals for student achievement. As rubrics define what performances students should do to demonstrate mastery of the mathematics standards, students learn the criteria for achievement levels through their use. Rubrics help learners to look at themselves in positive ways while continuing to take steps toward improving performance. Each student is provided feedback on his or her performance in a developmental continuum. In the continual improvement model, teachers need to supply quality feedback about what students are learning, what they can do to improve, and whether their mastery level is in line with expectations. Rubrics are tools to achieve this end. Teachers can determine mathematical error patterns and student strengths and specify next steps in the continuum of improvement of skills. With practice, students are eventually able to self-assess what is required to move from their present scoring levels to greater proficiency.

“Rubrics are a fantastic way to develop mathematical metacognition.”

A rubric is a scoring guide for evaluation of student work that includes specific performance criteria in a continuum of leveled descriptions from low to high.


One of the most significant changes in a standards-based classroom is the continual effort to revise and improve student work. The goal is mastery of the standards, not coverage of material. Each student requires coaching on his or her progress along the path to mastery. Students and teachers must be able to check the individual’s work against a scoring guide and determine what modifications are required. The process of checking and determining what steps are needed for further improvement is a unique and critical diagnostic interaction between the student and the teacher with the aim of mastery for all. The Process of Development The development of the Mathematics Instructional Rubrics was a collaborative process between teachers, intermediate unit personnel, and members of the Pennsylvania Department of Education who worked with national mathematics consultants to produce the end product. Initially, a core group of mathematics teachers working in primary, intermediate, middle, and high school teams developed a set of draft rubrics. A four-point rubric was selected, rather than the six data points in the state rubric. The rationale for this change came from teachers who reported that the four points represented what worked best in their classrooms. They also thought that the zero point tended to discourage students from working toward improvement. Working through intermediate units, teachers from across the state joined with the core group of teachers and met during the 2000-2001 school year to discuss appropriate mathematical problems and the process of field-testing the rubrics in their classrooms. The student rubrics were then piloted in PA schools in urban, suburban, and rural settings. Participating teachers maintained logs of their experiences and provided the feedback needed to further refine the rubrics. The rubrics were checked for coherence across grade levels and finalized. Field-test teachers also provided their anecdotal logs, general lesson plan outlines, mathematical problems that accompany each rubric, and sample student papers illustrating various score points of each rubric. Examples of these have been included in this document with each rubric. While the Mathematics Instructional Rubrics is a complete set of scoring tools that has been field-tested and revised by teachers across the state, district personnel should not hesitate to further revise the rubrics to meet their district and classroom needs.

“Student responsesimprove dramatically with the use of rubrics.”

“Practice is the key to success with students.”


A Description of the Rubrics The rubrics are written in appropriate language for instruction at four developmental levels: primary, intermediate, middle, and high school. They are not written at specific grade levels so that district educators can adapt and select the rubric that best fits their students. Each developmental level is encased in a separate binder. Within the developmental levels, there are rubrics written for the purpose of increasing students’ problem solving abilities in three skill areas: communication, reasoning, and representation. Communication is the part of a problem solving skill where a student is required to explain “how” they solve a problem using the language of mathematics. Reasoning is the skill area of explaining and defending “why” a student chooses to solve a problem using a selected strategy. Representation is the skill area of correctly “showing one’s work.” This last skill might include creating and using graphs, models, and drawings. To develop these skill areas there are three types of rubrics: analytic, holistic, and combination. Analytic rubrics include discrete criteria and specific traits. There is a score for each trait. Analytic rubrics lend themselves to formative evaluations of student skill development. The holistic rubrics include clusters of descriptors for a concluding or cumulative performance for a summative evaluation. The combination rubrics include all of the criteria from the holistic communication, reasoning, and representation skill areas in one rubric. The following paragraphs further describe the characteristics of each type of rubric. In the analytic rubric there are separate and discrete descriptive criteria for a skill development area, such as communication, across a range of score points and there are specific characteristics to be evaluated in separate columns. The four levels represent a range of performances from strongest to weakest. Separating the descriptors allows the teacher or student to look at the individual characteristics to be evaluated. The responses are viewed in a part-to-whole relationship, hence the term, “analytic.” The teacher and student must select the relevant score point that best matches the characteristic of the response. The benefits of this format are that it permits an evaluation of each characteristic of the response and asks the evaluator to analyze the response for strengths and weaknesses. This type of rubric is best suited to an analysis of the student’s work. As each component is considered separately, the analytic rubric format lends itself to formative evaluations of student work that can be used to guide the student to improve specific aspects of his or her work.

“As a first year teacher I learned some very important lessons while working with the rubrics. I learned that my students have done very little writing in mathematics.”

“It helps to developa chart in your room which explains ‘How to get a 4’ on a rubric.”


The holistic rubric clusters descriptive criteria for one skill development area, such as communication, around a range of score points, four through one, representing a range of performances from strongest to weakest. Clustering the descriptors enables the user to look at a response as a whole, hence the term holistic. The teacher or student using this rubric must select the score point that completely matches the overall response. All criteria of a given score point must be met to earn that score point. This allows the evaluator to look at the total or integrated response. This type of rubric is best suited to offering a single score response to a student’s work. As all criteria are considered as a group, this format lends itself to a summative assessment of student work on a given task. The combined rubric organizes descriptive criteria for all the skill development areas, communication, representation, and reasoning. It does this collectively in one rubric across a range of score points and combines the content included in the three holistic rubrics. By including the descriptors for all three of the skill development areas, this format enables the user to look at a student’s response as it relates to communication, representation, and reasoning. The responses are evaluated for each skill area as a part-to-whole relationship. The teacher and student must select the score point that generally best describes each aspect of the response. The benefit of the combination rubric is that it provides an evaluation of all three-skill development areas in one tool. Recommended Sequence for Introducing Rubrics to Students Figure One is designed to represent the types and difficulty levels of Mathematics Instructional Rubrics that can be used to assist students in responding to open-ended questions. When solving a problem, students’ responses need to include communication of “how” a problem was solved, “why” a specific strategy was selected and representation that supports the conclusion. This manual includes rubrics or tools to assist students in creating responses to an open- ended problem that includes communication, reasoning and representation. Figure One is designed as a flow chart to illustrate the recommended sequence for introducing the rubrics to students. Since analytic rubrics are generally considered to be the easiest of rubrics for students to use, they are shown in the first section of the flow chart. This section is shaded in yellow to remind teachers to introduce the rubrics with caution and to teach students how to use these tools. Notice that the analytic section includes rubrics to assist students in creating responses that communicate, reason, and represent their answers. These tools are usually used to diagnose student errors in solving problems and are formative in design. If students struggle with all aspects of solving open-ended problems then it is recommended that

“Students initially have a high resistance to the requirements of rubrics. However, with consistent use of rubrics they show improvement in their written explanations.”


Figure One

RECOMMENDED SEQUENCE OF RUBRIC INTRODUCTION

Analytic 1. Communication 2. Reasoning

3. Representation

Holistic 1. Communication 2. Reasoning 3. Representation

Combination


they be instructed in the separate components of a response, beginning with the communication rubric. If students are adept at communicating and representing their responses, but struggle with reasoning, then it is appropriate to use the reasoning rubric to diagnose their error patterns and instruct them on the criteria necessary to successfully explain “why” they chose a specific strategy. When students are comfortable with the analytic rubrics or if they have had experience in the use of rubrics it is then appropriate to use the holistic form. These rubrics are represented in Figure One in the blue section, since blue is a comfort color. This is to signify that when students are comfortable with the criteria that are specified in levels three and four of the analytic rubric it is time to assess them holistically on their responses. The holistic section of the flow chart includes rubrics for students to use when working on responses to communicate, reason and represent their answers. These tools are designed as summative tools to assess the total student response. They are generally more difficult to use and hold student responses to a higher level. Students must meet all the descriptive criteria of the response point in order to earn the score at that level. If students score at the lower levels of the rubric (one or two) the teacher may use the analytic form of the rubric to diagnose the error pattern and assist them in refining their skills. The combined rubric organizes the descriptive criteria for all of the skill development areas of communication, reasoning and representation into one rubric across a range of score points. These rubrics are represented on Figure One in the green section since green signifies the ability to move ahead. When students are comfortable with this rubric they are ready to “go” and respond to open ended questions with all of the required components of communication, reasoning and representation. This rubric is an excellent tool when students are comfortable in all of the skill areas for problem solving, however, it would be overwhelming to a student that has not had previous experience with rubrics. While this flow chart is a recommended sequence for the introduction of rubrics to students, this sequence is totally dependent upon students’ experiences with rubrics and their developmental level. Primary and intermediate students may spend much more time using the analytic and holistic rubrics until they are developmentally ready to use the combined rubric or until they have had experience with analytic and holistic. Once they are ready to use the combined rubric, it can always be folded so that only one or more of the sections are being used with the appropriate concepts of solving open-ended problems. Secondary students may use the combined rubric more easily as they have had more experience in solving open-ended problems as part of the curriculum and on the PSSA. If, however, they are experiencing difficulty in one aspect of

“Choose simple problems to begin introducing rubrics.”


problem solving (reasoning or representation) it would be appropriate to use the analytic rubric for diagnostic purposes. The ultimate goal of using the rubrics in this manual is to enhance students’ abilities to create responses to open-ended problems that include communication of “how” a problem was solved; “why” a specific strategy was selected; and representation that supports the conclusion. The Mathematics Instructional Rubrics will assist students and teachers in facilitating that process. The Mathematics Instructional Rubrics Format The Mathematics Instructional Rubrics are arranged by the four organizational levels - primary, intermediate, middle, and high school. Each document is divided into four sections.

• Section One includes the introduction and overview of the project; explanations of the development of the mathematics rubrics; and general guidelines to introduce rubrics to students.

• Section Two provides a set of all the rubrics, primary through high school, a copy of the PSSA Mathematics rubric, and an explanation of the difference between the PSSA six-point rubric and four-point instructional students rubrics.

• Section Three contains student rubrics for each organizational level (primary, intermediate, middle, or high school); teachers’ comments of how to use the rubric in their classroom; samples of student problems; and student anchor papers representing score points of the rubric.

• Section Four contains resources that would be helpful in learning more about the use and development of rubrics with students. These resources include: additional prompts, website addresses that provide more information on rubrics, and a glossary.

In Figure Two an outline is provided to guide the teacher in how to work with students through the initial stages of using rubrics to independent use of rubrics. The authors caution that these are only general suggestions and are not intended to take the place of individual teacher’s lesson designs. Additionally, there are teacher suggestions with each rubric in Section Three of this guide that have been provided by the classroom teachers who field-tested the rubrics in their classrooms.

“As a teacher with 35 years of experience, using these rubrics is most stimulating. It demands time and expertise and is rewarding.”


Figure Two

GENERAL GUIDELINES TO INTRODUCE STUDENTS TO RUBRICS

1. Introduce the concept of rubrics to students emphasizing that rubrics provide a guide of what is expected in a problem solving response. Use an analogy to help explain how rubrics are used such as the straw building activity. (A detailed version of a straw building lesson plan is located in section four, the resource section, of this manual.) Explain the rationale of how the rubrics can be used as a target for continual improvement, and that they can serve as a checklist to proof student work.

2. Using the overhead master of a rubric, present the rubric, reading each item

aloud and underlining key vocabulary words. Discuss vocabulary words in each line making sure students understand their meanings.

3. Explain the differences between each level on the rubric. Emphasize the use

of words such as, “all, most, some, few or none” or “completely, mostly, and partly” and their relationship to a 4, 3, 2, 1 score.

4. Present a practice problem and brainstorm together how to solve it. Once

students have chosen a solution, work through it with them emphasizing the use of the scoring guide to help write the solution. Check the student work and guide the responses. Place key mathematical terms on the board and tell students to use them in their written explanations.

5. Present another practice problem and have students read their responses

listing all the math terms they use. Create a list of reminders of what to do based on the discussions of the student responses. Create a list of problem solving procedures from this discussion. An example follows: • Read the problem and decide how to solve it. • Read the problem a second time rethinking the solution and what will be

needed to solve it. • Organize what needs to be done using the rubric as a checklist. • Solve the problem. • Use the rubric to check the response.


6. Have the students score their own responses using the rubric. Have students discuss how they could improve their response or score.

7. Present several more practice problems having students work in cooperative

groups using the rubric to guide their answers. Using the rubric have the groups exchange papers to score another group’s work. Discuss the rationale for their scores.

8. Utilize student papers from the anchor sets to illustrate the differences

between a 4, 3, 2, or 1 score.* 9. Have students individually solve a problem using the rubric. Give each

student feedback on their answer using the rubric. Guide students in what their next steps should be to improve their scores.

10. Continue to practice solving open-ended problems using rubrics. Encourage

students to improve; they will increase their skills with practice. Suggested Accommodations for Special Needs Students Allow extra time to complete the actual problem. Read the rubric and the problem or prompt orally to the student. Use the help of an aide to keep the student focused on the task. Provide a calculator or manipulative. Read the problem several times to the student emphasizing key words. Utilize dark-lined composition or graph paper for visually impaired students. Highlight important information and key words on the rubric. Add lines to the response pages. Use “post-it” notes to show students where to write parts of their work.

*Note: Teachers using student papers as examples should adhere to the Federal Educational Rights and Privacy Act (FERPA) guidelines.

Mathematics Instructional Rubrics – Section Two 10

HOW DO MATHEMATICS IHOW DO MATHEMATICS IHOW DO MATHEMATICS IHOW DO MATHEMATICS INSTRUCTIONAL RUBRICSNSTRUCTIONAL RUBRICSNSTRUCTIONAL RUBRICSNSTRUCTIONAL RUBRICS COMPARE TO THE PSSA COMPARE TO THE PSSA COMPARE TO THE PSSA COMPARE TO THE PSSA RUBRIC?RUBRIC?RUBRIC?RUBRIC?

The goal of the Mathematics Instructional Rubrics project was to develop a set of assessment tools students could use to improve their responses to open-ended problems both in the classroom and on the state assessment (the PSSA). While creating the rubrics, the core development team consistently referenced the expectations for student responses to the expectations for a level five on the PSSA; however, they chose to create four-point rubrics for two reasons. First, the team unanimously agreed that they did not want a zero on the instructional rubric because not completing a problem or being off task is unacceptable in daily classroom instruction. Second, as it is important for students to learn to evaluate their own work, there was some concern that an odd number on the rubrics (five rather than the state’s current six) might cause some students to lean toward the central tendency of a “3”. Given both of these considerations and teacher experience with four-point rubrics, the team elected to design a four-point rubric. According to the PA Mathematics Assessment Handbook, (p. 8, 2000) in order for a student to score at the level five on the PSSA rubric a student response must have the following characteristics:

“Correct answer with correct procedures/correct calculations shown or described and a written explanation that supports the work shown. The explanation tells what was done in the solution process and explains why the steps were done (or the reason(s) for the steps to be taken). No blemishes, that is, everything is correct. May have a minor omission in calculation or explanation where the omitted step or explanation may be of the level of 2 + 2 = 4 (something that is usually done mentally and considered trivial and understood).”

To achieve a five on the state rubric, the student response must have thoroughly addressed an explanation of their answer, a representation of the answer, and the reasoning for solving the problem. These three characteristics of the highest score on the state’s rubric were the impetus for the development of rubrics based on these three separate characteristics of quality mathematic performance (communication, representation, and reasoning). The Mathematics Instructional Rubrics were developed to be classroom tools and to be utilized by students so they were developed using “student appropriate language” to explain “how” and “why” a student solved a problem and chose to represent the answer. A comparison between the state’s scoring guide and the instructional rubrics is as follows: • A level four on the Mathematics Instructional Rubrics (MIR) is consistent with the PSSA

level five. • A level three on the MIR is consistent to a combination of the three and four on the PSSA

Rubric. • A level two on the MIR is comparable to a level two on the PSSA Rubric. The MIR level two

varies slightly from the PSSA level two in that the state rubric does allow for a correct answer at level two.

• A level one on the MIR is consistent with the criteria established on the PSSA rubric when levels one and zero are combined.


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s in

my

expl

anat

ion

.

1 M

y w

ork

is n

ot o

rgan

ized

, doe

s n

ot

mak

e se

nse

, an

d is

ver

y co

nfu

sin

g.

I in

clu

de a

n e

xpla

nat

ion

of

few

or

non

e of

th

e st

eps

nee

ded

to s

olve

th

e pr

oble

m.

I d

o n

ot u

se p

rope

r la

bels

, de

tail

s, s

ymbo

ls, a

nd

corr

ect

mat

h t

erm

s in

my

expl

anat

ion

.


Mat

hem

atic

al C

omm

un

icat

ion

- A

nal

ytic

Ru

bri

c -

Mid

dle

Sch

ool

Lev

el

Th

is is

how

I s

olve

th

e pr

oble

m.

O

rgan

izat

ion

Is

my

resp

onse

org

aniz

ed t

o sh

ow

how

I s

olve

th

e pr

oble

m?

E

xpla

nat

ion

D

oes

my

expl

anat

ion

incl

ude

how

I

solv

e th

e pr

oble

m?

U

se o

f M

ath

emat

ical

Ter

ms

Doe

s m

y re

spon

se in

clu

de p

rope

r co

nce

pts,

labe

ls, d

etai

ls, s

ymbo

ls,

and

corr

ect

mat

h t

erm

s?

4

My

resp

onse

is w

ell

orga

niz

ed

and

is lo

gica

l.

I in

clu

de a

n a

ccu

rate

, com

plet

e,

and

thor

ough

exp

lan

atio

n o

f al

l of

th

e st

eps

nee

ded

to c

orre

ctly

sol

ve

the

prob

lem

.

I u

se a

ll o

f th

e pr

oper

con

cept

s,

labe

ls, d

etai

ls, s

ymbo

ls, a

nd

corr

ect

mat

h t

erm

s in

my

expl

anat

ion

.

3 M

y re

spon

se is

mos

tly

orga

niz

ed

and

is lo

gica

l.

I in

clu

de a

n a

ccu

rate

exp

lan

atio

n o

f m

ost

of t

he

step

s n

eede

d to

co

rrec

tly

solv

e th

e pr

oble

m.

I u

se m

ost

of t

he

prop

er c

once

pts,

la

bels

, det

ails

, sym

bols

, an

d co

rrec

t m

ath

ter

ms

in m

y ex

plan

atio

n.

2 M

y re

spon

se is

poo

rly

orga

niz

ed

or is

illo

gica

l.

I in

clu

de a

n e

xpla

nat

ion

of

som

e of

th

e st

eps

nee

ded

to s

olve

th

e pr

oble

m.

I u

se s

ome

of t

he

prop

er c

once

pts,

la

bels

, det

ails

, sym

bols

, an

d co

rrec

t m

ath

ter

ms

in m

y ex

plan

atio

n.

1 M

y re

spon

se is

not

org

aniz

ed

and

is il

logi

cal.

I in

clu

de a

n e

xpla

nat

ion

of

few

or

non

e of

th

e st

eps

nee

ded

to s

olve

th

e pr

oble

m.

I u

se f

ew o

r n

one

of t

he

prop

er

con

cept

s, la

bels

, det

ails

, sym

bols

, an

d co

rrec

t m

ath

ter

ms

in m

y ex

plan

atio

n.


Mat

hem

atic

al C

omm

un

icat

ion

- A

nal

ytic

Ru

bri

c -

Hig

h S

choo

l L

evel

T

his

is h

ow I

sol

ve t

he

prob

lem

.

O

rgan

izat

ion

Is

my

resp

onse

org

aniz

ed t

o sh

ow h

ow I

so

lve

the

prob

lem

?

E

xpla

nat

ion

D

oes

my

expl

anat

ion

incl

ude

how

I s

olve

th

e pr

oble

m?

U

se o

f M

ath

emat

ical

Ter

ms

Doe

s m

y re

spon

se in

clu

de a

ccu

rate

labe

ls,

sym

bols

, con

cept

s, t

erm

inol

ogy,

an

d re

pres

enta

tion

s?

4

My

resp

onse

is t

hor

ough

, wel

l or

gan

ized

an

d lo

gica

l.

I in

clu

de a

com

plet

e an

d co

rrec

t ex

plan

atio

n u

sin

g al

l of

th

e re

leva

nt

and

spec

ific

det

ails

fro

m t

he

prob

lem

wh

en

desc

ribi

ng

the

proc

edu

res

use

d to

arr

ive

at t

he

corr

ect

solu

tion

.

I u

se a

ll o

f th

e la

bels

, sym

bols

, con

cept

s,

term

inol

ogy,

an

d re

pres

enta

tion

s ac

cura

tely

, cle

arly

, an

d su

ccin

ctly

in m

y re

spon

se.

3 M

y re

spon

se is

mos

tly

orga

niz

ed a

nd

logi

cal.

I in

clu

de a

cor

rect

exp

lan

atio

n u

sin

g m

ost

of t

he

rele

van

t an

d sp

ecif

ic d

etai

ls

from

th

e pr

oble

m w

hen

des

crib

ing

the

proc

edu

res

use

d to

arr

ive

at t

he

corr

ect

solu

tion

.

I u

se m

ost

of t

he

labe

ls, s

ymbo

ls,

con

cept

s, t

erm

inol

ogy,

an

d re

pres

enta

tion

s ac

cura

tely

, cle

arly

, an

d su

ccin

ctly

in m

y re

spon

se.

2 M

y re

spon

se is

poo

rly

orga

niz

ed o

r is

il

logi

cal.

I in

clu

de a

n e

xpla

nat

ion

usi

ng

som

e of

th

e re

leva

nt

and

spec

ific

det

ails

fro

m t

he

prob

lem

wh

en d

escr

ibin

g th

e pr

oced

ure

s u

sed

to a

rriv

e at

a s

olu

tion

.

I u

se s

ome

of t

he

labe

ls, s

ymbo

ls,

con

cept

s, t

erm

inol

ogy,

an

d re

pres

enta

tion

s ac

cura

tely

in m

y re

spon

se.

1 M

y re

spon

se is

not

org

aniz

ed a

nd

is

illo

gica

l.

I in

clu

de a

n e

xpla

nat

ion

usi

ng

few

or

non

e of

th

e re

leva

nt

or s

peci

fic

deta

ils

from

th

e pr

oble

m w

hen

des

crib

ing

the

proc

edu

res.

I u

se f

ew o

r n

one

of t

he

labe

ls, s

ymbo

ls,

con

cept

s, t

erm

inol

ogy,

or

repr

esen

tati

ons

in m

y re

spon

se.


Mat

hem

atic

al R

easo

nin

g -

An

alyt

ic R

ub

ric

– P

rim

ary

Lev

el

Th

is is

wh

y I

solv

e th

e pr

oble

m t

his

way

.

E

xpla

nat

ion

of

the

Ste

ps

Doe

s m

y ex

plan

atio

n in

clu

de

com

plet

e an

d or

gan

ized

in

form

atio

n?

R

easo

n f

or t

he

Ch

oice

of

Str

ateg

y D

oes

my

expl

anat

ion

tel

l wh

y I

chos

e th

is s

trat

egy?

U

se o

f M

ath

Ter

ms

Do

I u

se c

orre

ct la

bels

, det

ails

, sy

mbo

ls, a

nd

mat

h t

erm

s to

ex

plai

n m

y w

ork?

4 M

y ex

plan

atio

n in

clu

des

all

of

the

step

s, is

wel

l org

aniz

ed, a

nd

mak

es s

ense

.

I ex

plai

n w

hy

I ch

ose

this

str

ateg

y to

cor

rect

ly s

olve

th

e pr

oble

m

incl

udi

ng

all

the

info

rmat

ion

n

eede

d.

I u

se a

ll o

f th

e co

rrec

t la

bels

, de

tail

s, s

ymbo

ls, a

nd

mat

h t

erm

s to

exp

lain

my

wor

k.

3 M

y ex

plan

atio

n in

clu

des

mos

t of

th

e st

eps,

is o

rgan

ized

, an

d m

akes

sen

se.

I ex

plai

n w

hy

I ch

ose

this

str

ateg

y to

cor

rect

ly s

olve

th

e pr

oble

m a

nd

incl

ude

mos

t of

th

e in

form

atio

n

nee

ded.

I u

se m

ost

of t

he

corr

ect

labe

ls,

deta

ils,

sym

bols

, an

d m

ath

ter

ms

to e

xpla

in m

y w

ork.

2 M

y ex

plan

atio

n in

clu

des

som

e of

th

e st

eps,

is n

ot o

rgan

ized

, bu

t m

akes

som

e se

nse

.

I ex

plai

n w

hy

I ch

ose

this

str

ateg

y to

sol

ve t

he

prob

lem

an

d in

clu

de

som

e of

th

e in

form

atio

n n

eede

d.

I u

se s

ome

labe

ls, d

etai

ls,

sym

bols

, an

d m

ath

ter

ms

to

expl

ain

my

wor

k.

1 M

y ex

plan

atio

n in

clu

des

few

or

non

e of

th

e st

eps,

is n

ot

orga

niz

ed, a

nd

does

not

mak

e se

nse

.

I do

not

exp

lain

wh

y I

chos

e th

is

stra

tegy

to

solv

e th

e pr

oble

m a

nd

I in

clu

de li

ttle

or

no

info

rmat

ion

n

eede

d to

su

ppor

t m

y st

rate

gy.

I d

o n

ot u

se la

bels

, det

ails

, sy

mbo

ls, o

r m

ath

ter

ms

to e

xpla

in

my

wor

k.


M

ath

emat

ical

Rea

son

ing

- A

nal

ytic

Ru

bri

c –

Inte

rmed

iate

Lev

el

Th

is is

wh

y I

solv

e th

e pr

oble

m t

his

way

.

Exp

lan

atio

n o

f th

e S

trat

egy

Doe

s m

y ex

plan

atio

n in

clu

de

orga

niz

ed in

form

atio

n?

R

easo

n f

or t

he

Ch

oice

of

Str

ateg

y D

oes

my

expl

anat

ion

rev

eal w

hy

I ch

ose

this

str

ateg

y?

U

se o

f M

ath

Ter

ms

Doe

s m

y re

spon

se in

clu

de p

rope

r la

bels

, det

ails

, sym

bols

, an

d th

e u

se o

f th

e co

rrec

t m

ath

ter

ms?

4 M

y ex

plan

atio

n d

escr

ibes

my

stra

tegy

in a

hig

hly

sk

illf

ul

way

th

at is

cle

ar, o

rgan

ized

, an

d m

akes

se

nse

.

I co

mp

lete

ly e

xpla

in w

hy

I ch

ose

this

str

ateg

y to

cor

rect

ly s

olve

th

e pr

oble

m.

I u

se a

ll o

f th

e pr

oper

labe

ls,

deta

ils,

sym

bols

, an

d co

rrec

t m

ath

te

rms

in m

y ex

plan

atio

n.

3 M

y ex

plan

atio

n d

escr

ibes

my

stra

tegy

in a

mos

tly

skil

lfu

l w

ay

that

is o

rgan

ized

an

d m

akes

sen

se.

I m

ostl

y ex

plai

n w

hy

I ch

ose

this

st

rate

gy t

o co

rrec

tly

solv

e th

e pr

oble

m.

I u

se m

ost

of t

he

prop

er la

bels

, de

tail

s, s

ymbo

ls, a

nd

corr

ect

mat

h

term

s in

my

expl

anat

ion

.

2 M

y ex

plan

atio

n d

escr

ibes

my

stra

tegy

in a

som

ewh

at s

kil

lfu

l w

ay t

hat

is n

ot o

rgan

ized

bu

t m

akes

som

e se

nse

.

I p

arti

ally

exp

lain

wh

y I

chos

e th

is

stra

tegy

to

solv

e th

e pr

oble

m.

I u

se s

ome

of t

he

prop

er la

bels

, de

tail

s, s

ymbo

ls, a

nd

corr

ect

mat

h

term

s in

my

expl

anat

ion

.

1 M

y ex

plan

atio

n d

oes

not

des

crib

e m

y st

rate

gy in

a s

kill

ful w

ay, i

s n

ot o

rgan

ized

, an

d do

es n

ot m

ake

sen

se.

I d

o n

ot e

xpla

in w

hy

I ch

ose

this

st

rate

gy t

o so

lve

the

prob

lem

.

I d

o n

ot u

se p

rope

r la

bels

, det

ails

, sy

mbo

ls, a

nd

corr

ect

mat

h t

erm

s in

my

expl

anat

ion

.


M

ath

emat

ical

Rea

son

ing

- A

nal

ytic

Ru

bri

c –

Mid

dle

Sch

ool

Lev

el

Th

is is

wh

y I

solv

e th

e pr

oble

m u

sin

g a

sele

ct s

trat

egy.

Exp

lan

atio

n o

f th

e S

trat

egy

Doe

s m

y ex

plan

atio

n in

clu

de

orga

niz

ed in

form

atio

n?

R

atio

nal

e fo

r th

e S

trat

egy

Ch

oice

Doe

s m

y ex

plan

atio

n r

evea

l wh

y I

chos

e th

is s

trat

egy?

U

se o

f M

ath

emat

ical

Ter

ms

Doe

s m

y ex

plan

atio

n in

clu

de

prop

er c

once

pts,

labe

ls, d

etai

ls,

sym

bols

, an

d co

rrec

t m

ath

ter

ms?

4 M

y ex

plan

atio

n o

f th

e st

rate

gy

incl

ude

s al

l de

tail

s an

d is

wel

l or

gan

ized

.

I fu

lly

expl

ain

wh

y I

chos

e th

is

effe

ctiv

e an

d ef

fici

ent

stra

tegy

th

at

lead

s to

a c

omp

lete

ly c

orre

ct

con

clu

sion

or

solu

tion

.

I u

se a

ll o

f th

e pr

oper

con

cept

s,

labe

ls, d

etai

ls, s

ymbo

ls, a

nd

corr

ect

mat

h t

erm

s in

my

expl

anat

ion

.

3 M

y ex

plan

atio

n o

f th

e st

rate

gy

incl

ude

s m

ost

deta

ils

and

is

orga

niz

ed.

I m

ostl

y ex

plai

n w

hy

I ch

ose

this

ef

fect

ive

stra

tegy

th

at le

ads

to a

co

mp

lete

ly c

orre

ct c

oncl

usi

on o

r so

luti

on.

I u

se m

ost

of t

he

prop

er c

once

pts,

la

bels

, det

ails

, sym

bols

, an

d co

rrec

t m

ath

ter

ms

in m

y ex

plan

atio

n.

2 M

y ex

plan

atio

n o

f th

e st

rate

gy

incl

ude

s so

me

deta

ils

and

is

diso

rgan

ized

.

I pa

rtia

lly

expl

ain

wh

y I

chos

e th

is

stra

tegy

th

at le

ads

to a

par

tial

ly

corr

ect

con

clu

sion

or

solu

tion

.

I u

se s

ome

of t

he

prop

er c

once

pts,

la

bels

, det

ails

, sym

bols

, an

d co

rrec

t m

ath

ter

ms

in m

y ex

plan

atio

n.

1 M

y ex

plan

atio

n o

f th

e st

rate

gy

incl

ude

s fe

w o

r n

o de

tail

s an

d is

n

ot o

rgan

ized

.

I do

not

exp

lain

wh

y I

chos

e th

is

stra

tegy

th

at le

ads

to a

n i

nco

rrec

t co

ncl

usi

on o

r so

luti

on.

I u

se f

ew o

r n

one

of t

he

prop

er

con

cept

s, la

bels

, det

ails

, sym

bols

, an

d co

rrec

t m

ath

ter

ms

in m

y ex

plan

atio

n.


Mat

hem

atic

al R

easo

nin

g -

An

alyt

ic R

ub

ric

– H

igh

Sch

ool

My

impl

emen

tati

on in

clu

des

orga

niz

ed m

ath

emat

ical

ste

ps/p

roce

dure

s an

d re

leva

nt

deta

ils.

Im

ple

men

tati

on o

f th

e S

trat

egy

Doe

s my

impl

emen

tatio

n in

clud

e or

gani

zed

step

s, pr

oced

ures

, and

re

leva

nt d

etai

ls?

R

atio

nal

e fo

r th

e S

trat

egy

Ch

oice

D

oes m

y ex

plan

atio

n re

veal

why

I se

lect

th

e co

ncep

ts p

rese

nted

in m

y so

lutio

n?

U

se o

f M

ath

emat

ical

Ter

ms

Doe

s my

resp

onse

incl

ude

accu

rate

labe

ls,

sym

bols

, con

cept

s, te

rmin

olog

y, a

nd

repr

esen

tatio

ns?

4 M

y im

plem

enta

tion

is fu

lly

deve

lope

d an

d is

com

plet

ely

supp

orte

d by

rele

vant

and

spec

ific

deta

ils fr

om th

e pr

oble

m.

I inc

lude

a c

orre

ct, t

horo

ugh,

and

wel

l or

gani

zed

expl

anat

ion

com

plet

ely

base

d up

on m

athe

mat

ical

trut

hs o

f why

I se

lect

th

e co

ncep

ts a

nd re

pres

enta

tions

pre

sent

ed

in m

y co

rrec

t sol

utio

n.

I use

all

of th

e la

bels

, sym

bols

, con

cept

s, te

rmin

olog

y, a

nd re

pres

enta

tions

ac

cura

tely

, cle

arly

, and

succ

inct

ly in

my

resp

onse

.

3 M

y im

plem

enta

tion

is m

ostly

de

velo

ped

and

supp

orte

d by

rele

vant

an

d sp

ecifi

c de

tails

from

the

prob

lem

.

I inc

lude

a c

orre

ct e

xpla

natio

n ba

sed

on

mat

hem

atic

al tr

uths

of w

hy I

sele

ct th

e co

ncep

ts a

nd re

pres

enta

tions

pre

sent

ed in

m

y co

rrec

t sol

utio

n.

I use

mos

t of t

he la

bels

, sym

bols

, co

ncep

ts, t

erm

inol

ogy,

and

re

pres

enta

tions

acc

urat

ely,

cle

arly

, and

su

ccin

ctly

in m

y re

spon

se.

2 M

y im

plem

enta

tion

is so

mew

hat

deve

lope

d an

d su

ppor

ted

by re

leva

nt

and

spec

ific

deta

ils fr

om th

e pr

oble

m.

I inc

lude

a p

artia

lly c

orre

ct a

nd so

mew

hat

orga

nize

d ex

plan

atio

n of

why

I se

lect

the

conc

epts

and

repr

esen

tatio

ns p

rese

nted

in

my

solu

tion.

I use

som

e of

the

labe

ls, s

ymbo

ls,

conc

epts

, ter

min

olog

y, a

nd

repr

esen

tatio

ns a

ccur

atel

y in

my

resp

onse

.

1 M

y im

plem

enta

tion

is r

arel

y su

ppor

ted

by re

leva

nt a

nd sp

ecifi

c de

tails

from

the

prob

lem

.

I inc

lude

an

inco

rrec

t, di

sorg

aniz

ed, o

r m

inim

al e

xpla

natio

n of

why

I se

lect

the

conc

epts

and

repr

esen

tatio

ns p

rese

nted

in

my

solu

tion.

I use

few

or

none

of t

he la

bels

, sym

bols

, co

ncep

ts, t

erm

inol

ogy,

or r

epre

sent

atio

ns

in m

y re

spon

se.


Mat

hem

atic

al R

epre

sen

tati

on -

An

alyt

ic R

ub

ric

– P

rim

ary

Lev

el

Th

is is

how

I s

how

my

info

rmat

ion

in a

gra

ph o

r pi

ctu

re.

A

ccu

racy

D

oes

my

grap

h o

r pi

ctu

re

corr

ectl

y sh

ow t

he

info

rmat

ion

?

F

orm

at

Do

I co

rrec

tly

show

all

th

e pa

rts

I n

eed

in t

he

grap

h o

r pi

ctu

re?

C

oncl

usi

on

Do

I su

ppor

t m

y an

swer

wit

h t

he

grap

h o

r pi

ctu

re?

4

M

y gr

aph

or

pict

ure

an

d in

form

atio

n a

re

com

ple

tely

cor

rect

.

I

put

all

of t

he

part

s I

nee

d in

my

grap

h o

r pi

ctu

re.

I

com

ple

tely

su

ppor

t m

y co

rrec

t an

swer

wit

h t

he

grap

h

or p

ictu

re.

3

M

y gr

aph

or

pict

ure

an

d in

form

atio

n a

re m

ostl

y co

rrec

t.

I pu

t m

ost

of t

he

part

s I

nee

d in

my

grap

h o

r pi

ctu

re.

I

mos

tly

supp

ort

my

corr

ect

answ

er w

ith

th

e gr

aph

or

pict

ure

.

2

My

grap

h o

r pi

ctu

re o

r in

form

atio

n is

par

tly

corr

ect.

I pu

t so

me

of t

he

part

s I

nee

d in

my

grap

h o

r pi

ctu

re.

I

par

tly

supp

ort

my

answ

er

wit

h t

he

grap

h o

r pi

ctu

re.

1

My

grap

h o

r pi

ctu

re o

r in

form

atio

n is

not

cor

rect

.

I pu

t fe

w o

r n

one

of t

he

part

s I

nee

d in

my

grap

h

or p

ictu

re.

I

do n

ot s

upp

ort

my

answ

er

wit

h t

he

grap

h o

r pi

ctu

re.


Mat

hem

atic

al R

epre

sen

tati

on -

An

alyt

ic R

ub

ric

– In

term

edia

te L

evel

T

his

is h

ow I

rep

rese

nt

my

data

an

d an

swer

.

Acc

ura

cy

Doe

s m

y re

pres

enta

tion

cor

rect

ly

disp

lay

the

data

?

F

orm

at

Do

I re

pre

sen

t al

l of

the

labe

ls,

oper

atio

n s

ymbo

ls, t

itle

s, a

nd/

or

keys

for

the

type

of

disp

lay

or

grap

h I

ch

ose?

C

oncl

usi

on

Do

I st

ate

my

con

clu

sion

wit

h

supp

ort

from

my

repr

esen

tati

on?

4 M

y re

pres

enta

tion

is c

omp

lete

lyco

rrec

t in

dis

play

ing

all

of t

he

data

.

I in

clu

de a

ll o

f th

e la

bels

, op

erat

ion

sym

bols

, tit

les,

an

d/or

ke

ys fo

r th

e ty

pe o

f di

spla

y or

gr

aph

I c

hos

e.

I st

ate

my

corr

ect

con

clu

sion

co

mp

lete

lysu

ppor

ted

from

my

repr

esen

tati

on.

3 M

y re

pres

enta

tion

is m

ostl

y co

rrec

t in

dis

play

ing

mos

t of

th

e da

ta.

I in

clu

de m

ost

of t

he

labe

ls,

oper

atio

n s

ymbo

ls, t

itle

s, a

nd/

or

keys

for

th

e ty

pe o

f di

spla

y or

gr

aph

I c

hos

e.

I st

ate

my

corr

ect

con

clu

sion

m

ostl

y su

ppor

ted

from

my

repr

esen

tati

on.

2 M

y re

pres

enta

tion

is p

artl

y co

rrec

t in

dis

play

ing

som

e of

th

e da

ta.

I in

clu

de s

ome

of t

he

labe

ls,

oper

atio

n s

ymbo

ls, t

itle

s, a

nd/

or

keys

for

th

e ty

pe o

f di

spla

y or

gr

aph

I c

hos

e.

I st

ate

my

con

clu

sion

par

tly

supp

orte

d fr

om m

y re

pres

enta

tion

.

1

My

repr

esen

tati

on is

not

cor

rect

in

dis

play

ing

the

data

.

I in

clu

de f

ew o

r n

one

of t

he

labe

ls, o

pera

tion

sym

bols

, tit

les,

an

d/or

key

s fo

r th

e ty

pe o

f di

spla

y or

gra

ph I

ch

ose.

I st

ate

my

con

clu

sion

wit

hou

t su

ppor

t fr

om m

y re

pres

enta

tion

.


Mat

hem

atic

al R

epre

sen

tati

on -

An

alyt

ic R

ub

ric

– M

idd

le S

choo

l L

evel

T

his

is h

ow I

rep

rese

nt

the

prob

lem

an

d so

luti

on.

A

ccu

racy

D

oes

my

repr

esen

tati

on a

ccu

rate

ly

disp

lay

the

prob

lem

?

F

orm

at

Do

I in

clu

de a

ll o

f th

e la

bels

, ope

rati

on

sym

bols

, tit

les,

an

d/or

key

s fo

r th

e ty

pe o

f re

pres

enta

tion

I c

hos

e?

C

oncl

usi

on

Do

I st

ate

my

con

clu

sion

wit

h s

upp

ort

from

my

repr

esen

tati

on?

4

My

repr

esen

tati

on is

com

ple

tely

ac

cura

te a

nd

incl

ude

s al

l of

th

e da

ta a

nd

all

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

I in

clu

de a

ll o

f th

e la

bels

, ope

rati

on

sym

bols

, tit

les,

an

d/or

key

s fo

r th

e ty

pe

of r

epre

sen

tati

on I

ch

ose.

I st

ate

my

corr

ect

con

clu

sion

co

mp

lete

ly s

upp

orte

d fr

om m

y re

pres

enta

tion

.

3

My

repr

esen

tati

on is

mos

tly

accu

rate

an

d in

clu

des

mos

t of

th

e da

ta a

nd

mos

t of

th

e n

eces

sary

re

lati

onsh

ips

in t

he

prob

lem

.

I in

clu

de m

ost

of t

he

labe

ls, o

pera

tion

sy

mbo

ls, t

itle

s, a

nd/

or k

eys

for

the

type

of

rep

rese

nta

tion

I c

hos

e.

I st

ate

my

corr

ect

con

clu

sion

mos

tly

supp

orte

d fr

om m

y re

pres

enta

tion

.

2 M

y re

pres

enta

tion

is p

arti

ally

ac

cura

te a

nd

incl

ude

s so

me

of t

he

data

an

d so

me

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

I in

clu

de s

ome

of t

he

labe

ls, o

pera

tion

sy

mbo

ls, t

itle

s, a

nd/

or k

eys

for

the

type

of

rep

rese

nta

tion

I c

hos

e.

I st

ate

my

con

clu

sion

par

tly

supp

orte

d fr

om m

y re

pres

enta

tion

or

my

repr

esen

tati

on le

ads

to a

n

un

stat

ed c

oncl

usi

on.

1 M

y re

pres

enta

tion

is n

ot a

ccu

rate

an

d in

clu

des

few

or

non

e of

th

e da

ta o

r n

eces

sary

rel

atio

nsh

ips

in

the

prob

lem

.

I in

clu

de f

ew o

r n

one

of t

he

labe

ls,

oper

atio

n s

ymbo

ls, t

itle

s, a

nd/

or k

eys

for

the

type

of

repr

esen

tati

on I

ch

ose.

I st

ate

my

con

clu

sion

wit

hou

t su

ppor

t fr

om m

y re

pres

enta

tion

or

I do

not

sta

te a

con

clu

sion

.


Mat

hem

atic

al R

epre

sen

tati

on -

An

alyt

ic R

ub

ric

– H

igh

Sch

ool

Lev

el

Th

is is

how

I r

epre

sen

t th

e pr

oble

m a

nd

solu

tion

.

Acc

ura

cy

Do

I ac

cura

tely

rep

rese

nt

all o

f m

y da

ta?

F

orm

at

Do

I co

rrec

tly

rep

rese

nt

all n

eces

sary

re

lati

onsh

ips?

C

oncl

usi

on

Do

I st

ate

my

con

clu

sion

an

d/or

ge

ner

aliz

atio

n w

ith

su

ppor

t fr

om m

y re

pres

enta

tion

?

4

My

repr

esen

tati

on(s

) is

wel

l pr

esen

ted

wit

h a

ll d

etai

ls w

ell

exec

ute

d in

th

at it

is c

ompl

ete,

ac

cura

te, c

lear

, cor

rect

, an

d ea

sy

to in

terp

ret.

I re

pres

ent

the

elem

ents

in a

n

insi

ghtf

ul s

elec

tion

/for

mat

th

at

illu

stra

tes

all

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

I st

ate

my

corr

ect

con

clu

sion

an

d/or

gen

eral

izat

ion

co

mp

lete

ly s

upp

orte

d fr

om m

y re

pres

enta

tion

.

3

My

repr

esen

tati

on(s

) is

ap

prop

riat

e in

th

at it

is m

ostl

y co

mpl

ete,

acc

ura

te, c

lear

, cor

rect

, an

d ea

sy t

o in

terp

ret.

I re

pres

ent

the

elem

ents

in a

n

appr

opri

ate

sele

ctio

n/f

orm

at t

hat

il

lust

rate

s m

ost

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

I st

ate

my

corr

ect

con

clu

sion

an

d/or

gen

eral

izat

ion

mos

tly

supp

orte

d fr

om m

y re

pres

enta

tion

.

2 M

y re

pres

enta

tion

(s)

is

som

ewh

at c

ompl

ete,

acc

ura

te

and/

or p

arti

ally

cor

rect

, an

d so

me

part

s ar

e ea

sy t

o in

terp

ret.

I pa

rtia

lly

repr

esen

t th

e el

emen

ts

in a

sel

ecti

on/f

orm

at t

hat

il

lust

rate

s so

me

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

I st

ate

my

con

clu

sion

an

d/or

ge

ner

aliz

atio

n p

artl

y su

ppor

ted

from

my

repr

esen

tati

on.

1 M

y re

pres

enta

tion

(s)

is

inco

mpl

ete,

inac

cura

te, i

nco

rrec

t,

and

is d

iffi

cult

to

inte

rpre

t.

I re

pres

ent

the

elem

ents

in a

se

lect

ion

/for

mat

th

at il

lust

rate

few

or

non

e of

th

e n

eces

sary

re

lati

onsh

ips

in t

he

prob

lem

.

I m

ay o

r m

ay n

ot s

tate

my

con

clu

sion

an

d/or

gen

eral

izat

ion

w

ith

out

supp

ort

from

my

repr

esen

tati

on.


Mat

hem

atic

al C

omm

unic

atio

n H

olis

tic

Rub

ric

- Pri

mar

y Le

vel

This

is h

ow I

solv

e th

e pr

oble

m.

4

• M

y w

ork

is w

ell o

rgan

ized

and

eas

y to

und

erst

and.

•

I exp

lain

all

of th

e st

eps t

hat I

use

to g

et a

corr

ect a

nsw

er.

• I u

se a

ll of

the

corr

ect l

abel

s, de

tails

, sym

bols

, and

mat

h te

rms t

o ex

plai

n m

y w

ork.

3 •

My

wor

k is

mos

tly

orga

nize

d an

d ea

sy to

und

erst

and.

•

I exp

lain

mos

t of t

he st

eps t

hat I

use

to g

et a

corr

ect a

nsw

er.

• I u

se m

ost o

f the

corr

ect l

abel

s, de

tails

, sym

bols

, and

mat

h te

rms t

o ex

plai

n m

y w

ork.

2 •

My

wor

k is

poo

rly

orga

nize

d an

d is

har

d to

und

erst

and.

•

I exp

lain

som

e of

the

step

s tha

t I u

se to

get

an

answ

er.

• I u

se s

ome

labe

ls, d

etai

ls, s

ymbo

ls, a

nd m

ath

term

s to

expl

ain

my

wor

k.

1

• M

y w

ork

is n

ot o

rgan

ized

to sh

ow h

ow I

solv

e th

e pr

oble

m.

• I d

o no

t exp

lain

the

step

s tha

t I u

se to

get

an

answ

er.

• I d

o no

t use

labe

ls, d

etai

ls, s

ymbo

ls, o

r mat

h te

rms t

o ex

plai

n m

y w

ork.


M

athe

mat

ical

Com

mun

icat

ion

- Hol

isti

c R

ubri

c - I

nter

med

iate

Lev

el

This

is h

ow I

solv

e th

e pr

oble

m.

4

• M

y w

ork

is w

ell o

rgan

ized

, mak

es se

nse,

and

is e

asy

to u

nder

stan

d.

• I i

nclu

de a

n ac

cura

te e

xpla

natio

n of

all

of th

e st

eps n

eede

d to

corr

ectly

solv

e th

e pr

oble

m.

• I u

se a

ll of

the

prop

er la

bels

, det

ails

, sym

bols

, and

corr

ect m

ath

term

s in

my

expl

anat

ion.

3 •

My

wor

k is

mos

tly

orga

nize

d, m

akes

sens

e, a

nd is

eas

y to

und

erst

and.

•

I inc

lude

an

accu

rate

exp

lana

tion

of m

ost o

f the

step

s nee

ded

to co

rrec

tly so

lve

the

prob

lem

. •

I use

mos

t of t

he p

rope

r lab

els,

deta

ils, s

ymbo

ls, a

nd co

rrec

t mat

h te

rms i

n m

y ex

plan

atio

n.

2

• M

y w

ork

is p

oorl

y or

gani

zed,

har

d to

und

erst

and,

and

is co

nfus

ing.

•

I inc

lude

an

expl

anat

ion

of s

ome

of th

e st

eps n

eede

d to

solv

e th

e pr

oble

m.

• I u

se s

ome

of th

e pr

oper

labe

ls, d

etai

ls, s

ymbo

ls, a

nd co

rrec

t mat

h te

rms i

n m

y ex

plan

atio

n.

1

• M

y w

ork

is n

ot o

rgan

ized

, doe

s not

mak

e se

nse,

and

is v

ery

conf

usin

g.

• I i

nclu

de a

n ex

plan

atio

n of

few

or

none

of t

he st

eps n

eede

d to

solv

e th

e pr

oble

m.

• I d

o no

t use

pro

per l

abel

s, de

tails

, sym

bols

, and

corr

ect m

ath

term

s in

my

expl

anat

ion.


M

athe

mat

ical

Com

mun

icat

ion

- Hol

isti

c R

ubri

c - M

iddl

e Sc

hool

Lev

el

This

is h

ow I

solv

e th

e pr

oble

m.

4

• M

y re

spon

se is

wel

l org

aniz

ed a

nd is

logi

cal.

• I i

nclu

de a

n ac

cura

te, c

ompl

ete,

and

thor

ough

exp

lana

tion

of a

ll of

the

step

s nee

ded

to

corr

ectly

solv

e th

e pr

oble

m.

• I u

se a

ll of

the

prop

er co

ncep

ts, l

abel

s, de

tails

, sym

bols

, and

corr

ect m

ath

term

s in

my

expl

anat

ion.

3 •

My

resp

onse

is m

ostl

y or

gani

zed

and

is lo

gica

l. •

I inc

lude

an

accu

rate

exp

lana

tion

of m

ost o

f the

step

s nee

ded

to co

rrec

tly so

lve

the

prob

lem

. •

I use

mos

t of t

he p

rope

r con

cept

s, la

bels

, det

ails

, sym

bols

, and

corr

ect m

ath

term

s in

my

expl

anat

ion.

2 •

My

resp

onse

is p

oorl

y or

gani

zed

or is

illo

gica

l. •

I inc

lude

an

expl

anat

ion

of s

ome

of th

e st

eps n

eede

d to

solv

e th

e pr

oble

m.

• I u

se s

ome

of th

e pr

oper

conc

epts

, lab

els,

deta

ils, s

ymbo

ls, a

nd co

rrec

t mat

h te

rms i

n m

y ex

plan

atio

n.

1

• M

y re

spon

se is

not

org

aniz

ed a

nd is

illo

gica

l. •

I inc

lude

an

expl

anat

ion

of fe

w o

r no

ne o

f the

step

s nee

ded

to so

lve

the

prob

lem

. •

I use

few

or

none

of t

he p

rope

r con

cept

s, la

bels

, det

ails

, sym

bols

, and

corr

ect m

ath

term

s in

my

expl

anat

ion.


M

athe

mat

ical

Com

mun

icat

ion

- Hol

isti

c R

ubri

c - H

igh

Scho

ol L

evel

Th

is is

how

I so

lve

the

prob

lem

.

4 •

My

resp

onse

is th

orou

gh, w

ell o

rgan

ized

, and

logi

cal.

• I i

nclu

de a

com

plet

e an

d co

rrec

t exp

lana

tion

usin

g al

l of t

he re

leva

nt a

nd sp

ecifi

c det

ails

from

the

prob

lem

w

hen

desc

ribi

ng th

e pr

oced

ures

use

d to

arr

ive

at th

e cor

rect

solu

tion.

•

I use

all

of th

e la

bels

, sym

bols

, con

cept

s, te

rmin

olog

y, a

nd re

pres

enta

tions

acc

urat

ely,

clea

rly

and

succ

inct

ly in

my

resp

onse

.

3 •

My

resp

onse

is m

ostl

y or

gani

zed

and

logi

cal.

• I i

nclu

de a

corr

ect e

xpla

natio

n us

ing

mos

t of t

he re

leva

nt a

nd sp

ecifi

c det

ails

from

the

prob

lem

whe

n de

scri

bing

the

proc

edur

es u

sed

to a

rriv

e at

the

corr

ect s

olut

ion.

•

I use

mos

t of t

he la

bels

, sym

bols

, con

cept

s, te

rmin

olog

y, a

nd re

pres

enta

tions

acc

urat

ely,

clea

rly,

and

su

ccin

ctly

in m

y re

spon

se.

2

• M

y re

spon

se is

poo

rly

orga

nize

d or

is il

logi

cal.

• I i

nclu

de a

n ex

plan

atio

n us

ing

som

e of

the

rele

vant

and

spec

ific d

etai

ls fr

om th

e pr

oble

m w

hen

desc

ribi

ng

the

proc

edur

es u

sed

to a

rriv

e at

a so

lutio

n.

• I u

se s

ome

of th

e la

bels

, sym

bols

, con

cept

s, te

rmin

olog

y, a

nd re

pres

enta

tions

acc

urat

ely

in m

y re

spon

se.

1

• M

y re

spon

se is

not

org

aniz

ed a

nd is

illo

gica

l. •

I inc

lude

an

expl

anat

ion

usin

g fe

w o

r no

ne o

f the

rele

vant

or s

peci

fic d

etai

ls fr

om th

e pr

oble

m w

hen

desc

ribi

ng th

e pr

oced

ures

. •

I use

few

or

none

of t

he la

bels

, sym

bols

, con

cept

s, te

rmin

olog

y, o

r rep

rese

ntat

ions

in m

y re

spon

se.


Mat

hem

atic

al R

easo

ning

- H

olis

tic

Rub

ric

- Pri

mar

y Le

vel

This

is w

hy I

solv

e th

e pr

oble

m th

is w

ay.

4

• M

y ex

plan

atio

n in

clud

es a

ll of

the

step

s, is

wel

l org

aniz

ed, a

nd m

akes

sens

e.

• I e

xpla

in w

hy I

chos

e th

is st

rate

gy to

corr

ectly

solv

e th

e pr

oble

m in

clud

ing

all t

he

info

rmat

ion

need

ed.

• I u

se a

ll of

the

corr

ect l

abel

s, de

tails

, sym

bols

, and

mat

h te

rms t

o ex

plai

n m

y w

ork.

3 •

My

expl

anat

ion

incl

udes

mos

t of t

he st

eps,

is o

rgan

ized

, and

mak

es se

nse.

•

I exp

lain

why

I ch

ose

this

stra

tegy

to co

rrec

tly so

lve

the

prob

lem

and

incl

ude

mos

t of t

he

info

rmat

ion

need

ed.

• I u

se m

ost o

f the

corr

ect l

abel

s, de

tails

, sym

bols

, and

mat

h te

rms t

o ex

plai

n m

y w

ork.

2 •

My

expl

anat

ion

incl

udes

som

e of

the

step

s, is

not

org

aniz

ed, b

ut m

akes

som

e se

nse.

•

I exp

lain

why

I ch

ose

this

stra

tegy

to so

lve

the

prob

lem

and

incl

ude

som

e of

the

info

rmat

ion

need

ed.

• I u

se s

ome

labe

ls, d

etai

ls, s

ymbo

ls, a

nd m

ath

term

s to

expl

ain

my

wor

k.

1

• M

y ex

plan

atio

n in

clud

es fe

w o

r no

ne o

f the

step

s, is

not

org

aniz

ed, a

nd d

oes n

ot m

ake

sens

e.

• I d

o no

t exp

lain

why

I ch

ose

this

stra

tegy

to so

lve

the

prob

lem

and

I in

clud

e lit

tle o

r no

info

rmat

ion

need

ed to

supp

ort m

y st

rate

gy.

• I d

o no

t use

labe

ls, d

etai

ls, s

ymbo

ls, o

r mat

h te

rms t

o ex

plai

n m

y w

ork.


Mat

hem

atic

al R

easo

nin

g -

Hol

isti

c R

ub

ric

- In

term

edia

te L

evel

T

his

is w

hy

I so

lve

the

prob

lem

th

is w

ay.

4

• M

y ex

plan

atio

n d

escr

ibes

my

stra

tegy

in a

hig

hly

sk

illf

ul

way

th

at is

cle

ar, o

rgan

ized

, an

d m

akes

sen

se.

•

I co

mp

lete

ly e

xpla

in w

hy

I ch

ose

this

cor

rect

str

ateg

y to

sol

ve t

he

prob

lem

. •

I u

se a

ll o

f th

e pr

oper

labe

ls, d

etai

ls, s

ymbo

ls, a

nd

corr

ect

mat

h t

erm

s in

my

expl

anat

ion

.

3 •

My

expl

anat

ion

des

crib

es m

y st

rate

gy in

a m

ostl

y sk

illf

ul

way

th

at is

org

aniz

ed a

nd

mak

es s

ense

. •

I m

ostl

y ex

plai

n w

hy

I ch

ose

this

cor

rect

str

ateg

y to

sol

ve t

he

prob

lem

. •

I u

se m

ost

of t

he

prop

er la

bels

, det

ails

, sym

bols

, an

d co

rrec

t m

ath

ter

ms

in m

y ex

plan

atio

n.

2

• M

y ex

plan

atio

n d

escr

ibes

my

stra

tegy

in a

som

ewh

at s

kil

lfu

l w

ay t

hat

is n

ot o

rgan

ized

bu

t m

akes

som

e se

nse

. •

I p

arti

ally

exp

lain

wh

y I

chos

e th

is s

trat

egy

to s

olve

th

e pr

oble

m.

• I

use

som

e of

th

e pr

oper

labe

ls, d

etai

ls, s

ymbo

ls, a

nd

corr

ect

mat

h t

erm

s in

my

expl

anat

ion

.

1 •

My

expl

anat

ion

doe

s n

ot d

escr

ibe

my

stra

tegy

in a

ski

llfu

l way

, is

not

org

aniz

ed, a

nd

does

n

ot m

ake

sen

se.

• I

do

not

exp

lain

wh

y I

chos

e th

is s

trat

egy

to s

olve

th

e pr

oble

m.

• I

do

not

use

pro

per

labe

ls, d

etai

ls, s

ymbo

ls, a

nd

corr

ect

mat

h t

erm

s in

my

expl

anat

ion

.


Mat

hem

atic

al R

easo

nin

g -

Hol

isti

c R

ub

ric

- M

idd

le S

choo

l L

evel

T

his

is w

hy

I so

lve

the

prob

lem

usi

ng

a se

lect

str

ateg

y.

4

• M

y ex

plan

atio

n o

f th

e st

rate

gy in

clu

des

all

deta

ils

and

is w

ell o

rgan

ized

. •

I fu

lly

expl

ain

wh

y I

chos

e th

is e

ffec

tive

an

d ef

fici

ent

stra

tegy

th

at le

ads

to a

com

ple

tely

co

rrec

t co

ncl

usi

on o

r so

luti

on.

• I

use

all

of

the

prop

er c

once

pts,

labe

ls, d

etai

ls, s

ymbo

ls, a

nd

corr

ect

mat

h t

erm

s in

my

expl

anat

ion

.

3 •

My

expl

anat

ion

of

the

stra

tegy

incl

ude

s m

ost

deta

ils

and

is o

rgan

ized

. •

I m

ostl

y ex

plai

n w

hy

I ch

ose

this

eff

ecti

ve s

trat

egy

that

lead

s to

a c

omp

lete

ly c

orre

ct

con

clu

sion

or

solu

tion

. •

I u

se m

ost

of t

he

prop

er c

once

pts,

labe

ls, d

etai

ls, s

ymbo

ls, a

nd

corr

ect

mat

h t

erm

s in

my

expl

anat

ion

.

2 •

My

expl

anat

ion

of

the

stra

tegy

incl

ude

s so

me

deta

ils

and

is d

isor

gan

ized

. •

I pa

rtia

lly

expl

ain

wh

y I

chos

e th

is s

trat

egy

that

lead

s to

a p

arti

ally

cor

rect

con

clu

sion

or

solu

tion

. •

I u

se s

ome

of t

he

prop

er c

once

pts,

labe

ls, d

etai

ls, s

ymbo

ls, a

nd

corr

ect

mat

h t

erm

s in

my

expl

anat

ion

.

1 •

My

expl

anat

ion

of

the

stra

tegy

incl

ude

s fe

w o

r n

o de

tail

s an

d is

not

org

aniz

ed.

• I

do n

ot e

xpla

in w

hy

I ch

ose

this

str

ateg

y th

at le

ads

to a

n i

nco

rrec

t co

ncl

usi

on o

r so

luti

on.

• I

use

few

or

non

e of

th

e pr

oper

con

cept

s, la

bels

, det

ails

, sym

bols

, an

d co

rrec

t m

ath

ter

ms

in m

y ex

plan

atio

n.


Mat

hem

atic

al R

easo

nin

g -

Hol

isti

c R

ub

ric

- H

igh

Sch

ool

Lev

el

My

impl

emen

tati

on in

clu

des

orga

niz

ed m

ath

emat

ical

ste

ps/p

roce

dure

s an

d re

leva

nt

deta

ils.

4 •

My

impl

emen

tati

on is

fu

lly

deve

lope

d an

d co

mpl

etel

y su

ppor

ted

by r

elev

ant

and

spec

ific

de

tail

s fr

om t

he

prob

lem

. •

I in

clu

de a

cor

rect

, th

orou

gh, a

nd

wel

l org

aniz

ed e

xpla

nat

ion

bas

ed o

n m

ath

emat

ical

tru

ths

of

wh

y I

sele

ct t

he

con

cept

s an

d re

pres

enta

tion

s pr

esen

ted

in m

y co

rrec

t so

luti

on.

• I

use

all

of

the

labe

ls, s

ymbo

ls, c

once

pts,

ter

min

olog

y, a

nd

repr

esen

tati

ons

accu

rate

ly, c

lear

ly,

and

succ

inct

ly in

my

resp

onse

.

3 •

My

impl

emen

tati

on is

mos

tly

deve

lope

d an

d su

ppor

ted

by r

elev

ant

and

spec

ific

det

ails

fro

m

the

prob

lem

. •

I in

clu

de a

cor

rect

exp

lan

atio

n b

ased

on

mat

hem

atic

al t

ruth

s of

wh

y I

sele

ct t

he

con

cept

s an

d re

pres

enta

tion

s pr

esen

ted

in m

y co

rrec

t so

luti

on.

• I

use

mos

t of

th

e la

bels

, sym

bols

, con

cept

s, t

erm

inol

ogy,

an

d re

pres

enta

tion

s ac

cura

tely

, cl

earl

y, a

nd

succ

inct

ly in

my

resp

onse

.

2 •

My

impl

emen

tati

on is

som

ewh

at d

evel

oped

an

d su

ppor

ted

by r

elev

ant

and

spec

ific

det

ails

fr

om t

he

prob

lem

. •

I in

clu

de a

par

tial

ly c

orre

ct a

nd

som

ewh

at o

rgan

ized

exp

lan

atio

n o

f w

hy

I se

lect

th

e co

nce

pts

and

repr

esen

tati

ons

pres

ente

d in

my

solu

tion

. •

I u

se s

ome

of t

he

labe

ls, s

ymbo

ls, c

once

pts,

ter

min

olog

y, a

nd

repr

esen

tati

ons

accu

rate

ly in

my

resp

onse

.

1 •

My

impl

emen

tati

on is

rar

ely

supp

orte

d by

rel

evan

t an

d sp

ecif

ic d

etai

ls f

rom

th

e pr

oble

m.

• I

incl

ude

an

inco

rrec

t, d

isor

gan

ized

, or

min

imal

exp

lan

atio

n o

f w

hy

I se

lect

th

e co

nce

pts

and

repr

esen

tati

ons

pres

ente

d in

my

solu

tion

. •

I u

se f

ew o

r n

one

of t

he

labe

ls, s

ymbo

ls, c

once

pts,

ter

min

olog

y, o

r re

pres

enta

tion

s in

my

resp

onse

.


Mat

hem

atic

al R

epre

sen

tati

on -

Hol

isti

c R

ub

ric

- P

rim

ary

Lev

el

Th

is is

how

I s

how

my

info

rmat

ion

in a

gra

ph o

r pi

ctu

re.

4

•

My

grap

h o

r pi

ctu

re a

nd

info

rmat

ion

are

com

ple

tely

cor

rect

. •

I pu

t al

l of

th

e pa

rts

I n

eed

in m

y gr

aph

or

pict

ure

. •

I co

mp

lete

ly s

upp

ort

my

corr

ect

answ

er w

ith

th

e gr

aph

or

pict

ure

.

3 •

My

grap

h o

r pi

ctu

re a

nd

info

rmat

ion

are

mos

tly

corr

ect.

•

I pu

t m

ost

of t

he

part

s I

nee

d in

my

grap

h o

r pi

ctu

re.

• I

mos

tly

supp

ort

my

corr

ect

answ

er w

ith

th

e gr

aph

or

pict

ure

.

2 •

My

grap

h o

r pi

ctu

re o

r in

form

atio

n is

par

tly

corr

ect.

•

I pu

t so

me

of t

he

part

s I

nee

d in

my

grap

h o

r pi

ctu

re.

• I

par

tly

supp

ort

my

answ

er w

ith

th

e gr

aph

or

pict

ure

.

1 •

My

grap

h o

r pi

ctu

re o

r in

form

atio

n is

not

cor

rect

. •

I pu

t fe

w o

r n

one

of t

he

part

s I

nee

d in

my

grap

h o

r pi

ctu

re.

• I

do n

ot s

upp

ort

my

answ

er w

ith

th

e gr

aph

or

pict

ure

.


Mat

hem

atic

al R

epre

sen

tati

on -

Hol

isti

c R

ub

ric

- In

term

edia

te L

evel

T

his

is h

ow I

rep

rese

nt

my

data

an

d an

swer

.

4 •

My

repr

esen

tatio

n is

com

plet

ely

corr

ect i

n di

spla

ying

all

of th

e da

ta.

• I i

nclu

de a

ll of

the

labe

ls, o

pera

tion

sym

bols

, titl

es, a

nd/o

r key

s for

the

type

of d

ispl

ay o

r gra

ph I

chos

e.

• I s

tate

my

corr

ect c

oncl

usio

n co

mpl

etel

y su

ppor

ted

from

my

repr

esen

tatio

n.

3

• M

y re

pres

enta

tion

is m

ostly

cor

rect

in d

ispl

ayin

g m

ost o

f the

dat

a.

• I i

nclu

de m

ost o

f the

labe

ls, o

pera

tion

sym

bols

, titl

es, a

nd/o

r key

s for

the

type

of d

ispl

ay o

r gra

ph I

chos

e.

• I s

tate

my

corr

ect c

oncl

usio

n m

ostly

supp

orte

d fr

om m

y re

pres

enta

tion.

2 •

My

repr

esen

tatio

n is

par

tly c

orre

ct in

dis

play

ing

som

e of

the

data

. •

I inc

lude

som

e of

the

labe

ls, o

pera

tion

sym

bols

, titl

es, a

nd/o

r key

s for

the

type

of d

ispl

ay o

r gra

ph I

chos

e.

• I s

tate

my

conc

lusi

on p

artly

supp

orte

d fr

om m

y re

pres

enta

tion.

1 •

My

repr

esen

tatio

n is

not

cor

rect

in d

ispl

ayin

g th

e da

ta.

• I i

nclu

de fe

w o

r no

ne o

f the

labe

ls, o

pera

tion

sym

bols

, titl

es, a

nd/o

r key

s for

the

type

of d

ispl

ay o

r gr

aph

I cho

se.

• I s

tate

my

conc

lusi

on w

ithou

t sup

port

from

my

repr

esen

tatio

n.


Mat

hem

atic

al R

epre

sen

tati

on -

Hol

isti

c R

ub

ric

- M

idd

le S

choo

l L

evel

T

his

is h

ow I

rep

rese

nt

the

prob

lem

an

d so

luti

on.

4

• M

y re

pres

enta

tion

is c

omp

lete

ly a

ccu

rate

an

d in

clu

des

all

of t

he

data

an

d al

l of

th

e n

eces

sary

rel

atio

nsh

ips

in t

he

prob

lem

. •

I in

clu

de a

ll o

f th

e la

bels

, ope

rati

on s

ymbo

ls, t

itle

s, a

nd/

or k

eys

for

the

type

of

repr

esen

tati

on I

ch

ose.

•

I st

ate

my

corr

ect

con

clu

sion

com

ple

tely

su

ppor

ted

from

my

repr

esen

tati

on.

3

• M

y re

pres

enta

tion

is m

ostl

y ac

cura

te a

nd

incl

ude

s m

ost

of t

he

data

an

d m

ost

of t

he

nec

essa

ry r

elat

ion

ship

s in

th

e pr

oble

m.

• I

incl

ude

mos

t of

th

e la

bels

, ope

rati

on s

ymbo

ls, t

itle

s, a

nd/

or k

eys

for

the

type

of

repr

esen

tati

on I

ch

ose.

•

I st

ate

my

corr

ect

con

clu

sion

mos

tly

supp

orte

d fr

om m

y re

pres

enta

tion

.

2 •

My

repr

esen

tati

on is

par

tial

ly a

ccu

rate

an

d in

clu

des

som

e of

th

e da

ta a

nd

som

e of

th

e n

eces

sary

rel

atio

nsh

ips

in t

he

prob

lem

. •

I in

clu

de s

ome

of t

he

labe

ls, o

pera

tion

sym

bols

, tit

les,

an

d/or

key

s fo

r th

e ty

pe o

f re

pres

enta

tion

I c

hos

e.

• I

stat

e m

y co

ncl

usi

on p

artl

y su

ppor

ted

from

my

repr

esen

tati

on o

r m

y re

pres

enta

tion

lead

s to

an

un

stat

ed c

oncl

usi

on.

1

• M

y re

pres

enta

tion

is n

ot a

ccu

rate

an

d in

clu

des

few

or

non

e of

th

e da

ta o

r n

eces

sary

re

lati

onsh

ips

in t

he

prob

lem

. •

I in

clu

de f

ew o

r n

one

of t

he

labe

ls, o

pera

tion

sym

bols

, tit

les,

an

d/or

key

s fo

r th

e ty

pe o

f re

pres

enta

tion

I c

hos

e.

• I

stat

e m

y co

ncl

usi

on w

ith

out

supp

ort

from

my

repr

esen

tati

on o

r I

do n

ot s

tate

a c

oncl

usi

on.


Mat

hem

atic

al R

epre

sen

tati

on -

Hol

isti

c R

ub

ric

- H

igh

Sch

ool

Lev

el

Th

is is

how

I r

epre

sen

t th

e pr

oble

m a

nd

solu

tion

.

4 •

My

repr

esen

tati

on(s

) is

wel

l pre

sen

ted

wit

h a

ll d

etai

ls w

ell e

xecu

ted

in t

hat

it is

com

plet

e,

accu

rate

, cle

ar, c

orre

ct, a

nd

easy

to

inte

rpre

t.

• I

repr

esen

t th

e el

emen

ts in

an

insi

ghtf

ul s

elec

tion

/for

mat

th

at il

lust

rate

s al

l of

th

e n

eces

sary

re

lati

onsh

ips

in t

he

prob

lem

. •

I st

ate

my

corr

ect

con

clu

sion

an

d/or

gen

eral

izat

ion

com

ple

tely

su

ppor

ted

from

my

repr

esen

tati

on.

3

• M

y re

pres

enta

tion

(s)

is a

ppro

pria

te in

th

at it

is m

ostl

y co

mpl

ete,

acc

ura

te, c

lear

, cor

rect

, an

d ea

sy t

o in

terp

ret.

•

I re

pres

ent

the

elem

ents

in a

n a

ppro

pria

te s

elec

tion

/for

mat

th

at il

lust

rate

s m

ost

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

• I

stat

e m

y co

rrec

t co

ncl

usi

on a

nd/

or g

ener

aliz

atio

n m

ostl

y su

ppor

ted

from

my

repr

esen

tati

on.

2

• M

y re

pres

enta

tion

(s)

is s

omew

hat

com

plet

e, a

ccu

rate

, an

d/or

par

tial

ly c

orre

ct a

nd

som

e pa

rts

are

easy

to

inte

rpre

t.

• I

part

iall

y re

pres

ent

the

elem

ents

in a

sel

ecti

on/f

orm

at t

hat

illu

stra

tes

som

e of

th

e n

eces

sary

re

lati

onsh

ips

in t

he

prob

lem

. •

I st

ate

my

con

clu

sion

an

d/or

gen

eral

izat

ion

par

tly

supp

orte

d fr

om m

y re

pres

enta

tion

.

1 •

My

repr

esen

tati

on(s

) is

inco

mpl

ete,

inac

cura

te, i

nco

rrec

t, a

nd

is d

iffi

cult

to

inte

rpre

t •

I re

pres

ent

the

elem

ents

in a

sel

ecti

on/f

orm

at t

hat

illu

stra

te f

ew o

r n

one

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

• I

may

or

may

not

sta

te m

y co

ncl

usi

on a

nd/

or g

ener

aliz

atio

n w

ith

out

supp

ort

from

my

repr

esen

tati

on.


M

athe

mat

ics C

ombi

natio

n R

ubri

c –

Prim

ary

Lev

el

Com

mun

icat

ions

Th

is is

how

I so

lve

the

prob

lem

.

R

easo

ning

Th

is is

why

I so

lve

the

prob

lem

this

way

.

R

epre

sent

atio

n Th

is is

how

I sh

ow m

y in

form

atio

n in

a g

raph

or

pict

ure.

4

• M

y w

ork

is w

ell o

rgan

ized

and

eas

y to

un

ders

tand

. •

I exp

lain

all

of th

e st

eps t

hat I

use

to

get a

corr

ect a

nsw

er.

• M

y ex

plan

atio

n in

clud

es a

ll of

the

step

s, is

wel

l or

gani

zed,

and

mak

es se

nse.

•

I exp

lain

why

I ch

ose

this

stra

tegy

to co

rrec

tly

solv

e th

e pr

oble

m in

clud

ing

all t

he in

form

atio

n ne

eded

. •

I use

all

of th

e co

rrec

t lab

els,

deta

ils, s

ymbo

ls,

and

mat

h te

rms t

o ex

plai

n m

y w

ork.

•

My

grap

h or

pic

ture

and

info

rmat

ion

are

com

plet

ely

corr

ect.

• I p

ut a

ll of

the

part

s I n

eed

in m

y gr

aph

or

pict

ure.

•

I com

plet

ely

supp

ort m

y co

rrec

t ans

wer

w

ith th

e gr

aph

or p

ictu

re.

3

• M

y w

ork

is m

ostl

y or

gani

zed

and

easy

to

und

erst

and.

•

I exp

lain

mos

t of t

he st

eps t

hat I

use

to

get a

corr

ect a

nsw

er.

• M

y ex

plan

atio

n in

clud

es m

ost o

f the

step

s, is

or

gani

zed,

and

mak

es se

nse.

•

I exp

lain

why

I ch

ose

this

stra

tegy

to co

rrec

tly

solv

e th

e pr

oble

m a

nd in

clud

e m

ost o

f the

in

form

atio

n ne

eded

. •

I use

mos

t of t

he co

rrec

t lab

els,

deta

ils,

sym

bols

, and

mat

h te

rms t

o ex

plai

n m

y w

ork.

•

My

grap

h or

pic

ture

and

info

rmat

ion

are

mos

tly

corr

ect.

• I p

ut m

ost o

f the

par

ts I

need

in m

y gr

aph

or

pict

ure.

•

I mos

tly

supp

ort m

y co

rrec

t ans

wer

with

the

grap

h or

pic

ture

.

2

• M

y w

ork

is p

oorl

y or

gani

zed

and

is

hard

to u

nder

stan

d.

• I e

xpla

in s

ome

of th

e st

eps t

hat I

use

to

get

an

answ

er.

• M

y ex

plan

atio

n in

clud

es s

ome

of th

e st

eps,

is

not o

rgan

ized

, but

mak

es so

me

sens

e.

• I e

xpla

in w

hy I

chos

e th

is st

rate

gy to

solv

e th

e pr

oble

m a

nd in

clud

e so

me

of th

e in

form

atio

n ne

eded

. •

I use

som

e la

bels

, det

ails

, sym

bols

, and

mat

h te

rms t

o ex

plai

n m

y w

ork.

•

My

grap

h or

pic

ture

or i

nfor

mat

ion

is p

artl

y co

rrec

t. •

I put

som

e of

the

part

s I n

eed

in m

y gr

aph

or

pict

ure.

•

I par

tly

supp

ort m

y an

swer

with

the

grap

h or

pic

ture

.

1

• M

y w

ork

is n

ot o

rgan

ized

to sh

ow h

ow

I sol

ve th

e pr

oble

m.

• I d

o no

t exp

lain

the

step

s tha

t I u

se to

ge

t an

answ

er.

• M

y ex

plan

atio

n in

clud

es fe

w o

r no

ne o

f the

st

eps,

is n

ot o

rgan

ized

and

doe

s not

mak

e se

nse.

• I d

o no

t exp

lain

why

I ch

ose

this

stra

tegy

to

solv

e th

e pr

oble

m a

nd I

incl

ude

little

or n

o in

form

atio

n ne

eded

to su

ppor

t my

stra

tegy

. •

I do

not u

se la

bels

, det

ails

, sym

bols

, or m

ath

term

s to

expl

ain

my

wor

k.

•

My

grap

h or

pic

ture

or i

nfor

mat

ion

is n

ot

corr

ect.

• I p

ut fe

w o

r no

ne o

f the

par

ts I

need

in m

y gr

aph

or p

ictu

re.

• I d

o no

t sup

port

my

answ

er w

ith th

e gr

aph

or p

ictu

re.

W

hen

the

com

mun

icat

ion

and

reas

onin

g ru

bric

s are

use

d se

para

tely

, the

y bo

th a

sses

s a st

uden

ts’ a

bilit

y to

use

the

prop

er la

bels

, det

ails,

sym

bols,

and

mat

h te

rms i

n th

e ex

plan

atio

n. W

hen

the

indi

vidu

al ru

bric

s are

uni

ted

to

crea

te th

e co

mbi

natio

n ru

bric

the

stat

emen

t con

cern

ing

the

use

of la

bels,

etc

, bec

omes

redu

ndan

t. Th

eref

ore,

the

labe

ls st

atem

ent i

s writ

ten

only

in th

e re

ason

ing

colu

mn,

whe

re it

is m

ost a

ppro

pria

te.


M

athe

mat

ics C

ombi

natio

n R

ubri

c –

Inte

rmed

iate

Lev

el

Com

mun

icat

ion

This

is h

ow I

solv

e th

e pr

oble

m.

R

easo

ning

Th

is is

why

I so

lve

the

prob

lem

this

way

.

R

epre

sent

atio

n Th

is is

how

I re

pres

ent m

y da

ta a

nd a

nsw

er.

4 •

My

wor

k is

wel

l org

aniz

ed, m

akes

sens

e, a

nd is

ea

sy to

und

erst

and.

•

I inc

lude

an

accu

rate

exp

lana

tion

of a

ll of

the

step

s nee

ded

to c

orre

ctly

solv

e th

e pr

oble

m.

• M

y ex

plan

atio

n de

scrib

es m

y st

rate

gy in

a h

ighl

y sk

illfu

l way

that

is c

lear

, org

aniz

ed, a

nd m

akes

se

nse.

•

I com

plet

ely

expl

ain

why

I cho

se th

is c

orre

ct

stra

tegy

to so

lve

the

prob

lem

. •

I use

all

of th

e pr

oper

labe

ls, d

etai

ls, s

ymbo

ls,

and

corr

ect m

ath

term

s in

my

expl

anat

ion.

• M

y re

pres

enta

tion

is c

ompl

etel

y co

rrec

t in

disp

layi

ng a

ll of

the

data

. •

I inc

lude

all

of th

e la

bels

, ope

ratio

n sy

mbo

ls, t

itles

, and

/or k

eys f

or th

e ty

pe o

f di

spla

y or

gra

ph I

chos

e.

• I s

tate

my

corr

ect c

oncl

usio

n co

mpl

etel

y su

ppor

ted

from

my

repr

esen

tatio

n.

3

• M

y w

ork

is m

ostly

org

aniz

ed, m

akes

sens

e an

d is

ea

sy to

und

erst

and.

•

I inc

lude

an

accu

rate

exp

lana

tion

of m

ost o

f the

st

eps n

eede

d to

cor

rect

ly so

lve

the

prob

lem

.

• M

y ex

plan

atio

n de

scrib

es m

y st

rate

gy in

a

mos

tly sk

illfu

l way

that

is o

rgan

ized

and

mak

es

sens

e.

• I m

ostly

exp

lain

why

I ch

ose

this

cor

rect

stra

tegy

to

solv

e th

e pr

oble

m.

• I u

se m

ost o

f the

pro

per l

abel

s, de

tails

, sym

bols

, an

d co

rrec

t mat

h te

rms i

n m

y ex

plan

atio

n.

• M

y re

pres

enta

tion

is m

ostly

cor

rect

in

disp

layi

ng m

ost o

f the

dat

a.

• I i

nclu

de m

ost o

f the

labe

ls, o

pera

tion

sym

bols

, titl

es, a

nd/o

r key

s for

the

type

of

disp

lay

or g

raph

I ch

ose.

•

I sta

te m

y co

rrec

t con

clus

ion

mos

tly

supp

orte

d fr

om m

y re

pres

enta

tion.

2 •

My

wor

k is

poo

rly

orga

nize

d, h

ard

to u

nder

stan

d an

d is

con

fusi

ng.

• I i

nclu

de a

n ex

plan

atio

n of

som

e of

the

step

s ne

eded

to so

lve

the

prob

lem

.

• M

y ex

plan

atio

n de

scrib

es m

y st

rate

gy in

a

som

ewha

t ski

llful

way

that

is n

ot o

rgan

ized

but

m

akes

som

e se

nse.

•

I par

tially

exp

lain

why

I ch

ose

this

stra

tegy

to

solv

e th

e pr

oble

m a

nd in

clud

e so

me

of th

e in

form

atio

n ne

eded

to su

ppor

t my

stra

tegy

. •

I use

som

e of

the

prop

er la

bels

, det

ails

, sym

bols

, an

d co

rrec

t mat

h te

rms i

n m

y ex

plan

atio

n.

• M

y re

pres

enta

tion

is p

artly

cor

rect

in

disp

layi

ng so

me

of th

e da

ta.

• I i

nclu

de so

me

of th

e la

bels

, ope

ratio

n sy

mbo

ls, t

itles

, and

/or k

eys f

or th

e ty

pe o

f di

spla

y or

gra

ph I

chos

e.

• I s

tate

my

conc

lusi

on p

artly

supp

orte

d fr

om

my

repr

esen

tatio

n.

1

• M

y w

ork

is n

ot o

rgan

ized

, doe

s not

mak

e se

nse,

an

d is

ver

y co

nfus

ing.

•

I inc

lude

an

expl

anat

ion

of fe

w o

r no

ne o

f the

st

eps n

eede

d to

solv

e th

e pr

oble

m.

• M

y ex

plan

atio

n do

es n

ot d

escr

ibe

my

stra

tegy

in

a sk

illfu

l way

, is n

ot o

rgan

ized

, and

doe

s not

m

ake

sens

e.

• I d

o no

t exp

lain

why

I ch

ose

this

stra

tegy

to

solv

e th

e pr

oble

m a

nd I

incl

ude

little

or n

o in

form

atio

n ne

eded

to su

ppor

t my

stra

tegy

. •

I do

not u

se p

rope

r lab

els,

deta

ils, s

ymbo

ls, a

nd

corr

ect m

ath

term

s in

my

expl

anat

ion.

• M

y re

pres

enta

tion

is n

ot c

orre

ct in

di

spla

ying

the

data

. •

I inc

lude

few

or

none

of t

he la

bels

, op

erat

ion

sym

bols

, titl

es, a

nd/o

r key

s for

th

e ty

pe o

f dis

play

or g

raph

I ch

ose.

•

I sta

te m

y co

nclu

sion

with

out s

uppo

rt fr

om

my

repr

esen

tatio

n.

Whe

n th

e co

mm

unic

atio

n an

d re

ason

ing

rubr

ics a

re u

sed

sepa

rate

ly, t

hey

both

ass

ess a

stud

ents

’ abi

lity

to u

se th

e pr

oper

labe

ls, d

etai

ls, sy

mbo

ls, a

nd m

ath

term

s in

the

expl

anat

ion.

Whe

n th

e in

divi

dual

rubr

ics a

re u

nite

d to

cr

eate

the

com

bina

tion

rubr

ic th

e st

atem

ent c

once

rnin

g th

e us

e of

labe

ls, e

tc, b

ecom

es re

dund

ant.

Ther

efor

e, th

e la

bels

stat

emen

t is w

ritte

n on

ly in

the

reas

onin

g co

lum

n, w

here

it is

mos

t app

ropr

iate

.


Mat

hem

atic

s Com

bina

tion

Rub

ric

– M

iddl

e Sc

hool

Lev

el

Com

mun

icat

ions

Th

is is

how

I so

lve

the

prob

lem

.

Rea

soni

ng

This

is w

hy I

solv

e th

e pr

oble

m u

sing

a se

lect

stra

tegy

.

Rep

rese

ntat

ion

This

is h

ow I

repr

esen

t the

pro

blem

and

solu

tion.

4

• M

y re

spon

se is

wel

l org

aniz

ed a

nd is

lo

gica

l. •

I inc

lude

an

accu

rate

, com

plet

e, a

nd

thor

ough

exp

lana

tion

of a

ll of

the

step

s ne

eded

to c

orre

ctly

solv

e th

e pr

oble

m.

• M

y ex

plan

atio

n of

the

stra

tegy

incl

udes

all

deta

ils a

nd is

wel

l org

aniz

ed.

• I f

ully

exp

lain

why

I ch

ose

this

effe

ctiv

e an

d ef

ficie

nt st

rate

gy th

at le

ads t

o a

com

plet

ely

corr

ect c

oncl

usio

n or

solu

tion.

•

I use

all

of th

e pr

oper

con

cept

s, la

bels

, det

ails

, sy

mbo

ls, a

nd c

orre

ct m

ath

term

s in

my

expl

anat

ion.

• M

y re

pres

enta

tion

is c

ompl

etel

y ac

cura

te a

nd

incl

udes

all

of th

e da

ta a

nd a

ll of

the

nece

ssar

y re

latio

nshi

ps in

the

prob

lem

. •

I inc

lude

all

of th

e la

bels

, ope

ratio

n sy

mbo

ls,

title

s, an

d/or

key

s for

the

type

of r

epre

sent

atio

n I

chos

e.

• I s

tate

my

corr

ect c

oncl

usio

n co

mpl

etel

y su

ppor

ted

from

my

repr

esen

tatio

n.

3

• M

y re

spon

se is

mos

tly o

rgan

ized

or i

s lo

gica

l. •

I inc

lude

an

accu

rate

exp

lana

tion

of m

ost o

f th

e st

eps n

eede

d to

cor

rect

ly so

lve

the

prob

lem

.

• M

y ex

plan

atio

n of

the

stra

tegy

incl

udes

mos

t de

tails

and

is o

rgan

ized

. •

I mos

tly e

xpla

in w

hy I

chos

e th

is e

ffect

ive

stra

tegy

that

lead

s to

a co

mpl

etel

y co

rrec

t co

nclu

sion

or s

olut

ion.

•

I use

mos

t of t

he p

rope

r con

cept

s, la

bels

, de

tails

, sym

bols

, and

cor

rect

mat

h te

rms i

n m

y ex

plan

atio

n.

• M

y re

pres

enta

tion

is m

ostly

acc

urat

e an

d in

clud

es

mos

t of t

he d

ata

and

mos

t of t

he n

eces

sary

re

latio

nshi

ps in

the

prob

lem

. •

I inc

lude

mos

t of t

he la

bels

, ope

ratio

n sy

mbo

ls,

title

s, an

d/or

key

s for

the

type

of r

epre

sent

atio

n I

chos

e.

• I s

tate

my

corr

ect c

oncl

usio

n m

ostly

supp

orte

d fr

om m

y re

pres

enta

tion.

2

• M

y re

spon

se is

poo

rly

orga

nize

d or

is

illog

ical

. •

I inc

lude

an

expl

anat

ion

of so

me

of th

e st

eps n

eede

d to

solv

e th

e pr

oble

m.

• M

y ex

plan

atio

n of

the

stra

tegy

incl

udes

som

e de

tails

and

is d

isor

gani

zed.

•

I par

tially

exp

lain

why

I ch

ose

this

stra

tegy

that

le

ads t

o a

part

ially

cor

rect

con

clus

ion

or

solu

tion.

•

I use

som

e of

the

prop

er c

once

pts,

labe

ls,

deta

ils, s

ymbo

ls, a

nd c

orre

ct m

ath

term

s in

my

expl

anat

ion.

• M

y re

pres

enta

tion

is p

artia

lly a

ccur

ate

and

incl

udes

som

e of

the

data

and

som

e of

the

nece

ssar

y re

latio

nshi

ps in

the

prob

lem

. •

I inc

lude

som

e of

the

labe

ls, o

pera

tion

sym

bols

, tit

les,

and/

or k

eys f

or th

e ty

pe o

f rep

rese

ntat

ion

I ch

ose.

•

I sta

te m

y co

nclu

sion

par

tly su

ppor

ted

from

my

repr

esen

tatio

n or

my

repr

esen

tatio

n le

ads t

o an

un

stat

ed c

oncl

usio

n.

1

• M

y re

spon

se is

not

org

aniz

ed a

nd is

ill

ogic

al.

• I i

nclu

de a

n ex

plan

atio

n of

few

or

none

of

the

step

s nee

ded

to so

lve

the

prob

lem

.

• M

y ex

plan

atio

n of

the

stra

tegy

incl

udes

few

or

no d

etai

ls a

nd is

not

org

aniz

ed.

• I d

o no

t exp

lain

why

I ch

ose

this

stra

tegy

that

le

ads t

o an

inco

rrec

t con

clus

ion

or so

lutio

n.

• I u

se fe

w o

r no

ne o

f the

pro

per c

once

pts,

labe

ls, d

etai

ls, s

ymbo

ls, a

nd c

orre

ct m

ath

term

s in

my

expl

anat

ion.

• M

y re

pres

enta

tion

is n

ot a

ccur

ate

and

incl

udes

few

or

non

e of

the

data

or n

eces

sary

rela

tions

hips

in

the

prob

lem

. •

I inc

lude

few

or

none

of t

he la

bels

, ope

ratio

n sy

mbo

ls, t

itles

, and

/or k

eys f

or th

e ty

pe o

f re

pres

enta

tion

I cho

se.

• I s

tate

my

conc

lusi

on w

ithou

t sup

port

from

my

repr

esen

tatio

n or

I do

not

stat

e a

conc

lusi

on.

W

hen

the

com

mun

icat

ion

and

reas

onin

g ru

bric

s are

use

d se

para

tely

, the

y bo

th a

sses

s a st

uden

ts’ a

bilit

y to

use

the

prop

er la

bels

, det

ails,

sym

bols,

and

mat

h te

rms i

n th

e ex

plan

atio

n. W

hen

the

indi

vidu

al ru

bric

s are

uni

ted

to

crea

te th

e co

mbi

natio

n ru

bric

the

stat

emen

t con

cern

ing

the

use

of la

bels,

etc

, bec

omes

redu

ndan

t. Th

eref

ore,

the

labe

ls st

atem

ent i

s writ

ten

only

in th

e re

ason

ing

colu

mn,

whe

re it

is m

ost a

ppro

pria

te.


Whe

n th

e co

mm

unic

atio

n an

d re

ason

ing

rubr

ics a

re u

sed

sepa

rate

ly, t

hey

both

ass

ess a

stud

ents

’ abi

lity

to u

se th

e pr

oper

labe

ls, d

etai

ls, sy

mbo

ls, a

nd m

ath

term

s in

the

expl

anat

ion.

Whe

n th

e in

divi

dual

rubr

ics a

re u

nite

d to

cr

eate

the

com

bina

tion

rubr

ic th

e st

atem

ent c

once

rnin

g th

e us

e of

labe

ls, e

tc, b

ecom

es re

dund

ant.

Ther

efor

e, th

e st

atem

ent i

s lef

t in

the

reas

onin

g ru

bric

, whe

re it

is m

ost a

ppro

pria

te.

M

athe

mat

ics C

ombi

natio

n R

ubri

c –

Hig

h Sc

hool

Lev

el

Com

mun

icat

ion

This

is h

ow I

solv

e th

e pr

oble

m.

R

easo

ning

M

y im

plem

enta

tion

incl

udes

org

aniz

ed m

athe

mat

ical

st

eps/

proc

edur

es a

nd re

leva

nt d

etai

ls.

R

epre

sent

atio

n Th

is is

how

I re

pres

ent t

he p

robl

em a

nd so

lutio

n.

4 •

My

resp

onse

is th

orou

gh, w

ell o

rgan

ized

, and

lo

gica

l whe

n de

scrib

ing

all m

y pr

oced

ures

. •

I inc

lude

a c

ompl

ete

and

corr

ect e

xpla

natio

n us

ing

all o

f the

rele

vant

and

spec

ific

deta

ils

from

the

prob

lem

whe

n de

scrib

ing

the

proc

edur

es u

sed

to a

rriv

e at

the

corr

ect s

olut

ion.

• M

y im

plem

enta

tion

is fu

lly d

evel

oped

and

co

mpl

etel

y su

ppor

ted

by re

leva

nt a

nd sp

ecifi

c de

tails

from

the

prob

lem

. •

I inc

lude

a c

orre

ct e

xpla

natio

n ba

sed

on

mat

hem

atic

al tr

uths

of w

hy I

sele

ct th

e co

ncep

ts

and

repr

esen

tatio

ns p

rese

nted

in m

y co

rrec

t so

lutio

n.

• I u

se a

ll of

the

labe

ls, s

ymbo

ls, c

once

pts,

term

inol

ogy,

and

repr

esen

tatio

ns a

ccur

atel

y,

clea

rly, a

nd su

ccin

ctly

in m

y re

spon

se.

• M

y re

pres

enta

tion(

s) is

wel

l pre

sent

ed w

ith

all d

etai

ls w

ell e

xecu

ted

in th

at it

is c

ompl

ete,

ac

cura

te, c

lear

, cor

rect

, and

eas

y to

inte

rpre

t. •

I rep

rese

nt th

e el

emen

ts in

an

insi

ghtfu

l se

lect

ion/

form

at th

at il

lust

rate

s all

of th

e ne

cess

ary

rela

tions

hips

in th

e pr

oble

m.

• I s

tate

my

corr

ect c

oncl

usio

n an

d/or

ge

nera

lizat

ion

com

plet

ely

supp

orte

d fr

om

my

repr

esen

tatio

n.

3

• M

y re

spon

se is

mos

tly o

rgan

ized

and

logi

cal

whe

n de

scrib

ing

mos

t of m

y pr

oced

ures

. •

I inc

lude

a c

orre

ct e

xpla

natio

n us

ing

mos

t of t

he

rele

vant

and

spec

ific

deta

ils fr

om th

e pr

oble

m

whe

n de

scrib

ing

the

proc

edur

es u

sed

to a

rriv

e at

th

e co

rrec

t sol

utio

n.

• M

y im

plem

enta

tion

is m

ostly

dev

elop

ed a

nd

supp

orte

d by

rele

vant

and

spec

ific

deta

ils fr

om th

e pr

oble

m.

• I i

nclu

de a

cor

rect

, exp

lana

tion

base

d on

m

athe

mat

ical

trut

hs o

f why

I se

lect

the

conc

epts

an

d re

pres

enta

tions

pre

sent

ed in

my

corr

ect

solu

tion.

•

I use

mos

t of t

he la

bels

, sym

bols

, con

cept

s, te

rmin

olog

y, a

nd re

pres

enta

tions

acc

urat

ely,

cl

early

, and

succ

inct

ly in

my

resp

onse

.

• M

y re

pres

enta

tion(

s) is

app

ropr

iate

in th

at it

is

mos

tly c

ompl

ete,

acc

urat

e, c

lear

, cor

rect

, an

d ea

sy to

inte

rpre

t. •

I rep

rese

nt th

e el

emen

ts in

an

appr

opria

te

sele

ctio

n/fo

rmat

that

illu

stra

tes m

ost o

f the

ne

cess

ary

rela

tions

hips

in th

e pr

oble

m.

• I s

tate

my

corr

ect c

oncl

usio

n an

d/or

ge

nera

lizat

ion

mos

tly su

ppor

ted

from

my

repr

esen

tatio

n.

2

• M

y re

spon

se is

poo

rly

orga

nize

d or

is il

logi

cal

whe

n de

scrib

ing

som

e of

my

proc

edur

es.

• I i

nclu

de a

n ex

plan

atio

n us

ing

som

e of

the

rele

vant

and

spec

ific

deta

ils fr

om th

e pr

oble

m

whe

n de

scrib

ing

the

proc

edur

es u

sed

to a

rriv

e at

a

solu

tion.

• M

y im

plem

enta

tion

is so

mew

hat d

evel

oped

and

su

ppor

ted

by re

leva

nt a

nd sp

ecifi

c de

tails

from

the

prob

lem

. •

I inc

lude

a p

artia

lly c

orre

ct a

nd so

mew

hat

orga

nize

d ex

plan

atio

n of

why

I se

lect

the

conc

epts

an

d re

pres

enta

tions

pre

sent

ed in

my

solu

tion.

•

I use

som

e of

the

labe

ls, s

ymbo

ls, c

once

pts,

term

inol

ogy,

and

repr

esen

tatio

ns a

ccur

atel

y in

my

resp

onse

.

• M

y re

pres

enta

tion(

s) is

som

ewha

t com

plet

e,

accu

rate

, and

/or p

artia

lly c

orre

ct, a

nd so

me

parts

are

eas

y to

inte

rpre

t. •

I par

tially

repr

esen

t the

ele

men

ts in

a

sele

ctio

n/fo

rmat

that

illu

stra

tes s

ome

of th

e ne

cess

ary

rela

tions

hips

in th

e pr

oble

m.

• I s

tate

my

conc

lusi

on a

nd/o

r gen

eral

izat

ion

part

ly su

ppor

ted

from

my

repr

esen

tatio

n.

1

• M

y re

spon

se is

not

org

aniz

ed a

nd is

illo

gica

l w

hen

desc

ribin

g fe

w o

r no

ne o

f my

proc

edur

es.

• I i

nclu

de a

n ex

plan

atio

n us

ing

few

or

none

of

the

rele

vant

or s

peci

fic d

etai

ls fr

om th

e pr

oble

m

whe

n de

scrib

ing

the

proc

edur

es.

• M

y im

plem

enta

tion

is r

arel

y su

ppor

ted

by

rele

vant

and

spec

ific

deta

ils fr

om th

e pr

oble

m.

• I i

nclu

de a

n in

corr

ect,

diso

rgan

ized

, or m

inim

al

expl

anat

ion

of w

hy I

sele

ct th

e co

ncep

ts a

nd

repr

esen

tatio

ns p

rese

nted

in m

y so

lutio

n.

• I u

se fe

w o

r no

ne o

f the

labe

ls, s

ymbo

ls, c

once

pts,

term

inol

ogy,

or r

epre

sent

atio

ns in

my

resp

onse

.

• M

y re

pres

enta

tion(

s) is

inco

mpl

ete,

in

accu

rate

, inc

orre

ct, a

nd is

diff

icul

t to

inte

rpre

t. •

I rep

rese

nt th

e el

emen

ts in

a se

lect

ion/

form

at

that

illu

stra

te fe

w o

r no

ne o

f the

nec

essa

ry

rela

tions

hips

in th

e pr

oble

m.

• I s

tate

my

conc

lusi

on a

nd/o

r gen

eral

izat

ion

with

out s

uppo

rt fr

om m

y re

pres

enta

tion.

Mathematics Instructional Rubrics – Section Three 40

OVERVIEW OF THE RUBROVERVIEW OF THE RUBROVERVIEW OF THE RUBROVERVIEW OF THE RUBRIC, PROMPT, AND ANCHIC, PROMPT, AND ANCHIC, PROMPT, AND ANCHIC, PROMPT, AND ANCHOR OR OR OR

PAPER SECTIONPAPER SECTIONPAPER SECTIONPAPER SECTION

This section of the manual includes everything that is needed to get started using the Mathematics Instructional Rubrics (MIR) in the classroom. The following components are included in this section:

• Rubrics - scoring guides that can be used with students to instruct them on how to communicate, reason, and represent their answers to open-ended questions. Included with the rubrics are tips from teachers on how to introduce the rubrics and how to get students accustomed to using rubrics to improve their responses.

• Prompts - questions or problems that were used to pilot the rubrics with

students and orient them to the concept of scoring their own work. Please note that some prompts were used to pilot more than one rubric.

• Anchor Papers - examples of student papers that illustrate each level or

point on the rubric.* When beginning to use rubrics with students it is important to remember that they are designed to be student tools. Students must be taught how to use them and then be given feedback to encourage growth in their responses. It is through practice that students refine their responses and move to the proficient level. It is important to remember that students need to be comfortable with these tools. This comfort is gained through continual practice and feedback.

The anchor papers provide students with examples of how other students in the state solved the problem or prompt that is provided. Teachers are encouraged to create their own anchor papers and prompts to allow students to see what is considered an exemplary answer. Additional sample prompts are included in the resource section of this document, and others may also be found on the websites listed in Section Four. *Note: Teachers using student papers as examples in the classroom should adhere to the Federal Educational Rights and Privacy Act (FERPA) guidelines.


Rubric: Communication - Analytic – High School Level Problem: Take-Home Pay Pilot Teacher Tips to Introduce the Rubric: Present the Communications Analytic Rubric and explain that it is a four-point rubric. Help the students understand the analytic rubric for communication by examining each of the traits and the differences between levels. Emphasize to students that communication is the hallmark of success for employment in today’s world. Students’ ability to communicate mathematically truly demonstrates their depth of understanding of mathematical concepts. Additional Teacher Comments:

• As a teacher with 35 years experience, using these rubrics is most stimulating. It demands time and expertise, and is rewarding.

• Often students do not see the sense of having to do so much writing to substantiate a correct solution. They wonder if the rubrics are testing them on their mathematical ability or their language arts ability.

• Students need different levels of intensity and explicitness of instruction to master the use of the rubrics. Some students need only a brief explanation while others need consistent and explicit instruction, practice, and feedback.

• Some students need to be taught the vocabulary of the rubrics to understand them. The words “organized, logical, well, most, poorly, not,” etc., have to be taught.

• Some of the tasks need to be broken down into smaller units for some special education students.

Mathematics Instructional Rubrics – Section 42

Mat

hem

atic

al C

omm

unic

atio

n - A

naly

tic R

ubri

c - H

igh

Scho

ol L

evel

Th

is is

how

I so

lve

the

prob

lem

.

Org

aniz

atio

n Is

my

resp

onse

org

aniz

ed to

show

how

I so

lve

the

prob

lem

?

E

xpla

natio

n D

oes m

y ex

plan

atio

n in

clud

e ho

w I s

olve

the

prob

lem

?

U

se o

f Mat

hem

atic

al T

erm

s D

oes m

y re

spon

se in

clud

e ac

cura

te la

bels

, sy

mbo

ls, c

once

pts,

term

inol

ogy,

and

re

pres

enta

tions

?

4 M

y re

spon

se is

thor

ough

, wel

l org

aniz

ed a

nd

logi

cal.

I inc

lude

a c

ompl

ete

and

corr

ect e

xpla

natio

n us

ing

all o

f the

rele

vant

and

spec

ific

deta

ils

from

the

prob

lem

whe

n de

scrib

ing

the

proc

edur

es u

sed

to a

rriv

e at

the

corr

ect s

olut

ion.

I use

all

of th

e la

bels

, sym

bols

, con

cept

s, te

rmin

olog

y, a

nd re

pres

enta

tions

acc

urat

ely,

cl

early

, and

succ

inct

ly in

my

resp

onse

.

3 M

y re

spon

se is

mos

tly o

rgan

ized

and

logi

cal.

I inc

lude

a c

orre

ct e

xpla

natio

n us

ing

mos

t of t

he

rele

vant

and

spec

ific

deta

ils fr

om th

e pr

oble

m

whe

n de

scrib

ing

the

proc

edur

es u

sed

to a

rriv

e at

th

e co

rrec

t sol

utio

n.

I use

mos

t of t

he la

bels

, sym

bols

, con

cept

s, te

rmin

olog

y, a

nd re

pres

enta

tions

acc

urat

ely,

cl

early

, and

succ

inct

ly in

my

resp

onse

.

2 M

y re

spon

se is

poo

rly

orga

nize

d or

is

illog

ical

.

I inc

lude

an

expl

anat

ion

usin

g so

me

of th

e re

leva

nt a

nd sp

ecifi

c de

tails

from

the

prob

lem

w

hen

desc

ribin

g th

e pr

oced

ures

use

d to

arr

ive

at

a so

lutio

n.

I use

som

e of

the

labe

ls, s

ymbo

ls, c

once

pts,

term

inol

ogy,

and

repr

esen

tatio

ns a

ccur

atel

y in

m

y re

spon

se.

1 M

y re

spon

se is

not

org

aniz

ed a

nd is

illo

gica

l.

I inc

lude

an

expl

anat

ion

usin

g fe

w o

r no

ne o

f th

e re

leva

nt o

r spe

cific

det

ails

from

the

prob

lem

w

hen

desc

ribin

g th

e pr

oced

ures

.

I use

few

or

none

of t

he la

bels

, sym

bols

, co

ncep

ts, t

erm

inol

ogy,

or r

epre

sent

atio

ns in

my

resp

onse

.


Take-Home Pay Toni is paid $18 an hour as a plumber. For overtime (time beyond 40 hours) she earns 1 and 1/2 times her normal rate. The regular deductions from her pay are federal taxes (14%), state tax (3.1%), local tax (1%), social security tax (7.5%), and union dues (1.2%). Last week Toni worked 52 hours. What was her net (take-home) pay? Justify your answer by explaining all of the steps you used. Do all work for this problem on this page. Remember you must show all the steps you used to solve the problem even if you have used a calculator. To receive the highest score, all calculation steps must be shown and explained in writing. Numeric answers must always be labeled.

PromptCommunicationAnalytic Rubric


Mathematics Instructional Rubrics Explanation of Score Points for

Student Anchor Paper

Date: 3/10/01 Grade Level: High School

Title of Rubric:Title of Rubric:Title of Rubric:Title of Rubric: Communications - Analytic

Set of comments: Score Point isScore Point isScore Point isScore Point is 4 \ 4 \ 4 because:

The explanation is thorough, well organized, and logical throughout. A complete and correct explanation is provided, including specific details and computations. All labels and symbols ($, %, X, +, -) are provided. The paper includes the correct solution.


Student Anchor Paper Score Point 4/4/4







The response is thorough, well organized and logical. Most of the relevant and specific details were included when describing the procedures. Student neglected to include specific information about how the $27 overtime rate was computed. All labels, symbols, concepts, terms, and representations were included.







The explanation is thorough and well organized in describing all procedures. A complete and detailed explanation is given with one computational rounding error leading to an incorrect solution. All labels, symbols, and terminology (percent, multiplied, divided, deductions) are used clearly and accurately.







The work is mostly organized mathematically and logically, however description of categories are not specifically given. An explanation is completely lacking. All mathematical terms are accurately denoted.







Solution is mostly organized but difficult to follow. The procedure is correct, but the solution is incorrect. Labels are used, but are not clear.







The response is not organized and does not show the procedure followed. The response contains few relevant or specific details, including incorrect computation. There are few symbols shown and labeling is very limited.


Rubric: Reasoning - Analytic – High School Level Problem: Theater Tickets Pilot Teacher Tips to Introduce the Rubric: Prior to having students use the rubrics, have them experience the same activity as part of a rubrics team. Put students into groups of four or five and give them the Straw Building problem and group materials.*

In the straw building activity, students ask questions like: “Do the three shapes have to be different?” “Can we cut or bend the straws?” “What is a rubric?” “Can we have more time?” “What does self-supporting mean?”

After students complete the activity, present the rubric. Some students express anger that they had not known that height mattered. Give them five additional minutes and some extra tape to modify their building. Then evaluate the buildings based upon the rubric. This activity is a segue to the rational for using rubrics. Additional Teacher Comments:

• The analytic rubric seems to be the most straightforward and least intimidating for the students.

• Chose simple problems to begin introducing rubrics. • The students think that with the analytical rubric they have a better chance to pick up points

because of the way it is broken into accuracy, format, and conclusion. • Many of students are used to rubrics since they are utilized in performance-based

assessments in all disciplines. • The hardest part of using rubrics is picking out good questions. Once these are selected,

the rest is smooth sailing. The students are very good and the results are basically what one would expect.

• The vocabulary of the rubric must be taught. • Feedback regarding what the student has done well and its relationship to the rubric and

what the student needs to improve needs to be given.

* A lesson plan for this activity can be found in the resource section of this manual.


Mat

hem

atic

al R

easo

ning

- A

naly

tic R

ubri

c –

Hig

h Sc

hool

D

oes m

y im

plem

enta

tion

incl

ude

orga

nize

d m

athe

mat

ical

step

s/pr

oced

ures

and

rele

vant

det

ails

?

Impl

emen

tatio

n of

the

Stra

tegy

D

oes m

y im

plem

enta

tion

incl

ude

orga

nize

d st

eps,

proc

edur

es, a

nd

rele

vant

det

ails

?

R

atio

nale

for

the

Stra

tegy

Cho

ice

Doe

s my

expl

anat

ion

reve

al w

hy I

sele

ct

the

conc

epts

pre

sent

ed in

my

solu

tion?

U

se o

f Mat

hem

atic

al T

erm

s D

oes m

y re

spon

se in

clud

e ac

cura

te

labe

ls, s

ymbo

ls, c

once

pts,

term

inol

ogy,

and

repr

esen

tatio

ns?

4

My

impl

emen

tatio

n is

fully

de

velo

ped

and

is c

ompl

etel

y su

ppor

ted

by re

leva

nt a

nd sp

ecifi

c de

tails

from

the

prob

lem

.

I inc

lude

a c

orre

ct, t

horo

ugh,

and

wel

l-or

gani

zed

expl

anat

ion

com

plet

ely

base

d up

on m

athe

mat

ical

trut

hs o

f why

I se

lect

th

e co

ncep

ts a

nd re

pres

enta

tions

pre

sent

ed

in m

y co

rrec

t sol

utio

n.

I use

all

of th

e la

bels

, sym

bols

, co

ncep

ts, t

erm

inol

ogy,

and

re

pres

enta

tions

acc

urat

ely,

cle

arly

, and

su

ccin

ctly

in m

y re

spon

se.

3 M

y im

plem

enta

tion

is m

ostly

de

velo

ped

and

supp

orte

d by

rele

vant

an

d sp

ecifi

c de

tails

from

the

prob

lem

.

I inc

lude

a c

orre

ct e

xpla

natio

n ba

sed

on

mat

hem

atic

al tr

uths

of w

hy I

sele

ct th

e co

ncep

ts a

nd re

pres

enta

tions

pre

sent

ed in

m

y co

rrec

t sol

utio

n.

I use

mos

t of t

he la

bels

, sym

bols

, co

ncep

ts, t

erm

inol

ogy,

and

re

pres

enta

tions

acc

urat

ely,

cle

arly

, and

su

ccin

ctly

in m

y re

spon

se.

2 M

y im

plem

enta

tion

is so

mew

hat

deve

lope

d an

d su

ppor

ted

by re

leva

nt

and

spec

ific

deta

ils fr

om th

e pr

oble

m.

I inc

lude

a p

artia

lly c

orre

ct a

nd so

mew

hat

orga

nize

d ex

plan

atio

n of

why

I se

lect

the

conc

epts

and

repr

esen

tatio

ns p

rese

nted

in

my

solu

tion.

I use

som

e of

the

labe

ls, s

ymbo

ls,

conc

epts

, ter

min

olog

y, a

nd

repr

esen

tatio

ns a

ccur

atel

y in

my

resp

onse

.

1 M

y im

plem

enta

tion

is r

arel

y su

ppor

ted

by re

leva

nt a

nd sp

ecifi

c de

tails

from

the

prob

lem

.

I inc

lude

an

inco

rrec

t, di

sorg

aniz

ed, o

r m

inim

al e

xpla

natio

n of

why

I se

lect

the

conc

epts

and

repr

esen

tatio

ns p

rese

nted

in

my

solu

tion.

I use

few

or

none

of t

he la

bels

, sy

mbo

ls, c

once

pts,

term

inol

ogy,

or

repr

esen

tatio

ns in

my

resp

onse

.


Theater Tickets

Movie theaters keep track of how many tickets they sell for each show. The Penn Theater sells adult’s tickets for $7.00 and child’s tickets for $4.00. For a recent show, the Penn sold 272 tickets and collected $1,694 in ticket sales. How many of each type of ticket were sold? For this problem, show all of your steps (even if you used a calculator) and explain why you did each step.

PromptReasoning

Analytic Rubric





Title of Rubric:Title of Rubric:Title of Rubric:Title of Rubric: Reasoning - Analytic

Set of comments: Score Point isScore Point isScore Point isScore Point is 4 / 4 / 4 because:

The implementation is thorough and contains specific detail (e.g., total tickets, money, identified variables). The explanation is well organized and includes reasons for selecting the representation (2 variables – 2 equations, solving by substitution and check). Labels, concepts, symbols, and terms are accurate and clear (variables defined and solve system of equation, substitution).







The implementation is fully developed and contains specific details from the problem (identification of variables). The explanation is correct and organized, but not thorough. Reason for setting up 2 equations with 2 variables is missing. Correctly describes the process of elimination but never identifies it by name as elimination or linear combination. Labels, symbols, concepts, terms, and representations are accurate and clear (answers labeled, use of variables, and processes of substitution and linear combination).





Title of RuTitle of RuTitle of RuTitle of Rubric:bric:bric:bric: Reasoning - Analytic


Student has a thorough mathematical solution with some organization concerns. Student does not explain why they selected processes/procedures. Student labeled variables and solutions but did not use mathematical terminology.







The student’s work is somewhat developed and the method contains errors. Correct, well-organized step-by-step process leads to the solution. Labels are incorrect and are missing.







The implementation is sometimes supported (make an equation). Although the explanation is weak, it is not incorrect and it is not disorganized. Some label terms are used ($, answer labeled, system of equations, matrix).







Implementation is limited with insufficient connections to the problem. No explanation on why the matrix equation was used or how it was solved. The variables were identified, but solutions were not explained.


Rubric: Representation - Analytic – High School Level Problem: National Honor Society Luncheon Pilot Teacher Tips to Introduce the Rubric: Begin the process by giving the students the open-ended question to solve. Do not give them a rubric to follow at first, nor answer any of their questions. Essentially use this activity as a pre-test. Then present the analytic rubric to the students. Use the rubric to grade the pre-tests. Students are generally surprised to see how many aspects of the rubric are missing from their solutions. Next, have the students work through a problem together using the rubric as a guide. Students comment on how much explanation is necessary to get a “4.” It is then time to give them a problem to solve on their own using the rubric. Additional Teacher Comments:

• The analytic rubric seems to be the most straightforward and least intimidating for the students.

• The students like the format that separates it into “Accuracy, Format, and Conclusion.” • Present the PSSA rubric to a class along with various examples from last year’s PSSA

exam. This helps to show the students the type of responses that are expected. • Students have done very little writing in mathematics in the past. Most students seem

very hesitant to clearly explain their work and would rather the work stand on its own merit.

• Students seem to be scared to “problem solve.” They would much rather be presented with an idea or topic, learn about it, and be quizzed or tested on it. They hesitate to put the knowledge they have previously learned to use and apply it to a current situation.

• The analytic rubrics are much easier to use and students would rather be graded using them because they offer more of an opportunity to score well since the students’ work is scored in more than one category.


Mat

hem

atic

al R

epre

sen

tati

on -

An

alyt

ic R

ub

ric

– Hig

h S

choo

l L

evel

T

his

is h

ow I

rep

rese

nt

the

prob

lem

an

d so

luti

on.

Acc

ura

cy

Do

I ac

cura

tely

rep

rese

nt

all o

f m

y da

ta?

F

orm

at

Do

I co

rrec

tly

rep

rese

nt

all n

eces

sary

re

lati

onsh

ips?

C

oncl

usi

on

Do

I st

ate

my

con

clu

sion

an

d/or

ge

ner

aliz

atio

n w

ith

su

ppor

t fr

om m

y re

pres

enta

tion

?

4

My

repr

esen

tati

on(s

) is

wel

l pr

esen

ted

wit

h a

ll d

etai

ls w

ell

exec

ute

d in

th

at it

is c

ompl

ete,

ac

cura

te, c

lear

, cor

rect

, an

d ea

sy

to in

terp

ret.

I re

pres

ent

the

elem

ents

in a

n

insi

ghtf

ul s

elec

tion

/for

mat

th

at

illu

stra

tes

all

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

I st

ate

my

corr

ect

con

clu

sion

an

d/or

gen

eral

izat

ion

co

mp

lete

ly s

upp

orte

d fr

om m

y re

pres

enta

tion

.

3

My

repr

esen

tati

on(s

) is

ap

prop

riat

e in

th

at it

is m

ostl

y co

mpl

ete,

acc

ura

te, c

lear

, cor

rect

, an

d ea

sy t

o in

terp

ret.

I re

pres

ent

the

elem

ents

in a

n

appr

opri

ate

sele

ctio

n/f

orm

at t

hat

il

lust

rate

s m

ost

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

I st

ate

my

corr

ect

con

clu

sion

an

d/or

gen

eral

izat

ion

mos

tly

supp

orte

d fr

om m

y re

pres

enta

tion

.

2 M

y re

pres

enta

tion

(s)

is

som

ewh

at c

ompl

ete,

acc

ura

te

and/

or p

arti

ally

cor

rect

, an

d so

me

part

s ar

e ea

sy t

o in

terp

ret.

I pa

rtia

lly

repr

esen

t th

e el

emen

ts

in a

sel

ecti

on/f

orm

at t

hat

il

lust

rate

s so

me

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

I st

ate

my

con

clu

sion

an

d/or

ge

ner

aliz

atio

n p

artl

y su

ppor

ted

from

my

repr

esen

tati

on.

1 M

y re

pres

enta

tion

(s)

is

inco

mpl

ete,

inac

cura

te, i

nco

rrec

t,

and

is d

iffi

cult

to

inte

rpre

t.

I re

pres

ent

the

elem

ents

in a

se

lect

ion

/for

mat

th

at il

lust

rate

few

or

non

e of

th

e n

eces

sary

re

lati

onsh

ips

in t

he

prob

lem

.

I m

ay o

r m

ay n

ot s

tate

my

con

clu

sion

an

d/or

gen

eral

izat

ion

w

ith

out

supp

ort

from

my

repr

esen

tati

on.


National Honor Society Luncheon The National Honor Society is planning their annual luncheon honoring new members and their families. Costs from two catering companies are being considered by the club. Delicious Catering Services charges $20 per person and Tastee Caterers charge a flat fee of $800 plus $10 per person. Write a system of equations to represent this situation and solve the system by graphing. Show all of your work. What advice would you give the National Honor Society to help them decide what caterer to use? Include an explanation of why you chose to give this advice.

PromptRepresentation

Analytic Rubric





Title of Rubric:Title of Rubric:Title of Rubric:Title of Rubric: Representation - Analytic


The table and graph are accurate with all details included. All elements are represented. The conclusion is completely supported by the representations.







The table and graph are accurate with all details included (labels, numeric increments, etc.). All necessary relationships are identified with one exception. Although the 2 equations are correct they are never appropriately associated to the companies (Delicious and Tastee). The correct conclusion is completely supported from the representation (use of “according to the graph,” “the line is lower,” the “line climbs slower”).







The graph is correct but sideways, making it difficult to interpret. The format selected is appropriate however the table does not show the point of intersection. The conclusion is partially supported. The point of intersection (80 people) is not mentioned.







The graph’s scale and labels are missing. The table and equations are accurate. The graph poorly represents data from the table. Most elements are represented in an appropriate format. Incorrect conclusion is not supported.







Variables are not identified. Graph is not labeled. The equations partially represent elements of the problem. The graph shows the intersection of two appropriate lines but it is not labeled. The conclusion is incorrect and is not supported by the representation.


Rubric: Communication - Holistic – High School Level Problem: Take-Home Pay Pilot Teacher Tips to Introduce the Rubric: It is helpful to introduce rubrics to students by writing a number of open-ended problems. Select several to use with your classes. Many students are already familiar with the PSSA Mathematics Test. Present the PSSA rubric to your classes, along with various released problems form last year’s PSSA exam. Present this rubric. Explain the differences between this rubric and the PSSA rubric. Then give this problem to solve using the holistic four-point scale. Additional Teacher Comments:

• After using the rubric, ask students what additional information can be put into the rubric to assist them in obtaining better scores. The big question seems to surround the difference between “how” a solution is computed and “why” that solution was selected. This emphasizes the need to have students continually explain why they do what they do.

• As a first year teacher, working with rubrics revealed some very important lessons. The first discovery is that students have done very little writing in mathematics in the past. Most seem very hesitant to clearly explain their work. On the other hand, the enthusiasm that is shown by most students in working with rubrics is very moving. They try very hard to do their best in completing the open-ended tasks. All in all, rubrics work very well to improve student learning.


Mat

hem

atic

al C

omm

unic

atio

n - H

olis

tic R

ubri

c - H

igh

Scho

ol L

evel

Th

is is

how

I so

lve

the

prob

lem

.

4 •

My

resp

onse

is th

orou

gh, w

ell o

rgan

ized

, and

logi

cal.

• I i

nclu

de a

com

plet

e an

d co

rrec

t exp

lana

tion

usin

g al

l of t

he re

leva

nt a

nd sp

ecifi

c det

ails

from

the

prob

lem

w

hen

desc

ribi

ng th

e pr

oced

ures

use

d to

arr

ive

at th

e cor

rect

solu

tion.

•

I use

all

of th

e la

bels

, sym

bols

, con

cept

s, te

rmin

olog

y, a

nd re

pres

enta

tions

acc

urat

ely,

clea

rly

and

succ

inct

ly in

my

resp

onse

.

3 •

My

resp

onse

is m

ostl

y or

gani

zed

and

logi

cal.

• I i

nclu

de a

corr

ect e

xpla

natio

n us

ing

mos

t of t

he re

leva

nt a

nd sp

ecifi

c det

ails

from

the

prob

lem

whe

n de

scri

bing

the

proc

edur

es u

sed

to a

rriv

e at

the

corr

ect s

olut

ion.

•

I use

mos

t of t

he la

bels

, sym

bols

, con

cept

s, te

rmin

olog

y, a

nd re

pres

enta

tions

acc

urat

ely,

clea

rly,

and

su

ccin

ctly

in m

y re

spon

se.

2

• M

y re

spon

se is

poo

rly

orga

nize

d or

is il

logi

cal.

• I i

nclu

de a

n ex

plan

atio

n us

ing

som

e of

the

rele

vant

and

spec

ific d

etai

ls fr

om th

e pr

oble

m w

hen

desc

ribi

ng

the

proc

edur

es u

sed

to a

rriv

e at

a so

lutio

n.

• I u

se s

ome

of th

e la

bels

, sym

bols

, con

cept

s, te

rmin

olog

y, a

nd re

pres

enta

tions

acc

urat

ely

in m

y re

spon

se.

1

• M

y re

spon

se is

not

org

aniz

ed a

nd is

illo

gica

l. •

I inc

lude

an

expl

anat

ion

usin

g fe

w o

r no

ne o

f the

rele

vant

or s

peci

fic d

etai

ls fr

om th

e pr

oble

m w

hen

desc

ribi

ng th

e pr

oced

ures

. •

I use

few

or

none

of t

he la

bels

, sym

bols

, con

cept

s, te

rmin

olog

y, o

r rep

rese

ntat

ions

in m

y re

spon

se.


Take-Home Pay Toni is paid $18 an hour as a plumber. For overtime (time beyond 40 hours) she earns 1 and 1/2 times her normal rate. The regular deductions from her pay are federal taxes (14%), state tax (3.1%), local tax (1%), social security tax (7.5%), and union dues (1.2%). Last week Toni worked 52 hours. What was her net (take-home) pay? Justify your answer by explaining all of the steps you used. Do all work for this problem on this page. Remember you must show all the steps you used to solve the problem even if you have used a calculator. To receive the highest score, all calculation steps must be shown and explained in writing. Numerical answers must always be labeled.

PromptCommunicationHolistic Rubric





Title of Rubric:Title of Rubric:Title of Rubric:Title of Rubric: Communication - Holistic

Set of comments: Score Point isScore Point isScore Point isScore Point is 4 because:

The explanation is well organized and describes all procedures logically and sequentially. All of the relevant and specific details from the problem are noted with correct terms (regular pay, overtime pay, percentages, decimals). The paper includes the correct solution.


Student Anchor Paper Score Point 4







The explanation is mostly organized and describes most of the procedures logically. It lacks an explanation of how the overtime rate and number of hours was found. The explanation includes proper concepts and labels. Mathematical terms used are correct (percentages, money deducted, add, multiple, divide). The paper includes the correct solution.





Title of Title of Title of Title of Rubric:Rubric:Rubric:Rubric: Communication - Holistic


The computation is partially accurate. There are errors in computing tax deductions result in an incorrect solution (net pay). The explanations of how the tax deductions were computed are unclear. There is minimal use of labeling and poor use of mathematical terminology.







Although the student gives the correct answer, the response is not organized with few procedures shown. Details are lacking in the computation of individual totals. There is minimal labeling. The representation of the process of finding total tax deductions is incorrect.


Rubric: Reasoning - Holistic – High School Level Problem: Theater Tickets Pilot Teacher Tips so Introduce the Rubric: Students need to understand what mathematical reasoning is. Reasoning is about “why I did what I did” and not about how the problem was solved. Teach your students to connect the steps to the solution with justifications. To prepare for the use of rubrics and this problem, discuss the Holistic Reasoning Rubric on an overhead. Have the students read it and discuss it while working through it. Hand out the Holistic Reasoning Rubric to the students, the formula page from the PSSA, and a blank piece of scrap paper. Give students adequate time to complete the problem (most need about 20 minutes). Additional Teacher Comments:

• Use the Holistic Reasoning Rubric with a geometry class. Provide the students with a copy of the rubric and stress to the class what a “4” represents.

• For additional practice with rubrics create a four-point rubric that students use for completing their homework assignments.

• The vocabulary of the rubrics must be taught. • Students need different amounts of practice and feedback with rubrics.


Mat

hem

atic

al R

easo

nin

g -

Hol

isti

c R

ub

ric

- H

igh

Sch

ool

Lev

el

My

impl

emen

tati

on in

clu

des

orga

niz

ed m

ath

emat

ical

ste

ps/p

roce

dure

s an

d re

leva

nt

deta

ils.

4 •

My

impl

emen

tati

on is

fu

lly

deve

lope

d an

d co

mpl

etel

y su

ppor

ted

by r

elev

ant

and

spec

ific

de

tail

s fr

om t

he

prob

lem

. •

I in

clu

de a

cor

rect

, th

orou

gh, a

nd

wel

l org

aniz

ed e

xpla

nat

ion

bas

ed o

n m

ath

emat

ical

tru

ths

of

wh

y I

sele

ct t

he

con

cept

s an

d re

pres

enta

tion

s pr

esen

ted

in m

y co

rrec

t so

luti

on.

• I

use

all

of

the

labe

ls, s

ymbo

ls, c

once

pts,

ter

min

olog

y, a

nd

repr

esen

tati

ons

accu

rate

ly, c

lear

ly,

and

succ

inct

ly in

my

resp

onse

.

3 •

My

impl

emen

tati

on is

mos

tly

deve

lope

d an

d su

ppor

ted

by r

elev

ant

and

spec

ific

det

ails

fro

m

the

prob

lem

. •

I in

clu

de a

cor

rect

exp

lan

atio

n b

ased

on

mat

hem

atic

al t

ruth

s of

wh

y I

sele

ct t

he

con

cept

s an

d re

pres

enta

tion

s pr

esen

ted

in m

y co

rrec

t so

luti

on.

• I

use

mos

t of

th

e la

bels

, sym

bols

, con

cept

s, t

erm

inol

ogy,

an

d re

pres

enta

tion

s ac

cura

tely

, cl

earl

y, a

nd

succ

inct

ly in

my

resp

onse

.

2 •

My

impl

emen

tati

on is

som

ewh

at d

evel

oped

an

d su

ppor

ted

by r

elev

ant

and

spec

ific

det

ails

fr

om t

he

prob

lem

. •

I in

clu

de a

par

tial

ly c

orre

ct a

nd

som

ewh

at o

rgan

ized

exp

lan

atio

n o

f w

hy

I se

lect

th

e co

nce

pts

and

repr

esen

tati

ons

pres

ente

d in

my

solu

tion

. •

I u

se s

ome

of t

he

labe

ls, s

ymbo

ls, c

once

pts,

ter

min

olog

y, a

nd

repr

esen

tati

ons

accu

rate

ly in

my

resp

onse

.

1 •

My

impl

emen

tati

on is

rar

ely

supp

orte

d by

rel

evan

t an

d sp

ecif

ic d

etai

ls f

rom

th

e pr

oble

m.

• I

incl

ude

an

inco

rrec

t, d

isor

gan

ized

, or

min

imal

exp

lan

atio

n o

f w

hy

I se

lect

th

e co

nce

pts

and

repr

esen

tati

ons

pres

ente

d in

my

solu

tion

. •

I u

se f

ew o

r n

one

of t

he

labe

ls, s

ymbo

ls, c

once

pts,

ter

min

olog

y, o

r re

pres

enta

tion

s in

my

resp

onse

.


Theater Tickets

Movie theaters keep track of how many tickets they sell for each show. The Penn Theater sells adult’s tickets for $7.00 and child’s tickets for $4.00. For a recent show, the Penn sold 272 tickets and collected $1694 in ticket sales. How many of each type of ticket were sold? For this problem, show all of your steps (even if you used a calculator) and explain why you did each step.

PromptReasoning

Holistic Rubric





Title of Rubric:Title of Rubric:Title of Rubric:Title of Rubric: Reasoning - Holistic


The implementation is thorough and contains specific detail (total tickets, money, identified adult and children’s tickets). The explanation is well organized and includes reasons for selecting the representation (two variables, two equations, solving by substitution, checking, correct solution). Labels, concepts, symbols, and terms are accurate and clear (variables defined, solve system of equation, substitution).







The implementation is mostly supported by the problem (division by seven is unclear). It is correct and well organized and the solution is correct. Reasons for selecting operations and processes are missing. Most of the labels, concepts and terms are clear. The use of variables (a, c, x) is inconsistent and unclear.







The implementation is mostly supported by details from the problem (“this means that”). A correct and organized explanation is included with a correct solution, however the explanation is not thorough. Most of the symbols and concepts are used accurately. Money is not labeled and there is some inconsistent use of dollars and cents (7.00, 1694).







The implementation is sometimes supported by the problem (system of equations, matrix). A somewhat organized explanation of why the matrix representation was chosen is given. Although the solution is correct, the explanation of the reasoning is weak. Some concepts and representations are accurate.







The implementation is rarely supported by detail (multiplied the number of adults by ....). The explanation is incorrect and disorganized. Few labels, concepts, or terms are used in the response.


Rubric: Representation - Holistic – High School Level Problem: National Honor Society Pilot Teacher Tips to Introduce the Rubric: Teach your students that representations take on many forms. It is important that students understand the essential characteristics of each form (e.g., graphs, symbols, diagrams, tables). Explain rubrics to students. Hand out the rubric and ask students to read it. Discuss how a rubric tells them what to do. When the students have no more questions, hand out a practice problem. Grade the practice problem as a group and discuss the criteria necessary to score at the level 4. Additional Teacher Comments:

• There are usually no problems using the rubrics if students are experienced at using them in mathematics.

• The hardest part of the experience is picking out good questions to use.


Mat

hem

atic

al R

epre

sen

tati

on -

Hol

isti

c R

ub

ric

– Hig

h S

choo

l L

evel

T

his

is h

ow I

rep

rese

nt

the

prob

lem

an

d so

luti

on.

4

• M

y re

pres

enta

tion

(s)

is w

ell p

rese

nte

d w

ith

all

det

ails

wel

l exe

cute

d in

th

at it

is c

ompl

ete,

ac

cura

te, c

lear

, cor

rect

, an

d ea

sy t

o in

terp

ret.

•

I re

pres

ent

the

elem

ents

in a

n in

sigh

tfu

l sel

ecti

on/f

orm

at t

hat

illu

stra

tes

all

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

• I

stat

e m

y co

rrec

t co

ncl

usi

on a

nd/

or g

ener

aliz

atio

n c

omp

lete

ly s

upp

orte

d fr

om m

y re

pres

enta

tion

.

3 •

My

repr

esen

tati

on(s

) is

app

ropr

iate

in t

hat

it is

mos

tly

com

plet

e, a

ccu

rate

, cle

ar, c

orre

ct, a

nd

easy

to

inte

rpre

t.

• I

repr

esen

t th

e el

emen

ts in

an

app

ropr

iate

sel

ecti

on/f

orm

at t

hat

illu

stra

tes

mos

t of

th

e n

eces

sary

re

lati

onsh

ips

in t

he

prob

lem

. •

I st

ate

my

corr

ect

con

clu

sion

an

d/or

gen

eral

izat

ion

mos

tly

supp

orte

d fr

om m

y re

pres

enta

tion

.

2 •

My

repr

esen

tati

on(s

) is

som

ewh

at c

ompl

ete,

acc

ura

te, a

nd/

or p

arti

ally

cor

rect

an

d so

me

part

s ar

e ea

sy t

o in

terp

ret.

•

I pa

rtia

lly

repr

esen

t th

e el

emen

ts in

a s

elec

tion

/for

mat

th

at il

lust

rate

s so

me

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

• I

stat

e m

y co

ncl

usi

on a

nd/

or g

ener

aliz

atio

n p

artl

y su

ppor

ted

from

my

repr

esen

tati

on.

1

• M

y re

pres

enta

tion

(s)

is in

com

plet

e, in

accu

rate

, in

corr

ect,

an

d is

dif

ficu

lt t

o in

terp

ret.

•

I re

pres

ent

the

elem

ents

in a

sel

ecti

on/f

orm

at t

hat

illu

stra

te f

ew o

r n

one

of t

he

nec

essa

ry

rela

tion

ship

s in

th

e pr

oble

m.

• I

may

or

may

not

sta

te m

y co

ncl

usi

on a

nd/

or g

ener

aliz

atio

n w

ith

out

supp

ort

from

my

repr

esen

tati

on.


National Honor Society Luncheon The National Honor Society is planning their annual luncheon honoring new members and their families. Costs from two catering companies are being considered by the club. Delicious Catering Services charges $20 per person and Tastee Caterers charge a flat fee of $800 plus $10 per person. Write a system of equations to represent this situation and solve the system by graphing. Show all of your work. What advice would you give the National Honor Society to help them decide what caterer to use? Include an explanation of why you chose to give this advice.

PromptRepresentationHolistic Rubric





Title Title Title Title of Rubric:of Rubric:of Rubric:of Rubric: Representation - Holistic


All details are well presented and represented. The correct conclusion is well supported by the representation.





Title of Rubric:Title of Rubric:Title of Rubric:Title of Rubric: Representation - Holistic

Set of comments: ScoScoScoScore Point isre Point isre Point isre Point is 4 because:

All details are well presented. All necessary relationships are represented. The conclusion is completely supported by the representation.







The explanation is supported but the conclusion stating why the advice is given is unclear. The graph is not labeled.






Set of comments: Score PScore PScore PScore Point isoint isoint isoint is 2 because:

The incorrect conclusion is supported by the inaccurately drawn graph, but is not supported by the correct table.







The general conclusion is not specifically supported by the correct table and graph. The graph is not labeled.







Although the table is correct and the graph is correct (but not labeled), the conclusion is incorrect and not supported by the representation.


Rubric: Combination - High School Level Problem: Linear Programming Problem Pilot Teacher Tips to Introduce the Rubric: To use the combination rubric, carefully select problems that require all traits of the communication, reasoning, and representation rubrics. Provide an overview and/or a review on the framework of solving the problem before students begin the problem. A suggested framework follows:

1. Assign variables, x=, y= 2. Write inequalities 3. Graph inequalities 4. Find maximum/minimum values 5. Evaluate maximum/minimum values into cost function.

After students are given the framework, instruct them to work alone or with a partner to develop a solution. Initially, all students are able to start the problem, but not solve it. Of the students who solve the problem, some include all of the necessary work and explanations, while some only include partial work and explanations. Use these student papers with the class to illustrate what additional steps they need to take to improve their work.

Additional Teacher Comments:

• Follow the procedure of presenting the rubric first and then having the students do a problem using the rubric as a guide.

• Distribute the rubric to the students and again review the 3-column idea. Remind the students when they solve a problem they are to think in terms of three columns: “How” (what we are doing); “Why” (why we use these steps) and “Representation” (the mathematics). Practice solving problems selected from SAT materials.

• As the students use the rubrics, they get better at explaining the “why.” Typical comments from students include the fact that they are able to get an expression, but are unable to explain why it works. They can understand what they are looking for, but cannot explain or show it.

• The most difficult part of this experience is trying to find additional problems that fit the rubrics. It is helpful to work out a problem first, decide what kind of answer you are looking for, and then design the rubric.


Whe

n th

e co

mm

unic

atio

n an

d re

ason

ing

rubr

ics a

re u

sed

sepa

rate

ly, t

hey

both

ass

ess a

stud

ents

’ abi

lity

to u

se th

e pr

oper

labe

ls, d

etai

ls, sy

mbo

ls, a

nd m

ath

term

s in

the

expl

anat

ion.

Whe

n th

e in

divi

dual

rubr

ics a

re u

nite

d to

cr

eate

the

com

bina

tion

rubr

ic th

e st

atem

ent c

once

rnin

g th

e us

e of

labe

ls, e

tc, b

ecom

es re

dund

ant.

Ther

efor

e, th

e st

atem

ent i

s lef

t in

the

reas

onin

g ru

bric

, whe

re it

is m

ost a

ppro

pria

te.

Mat

hem

atic

s Com

bina

tion

Rub

ric

– H

igh

Scho

ol L

evel

Com

mun

icat

ion

This

is h

ow I

solv

e th

e pr

oble

m.

Rea

soni

ng

My

impl

emen

tati

on in

clu

des

orga

niz

ed m

ath

emat

ical

st

eps/

proc

edu

res

and

rele

van

t de

tail

s.

Rep

rese

ntat

ion

Th

is is

how

I r

epre

sen

t th

e pr

oble

m a

nd

solu

tion

.

4

• M

y re

spon

se is

thor

ough

, wel

l org

aniz

ed, a

nd

logi

cal w

hen

desc

ribi

ng a

ll m

y pr

oced

ures

. •

I inc

lude

a co

mpl

ete

and

corr

ect e

xpla

natio

n us

ing

all o

f the

rele

vant

and

spec

ific d

etai

ls

from

the

prob

lem

whe

n de

scri

bing

the

proc

edur

es u

sed

to a

rriv

e at

the

corr

ect

solu

tion.

• M

y im

plem

enta

tion

is f

ull

y de

velo

ped

and

com

plet

ely

supp

orte

d by

rel

evan

t an

d sp

ecif

ic

deta

ils

from

th

e pr

oble

m.

• I

incl

ude

a c

orre

ct e

xpla

nat

ion

bas

ed o

n

mat

hem

atic

al t

ruth

s of

wh

y I

sele

ct t

he

con

cept

s an

d re

pres

enta

tion

s pr

esen

ted

in m

y co

rrec

t so

luti

on.

• I

use

all

of

the

labe

ls, s

ymbo

ls, c

once

pts,

te

rmin

olog

y, a

nd

repr

esen

tati

ons

accu

rate

ly,

clea

rly,

an

d su

ccin

ctly

in m

y re

spon

se.

• M

y re

pres

enta

tion

(s)

is w

ell p

rese

nte

d w

ith

al

l de

tail

s w

ell e

xecu

ted

in t

hat

it is

co

mpl

ete,

acc

ura

te, c

lear

, cor

rect

, an

d ea

sy

to in

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.


Linear Programming Problem

The Industrial Arts teacher works with students after school to make tables and chairs to sell so they can raise funds to go on a trip. They can make at most five items per week. Materials cost $40 for tables and $20 for chairs. They have to stay within a budget of $120 per week for materials. Each table sells for $50 and each chair for $30. How many of each can the students make each week to maximize their funds? Show all of your work, fully explain how you solved the problem and explain why you chose the steps you used.

PromptCombination Rubric





Title of Rubric:Title of Rubric:Title of Rubric:Title of Rubric: Combination


The explanation is organized to show how the problem is solved. The implementation is complete and includes organized mathematical steps and procedures and relevant details. The problem is accurately represented graphically and algebraically. The solution is accurate and supported by the work.







A correct explanation using most of the procedures is included. The specific details as to how (1,4) in the solution is missing. The work is mostly developed. Explanations as to why (1,4) is the solution was not justified. All elements of the problem are represented.







A correct explanation using most of the relevant details is included. Most concepts are developed. Why the concepts were selected is included. The inequalities x > 0, y > 0 are not stated. The problem and solution are accurately represented graphically and algebraically.







The explanation includes some details from the problem in the beginning. The explanation describing the procedures used to arrive at the solution is unclear. The implementation is somewhat developed and supported. Some labels and concepts are used accurately. Elements are partially represented in a graph. Some inequalities are represented. The conclusion is partly supported by the graph.



Answer continued on next page







An explanation using a few of the relevant details is included. A few concepts and representations are included. The conclusion is stated without support form the representation.

Mathematics Instructional Rubrics – Section Four 137

HIGH SCHOOL PROMPTS

The New Soccer Field (from the Summer 2000 Math Assessment Pilot)

Your company is constructing a soccer field for a high school. The field is 110 yards long and 80 yards wide. You receive the following note from your boss: The Board of Zoning requires that a 6” layer of gravel must be laid on all athletic fields before top soil is added, to give adequate drainage. Our gravel supplier says that each truck load contains 12 cubic yards of gravel, at a cost of $9.25/cubic yard delivered. Calculate how many truckloads of gravel we should order for the soccer field and estimate how much it will cost. I need to have your background calculations, clearly explained, as well as the total cost in order to get budget approval.

High School PromptCommunication

Analytic and Holistic Rubrics


Sale (from Summer 2000 Math Assessment Pilot)

For a sale, a shopkeeper lowered the original price of an item by 30 percent. After the sale, the shopkeeper told this clerk, Mike, to raise the price of that item by 30 percent of its sale price. So Mike marked the item with its original price. Was Mike right or wrong in doing that? Present a convincing argument to support your answer: your may wish to include a specific example as part of your argument.




The Budget Mystery (from Summer 2000 Math Assessment Pilot)

In 1990, the maintenance budget for a school was $30,000 out of a total budget of $500,000. In 1991, the figure was $31,200 out of a total budget of $520,000. Inflation between 1990 and 1991 was 8%. Parents complain that the money spent on maintenance increased. The maintenance manager complained that the money spent on maintenance was decreased. The principal claimed that, in fact, there has been no change in spending for maintenance.

1. Write what the parents could say to justify their claim of an increase 2. Write what the maintenance manager could say to justify his claim of a decrease. 3. Write what the principal could say to justify her claim of no change.

High School PromptReasoning



Ebony’s Medicine (from Summer 2000 Math Assessment Pilot)

Ebony is taking medicine for an illness. Her doctor told her to begin to take 500 milligrams (mg) of this medicine at 8 a.m. The amount of the medicine still active in Ebony’s system at the end of any given hour is reduced by 25% of that amount that was present at the beginning of that hour. At 12:00 noon, how many milligrams (mg) of the medicine is still active (to the nearest milligram)? Show all of your work and explain the steps you used to justify your answer. Numeric answers must always be labeled.






(from PA Department of Education)


High School PromptReasoning and RepresentationAnalytic and Holistic Rubrics


Almanac (from Mathematics Connections Kit, Page 39)

Students will use an almanac to collect data on any of the following: Women’s Olympic 400-meter Freestyle Swim Men’s Mile Record Winning Times for the Indianapolis 500

1. Construct a scatter plot on graph paper and on a graphing calculator with “year” as the independent variable and “winning time” as the dependent variable.

2. Complete a linear regression and write the equation. 3. What is the slope of your model and what does it mean? Test your model for accuracy

with at least three of the actual data points. Comment on the accuracy. Predict the winning time for next running of your event. Is the prediction reasonable? Why or why not?

High School PromptRepresentation



French Fries (from Summer 2000 Math Assessment Pilot)

You and your friends think that sometimes you get ripped off when you buy fries. Some portions seem to have a lot fewer french fries than others, so you decide to do a study. For a week, after school, you and your friends count the number of french fries in 20 different orders. Here is what you found:

Portion # # of Fries Portion # # off Fries 1 30 11 40 2 35 12 32 3 35 13 32 4 38 14 30 5 31 15 35 6 43 16 33 7 32 17 33 8 32 18 31 9 29 19 38 10 40 20 31

1. Construct a graph representing the information from your study. 2. About how many french fries would you expect to get next time? Explain your

reasoning. 3. Based on your date, how few fries would you need to get before feeling ripped off?

Explain your reasoning.




Cow Grazing (from Mathematics Assessment Handbook, Page 42)

A cow is tied to the long side of a barn 10 feet from the corner. The barn measures 11 feet wide and 28 feet long. If the rope is 21 feet long, what is the total area of the space in which the cow can graze? Draw a picture which includes the grazing area to show how you arrived at you answer.




Emilio’s Bookcases (from Summer 2000 Math Assessment Pilot)

Emilio has a small carpentry shop in his basement to make bookcases. He makes two sizes of bookcases, large and small. His profit on a large bookcase is $80, and his profit on a small bookcase in $50. It takes Emilio six hours to make a large bookcase and two hours to make a small one. He can spend only 24 hours each week on his carpentry work. He must make at least two of each size each week. What is the maximum weekly profit?




Population Survey (from Performance Events, 1993-94. Kentucky Department of Education.)

High School PromptCombination Rubric


RRRRESOURCESESOURCESESOURCESESOURCES

Websites National Council of Teachers of Mathematics http://www.nctm.org Pennsylvania Council of Teachers of Math http://www.pctm.org Pennsylvania Department of Education http://www.pde.psu.edu Pennsylvania Academic Math Standards http://www.pde.psu.edu/standard/mathstan.doc PDE Review & Eval. For Select.Textbooks http://www.pde.psu.edu/mathreveval.pdf PDE Math Assessment Handbook http://www.pde.psu.edu/pssa/mathbook.pdf TIMSS Released Test Items 1995 http://timss.bc.edu/timss1995i/Items.html Glenn Commission Report http://www.ed.gov/americacounts/glenn/report.doc Exemplary and Promising Programs http://www.ed.gov/offices/OERI/ORAD/KAD/expert_panel/math-science.html K-12 Math Curriculum Center http://www.edc.org/mcc/ Elementary ARC Center http://www.comap.com/elementary/projects/arc/ Middle School Show Me Center http://www.showmecenter.missouri.edu/ Secondary Compass Center http://www.ithaca.edu/compass/frames.htm Project 2061 Textbook Rating http://www.project2061.org/tools/textbook/algebra/index.htm


Websites (continued)

Council of Chief State School Officers http://www.ccsso.org (Select tab at top of home page labeled state agencies) National Center for Educational Statistics http://www.nces.ed.gov Mathematics Forum http://www.mathforum.com TIMSS http://nces.ed.gov/TIMSS TIMSS http://timss.bc.edu/ NAEP http://nces.ed.gov/nationsreportcard/ Eisenhower National Clearinghouse http://www.enc.org National Science Foundation http://nsf.gov Research for Better Schools http://www.rbs.org Math Problems Assessment 1999/2000 http://www.apiu.k12.pa.us/downloads/map.html


References

Badger, Elizabeth. (May 1992). “More than Testing,” Arithmetic teacher. National Council of Teachers of Mathematics. Blum, R., & Arter, J. (eds.). (1996). A handbook for student performance assessment in an era of restructuring. (Section VI). Alexandria, VA: Association for Supervision and Curriculum Development. Charles, R., and Silver, E. (eds.). (1988). The teaching and assessing of mathematical problem solving. Vol. 3. Reston, VA: National Council of Teachers of Mathematics. Goldberg, Gail, Maryland Department of Education; telephone 410-767-0100. Illinois State Board of Education. (1995). Effective scoring rubrics – A guide to their development and use. (Available from Illinois State Board of Education, 100 N. First Street, Springfield, IL 62777) Lesh, R., and Lamon, S. (eds.). (1992). Assessment of authentic performance in school mathematics. Washington, D.C.: American Association for the Advancement of Science. Marzano, R., Pickering, D., and McTighe, J. (1993). Assessing student outcomes: performance assessment using the dimensions of learning model. Alexandria, VA: Association for Supervision and Curriculum Development. National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA. Newmann, F. Secada, W., and Wehlage, G. A guide to authentic instruction and assessment; vision, standards and scoring. Madison: Wisconsin Center for Education Research. NWREL. (1999). Seeing with new eyes (Video). IOX; telephone 310-822-3225. Resnick L.B., and Resnick, D. P. (1991). “Assessing the Thinking Curriculum: New Tools for Educational Reform. In B. Gifford (ed.), Changing assessments: alternative views of aptitude, achievement and instruction. Norwell, Mass.: Kluwer. Stenmark, Jean Kerr (ed.). (1991). “Mathematics Assessment” Myths, models, good questions, and practical suggestions. Reston, VA: National Council of Teachers of Mathematics.


References (continued) Stiggins, R. (2001). Student-involved classroom assessment (3rd ed.). New York: Merrill. Stiggins, R. (1994). Student-centered classroom assessment. New York: Merrill. Wiggins, G. (1998). Educative assessment. San Francisco: Jossey-Bass. Wiggins, G. (1989a). “A True Test: Toward More Authentic and Equitable Assessment.” Phi Delta Kappan, 70(9), 703-713. Wiggins, G. (1989b). “Teaching to the (Authentic) Test.” Educational Leadership, 46(7), 41-47. Wiggins, G., (1992). “Creating Tests Worth Taking.” Educational Leadership, 49(8), 26-33. Wiggins, G., (1991). “Standards, Not Standardization: Evoking Quality Student Work.” Educational Leadership, 48(5), 18-25. Wolf, D., Bixby, J., Glen, Jr. III, Gardner, H. (1991). “To Use Their Minds Well: Investigating New Forms of Student Assessment.” In G. Grant (ed.), Review of Research in Education. Washington, D.C.: American Educational Research Association.


Glossary Analytic Rubric A scoring guide that contains separate and discrete descriptive

traits with a score point for each trait; separate and discrete criteria allow a response to be viewed in a part-to-whole relationship

Anchor Papers Examples of student work that illustrate each level or point on a

rubric Combination Rubric A scoring guide that contains all the skill development traits from

the holistic rubrics Criteria The specific concepts that are important in a performance Descriptors Statements of the various levels of a performance Formative Evaluation An assessment of student work intended to provide information

and guidance for future growth and development

Holistic Rubric A scoring guide that clusters multiple traits across a range of score points; clustering the traits enables the user to assess a response as a whole

Prompt A question or problem posed to the student Rubric A scoring guide for evaluation of student work that includes

specific performance criteria in a continuum of leveled descriptions from high to low

Score Point A designated value assigned to a descriptor Summative Evaluation An assessment of student work used for the purpose of providing a

concluding or cumulative rating

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