PPA Loneck final

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The Commonwealth of Massachusetts
Department of Education
350 Main Street, Malden, Massachusetts 02148-5023 Telephone: (781) 338-3000
Preservice Performance Assessment for Practicum or Practicum Equivalent
Professional Standards for Teachers: See 603 CMR 7.08.
Part I –To be completed by the applicant. Practicum:_____X_______Practicum Equivalent: ___________
1. Legal Name: (print)___Stephanie Loneck________________________________________2. SSN: ____________________
3. Address: __________________________________ _____________________________________________________________
4. Sponsoring Organization: __Northeastern University__________________________Program & Level: _MED Learning and Instruction_
5. Practicum/Equivalent Course Number: ___EDU 6866_____________________Credit Hours: _8 QH credits ________________________
Course Title: ___Teaching Practicum and Seminar________________________________________________________________________
6. Practicum/Equivalent Site: __Richard J. Murphy School, 1 Worrell Street, Dorchester, MA 02122__
7: Grade Levels of Students: __Sixth/Seventh Grade______
8. Total number of practicum hours: _________________Number of hours assumed full responsibility in the role: ______________________
9. Other Massachusetts licenses held if any: _________________________________________________________________________________
10. Have any components of the approved program been waived (see Regulations 7.03(1)(b)): Yes _______________No__X_ _____________
Part II – To be completed by the Program Supervisor
Name: (print)___________________________________________________________________Position/Title_____________________________
The Applicant completed a practicum/equivalent designed by the Sponsoring organization as partial preparation for the following license:
Applicant’s License Field: ___________________________________________________________Grade Level: __________________________
Part III – To be completed by the Supervising Practitioner
Name: (print)_____________________________________________________________________Position: _______________________________
School System: _____________________________________________________License: Initial (# yrs. experience): ______or Professional: _____
Massachusetts License #: ______________________________________________________Field(s): ____________________________________
Part IV – Initial 1, 2, and 3.
1. Initial meeting held at which the Professional Standards and the procedures for evaluation were explained to the Applicant.
Date: ________Applicant: _________________ Program Supervisor: __________________ Supervising Practitioner: __________________
2. Meeting held midway through the practicum at which the Applicant’s progress toward the Professional Standards was discussed.
Date: ________Applicant: __________________ Program Supervisor: _________________ Supervising Practitioner: __________________
3. Final meeting held to complete evaluation and to allow Applicant an opportunity to raise questions and make comments.
Date: ________Applicant: __________________ Program Supervisor: _________________ Supervising Practitioner: __________________
Part V
Candidate has successfully completed the Preservice Performance Assessment (Sections: 7.03(2)(a)(4) & 7.04(2)(b)(4)(b)) Yes: _____No: _____
Program Supervisor (sign): ____________________________________________________________________ Date: _____________________
Supervising Practitioner (sign): _________________________________________________________________ Date: _____________________
Mediator (if necessary: see 7.04(4))(sign): _________________________________________________________ Date: ____________________

Professional Standards for Teachers: See 603 CMR 7.08
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Please use this assessment in conjunction with the Preservice Performance Assessment
Guidelines: the rating scale is described on page 4; evaluation questions relating to the
standards are pages 5 - 12, and license-specific questions per standard B2c are pages 13-44.
Standard A - Plans Curriculum and Instruction
Indicators Evidence
1. Draws on content standards of the
relevant curriculum frameworks to plan
sequential units of study, individual
lessons, and learning activities that make
learning cumulative and advance
students’ level of content knowledge.
(Specify Curriculum Framework title,
learning standards, and concept and
skills used [attach list if necessary]).
2. Draws on results of formal and
informal assessments as well as
knowledge of human development to
identify teaching strategies and learning
activities appropriate to the specific
discipline, age, level of English language
proficiency, and range of cognitive
levels being taught.
3. Identifies appropriate reading
materials, other resources, and writing
activities for promoting further learning
by the full range of students within the
classroom.
4. Identifies prerequisite skills, concepts,
and vocabulary needed for the learning
activities and design lessons that
strengthen student reading and writing
skills.
5. Plans lessons with clear objectives
and relevant measurable outcomes.
6. Draws on resources from colleagues,
families, and the community to enhance
learning.
7. Incorporates appropriate technology
and media in lesson planning.
8. Uses information in Individualized
Education Programs (IEPs) to plan
strategies for integrating students with
disabilities into general education
classrooms.
1. The following standards from Common Core Curriculum Standards
(implemented as State Standards in Massachusetts) were the basis of the
ratio, rate, unit rate, and proportion unit:
• 6.NS.A.1 Interpret and compute quotients of fractions, and solve
word problems involving division of fractions by fractions, e.g.,
by using visual fraction models and equations to represent the
problem.
• 6.NS.2: Fluently divide multi-digit numbers using the standard
algorithm (scaffold)
• 6.RP.A.1: Understand the concept of a ratio and use ratio language
to describe a ratio relationship between two quantities.
• 6.RP.A.2 Understand the concept of a unit rate a/b associated with
a ratio a:b with b ≠ 0, and use rate language in the context of a
ratio relationship.
• 6.RP.A.3.b Solve unit rate problems including those involving
unit pricing and constant speed.
• 6.RP.A.3: Use ratio and rate reasoning to solve real-world and
mathematical problems, e.g., by reasoning about tables of
equivalent ratios, tape diagrams, double number line diagrams, or
equations.
(See Lesson Plans section in Appendix)
2. During my practicum, I have incorporated both formal and informal
assessment in order to adjust my instruction. Students are regularly asked
to show their understanding through a “thumbs assessment” in which they
show their thumbs up, to the side, or down to illustrate deep understanding,
needing more practice, or no understanding respectively. This allows me to
assess what topics need more review or analysis, or if the class can proceed
to the next lesson.
Students also complete exit tickets at the end of most lessons that contains
a question regarding instruction, including asking students what methods of
instruction worked best for them. Furthermore, students complete a
“Questions/Comments/Concerns” poster during Round Robin activities in
order to formalize their level of comfort and preferred method of
instruction. In exit tickets and Round Robin posters, students referenced the
preference of using candy to model mathematics curriculum based on
lesson of ratios with Skittles candy, which was then adapted to incorporate
colored candies as a model for negative and positive integers. (See
Appendix ET2, ET3, RRP1, RRP6, LP4)
3. Lessons often stem from the Connected Mathematics Project 2
Curriculum in which students reference mathematical concepts, word
problems, and reflections to deepen their understanding. Activities like
group-collaborated posters also promote student learning for a full range of
students in the classroom.

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The lesson on percent word problems in particular fostered deeper
understanding by incorporating visuals, written text, and aural
interpretations. Student groups were provided with a word problem that
applied the concepts of discounts, tax, and tip and an associated grading
rubric to create a group poster illustrating a description of their assigned
word problem, an identified strategy from class to solve the word problem,
the work and solution to the word problem, a model (illustration) of the
word problem, and the Standards of Mathematical Practice (SMP) used to
solve the word problem. (See Appendix RRP2, RRP3, RRP4). In learning
the SMP standards by projecting the SMP webpage
(http://www.corestandards.org/Math/Practice/) on front board and
reviewing each standard individually, students were also directed to visit
the SMP website to read standards in greater detail.
4. During the review of each new textbook, students complete a Round
Robin Activity that introduces or reviews relevant terminology. Students
have completed Round Robin posters for vocabulary related to Ratios,
Rates and Proportions, as well as Positive, Negative and Rational Number
curriculum units (See Appendix RRP1, RRP5, RRP6, RRP7, RRP8).
Handouts were also provided to help students identify the differences
between terms (students complete definitions in their own words) and
terms are reviewed and written on the board throughout lessons for students
to record (See Appendix RH1, RH2). In beginning to learn the concepts of
Greatest Common Factor and Least Common Multiple, students examined
word parts to describe the meaning of each part in their own words.
5. Students are provided daily with a learning and language objective
related to each lesson. Exit tickets are administered at the end of most
lessons that review student understandings. In learning about Tax, Tip, and
Discount, students were provided with the learning objective to calculate
tax and discount amounts in word problems. Each table group completed a
group poster to illustrate problem solving for a discount and tax word
problem and were provided a rubric that their poster must abide to. (See
Appendix LP6, RRP2, RRP3, RRP4, RH3).
6. In addition to using and recording feedback from supervising teacher, I
have incorporated resources from sixth grade team meetings into my
instruction. Based on the Core Action document and suggestion from
colleague, I implemented the use of a projected internet timer in order to
keep students on task to achieve learning goals (See Appendix AM1).
I have also incorporated previous methodologies and resources from
supervising teacher including the Student Buy-Back Point form for students
to use for quiz correction in order to earn points back on quizzes and tests.
(See Appendix SGQM1h)
7. Lessons often incorporated the use of a document camera and projector
to illustrate mathematics concepts and to increase the size and visibility of
demonstrations with manipulatives. Lesson on comparing and combining
positive and negative numbers used document camera and projector to
exhibit the use of candies as representing negative and positive numbers,
and to illustrate the process of matching one white colored candy with one
purple colored candy in order to find the leftover (difference of) candies.
My example of candies and “leftover candies” were projected on the board
for students to reference as they completed their own candy comparison

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with their individual bags of candies (See Appendix CSU1, CSU2)
Students also viewed Exploring Integers and Temperature video
(http://www.learnalberta.ca/content/mejhm/index.html?ID1=AB.MATH.JR
.NUMB&ID2=AB.MATH.JR.NUMB.INTE&lesson=html/video_interactiv
es/integers/integersSmall.html) with Math Interactives via a laptop
connected to a projector. Students also participated as a class to complete
interactive page
(http://www.learnalberta.ca/content/mejhm/index.html?ID1=AB.MATH.JR
.NUMB&ID2=AB.MATH.JR.NUMB.INTE&lesson=html/video_interactiv
es/integers/integersInteractive.html) linked with video web page.
8. Based on visual needs of one student, enlarged copies or class materials
were provided to student A, as well as large-print versions of the class
textbook. Based on the social-emotional needs of student R as identified in
his IEP, classmate seating and partner pairings were adjusted in order to
improve engagement and participation.
Rating: Explanation of Rating for Standard A - Plans Curriculum and Instruction
Rating Scale: 1=Does Not Meet the Standard; 2=Meets the Standard, 3=Exceeds the Standard; NA=Not Applicable.
Candidate’s Name: _____________________________________________________License: _____________________________
Program Supervisor (initial): ______________________________________________________Date: ______________________
Supervising Practitioner (initial): ___________________________________________________Date: _____________________

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Standard B – Delivers Effective Instruction
Indicators Evidence
1. Communicates high standards and
expectations when beginning the lesson.
a) Makes learning objectives clear to
students.
b) Communicates clearly in writing and
speaking.
c) Uses engaging ways to begin a new unit
of study or lesson.
d) Builds on students’ prior knowledge and
experience.
expectations when
carrying out the lesson.
a) Uses a balanced approach to teaching
skills and concepts of elementary reading
and writing.
b) Employs a variety of content-based and
content-oriented teaching techniques
from more teacher-directed strategies
such as direct instruction, practice, and
Socratic dialogue, to less teacher-directed
approaches such as discussion, problem
solving, cooperative learning, and
research projects (among others).
c) Demonstrates an adequate knowledge
of and approach to the academic
content of lessons. (See license-specific
questions in Guidelines, pp. 13-44)
d) Employs a variety of reading and writing
strategies for addressing learning
objectives.
e) Uses questioning to stimulate thinking
and encourages all students to respond.
f) Uses instructional technology
appropriately.
g) Employs appropriate sheltered English or
subject matter strategies for English
learners.
expectations when extending and completing
the lesson.
a) Assigns homework or practice that
furthers student learning and checks it.
b) Provides regular and frequent feedback to
students on their progress.
c) Provides many and varied opportunities
for students to achieve competence.
expectations when evaluating student learning.
a) Accurately measures student achievement
of, and progress toward, the learning
objectives with a variety of formal and
informal assessments, and uses results to
plan further instruction.
b) Translates evaluations of student work
into records that accurately convey the
level of student achievement to students,
parents or guardians, and school
personnel.
1a. Objectives are always written before students arrive on board. A
specific area of the board is designated for the learning objective. In
reviewing operations with decimals and introducing word problems with
decimals, the learning objective was written as and read aloud as “Solve
addition, subtraction, multiplication, and division problems with decimals;
Identify key words to solve word problems” (See Appendix OB3, OB4)
1b. Lesson is always introduced with the statement, “today we are going
to learn…”. I point to the learning objective, written on board, and read
objective aloud verbatim. I then reword this objective into easier terms or
prompt students to interpret what this objective means to them.
1c. Many of the introductory activities, “hooks” include a visual
representation, an activity requiring movement, and/or a tangible item. In
learning how to identify key words to solve word problems, students were
presented with the scenario called “Lava Crossing”, in which students are
given objective (cross the river of lava without touching the lava, i.e. the
floor), and the parameters (student has two “safety gems”, i.e. two piece
of paper, to step on in order to cross the lava). After choosing a volunteer
to cross the “lava river”, I recorded student observations of the problem at
hand, the scenario and parameters, and possible solutions. Students then
crossed out and eliminated irrelevant information (i.e. student is wearing
blue sweater) as a class. Using relevant information, students worked
together to develop a strategy to solve while still abiding by the
limitations of the lava scenario. Student volunteer tested the strategies
until one of the suggested strategies worked to cross the room. After
successful completion of lava crossing, students were prompted to connect
the process of crossing the river (reviewing all the information given and
observed, eliminating unnecessary details, and using the relevant details to
solve the scenario) to the process of problem solving with word problems
with decimals in mathematics. (See Appendix LP5)
1d. For lesson on Word Problems with Decimals Problem-Solving, I
related the concept of eliminating irrelevant information and strategizing
with useful information to evacuating from a volcano. Although students
have not necessarily been inside a volcano, I assessed the students on
knowing when a volcano is, and explaining the dangers of a volcano by
using descriptors like “hot”, “fire”, and “unpredictable”.
2a. Students are directed and transitioned when notes are required for
recording and writing key concepts of a lesson. When learning how to
add, subtract, multiply and divide decimal numbers, students wrote notes
that I scribed on the board; these notes were filed into their Class Notes
section of their binder. Similarly, students illustrated their skills on
reading and indicating key terms and phrases of word problems by
highlighting such terms and phrases on class worksheet. (See Appendix
AS1).
2b. In designing lessons, exploration includes direct instruction by me as
well as guiding questions and Socratic dialog. My instruction also utilizes
group work collaboration and group projects, in which I move around
classroom to prompt discussion, but students problem solve themselves.

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Group-based instruction (less teacher-directed) was observable within the
Percent Word Problem Poster activity. (See Appendix CSU 1-10)
2c. In learning how to add and subtract negative numbers, students were
able to learn multiple strategies to illustrate their understandings. The
hook, Where’s the Cheese, allowed students to visually see how to add
integers by explaining how a mouse can move from one point on a
number line to another point on the number line that the cheese is located.
Students also developed rules to adding negative and positive numbers for
similar reference, as well as the use of a chipboard. (See Appendix ET8)
2d. In addition to rephrasing problem wording and terminology, I often
prompt students to explain readings in their own words. Students achieved
the learning objective “identify key words to solving word problems” with
percents by highlighting key words in word problems and finding a
solution to addition, subtraction, multiplication, and division. (See
Appendix AS1) Additionally, students complete Math Reflections
(incorporated in the CMP2 Curriculum), which call for explanations,
details, and examples in written form. (See Appendix MR1a, MR1b,
MR2a, MR2b)
2e. My instruction has supported my practice in using questions to
encourage learning and student responses. In creating lessons that support
participation and real-world application, lessons like one comparing “Air
Head” candy size and pricing hooks students into lesson. My prompting
for this lesson included questions such as “which bag of Air Heads is the
better buy and why?”, and implementing a vote by stating “who agrees
with student X about the better buy?”, “who does not agree? Why?”, and
“what additional information will help us decide exactly which one is a
better buy?”. (See Appendix LP2)
2f. The use of a document reader and projector are often used to magnify
and show an image on the white board for all students to see from their
desk spots. Projector and document reader was used to magnify candies as
representations of positive and negative numbers. (See Appendix CSU1,
CSU2) Students were also sent an email on the Boston Public School
system to remind them of an upcoming Math Reflection due date.
2g. For English Language Leaners, language objectives are written on
board daily, and verbally repeated by me in the beginning of class. (See
Appendix OB1, OB2, OB4, OB6, OB7, OB9 ) Language-based prompts
are incorporated into instruction by asking ELL students to explain their
understandings in their own words. Assignment on definition of ratio, rate,
and unit rate was given for students to express their understandings, and
credit was given to students that expressed coherent and accurate
reasoning. (See Appendix RH1, RH2)
3a. Homework is assigned and written on board in designated homework
board space daily. (See Appendix OB8, OB9). Homework is reviewed
and recorded when completed.
3b. Math Reflections are assigned for students to review their
understanding and exhibit their knowledge through logical reasoning and
justifiable explanations. Students were assigned on October 16th
, and
collected on October 24th
. After reviewing, feedback is provided to
student on their work, what was shown well, what can be improved, and

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the grade they received for their work.
3c. Students are often given opportunities to improve their competency.
Students are able to spend additional time during their lunch and recess
breaks to review class material, and have their questions answered.
Student X regularly attends lunch and recess help hours to receive and
learn more challenging concepts. Students are also able to improve
competency by completing Buy Back Points, in which they review,
correct, and identify their mistakes from a previous quiz or test. (See
Appendix SGQM1h).
4a. Students complete frequent exit tickets that address lesson concepts.
Students are able to express their understanding in a way that works best
for them, allowing for me to adjust my lessons according to student
preference. Students also complete a “thumbs to decide” assessment, in
which they signal a thumbs up, thumbs to the side, or thumbs down to
indicate comfortable/fluent, needing more practice, and
uncomfortable/confused respectively. Grades are updated daily on the
Boston Public Schools Student Information System (SIS). Upon viewing
assignment averages and individual student progress and performance,
adjustments and reiterations are planned accordingly.
4b. I enter and update grades for student work (homework, projects, and
quizzes/tests) daily to accurately reflect overall student grades, and make
notes of missing work or incompleteness accordingly. Communication
with parents is facilitated as needed. Phone call with parent was placed on
October 18th
regarding many missing assignments, and concern for grade
progress.
Rating: Explanation of Rating for Standard B – Delivers Effective Instruction
Candidate’s Name: _____________________________________________________License: __________________
Program Supervisor (initial): ______________________________________________________Date: __________
Supervising Practitioner (initial): ___________________________________________________Date: __________

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Standard C – Manages Classroom Climate and Operation
Indicators Evidence
1. Creates an environment that is
conducive to learning.
2. Creates a physical environment
appropriate to a range of learning
activities.
3. Maintains appropriate standards of
behavior, mutual respect, and safety.
4. Manages classroom routines and
procedures without loss of significant
instructional time.
1. During the start of the day, I pick up the students from the front of the
school and greet each student as they enter the school and classroom. The
classroom contains specified board space with the day’s objective(s) and
language objective(s), in which I update daily according to the lesson and
class schedule. (See Appendix OB1-7). This board space also includes a
spot designated for the homework assigned to each class section.
Furthermore, desks are arranged into clusters of four with visibility of
both classroom boards used during instruction to allow for variability in
movement and board space. (See Appendix CSU15, CSU16, CSU17)
Student work and Standards for Mathematical Practice (SMP) posters are
displayed on walls to encourage students to view previous learning, and
connect their learning to mathematical standards. (See Appendix CSU18,
CSU19, CSU20)
2. The classroom contains artifacts from prior lessons including chart
paper with word-definition-examples relevant to curriculum topics. For
example, students reviewed the definition and examples of the terms
‘ratio’, ‘rate’, ‘unit rate’, ‘proportion’, ‘scale factor’, and ‘equivalent’. In
addition to student and class work, the classroom desk space is arranged
into clusters of four desks to allow for group work and independent work
as needed. Desks are also arranged into clusters of four to allow for easy
view of all instructional boards, and to allow easy movement around the
room while observing student work. These clusters position desks so they
are facing inward toward each other to allow for easy and intimate
learning conversations. (See Appendix CSU5, CSU6, CSU10, CSU15,
CSU16, CSU17)
3. Beginning on the first day of school, all class sections reviewed the
three aspects of a learning community: personal best, honesty, and respect.
Each class defined the three aspects in their own words, responses were
recorded on poster paper, and hung in a visible area within the classroom.
These Class Norms are referenced regularly, especially when issues arise
between students. (See Appendix CSU11, CSU12)
During instances of issues or conflict between students, proper action is
taken to speak with students in individual and group interventions within
the classroom. The Boston Public School Student Handbook and Class
Norms are referenced during these interventions.
Similarly, students are provided with details and information regarding
redirection within the classroom. With three levels of intervention
(reminder, warning, conference/call home), students are given a verbal
warning if their negative behavior persists. These levels are placed on a
designated board space. (See Appendix CSU13)
In addition to class-developed Norms and a system of redirection, students
are recognized and rewarded for displaying positive behavior within the
classroom. In particular, instructor will signal the “quiet coyote” hand
gesture to which students must also gesture the “quiet coyote” signal, and
remain silent with eyes on instructor. The first student to respond and
signal the “quiet coyote” will be recorded on the board. Should they
receive recognition for this notion, students will receive a reward such as a

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sticker or candy treat. (See Appendix CSU14)
4. During the beginning of class, I remind students about the norm of
completing the Do Now and taking out homework from previous night.
Following the review of this homework, I review the agenda for the day,
including the learning objective, language objective, the type of activity to
introduce the lesson (the “hook”), lesson number (referenced in CMP2
text) , and the style of work to be completed (i.e. group work, individual
work, team competitions, and so on).
Throughout the lesson, I check the time, and clarify with the students if
we are running on time, running behind time, or running ahead of the
planned schedule in accordance to the timing listed within my lesson plans
(See Appendix LP1-6). In the event that we are running behind the
planned schedule, I verbally express any adjustments that need to be made
(such as less time to review questions on homework, less time to complete
concluding activity, and so on).
Furthermore, I verbalize transitions throughout the lesson so that students
may adjust themselves accordingly. This includes instructing students to
“file away” their Do Now worksheets, homework, and classwork into
their binders as needed, placing homework or other materials in the
middle of the table to be collected as needed, and transitional phrases to
capture every student’s attention (i.e. “quiet coyote” hand gesture) when
moving on throughout a lesson.
Rating: Explanation of Rating for Standard C – Manages Classroom Climate and Operation

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Standard D – Promotes Equity
Indicators Evidence
1. Encourages all students to believe that
effort is a key to achievement.
2. Works to promote achievement by all
students without exception.
3. Assesses the significance of student
differences in home experiences,
background knowledge, learning skills,
learning pace, and proficiency in the
English language for learning the
curriculum at hand and uses professional
judgment to determine if instructional
adjustments are necessary.
4. Helps all students to understand
American civic culture, its underlying
ideals, founding political principles and
political institutions, and to see
themselves as members of a local, state,
national, and international civic
community.
1. During class discussion and hook activities, I encourage all students to
participate as a learning community member. I intentionally select
students to show their work and answers on the board for the Do Now
worksheet on a daily basis, and often select students that have not been
vocal as much as others. In the event that students make a mistake in their
work or struggle to find an answer, I provide guiding questions in order to
help them arrive at an answer without directly showing them how and
without indicating that they are wrong. Additionally, I often ask for
alternative strategies, views, and perspectives from other classmates in
order to help each student arrive at the correct answer in a way that is best
for them (See Appendix CSU3, CSU4). Additionally, I grade quizzes and
tests based on the components of effort and accuracy. Students receive
partial credit for showing work on their test and attempting to find an
answer, which is explicitly stated in quiz directions. (See Appendix
SGQM1a-f).
2. Students were provided an outline of their grade weight on the first day
of school, and are given grading rubrics as needed (See Appendix RH3).
Additionally, students are given opportunities to review work and redeem
their understandings by completing additional work as well as completing
Buy-Back Points for quizzes and tests, which allows students to gain a
sense of achievement and improve their grade. (See Appendix SGMW1)
Furthermore, I allow students to spend extra time (lunch and recess time)
with me to review any material they may be questioning and to assist them
in starting their math work for that day. This time is also dedicated for
students to complete any make-up work that they are missing or did not
quite understand with the intention of changing their assignment/quiz
grade accordingly.
Student seating arrangements also change every month in their cluster of
four desks. With these seating changes, students receive a role of team
leader, recorder, materials manager, or team floater, with roles switching
each month when seating arrangements switch. This role rotation allows
students to have the opportunity to succeed in each table group role. (See
Appendix, CSU 21a-CSU21d)
3. In assessing the significance of student differences, I often give
students the opportunity to express their preference in learning and
method of learning in order to accommodate their differences. I have
incorporated prompts that allow students to share their voice in the form
of exit tickets, end-of-test assessments, and within Round Robin activities
(See Appendix ET1, ET2, ET3, ET7, RRP1, RRP6, SGQM1g). From
these forms of assessment, I am also able to adjust and differentiate my
instruction accordingly. Throughout my practicum, I have made changes
such as using an overhead projector, bringing in visuals and manipulatives
that students can touch and see, and created various study guides for
quizzes and tests in order to best prepare them for the quiz/test questions
(See Appendix SGQM2, SGQM3, SGQM4). These adjustments, along
with many more, are a direct result of student preference as indicated on
exit tickets and lesson activities.
4. During group activities, I have incorporated terminology related to

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American civic culture such as “elect”, “representative” and “speaking on
behalf of the larger group” for students to speak to and show the work of
their group on an assigned question. When including this approach in
group work, I remind students about the role election, representations, and
populations play a role in American and global culture. After
collaborating on an assigned question and coming to a consensus on the
strategy and solution as a table group, an elected representative from each
table illustrates and presents their work to the class. This process was used
for the hook activity that required students to collaborate and develop a
story that illustrated a real-world application of a positive or negative
number that I assigned to the group. (See Appendix LP7)
Similarly, students participate in group votes on content-related choices
for the purpose of satisfying a lesson objective. When learning about rate
and unit rate, students were presented with the problem of finding which
package of “Air Head” candy was a better deal. Based on two packages of
candy differing in size and price, all students were instructed to vote on
which deal they thought was better and provide a clear and thought-out
process of reasoning. (See Appendix LP2)
Rating: Explanation of Rating for Standard D – Promotes Equity
Program Supervisor (initial): ______________________________________________________Date: ___________
Supervising Practitioner (initial): ___________________________________________________Date: __________

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Standard E – Meets Professional Responsibilities
Indicators Evidence
1. Understands his or her legal and moral
responsibilities.
2. Conveys knowledge of and enthusiasm
for his/her academic discipline to
students.
3. Maintains interest in current theory,
research, and developments in the
academic discipline and exercises
judgment in accepting implications or
findings as valid for application in
classroom practice.
4. Collaborates with colleagues to
improve instruction, assessment, and
student achievement.
5. Works actively to involve parents in
their child’s academic activities and
performance, and communicates clearly
with them.
6. Reflects critically upon his or her
teaching experience, identifies areas for
further professional development as part
of a professional development plan that is
linked to grade level, school, and district
goals, and is receptive to suggestions for
growth.
7. Understands legal and ethical issues as
they apply to responsible and acceptable
use of the Internet and other resources.
1. Instruction and differentiation is based on IEPs and 504s available, as
well as based on the collaboration within the weekly sixth grade team
meetings. Outreach to parents/guardians is implemented upon multiple
offenses by a student (e.g. missing homework, disruptive behavior, lack
of participation). (See Appendix EC1)
2. In conveying knowledge and enthusiasm for mathematics to students, I
often ask students where they see a particular concept in real-world
application. These questions are often included within a lesson plan in
which I emphasized as one of many underlying reasons to practice and
understand core mathematics standards. (See Summary Questions asked
in Appendix LP1, L22, LP3, LP4, LP6)
In order to provide real-world application and context, I have facilitated
various activities and medias related to ratios, rates, and proportions in
order to illustrate the array of content relativity. Hook activities included
rate and unit rate within a grocery shopping ad, using dice to create a ratio
and proportion, baking mix to illustrate multiple batches, and Round
Robin with terminology posters. In displaying my enthusiasm in the hook
activity designs, I encourage students to become excited about the
application of mathematics in a way they can see, feel, and talk about (See
Appendix LP1, LP3, LP8)
3. In reviewing current theory and developments on educational practice, I
have often incorporated practices from Teach Like a Champion, by Doug
Lemov, in order to create classroom culture, give structure in how I
deliver lessons, and engage students in my lessons. More specifically, I
have focused on engaging students in lessons through techniques like cold
calling, call and response, and “Vegas”. My lesson facilitation
incorporates “Vegas” attributes by adding some theatrical presentation
(such as varying my linguistic accent to a thick New York City accent or
fluctuating my tone of voice to add emphasis on a word or phrase).
I have further included some sociocultural references into lessons,
allowing for material to resonate with students in a more memorable
manner. In learning how to convert a percent into a decimal number, my
reference to the opening line “to the left, to the left,” in the popular
Beyoncé song, “Irreplaceable”, created a lasting meaning and
unforgettable process of conversion. One student refers to this process in a
Mathematics Reflection assignment. (See Appendix MR3)
4. I collaborate weekly with the sixth grade teaching team to improve
communication and consistency for the students. I also meet regularly
with supervising teacher during free periods throughout the day and at the
end of the day to discuss the fluidity of the day’s lessons,
accomplishments and wonderments, and feedback from her observations
of my instruction in order to improve future lessons. Similarly, my
supervising teacher provides verbal and written (email) feedback in order
to improve my instruction and to call my attention to student concerns and
behavioral/academic issues (See Appendix, EC2).
5. I attended Open House night on September 18th
, 2014 to introduce
myself in person and to provide an introductory letter for parents. (See

Page 13 of 76
Appendix AM2) This opportunity was also used to review the course
outline, grading, and expectations. Outreach is made with parents via
phone and email regarding academic performance and concerns as
needed. Progress and quarter reports are sent home for parents/guardians
to review, sign, and send back. Additionally, contact is made with home
when students display behaviors of concern (homework not being handed
in, disruptive in class, lack of participation). (See Appendix EC1)
6. Throughout practicum, I recorded regular journal entries as evidenced
by the seminar platform on Blackboard. Included in this journal, I was
able to reflect on each component of learning and instruction.
Additionally, I document reflections on my lesson implementations daily
and send to my supervising teacher to receive feedback and suggestions to
improve my instruction. These reflections address the questions: What did
I intend to teach?; What did students learn?; How do I know they learned
it? And; What would I do differently next time? (See Appendix EC2)
7. In using technology and the Internet in the classroom, I have carefully
reviewed and implemented appropriate actions as cited in the Guide to
BPS: Using Technology in School- Middle School, Grades 6-8
(http://bpscybersafety.org/aup/aup-6-8.pdf) and the 2014-2015 Guide to
the Boston Public Schools for Families and Students
(http://www.excelhigh.org/pdf/BPS%20Fam%20Guide%202013-14.pdf).
All lessons that incorporate the Internet are planned carefully so as to
abide by the rules and expectations cited by Boston Public School, and I
review websites used before lesson implementation to ensure material is
relevant, appropriate, and scaffolds the lesson content.
Rating: Explanation of Rating for Standard E – Meets Professional Responsibilities
Program Supervisor (initial): _____________________________________________________Date: ____________
Supervising Practitioner (initial): __________________________________________________Date: ___________

Page 14 of 76
Summary Decision for Preservice Performance Assessment
Teacher candidate’s Preservice Performance Assessment in the practicum or practicum
equivalent meets the Professional Standards for Teachers: Yes ________ or No ________.
Candidate (sign): _______________________________________________________License: ________________
Program Supervisor (sign): _______________________________________________________Date: __________
Supervising Practitioner (sign): ____________________________________________________Date: __________
Standard Rating (from pp. 2-5)
(a) Plans Curriculum
(b) Delivers Effective Instruction
(c) Manages Classroom Climate
(d) Promotes Equity
(e) Meets Professional Responsibilities
Summary Comments (integrated assessment of performance):
The sponsoring organization should maintain this assessment record as part of its candidate’s
permanent file. Copies do not have to be sent to the Department of Education.

Page 15 of 76
Appendix

Page 16 of 76
Lesson Plans
LP1.
Lesson Plan : Comparing and Scaling 2.3 and 3.1- 315; 10/8/14
TheSet-up
Unit Goals: What essential questions are driving this unit?
- How can ratios be used to compare unit rates?
- What is the meaning and real world application of rate, and how can it be
represented graphically?
- How can you calculate a unit rate?
Learning Objective(s): What will students be able to do by the end of class?
- Understand how to write rate tables as a way to scale rates
- Know strategies for finding a number of units for a given unit rate (a limited/fixed
unit rate)
Materials: What do you need? How will the room be set up?
Students will work in a group of 2 or 4
- Pencil/pens/dry erase
- CMP Comparing and Scaling Book
- Lined paper for notes
- Catalog (for hook)
Common Core Standards:
6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of
fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
6.NS.2: Fluently divide multi-digit numbers using the standard algorithm (scaffold)
6.RP.A.1:Understand the concept of a ratio and use ratio language to describe a ratio relationship between two
quantities.
6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate
language in the context of a ratio relationship.
6.RP.A.3.b Solve unit rate problems including those involving unit pricing and constant speed.
6.RP.A.3: Use ratio and rate reasoning to solve real-world and mathematical problems,
e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line
diagrams, or equations.
SMP: Standard Mathematical Practices:
1, 2, 3, and 6 are aspects of mathematical thinking that are emphasized in this lesson.
Students will build on prior knowledge of ratios and compare unit rates based on given
information. They will need to attend to precision to compare.
ELL Content Standards:
Students will comprehend and use vocabulary pertaining to ratios, tables and unit rates.
Students will understand the terminology associated with calculating a unit rate, and
interpreting unit rate.
ELL Language Objectives:
Students will orally articulate and describe unit rates using tables and scale cost based on
the unit rate.

Page 17 of 76
Time
TheLesson
Do now and Collect Homework
- Students will be given a ratio table and will complete missing parts.
Students will also complete a division problem and will compare two
fractions to find the higher valued fraction.
- Worksheet homework will be collected, and ACE question homework
checked and reviewed (only most difficult 2 questions)
- Review 2.3 questions and summarize lesson (What would you do to
find the perfect amount to feed a larger number of chimps (ex. 50
baby chimps)? What is an efficient way to find an equivalent ratio?
How do you know when you need to multiply or divide to find an
equivalent ratio?)
-10 (Do Now
and HW
review)
-10 minutes
(2.3 review)
The Hook:
q Do you anchor the lesson to prior knowledge?
- Instructor will have shopping catalog(s) for students to view- either
copies will be passed around, or one copy will be projected on white
board.
- Students will be asked to pick their favorite item listed in catalog (2-3
volunteers will be chosen), and discuss the price of the item.
- Students will be asked to calculate cost if two of those items were
purchase, three items, four items, and so on. Students will need to
calculate the cost to purchase enough items to supply the whole
class (28 students). Instructor will create a table to illustrate pricing.
10
Exploration:
- Students will explore 3.1 in their table groups.
- 2.3 questions will be reviewed as a class, with a summary to follow.
- Students will practice unit rates by playing “How Much” (each ratio
card gives the unit rate that the students must calculate. The LCM
War cards will provide the number of units. One student has Ratio
cards, while the other has LCM cards- at the same time, students flip
their top card and must use the unit rate (the cost per unit for this
game) and the number of units to find the total cost.)
- 30 (3.1)
- 15 (review
of 3.1)
- 30 minutes
(“How
Much”
game)
Practice:
q Do you differentiate for language and learning needs? If need be, the
numbers will be smaller in quantity and scaffold vocabulary and have
students verbally express what they know
q Auditory, visual and kinesthetic modalities? Mostly kinesthetic, with
visual and auditory
q Independent, small and large group learning? Groups of 2 and 4
q Are students doing the heavy-lifting rather than you? They should be
working together in groups while teacher guides students to compare
fractions
q Are there checks for student learning? Thumbs up/summary
Included in
exploration

Page 18 of 76
Summary:
- What are other examples of unit rates? What two units are being
compared in these examples?
- What patterns did you see in the tables you made? How can you
predict the cost of something if you know the unit rate?
5
Exit Ticket (used from previous day)
- One class (Class W) has a ratio of 210 girls to 240 boys. Another
class (Class S) has a ratio of 95 girls to 120 boys. Which grade has
the greater proportion of girls?
- Fill in the blank: 5/16 = ____/48
5
Homework:
ACE: Pg. 1-2, 13-18, 33; Fractions/Decimals/Percents worksheet
LP2.
Lesson Plan : Comparing and Scaling 3.2 Review/3.3- 315; 10/15/14
TheSet-up
- How can ratios be used to compare unit rates?
- What is the meaning and real world application of rate?
- How can you calculate a unit rate?
- Understand how to write and interpret unit rates
- Air head packages (for hook)
6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate
language in the context of a ratio relationship.
6.RP.A.3.b Solve unit rate problems including those involving unit pricing and constant speed.
1, 2, 3, 4 and 6 are aspects of mathematical thinking that are emphasized in this lesson.
Students will build on prior knowledge of unit rates based on given information to apply to
unit pricing and the slope of a line. They will need to attend to precision and model their
understandings of unit rate graphically.

Page 19 of 76
Students will comprehend and use vocabulary pertaining to unit rates and unit pricing.
Students will understand the terminology associated with calculating a unit rate, and
interpreting unit rate as a cost per item.
Students will orally articulate and describe unit rate as the cost per one item, and relate the
unit rate to a graph.
Time
TheLesson
- Students will find unit rate for 2 different problems
- Have students swap homework worksheet, review answers and collect
- Review 3.2 lesson problems
- Summarize 3.2
-15 (Do Now
and HW
review)
-20 (Review
3.2)
The Hook:
- Instructor will bring in two similar items, one larger than the other (possible
examples include a party pack of candy and a single serving size of
candy,) Given a price for each item, instructor will prompt students to vote
on which item is the better deal.
- Instructor will allow 2-3 volunteers to explain their reasoning for why one is
the better deal than the other. If not mentioned, instructor will guide
students to calculate the unit rate (the unit price, or price per pound).
10
Exploration:
- Students will explore 3.3 in their table groups, then review 3.3 as a class. If
time allows, ask for additional examples of rates and speed.
- Summarize 3.3
- If time allows, students will practice unit rates by playing “How Much” (each
ratio card gives the unit rate that the students must calculate. The LCM
War cards will provide the number of units. One student has Ratio cards,
while the other has LCM cards- at the same time, students flip their top
card and must use the unit rate (the cost per unit for this game) and the
number of units to find the total cost.)
- Students will compete in table groups to solve for unit rates given by
instructor
- 20 (3.3
work and
review)
- 5
(summarize
3.3)
- 30 (How
Much
game)
- 20
(compete)
Practice:
q Do you differentiate for language and learning needs? If need be, the numbers
will be smaller in quantity and scaffold vocabulary and have students verbally
express what they know
q Auditory, visual and kinesthetic modalities? Mostly kinesthetic, with visual and
auditory
q Are students doing the heavy-lifting rather than you? They should be working
together in groups while teacher guides students to compare fractions
Included in
exploration

Page 20 of 76
Summary:
- What is a rate? What does unit rate mean
- What units did you work with in this problem, and how did you decide the
unit rate units?
- What strategies did you use to compare the cost of the CDs?
5
Exit Ticket
- One problem that asks students to find the unit rate for a box of 36 cookies
that cost $4.50
5
Homework: ACE, pg 41 #9, 11, 26, 34, Rate word problems Worksheet
LP3.
Lesson Plan : Comparing and Scaling 4.1- 315; 10/20/14
TheSet-up
- How are ratios related to proportions?
- How can you use scaling (i.e. equivalent ratios) to find a missing part in a
proportion?
- What are strategies to using proportions in real world application?
- Understand how to use a scaling factor in proportions
- Problem solve to find missing part in two equivalent ratios
- Colored counters (for hook)
- Chart paper (for round robin if time allows)
- Cards (for multiplication war if time allows)
diagrams, or equations. (scaffold)
6.RP.A.3.d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately
when multiplying or dividing quantities.
1, 2, and 4 are aspects of mathematical thinking that are emphasized in this lesson.
Students will build on prior knowledge of ratios and rates to make sense of proportions and
apply them to ratios with missing parts. They will need to attend to precision and model
their understandings by finding missing parts of proportions and missing lengths of
geometric shapes.
Students will comprehend and use vocabulary related to proportions and scaling. Students
will understand the terminology associated with finding a proportional value.

Page 21 of 76
Students will orally articulate and describe proportion as two ratios that are equivalent.
Time
TheLesson
- Students will complete 2 ratio problems (scaffold), and 1 unit rate problem
- Review 2-3 difficult problems from the homework (worksheet) as a class.
- Collect homework (worksheet and quiz corrections)
-10 (Do Now
and HW
review)
The Hook:
- Instructor will show a sample of two different items (red counters and
yellow counters) with a ratio of 2:5.
- Instructor will add 2 more red counters- how many more yellow counters
should be added?
- Instructor will remove the added counters to get back to the 2:5 ratio. If
there are 100 red counters, how many yellow counters would there be?
Why? If there were a total of 100 counters, how many would be red, and
how many would be yellow? What is the difference between these two
scenarios?
10
Exploration:
- Students will explore 4.1 in their table groups, then review 4.1 as a class.
- If time allows, ask for additional examples of proportions, and strategies to
finding proportional values.
- If time allows, students will complete a round robin of vocabulary posters
(ratio, rate, unit rate, proportion, scale factor, similar and equivalent)
- If time allows, students complete rounds of multiplication war (to scaffold
proportions and scale factors)
- 20 (4.1 work
and review)
- 10 minutes
(additional
examples
and
strategies)
- 40 mins
(round
robin)
- 20 mins
(multiplicati
on war)
Practice:
q Auditory, visual and kinesthetic modalities? Mostly kinesthetic, with visual and
auditory
together in groups while teacher guides students to compare fractions
q Are there checks for student learning? Thumbs up/summary/exit ticket
Included in
exploration
Summary:
- What does it mean to be proportional?
- Where do we see proportional things in the real world? Why is it
important?
- How do you find a missing side when you have two corresponding parts
of similar shapes?
5

Page 22 of 76
Exit Ticket
- One problem gives a ratio (5/10). Students will need to give 1 proportional
ratio.
- One problem illustrates a rectangle with 2 side lengths provided (4 cm
and 2 cm), and a larger rectangle with one side length provided (8 cm).
Students will find the missing length.
5
Homework: ACE, pg. 55 #1-2, 15-17, 22, Proportions worksheet
LP4.
Lesson Plan : Accentuate the Negative, 1.1 – 315; 11/12/14
TheSet-up
- How can we use negative and positive numbers?
- How can we add, subtract, multiply, and divide negative and positive numbers?
- What strategies can model operations between negative and positive numbers?
- Find relationships between integers by comparing, ordering, and adding other
integers to them
- Colored candy (for hook)
- Elmo and Projector (for hook)
- Playing cards
6.NS.C.5: Understand that positive and negative numbers are used together to describe quantities having
opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level,
credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in
real-world contexts, explaining the meaning of 0 in each situation.
6.NS.C.6.a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number
line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its
own opposite.
1, 4, 6 and 8 are aspects of mathematical thinking that are emphasized in this lesson. They
will need to make sense of negative and positive numbers and persist in comparing them,
as well as attend to precision while forming their answers. They will be using repeated
reasoning when adding positive and negative numbers together. They will also model their
understandings with number lines, and pictures.
Students will compare and order positive and negative integers. Students will also be
adding negative and positive integers to other integers.
Students will be able to compare integers and arrange them in order from lowest to
highest.

Page 23 of 76
Time
TheLesson
Do now and Review of new book
- Students will complete Do Now: One problem labeling 5 points on the
number line, set of 5 negative and positive comparisons
-10 mins (Do
Now)
The Hook:
- On the projector, instructor displays a pack of candy on board, placing
colors in separate groups. Instructor assigns one color as negatives, and
another color as positives.
- Based on the number of each color, instructor guides students in writing
an addition problem based on the number of candies shown on board.
- After guiding students through addition problem and identifying a
solution, each student is given their own baggie of candy, in which they
separate and write their algorithm using positive and negative numbers.
- Several volunteers are asked to present their problem and solution on
the board.
- Instructor asks students to find different algorithms to find a target
number using negatives, positives, and addition. (Write steps and have
students record steps in their notes)
10 mins
Exploration:
- Students work on 1.1 with their group.
- After completing group work, #2s in each group write their solution to an
assigned problem on the board.
- Review solutions and strategies as a class
- Summary of 1.1
- Integer Addition War
- 20 mins
(group work)
- 10 mins
(work review)
- 5 mins
(summary)
- 20 mins
(integer
addition war)
Practice:
q Do you differentiate for language and learning needs? Scaffold vocabulary,
use simpler numbers, and have students come to board to show work/mark
points
q Auditory, visual and kinesthetic modalities? Mostly kinesthetic, with visual
and auditory
q Are students doing the heavy-lifting rather than you? Students will be
working together to develop a solution to adding with negative and positive
integers, and then working together to build this understanding.
Included in
exploration
Summary:
- What is the best strategy that helped you add integers, negative and
positive?
- How can we use addition of negative and positive numbers in the real
world? For example, what is a story you can tell for -5 + +11?
- Did anyone in your group disagree about an answer? How did you solve
this disagreement?
5

Page 24 of 76
Exit Ticket
- One problem asking for students to find the which number is greater,
-3000 or -1500.
- One addition of integers problem (-25 + +60)
5
Homework: Addition of integers worksheet, Addition of fractions worksheet (negative and positive)
LP5.
Lesson Plan : Bits and Pieces I – 315; 11/4/15
TheSet-up
- How are fractions, decimals and percents related to one another?
- How do you write, compare and order fractions, decimals and percents?
- How can fractions, decimals, and percents be modeled with number lines, fraction
strips, and grids?
- Model fraction and percent operations with pictures
- Set up and solve percent word problems
- Paper to take notes
- Colored paper, slide with background information (for Lava Cross hook)
- Word problem worksheets
- Highlighter
6.RP.A.3.c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the
quantity); solve problems involving finding the whole, given a part and the percent.
1, 4, 6 and 8 are aspects of mathematical thinking that are emphasized in this lesson.
Students will analyze the given constraints to find a solution to a real world application of
percents. They will need to attend to precision while calculating their answers. They will be
using repeated reasoning when calculating the percent of a given number. They will also
model fraction multiplication with pictures.
Students will comprehend and use vocabulary related to word problem key words,
percents, and finding the percent of a given number.
Students will show pictures to solve word problems and describe strategies to solve
percent word problems.

Page 25 of 76
Time
TheLesson
- Allow students to complete a Do Now: One question on finding the
percent of a number. One question on finding the whole number given
the percent and number representing the percent of the whole. One
problem on dividing decimals.
- Review Do Now
- Review homework (read out answers, have students self-correct), collect
homework.
-10 (Do Now,
collect hw)
The Hook:
- Instructor takes out two colored pieces of paper and selects one
volunteer (possibly advanced student?)
- Instructor gives objective for the Lava Cross: Student X must cross the
lava river (the floor) using the two safety gems (two pieces of paper).
Student X is trying to get from the inner edge of the volcano to the exit of
the volcano (signs will be posted with inner volcano and exit).
- Instructor asks for students to give a few observations, with instructor
giving a few examples. (Instructor will give “there are 2 pieces of paper,
student x is about 5 feet tall, the papers are red and blue, the student
can’t touch the lava or they need to start over)
- Instructor will project these given observations on board in PPT
- Instructor will type observations students give in PPT for all to see
- Instructor will ask for students to sift through information- what is useful
to solving this objective? (instructor will highlight each piece that is
useful)
- What are strategies to help student x cross the lava?
- How does this relate to word problems?
10
Exploration:
- Hand out percent word problems. Allow students to work in their table
groups. Students must highlight/underline important information, and
write a strategy to solving the word problem. (They must not solve yet!)
- Review highlighted information as a class and strategies.
- Allow more table time to actually solve the problems. After completing
worksheet, review word problem solutions as a class.
- Review modeling with mathematics by drawing a picture to show fraction
multiplication (have a competition if time allows showing multiplication
with pictures).
- 10 minutes
(read and
highlight
problems)
- 20 mins
(review
strategies
and solve)

Page 26 of 76
Practice:
and auditory
together in groups while teacher guides students to set up and solve percent
word problems
Included in
exploration
Summary:
- Why is it important to find relevant details to problem solve?
- How can you use modeling beyond mathematics, and in every day life?
5
Exit Ticket (was not used on Tuesday, so pushed to this lesson)
- One problem finding the percent of a number
- One problem asking students to find the product of two fractions using
modeling
5
Homework: Percent word problems worksheet
LP6.
Lesson Plan : Bits and Pieces I – 315; 11/5/14
TheSet-up
- How are fractions, decimals and percents related to one another?
- How do you write, compare and order fractions, decimals and percents?
- How can fractions, decimals, and percents be modeled with number lines, fraction
strips, and grids?
- How can you calculate percents of a number in real-world application?
- Calculate a discount and tax amounts
- Paper to take notes
- Laptop (http://threeacts.mrmeyer.com/duelingdiscounts/)
- Projector
- Word problem worksheets with tax/discounts, poster paper
- Practice Problems (for math baseball)
6.RP.A.3.c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the
quantity); solve problems involving finding the whole, given a part and the percent.
6.NS.B.: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for
each operation. (scaffold)

Page 27 of 76
1, 4, 6 and 8 are aspects of mathematical thinking that are emphasized in this lesson.
Students will analyze the given constraints to find a solution to a real world application of
percents. They will need to attend to precision while calculating their answers. They will be
using repeated reasoning when calculating the percent of a given number. They will also
model their understandings with pictures on their poster.
Students will comprehend and solve to find final pricing after discounts and tax
adjustments.
Students will be able to show how to find final cost with discount and tax amounts.
Time
TheLesson
- Allow students to complete a Do Now: One word problem question, two
questions to find 35% of 190, and find 12% of 48.
- Review Do Now
- Review homework (read out answers, have students self-correct), collect
homework.
-10 mins (Do
Now, collect
hw)
The Hook:
- Instructor projects Dueling Discounts webpage on board, and prompts
students’ initial thoughts on calculating discounts.
- Instructor guides students through activity to sort through which discount
is the better buy.
- What is the process of finding a discount and/or tax amount?
10 mins
Exploration:
- Hand out worksheet of problems working with discounts. Allow students
to work with their table groups to solve one assigned problem. Students
show their work on poster paper to hang. Posters must include:
description of the problem (i.e. important details), the strategy and set up
to solve the problem, a picture modeling the problem/solution, and the
SMP standards they are using on their posters.
- “Rubric” for posters will be provided and written on the board for students
to see
- Review posters as a class (#4s at each table must present their poster in
under 2 minutes). Self assessment of group poster (check list style
assessment).
- Math baseball: Split class into 2 teams. One team starts as batting, and
one as pitching. Pitching team pitches a math question ( list of questions
prepared by instructor), and “batter” on Batting team goes to the board to
solve the problem. Batting team may not help “tap in” for student up to
bat. For a correct answer, it is a base hit. If incorrect, it counts as strike.
Just as in regular baseball, when Batting team gets three strikes, they
switch to pitching, and other team switches to batting.
- Review strategies to finding discount/tax amounts with more example
problems
- 20 mins
(poster work)
- 15 mins
(poster
reviews, self
assess)
- 35 mins
(math
baseball)
- 15 mins
(review
strategies)

Page 28 of 76
Practice:
use simpler numbers, and have students verbally express what they know
and auditory
together in groups to create poster while instructor guides them to
q Are there checks for student learning? Thumbs up/self
assessment/summary/exit ticket
Included in
exploration
Summary:
- How do discounts and taxes play a role in real world problems?
- Did anyone disagree or have alternative strategies to solve their table
group problems? How did you settle on what was put on your poster?
- Where will you need to “go up to bat” with your math skills? How can you
bounce back if you “strike out”?
5
Exit Ticket (was not used on Monday, so pushed and used for this lesson)
- One problem finding the discount amount of a number
- One problem asking students to identify their favorite lesson/topic so far.
5
Homework: Discount/Tax problem worksheet
LP7.
Lesson Plan : Accentuate the Negative, 1.2 – 315; 11/13/14
TheSet-up
- How can we use negative and positive numbers?
- How can we add, subtract, multiply, and divide negative and positive numbers?
- What strategies can model operations between negative and positive numbers?
- Place and locate positive and negative rational numbers on a number line
- Thermometer poster
- Stickies
- Playing cards
6.NS.C.5: Understand that positive and negative numbers are used together to describe quantities having
opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level,
credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in
real-world contexts, explaining the meaning of 0 in each situation.
6.NS.C.6.a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number
line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its
own opposite.

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1, 4, 6 and 8 are aspects of mathematical thinking that are emphasized in this lesson. They
will need to make sense of negative and positive numbers and persist in comparing them,
as well as attend to precision while forming their answers. They will be using repeated
reasoning when adding positive and negative numbers together. They will also model their
understandings with number lines, and pictures.
Students will be comparing negative and positive rational numbers to other numbers and
placing integers on a number line.
Students will locate positive and negative numbers on a number line.
Time
TheLesson
- Students will complete Do Now: One problem having students place 10
numbers on a number line. Another problem asks students to order a list
of numbers from least to greatest.
-10 mins (Do
Now)
The Hook:
- Draw thermometer on poster paper, and ask students what they think
the temperature is on a hot day. Place temperature at this degree level.
- Next, ask students what it means to be -10 degrees outside. What does
it feel like? Where would this go on a thermometer?
- Next, tip/turn thermometer so it is positioned like a number line- what are
their observations?
- Provide each table with an integer on a stickie, and give them 2 minutes
to provide an example of this number in the real world other than
temperature and money. After the two minutes are up, one elected
representative shares their example, and places stickie on number line
(on board). Ask students, which is the greatest/least number? Which
number is furthest from ______.
-10 mins
Exploration:
- Students work on 1.2 with their group, with timer on board. Share
answers as a group.
- Summary of 1.2
- As time allows, Integer Addition War
- 20 mins
(group work,
1.1)
- 10 mins
(work review,
1.1)
- 5 mins
(summary)
- 20 mins
(integer
addition war)

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Practice:
use simpler numbers, and have students come to board to show work/mark
points
and auditory
q Are students doing the heavy-lifting rather than you? Students will be
working together to develop a solution to adding with negative and positive
integers, and then working together to build this understanding.
Included in
exploration
Summary:
- Did anyone in your group disagree about an answer? How did you solve
this disagreement?
- What are strategies that helped you answer 1.2 B and C? Did anyone
use a method other than a number line?
5
Exit Ticket
- One problem asking students to list the opposite of 3 different numbers
(- ½ , 1267, and 8.475)
- One problem asking for students to list any rational number between -5
and ½ .
5
Homework: ACE pg 16 #9-19, worksheet on integers (?)
LP8.
Lesson Plan : Comparing and Scaling 2.3- 315; 10/7/14
TheSet-up
- Identify strategies to compare ratios in terms of decimal, fraction, and percent
- Identify strategies to compare ratios with fractions, decimals, and percents
- Develop strategies on when to use which comparison method
- Understand how to compare ratios with a table to find a pattern
- Understand how to scale ratios so they are different numbers but also equivalent
- Food items with portion directions (for hook)

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6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of
fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
6.RP.A.1:Understand the concept of a ratio and use ratio language to describe a ratio relationship between two
quantities.
1, 2, 3, and 6 are aspects of mathematical thinking that are emphasized in this lesson.
Students will build on prior knowledge of ratios and comparing fractions to determine ratios
of higher value.
Students will comprehend and use vocabulary pertaining to ratios, tables and scaling.
Students will understand the terminology associated with comparing ratios and strategies
to scale ratios.
Students will orally articulate and describe ratios using tables and scale ratios using
larger/smaller, but still being equal.
Time
TheLesson
- Students will be given a scenario comparing two tables with differing
numbers of seats and differing numbers of trays of mac and cheese,
all equal in size. Students must find the table that they would sit at so
they can get the largest portion of mac and cheese.
- Review homework (only answer questions that students struggled on
most- 2 to 3 questions); provide answers for other questions.
10 (Do Now
and HW
review)
The Hook:
- Instructor will have several food items that will either be projected on
the white board or passed around. Each item contains instructions to
make a batch by adding certain parts of water.
- Students will be prompted to give examples of a mixture they have
made before—perhaps in a candy store, or with water and dirt. How
much of each item did they add to make the mixture? If they wanted
to double the mixture, what amount of each part would they need,
and is their answer for the item’s fraction within the mixture (part to
whole) equivalent to a single batch?
10
Exploration:
- Students to explore 2.3 with their table groups. Once complete,
students will review 2.3 as a class. Summary to follow.
- As time allows, review alternative strategies to scaling ratios
(multiplying a fraction with a multiplier factor, tables, etc.)
- 20
- 10
(alternate
strategies)

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Practice:
q Auditory, visual and kinesthetic modalities? Mostly kinesthetic, with
visual and auditory
q Are students doing the heavy-lifting rather than you? They should be
working together in groups while teacher guides students to compare
fractions
Included in
exploration
Summary:
- What would you do to find the perfect amount to feed a larger
number of chimps (ex. 50 baby chimps)?
- What is an efficient way to find an equivalent ratio?
- How do you know when you need to multiply or divide to find an
equivalent ratio?
5
Exit Ticket
- One class (Class W) has a ratio of 210 girls to 240 boys. Another
class (Class S) has a ratio of 95 girls to 120 boys. Which grade has
the greater proportion of girls?
- Fill in the blank: 5/16 = ____/48
5
Homework:
(pg. 26, #7-8, 20-21,24, possible ratios worksheet

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Objectives
OB1. OB2.
OB3. OB4.

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OB5. OB6.
OB7. OB8.

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OB9.

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Exit Tickets
ET1.
ET2.

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ET3.
ET4.

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ET5.
ET6.

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ET7.
ET8.

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Posters (Classwork and Round Robin)
RRP1. RRP2.
RRP3. RRP4.

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RRP5. RRP6.
RRP7. RRP8.

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Rubrics and Handouts
RH1.

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RH2.

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RH3.

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Assignments
AS1.

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Study Guides and Quiz Material
SGQM1a.

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SGQM1b.

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SGQM1c.

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SGQM1d.

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SGQM1e.

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SGQM1f.

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SGQM1g.

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SGQM1h.

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SGQM2.

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SGQM3.

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SGQM4.

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Math Reflections
MR1a.

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MR1b.

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MR2a.

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MR2b.

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MR3.

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Additional Material
AM1.

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AM2.
September 18th
, 2014
Dear Families and Caregivers,
Welcome to a new school year at the Richard J. Murphy School! Since the school
year has only just started, I want to take the opportunity to introduce myself and
to discuss my role in your student’s classroom.
My name is Stephanie Loneck, and I am currently a student of the Northeastern
University Master of Education program. As a graduate student and teacher
candidate, I am working toward completing my degree and license to teach middle
school mathematics. I recently completed my second year of AmeriCorps with the
Massachusetts Promise Fellowship, and served as a Site Director of a mathematics-
focused afterschool program in Roxbury. Although I have enjoyed the educational
experiences I have had thus far, I am excited to build on my teaching knowledge
and practice with the Richard J. Murphy School!
I have the privilege of observing, collaborating, and teaching your student during
the months of September to mid-December as I prepare to become a certified
teacher in Massachusetts. As part of my student teaching practicum, I provide
support to Mrs. Cross and implement individual and group support during their
mathematics lessons. I will soon be transitioning into an instructional role within
the classroom, and will share the responsibilities of designing and facilitating
mathematics lessons.
During my instructional time, my Northeastern University supervising staff will visit
the classroom to observe my instruction with your student and provide
constructional feedback in order to improve my practices. In addition to
collaborating with Northeastern University and Mrs. Cross, I hope to build a strong
network of communication with you in order to best support your student and to
help them achieve academic success.
Thank you for allowing me to be a part of your student’s learning community. I
look forward to connecting with you this year!
Sincerely,
Stephanie Loneck
P: (518) 307-2394 | E: loneck.stephanie@gmail.com

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Classroom Set Up
CSU1.
CSU2.

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CSU3. CSU4.
CSU5.

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CSU6.
CSU7.

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CSU8.
CSU9.

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CSU10.

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CSU11. CSU12.
CSU13. CSU14.

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CSU15. CSU16.
CSU17.
CSU 18.

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CSU19.
CSU20.

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CSU21a.
CSU21b.

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CSU21c.
CSU21d.

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Email Communications
EC1.

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EC2.

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