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Project Based LearningA Stitch in Time

Math I

Project Title: A Stitch in Time

Project Idea: The non-profit Historical Society of the state is trying to preserve its tradition, culture and history. Money is needed to establish a museum where artifacts that depict aspects of each community’s heritage (such as agriculture or family) will be displayed. Your team of society members will create at least one sample of an historical quilt square, a stained glass square, a barn quilt, or a symmetrical egg (Pysanky), to be placed in the museum. In addition to the artifact, you will prepare a presentation for the fundraiser, which highlights the geometry and historical significance in the design.

Entry Event: (Several options are listed)1. Read “The Quilt Makers Gift” by Jeff Brumbeau and Gail de Marcken or some other book of this nature.2. Show pictures of stained glass mosaics that portray the culture of the community

A Stitch in Time Pictures are provided.3. The following site has pictures from the work of Isaiah Zagar. These pictures show community projects using

mosaics.http://www.images?hl=en&expIds=25657,26613,27015&sugexp=ldymls&xhr=t&q=isaiah+zagar&cp=8&wrapid=tljp1286804968955114&um=1&ie=UTF-8&source=univ&ei=7xWzTIm8JYP_8Aaq79ChCQ&sa=X&oi=image_result_group&ct=title&resnum=4&sqi=2&ved=0CDAQsAQwAw&biw=1020&bih=603 Discussion: How can mathematics make art pleasant and useful?

West Virginia College- and Career Readiness Standards:

Objectives Directly Taught or Learned Through Inquiry/Discovery

Evidence of Student Mastery of Content

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the

reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated

reasoning.

Proficient students clarify the meaning of real world problems and identify entry points to their solution. They choose appropriate tools and make sense of quantities and relationships in problem situations. Students use assumptions and previously-established results to construct arguments and explore them. They justify conclusions, communicate using clear definitions, and respond to arguments, deciding if the arguments make sense. They ask clarifying questions. Students reflect on solutions to decide if outcomes make sense. They discern a pattern or structure and notice if calculations are repeated, while looking for both general methods and shortcuts. As they monitor and evaluate their progress, they will change course if necessary.

M.1HS.40 represent transformations in the plane using, for example, transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Instructional note: Build on student experience with rigid motions from earlier grades Point out the basis of rigid motions in geometric concepts, (e.g., translations move points a specified distance along a line parallel to a specified line; rotations move objects along a circular arc with a specified center through a specified angle).

The student meets the teacher set criteria on The Respond Sheet located at SAS® Curriculum Pathways ® - http://www.sascurriculumpathways.com/ >Mathematics>Geometry > 2D Figures > Web Inquiry 110

M.1HS.43 Given a geometric figure and a rotation, reflection or translation, draw the transformed figure using, e.g., graph paper,

The student meets the teacher set criteria on The Respond Sheet located at SAS® Curriculum Pathways ® - http://www.sascurriculumpathways.com/ >Mathematics>Geometry

Created by Cheryl Reger, NBCT

http://www.sascurriculumpathways.com/


http://www.google.com/images?hl=en&expIds=25657,26613,27015&sugexp=ldymls&xhr=t&q=isaiah+zagar&cp=8&wrapid=tljp1286804968955114&um=1&ie=UTF-8&source=univ&ei=7xWzTIm8JYP_8Aaq79ChCQ&sa=X&oi=image_result_group&ct=title&resnum=4&sqi=2&ved=0CDAQsAQwAw&biw=1020&bih=603



tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Instructional Note: Build on student experience with rigid motions from earlier grades. Point out the basis of rigid options in geometric concepts (e.g. translations move points a specified distance along a line parallel to a specified line; rotations move objects along a circular arc with a specified center through a specified angle).

> Points, Lines & Planes > Web Inquiry 104.

M.1HS.47 make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Instructional Note: Build on prior student experience with simple constructions. Emphasize the ability to formalize and defend how these constructions result in the desired objects. Some of these constructions are closely related to previous standards and can be introduced in conjunction with them.

The student completes A Stitch in Time Project at a level of success designated by the teacher.The student completes the Transformation Constructions at a level of success designated by the teacher.

Performance Objectives:

KnowKnow the definitions of reflection, translation, rotation, glide reflection, and dilation of a figureKnow the types of symmetryKnow that symbols are sometimes used to represent a community’s heritage or traditionKnow what type of art work is used to portray history or culture

DoDetermine the relationship of figures transformed on a planeIdentify the transformations of a given figure Determine the types of symmetry for a given figureDistinguish between the different types of transformationsDistinguish between the different types of symmetryRepresent a transformation with a mapping (for example (x,y)(-x,y))Construct a reflection Construct a rotationCreate a piece of art work that models transformations and symmetry

Driving Question: How can mathematics be used to preserve the culture of a group of people?

Assessment Plan:

Major Group ProductsTeam Group Roles and contractA Stitch in Time Project

Major Individual ProjectsThe Respond Sheet located at SAS® Curriculum Pathways ® - http://www.sascurriculumpathways.com/>Mathematics>Geometry > 2D Figures > Web Inquiry 110



Constructions performed in the Transformation Constructions activityThe Respond Sheet located at SAS® Curriculum Pathways ® - http://www.sascurriculumpathways.com/>Mathematics>Geometry > Points, Lines & Planes > Web Inquiry 104Artifact Essay using the WV Grade 9 Writing Rubric

Assessment and Reflection:

Rubric(s) I will use: (Check all that apply.)

Collaboration Written CommunicationArtifact Essay

X

Critical Thinking & Problem SolvingA Stitch in Time Project

X Content KnowledgeA Stitch in Time Project

X

Oral Communication OtherOther classroom assessments for learning: (Check all that apply)

Quizzes/ tests Practice presentationsPractice Presentation Checklist

X

Self-evaluationStudent Reflection

X NotesKnowledge Rating Scale

X

Peer evaluationTeam Final Evaluation

X Checklists/observationsCollaboration Checklist

X

Online tests and exams Concept mapsReflections: (Check all that apply)

SurveyProject Debrief

X Focus Group

Discussion Task Management ChartTask Checklist

X

Journal Writing/ Learning LogResearch Log

X Other

Map the Project:

Product:

Knowledge and Skills Needed Already Have Learned

Taught Before the Project

Taught During the Project

1. Collaboration skills X2.Search and navigate the internet X3.Presentation skills X4.Identify similar and congruent shapes X5.Basic constructions X6.Basic transformations X7. Types of symmetry X8. Justify arguments X

Resources:

School-based Individuals:Art teacher

Technology:Computers with Internet access and printer Word processing/spreadsheet/publishing software

Community: Local artist or quilterMember of local historical society



Materials:Materials to construct an artifactHandouts for students

Websites:

An investigation on transformations: SAS® Curriculum Pathways ® - http://www.sascurriculumpathways.com/ >Mathematics>Geometry > 2D Figures > Web Inquiry 110

Frieze Patterns - http://illuminations.nctm.org/Activity.aspx?id=6608

An investigation on symmetry in nature: SAS® Curriculum Pathways ® - http://www.sascurriculumpathways.com/ >Mathematics>Geometry > Points, Lines & Planes > Web Inquiry 104.

e-Tutor-Transformations In The Coordinate Plane - http://www.e-tutor.com/et3/lessons/view/54501/print (tutorial on transformations on the coordinate plane)

Manage the Process: See A Stitch in Time Storyboard (approximately 3 to 4 weeks)

The following description contains many opportunities for students to learn about geometric transformations, symmetry and connections to the real world. In some cases, activities are suggested that could be added for students who need more hands on or visual investigations. The suggested scaffolding is here if needed. If something is eliminated or added, the Task Checklist should be adjusted as well.

Launch:Assign students to groups according to their personal style. The activity to determine this style can be found at nsrfharmony.org - http://www.nsrfharmony.org/system/files/protocols/north_south_1.pdf. Assign groups by mixing up the styles as much as possible. One of each style per group works well.After assigning groups, give them time to talk to each other about their individual style, strengths, and weaknesses. Students will take notes about members of the group and keep this as an artifact for the project.Plan other activities as necessary to help students see the importance and meaning of collaboration. Some team building activities can be found at Index to Group Activities, Games, Exercises, & Initiatives - http://wilderdom.com/games/ Note: These activities may not be necessary if students in the class have experience working together in groups.

Launch the project by choosing from the provided activities. Reading a story and showing pictures is a good combination. You can add your own local photographs or use those provided.

Next invite a member of the community to talk to the students about their art form and how it relates to this project. Distribute the project scenario and have groups complete a KWL. Discuss the goals of the project so that the learning targets are clear.

Each group is expected to compose their own contract. They can use the internet as a resource to help them with ideas to include. After they determine the role of each student in the group, this should be included in the contract. Each student will sign the contract and it will be kept on file in the group folder.

Investigate and Research:The SAS Curriculum Pathways is an interactive web inquiry that requires the student to carry out research on the resource pages provided while completing a response sheet. Web Inquiry 110 assists students in defining the types of transformations and familiarizes them with mapping notation.

Some students need a more hands-on experience to help visualize the mapping notation. Transformations on the Geoboard will let students create the transformation and see the pattern in the coordinates. This is a good way to differentiate for students with different learning styles.

At this point students will have enough information to begin to investigate different art forms so that they can decide what type of artifact they want to create. Students should also be working on the vocabulary on the Knowledge Rating Scale. Differentiate by providing some additional resources for students who need help finding definitions.Created by Cheryl Reger, NBCT

http://wilderdom.com/games/

http://www.nsrfharmony.org/system/files/protocols/north_south_1.pdf

http://www.e-tutor.com/et3/lessons/view/54501/print


http://illuminations.nctm.org/Activity.aspx?id=6608


Before beginning the “Frieze Patterns” Illuminations Activity (http://illuminations.nctm.org/Activity.aspx?id=6608 ), you might share some wallpaper samples. Most dealers will give you samples that they have retired so that you have a wide variety to show. Discuss some of the patterns you see before doing the Illuminations activity.

Investigate and Create:Another way to develop basic understanding of transformations is to construct them. This can be done with compass and straightedge on the Transformation Constructions. Differentiate here by performing the transformations using graph paper, miras, or paper folding where possible. These are all hands-on approaches to creating these patterns.

Another SAS Curriculum Pathways web inquiry can be helpful here to learn more about the types of symmetry. Web inquiry 104 provides a real world exploration of symmetry.

By this time students should have chosen the art form they will create and will complete the research required to design an artifact that meets the criteria as outlined in the rubric.

Present:One focus of A Stitch in Time Project is to highlight connections between geometry, art and history. Groups will need time to collaborate as each member carries out their tasks. Students should also be working on the Artifact Essay. This will help them pull together information for their presentation.Feedback from the Practice Presentation Checklist can help teams improve their final product. Invite members of the community (especially those involved in the arts) to attend the presentations.After final projects are presented, students will complete the Student Reflection, Team Final Evaluation, and Project Debrief.

Project Evaluation: Feedback from the Practice Presentation Checklist can help teams improve their final product.After final projects are presented, students will complete the Student Reflection Report, Team Final Evaluation, and Project Debrief.

Key Words: symmetrytranformationstranslationrotationreflectiongeometric constructions


http://illuminations.nctm.org/Activity.aspx?id=6608

Pictures from The River Walk in Morgantown, WV


A Stitch in Time Storyboard

Launch

Form groups

Team building activities as necessary ==>

Launch the project

Goals ==>KWL

Team roles

Team contract ==>

Investigate and

Research

SAS Curriculum Pathways Web Inquiry 110: Comparing Translations, Reflections, and Rotations ==>

Transformations on the geoboard

==>Distribute Knowledge Rating Scale

Begin research of artwork and history

“Frieze Patterns” Illuminations Activity

==> Progress check with each team

Investigate and Create

Transformation constructions Choose art form for artifact ==>

SAS Curriculum Pathways Web Inquiry 104: Types of Symmetry

==> Begin to create artifact

Revisit KWL and revise ==>Continue work on artifact

Present

Prepare Artifact Essay

==>Finalize artifact

Prepare presentation of the project

Peer review of projects

==>Begin making final presentations

Peer evaluation

Project reflection


Task Checklist - Individual

A Stitch in Time

o Team summary of individual styles, strengths, and weaknesses

o Respond sheet from SAS Web Inquiry 110

o Transformation Constructions

o Respond sheet from SAS Web Inquiry 104

o Research Log

o Artifact Essay

o Knowledge Rating Scale

o Peer evaluation

o Student reflection report

o Project Debrief

o Other artifacts

Task Checklist - Group

o Team contract

o KWL

o Team notes

o Research source list

o Artifact for the museum

o Group Presentation of A Stitch in Time Project


Team Group Roles

Members of the group will assume the following roles. The responsibilities of each role include, but are not limited to the following:

Team leader: The team leader keeps all members of the group on task and keeps a task management chart. They make sure that each member participates fully and shows respect for one another.

Recorder: The recorder maintains the group work folder, writes out solutions to problems, and facilitates the preparation of materials for presentations.

Reporter: The reporter reports progress to the group, class, and instructor. They facilitate any oral presentations required for the project.

Process director: The process director maintains the ground rules, monitors time, cleans up materials, and makes sure each group member is mastering concepts.

Floater (in groups of five): The floater assists the leader or other group members as needed. They will substitute for any absent member and assume their duties.

Participant: All members of the group are expected to participate fully. As a participant, they will take part in all activities of the group and keep a journal.

Team Expectations

Each member of the group is expected to pull their weight as part of the group. To prevent any member of the group from receiving a lower grade as a result of group learning, you will compose a group contract that every member will sign. Use the Internet to research contracts that could help you with some ideas. Be sure to include behaviors you expect from each individual as well as the group as a whole. Each member must sign the contract and designate which of the above roles they will be assuming.


What do we know? What do we need to know? What should wedo to learn more?

KWL


A Stitch in Time Project

The non-profit Historical Society of the state is trying to preserve its tradition, culture and history. Money is needed to establish a museum where artifacts that depict aspects of each community’s heritage (such as agriculture or family) will be displayed. Your team of society members will create at least one sample of an historical quilt square, a stained glass square, a barn quilt, or a symmetrical egg (Pysanky), to be placed in the museum. In addition to the artifact, you will prepare a presentation for the fundraiser, which highlights the geometry and historical significance in the design.


Mathematical Reasoning

and Problem Solving

InterdisciplinaryConnections Modeling

Mathematical Concepts

TechnologyNeatness

and Organization

30% 10% 20% 20% 10% 10%

4

Our artifact contains more than the minimum of 2 transformations and 2 types of symmetry and they are accurately constructed.

Our presentation includes detailed and accurate interpretations about the historical background of our artwork.

Our presentation includes accurate graphs or mappings that model the patterns in our artifact.

Our presentation includes a detailed explanation, using correct mathematical terminology, of the relationship between each transformation and its corresponding artwork.

Our final product shows evidence that advanced features of multiple technology tools and electronic resources were used.

Our work is presented in a neat, clear, organized fashion that is easy to understand.

3

Our artifact contains the minimum of 2 transformations and 2 types of symmetry and at least 3 are accurately constructed.

Our presentation includes partially accurate interpretations about the historical background of our artwork.

Our presentation includes somewhat accurate graphs or mappings that model the patterns in our artifact.

Our presentation shows substantial understanding of the relationship between each transformation and its corresponding artwork.

Our final product shows effective use of several technology tools and electronic resources.

Our work is presented in a neat and organized fashion that is usually easy to understand.

2

Our artifact contains less than the minimum of 2 transformations and 2 types of symmetry and at least 2 are accurately constructed.

Our presentation includes unclear or limited interpretations about the historical background of our artwork.

Our presentation includes somewhat accurate graphs or mappings that model part of the patterns in our artifact.

Our presentation shows some understanding of the relationship between each transformation and its corresponding artwork.

Our final product shows some evidence of effective use of technology tools and electronic resources.

Our work is presented in an organized fashion but may be hard to understand at times.

1

Our artifact contains less than 2 transformations and 2 types of symmetry and one or less are accurately constructed.

Our presentation did not include any interpretations about the historical background of our artwork. .

The graphs or mappings in our presentation are inaccurate or incomplete.

Our presentation shows very limited understanding of the relationship between the patterns and the artwork.

Our product shows little evidence of effective use of technology tools and electronic resources.

Our work appears sloppy and unorganized. It is hard to know what information goes together.

A Stitch in Time Project Rubric


Knowledge Rating Scale

As you learn the definition write the definition under “What It Means.”

WordKnow It

WellHave Seen or Heard It

Have No

ClueWhat It Means

dilation

glide reflection

isometry

line of symmetry

order of rotation symmetry

point symmetry

reflection

reflection symmetry

rigid motion

rotation

rotation symmetry

symmetry


transformation

translation


Transformations on the Geoboard

Materials needed: Each group or pair of students will need: 1 geoboard and 2 geobands, 6 pieces of circular cereal (3 colors), data chart

Groups (or pairs) of students will perform different transformations using the colored cereal. In each transformation, a triangle will serve as the original figure, and the cereal will mark the vertices of the triangle. The 2 geobands will mark the x and y axes with the origin being in the center of the geoboard. The group will determine if the triangle and its image are congruent and will show relationships between the points on the original triangle and the image.

Procedure:a) Place three different colored cereal pieces on the geoboard at A(-1,1), B(-2,1), C(0,2). These

three points represent the vertices of the original triangle ABC.b) Make a chart as shown to record the required data for each procedure.c) Reflect triangle ABC about the y-axis. Place the cereal of corresponding color to show the

vertices of the image triangle A1B1C1 on the geoboard. Record the required data in the chart.d) Reflect triangle ABC about the x-axis. Place cereal of corresponding color to show the vertices of

the image triangle A2B2C2 on the geoboard. Record the required data in the chart.e) Translate triangle ABC using the translation vector (2,-3). Place cereal of corresponding color to

show the vertices of the image triangle A3B3C3 on the geoboard. Record the required data in the chart.

f) Rotate triangle ABC as a whole, 90 degrees clockwise, with the origin as the center of rotation. Place cereal of corresponding color to show the vertices of the image triangle A4B4C4 on the geoboard. Record the required data in the chart.

g) Rotate triangle ABC, counterclockwise 90 degrees, with the origin as the center of rotation. Place cereal of corresponding color to show the vertices of the image triangle A5B5C5 on the geoboard. Record the required data in the chart.

h) Determine if the triangles in Steps c through g are congruent by examining the data. Record your decision on the chart.

i) Determine the relationship of the coordinates (x,y) of the original triangle and the coordinates of the image point in steps c through g using the data collected. Record your decision on he chart.

j) Each group will compare its data with the data of the other groups and resolve any differences.


Step Originaltrianglecoordinates

Image triangle coordinates

Length of sides of original

Length of sides of image

Congruent (x,y)(?,?)

c A(-1,1)B(-2,1)C(0,2)

AB=AC=BC=

d A(-1,1)B(-2,1)C(0,2)

AB=AC=BC=

e A(-1,1)B(-2,1)C(0,2)

AB=AC=BC=

f A(-1,1)B(-2,1)C(0,2)

AB=AC=BC=

g A(-1,1)B(-2,1)C(0,2)

AB=AC=BC=


Transformation Constructions

Use a compass and straight edge to complete each of the following constructions.

1. The reflection of a point in a line

2. The reflection of a circle in a line

3. A halfturn of a circle about a given point

4. The rotation of a point 90 degrees about a given point

5. The reflection of a square in a given line

6. The reflection of a square in a line through opposite vertices of the square

7. The reflection of a rectangle in the line through opposite vertices of the rectangle

8. The reflection of a circle in 2 given lines

9. A rotation of a segment 45 degrees about a given point


Collaboration Checklist

Not at all 1

Sometimes 2

Often3

Displays a positive attitude

Participates in discussion

Stays on task/uses time wisely

Organizes results/completes tasks

Engages in cooperative behavior

Comments _____________________________________________________________

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________


Artifact Essay

Prepare and submit a brief research paper about your design. Try to limit the length to one typed page, as it may eventually be on display with the artifact in the museum. Include the following:

Name the culture/area on which you focused your research. Give a brief history of quilting (stained glass, etc.) in this culture and describe how this

form of art may have changed in the area. Identify the geometric shapes used. What symbols are present in the design that depicts a message? Is congruence or similarity present? Identify the transformations and symmetries present in the design.


Research Log

Date Address of the Website Information


Practice Presentation Checklist

Compelling Evidence

Little Evidence No Evidence

Spelling and grammar in product(s)

Use of technology

Artifact clearly explained

Shares historical information

Includes well designed graphics

Supports designs with accurate mathematical analysis

Comments

_____________________________________________________________________________

_________________________________________________________________________

_____________________________________________________________________________


Student Reflection

Not at all Sometimes Often

I listened to the ideas of others

I offered suggestions

I worked on the project at home

I stayed on task

I met deadlines

I encouraged and complimented others

I did my best work

I enjoyed the project

I cooperated with my group

Some ways we worked well were

_____________________________________________________________________________

_________________________________________________________________________

We could have worked better by

_____________________________________________________________________________

_________________________________________________________________________

I am proud of this project because

_____________________________________________________________________________

_________________________________________________________________________

This project could have been better if I had

_____________________________________________________________________________

_____________________________________________________________________________


Team Final EvaluationA Stitch in Time Project

Name ________________________________ Role ___________________ Score ______

Name ________________________________ Role ___________________ Score ______

Name ________________________________ Role ___________________ Score ______

Name ________________________________ Role ___________________ Score ______

Name ________________________________ Role ___________________ Score ______

How well do you think you met the requirements of the project?

Component

Level

CommentsYour

Estimate ActualCombined research with mathematical reasoning to create an artifact that accurately displays the required transformations and symmetry.

30

Presented the project usingaccurate historical interpretations

10 .

Analyzed the graphs to create accurate mappings that model the patterns in the artifact

20

Explained, with correct mathematical terminology, the relationship between the transformation and the corresponding art work.

20

Demonstrated skill in the use of multiple technology tools and resources.

10

Created a neat, clear, organized presentation.

10

Total 100


Rate yourself and your colleagues using the following levels: A: Accomplished (unusually good) C: Competent (consistent) E: Emerging (inconsistent, but evident) N: Novice (not evident)

How well did you work with your team?

Component

Level

CommentsYour

Estimate ActualWork distribution and task completion 10

Participation in the problem-solving process and discussion

20

Cooperative behavior 20

Total 50

WORK DISTRIBUTION GRAPH: As you think about the project, make a circle graph that shows the percentage you think each of your team members contributed.


As you reflect on this project, rate each person in your team?

Team LeaderPerson responsible:

Component

Level

CommentsYour

Estimate ActualKeeps all members of the group on task

10

Makes sure that each member participates fully

10

Makes sure that each member shows respect for one another

10

Participates fully 10

Takes part in all activities of the group 10

Keeps a journal and a task management chart

10

Pulls their weight as part of the group 10

Meets the requirements included in the group contract

30

Total 100


RecorderPerson responsible:

Component

Level

CommentsYour

Estimate ActualMaintains the group work folder 10

Writes out solutions to problems 10

Facilitates the preparation of materials for presentations

10




10



30

Total 100


ReporterPerson responsible:

Component

Level

CommentsYour

Estimate ActualReports progress to the group 10

Reports progress to the class and/or instructor

10

Facilitates any oral presentations required for the project

10




10



30

Total 100


Process directorPerson responsible:

Component

Level

CommentsYour

Estimate ActualMaintains the ground rules and monitors time

10

Cleans up materials 10

Makes sure each group member is mastering concepts

10




10



30

Total 100


FloaterPerson responsible:

Component

Level

CommentsYour

Estimate ActualAssists the leader or other group members as needed

20

Substitutes for any absent member and assumes their duties

10




10



30

Total 100


Project Debrief: A Stitch in Time

Name _____________________________________

Reflection is an important part of any project. Please answer the following questions in a thoughtful manner. Be specific with your comments.

What are some things you learned during the project?

Was there a part of the project you liked or did not like? Explain.

What could be added or dropped to make the project better?

Was enough time allocated for each task in the project? Give details.

Are there any assignments you still don’t understand?

Other comments?


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