Olson –Teamwork
Projects – General Information - Last Revised Spring, 2007
Cooperative Teamwork: Regular participation in class and in small-team activities is expected.
One or more major long-term cooperative projects will be graded based on the presentation
and/or work collected from the team. THE longer MAJOR TEAMWORK GRADES CAN
NEITHER BE DROPPED NOR MADE UP. Each member’s absence during class periods which
have any time devoted to these projects drops your team’s total score by 2% (i.e., your team
counts on you). Your overall individual team project grade will be composed of the average
score from all separate Teamwork Projects done throughout the semester.
Guidelines For Working Together
1. Agree on what your team must do and how you will get it done.
2. Be courteous and listen carefully to the other team members.
3. Create a team atmosphere that allows team members to be comfortable asking for help when
needed.
4. Don’t assume the other members know more/less than you do. Your backgrounds are
different and you all have strengths to bring to the table.
5. Everyone has their own pace. Be patient. Offer your help. Receive help graciously.
6. Focus on the value of all contributions made.
7. Get help via the “order of three”: 1. Look it up, 2. Ask a team member, 3. Ask the instructor.
8. Help double-check the teams’ combined work. Can the team see a general rule about the
process or describe a real-world use for what you learned?
I will be assigning you to a specific team for each major project. (These teams will each
have 3-5 members.)
1. Once in your assigned team – get the other members phone numbers and email contacts.
2. Also find a time in common you can meet outside class (live or electronically via
phone/chat/etc).
NOTE: IF your team wants to/needs to meet on-line, WebCT has a chat facility, or I can set your
team up with a discussion board in there.
3. For each separate activity, you each will need to adopt a specific team role:
Standard team roles are: Facilitator (1 member), Recorder (1-2 members), and Questioner (12 members).
These roles are explained here:
Facilitator – leads the team, helping direct the activity.
Recorder – writes the information down that gets turned in for the team as a whole. This could
also include creating the visual aide for the team’s presentation.
Questioner – asks questions: during the process, to help the team clarify results, and the
questioner is on the lookout for errors.
You will be graded individually on the role you adopt as well as your overall effort.
1
4. Presentations: For some projects, findings are to be presented to the whole class. The whole
team stands together for this (for support), but not everyone has to speak,. Your team will need to
decide how it wants to do this.
Your individual teamwork grade (also see Grading below for how the teams’ grade is
calculated):
Team Scoring: Individual accountability is the key to success of the whole team here. Toward
that end, to guard against “freeloading”, your participation will be decided by your fellow team
members and by your attendance in class. Your entire team will earn between 0% and 100% of
the total points possible (number possible/individual* number of team members). I will allocate
the total number of points earned by the entire team. Then, as a team, you will help allocate how
the points are divided among your members.
You will do this by scoring each other via a scoring rubric and a peer scoring form. Here are
some guidelines to keep in mind for this part of the process:
1) No one person can get more than 100% of an individual score.
2) No one can get less than 0%.
3) In case of disputes, i.e., you can’t come to consensus as a team (not just majority), the
instructor will act as arbiter.
You will need to grade yourself and each team member fairly based on the items listed when
completing the rubric (also see those pages for more details on how you will score yourself and
each other).
Grading: Your grade will be composed from the parts below (apart from attendance).
Total possible for the Team = individual total possible * number of assigned team
members.
Presented Projects:
1. 50% The mathematics for the situation is correct (graded by the teacher).
2. 25% All data collected and records are clear, neat, and complete (all required parts
turned in)
– this includes proper use of the English language in the descriptive
paragraph (see below) (graded by the teacher).
3. 25% The class report for the problem is well-presented
(graded by classmates not in your team and by the teacher).
Projects w/o Classroom Presentations:
1. 66 2/3 % The mathematics for the situation is correct (graded by the teacher).
2. 33 1/3 % All data collected and records are clear, neat, and complete (all required parts
turned in)
– this includes proper use of the English language in the descriptive
paragraph (see below) (graded by the teacher).
Absence during teamwork times deducts from the above team total possible at a rate of
2%/single absence (i.e., if 2 members are absent the same day, that’s 4% lost). (Exception –
if an assigned team member is pretty much missing during the entire project, I will not hold
that against the total team, but that fact must be reflected accurately in that team member’s
peer scoring record.)
2
Projects –
MODELING IN THE REAL WORLD via data collection and analysis and algebraic methods.
This will be done in stages over several class periods (usually over a few weeks) and will
take some individual and team time outside class. You will be allowed adequate time for
report/results to come in before your team needs to report to the whole class.
1. Preparation: All teams will work on a specific problem below as a team when (and if)
it’s assigned over several days and even weeks. You will need to do some field-work to
collect real data, so some time outside class is necessary.
Once the data is collected, your team should use the data and an algebraic process to try
to find the requested results. NOTE: one goal here is a hands-on and teamwork approach
toward helping the entire team toward a deeper understanding of some applications
already studied or to be studied.
2. Paragraph: For your team’s problem, you must write a paragraph discussing your work
and any results in words (at least three sentences). The paragraph must be in formal
English (correct grammar and punctuation, no abbreviations). Please feel free to visit the
Writing Center for help with this component.
3. Presentation: For projects where your instructor states the team will present to the class,
your team will plan to present the data collected, the algebraic work, and the results to the
whole class once you’ve had a chance to prepare (typically two or more weeks). You will
have the choice as a team on format and who speaks. For your team’s presentation, you
need to create some sort of
visual aide: a poster, an over-head (on film), a handout, or a power-point (with handouts). Don’t plan to just write on the board, as this needs to be part of the over-all record
turned in (the board may be used in addition to whatever you do create). If using
PowerPoint, the instructor must be notified well in advance of your presentation day, to
reserve a computer and projector for that purpose.
Note: This does not mean once your team has presented, it’s any less responsible for
listening to the other presentations. During presentations given by other teams, you will
be responsible for grading them per a presentation rubric. (Absence here counts off the
same as any other teamwork activity time in class.) Also, EVERYONE in the team needs
to take note of and review the problems any team worked, since any presented problem
may be used or referred to in some form on any quiz, test, or the final exam.
4. What to turn in:
Your team must turn in
 all the RAW data your team collects (that’s every rough draft from every team
member). Include EVERYTHING, no matter how messy, and label that with “field
collection”
 all preparation work (including all scrap-work and any drafts and the algebraic process
used, even ones with errors),
 the organized, polished data and results
 be sure to include a paragraph in your results (see # 2 above),
 and the visual aides used in any presentation (if the project required one).
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5. When to turn it all in:
 I will periodically check in on your team’s progress with data collection and preparation
during class (those DO act as attendance-factor days). See the Timeline below. These
check-ins will be announced ahead of time (print off this form for each project and
complete the dates as announced for simplest tracking).
 All items listed above are due on the due date or at the time of your team’s
presentation, if that’s part of the project (last line in the Timeline below).
 IF late/unprepared for the due date/by the assigned presentation day, your team loses
10% per DAY (not per class meeting, per business day)!
TIMELINE for project
DATE:
Teams assigned:
Exchange contact info
Receive preliminary project problem definition and directions.
Finds a common meeting time for whole team, if possible (or the majority)
Team gets items required (check ones required for that project) to all members:
Team Project General Info
Team Project (for your course) Problem Set
Teams Scoring Rubric
Teams Peer Grading Forms
Oral Presentation Rubric
Presentation Scoring Sheets
Team meets and gathers preliminary data by this date.
Team meets and works on the mathematics required.
Team meets and works on the project for presentation or delivery (final draft).
Teem meets and rehearses presentation (this cannot occur in the classroom, but
this is only required for projects which will be presented to the class orally).
Project is due = Presentation date (if presenting) (you will have some input in any
“presentation date”).
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Collaborative Work Skills : PEER Scoring Rubric for Project Work - Olson - revised: Spring, ‘07


Use this to determine your team-mates’ scores.
Put their score for each category on the Scoring Sheet.
CATEGORY
1. Attends
meetings/
conferences
5
Is always
punctual and
prepared.
4
Is always
present.
2.
Contributions
Routinely
provides useful
ideas when
participating in
group discussion.
A definite leader
who contributes
a lot of effort and
does a lot more
than what’s
required of them.
Provides work of
the highest
quality.
Usually provides
useful ideas
when
participating in
group
discussion. A
strong group
member who
tries hard and
does more than
what’s required.
Provides high
quality work.
4. Time
Management
Routinely uses
time well
throughout the
project to ensure
things get done
on time. Group
does not have to
adjust deadlines
or work
responsibilities
because of this
person’s
procrastination.
5. Problemsolving
Actively looks
for and suggests
solutions to
problems.
Usually uses
time well
throughout the
project, but may
have
procrastinated on
one thing. Group
does not have to
adjust deadlines
or work
responsibilities
because of this
person’s
procrastination.
Refines
solutions
suggested by
others.
3. Quality of
Work
3
Is present most
of the time, or is
always present
but frequently is
tardy or leaves
early.
Sometimes
provides useful
ideas when
participating in
group
discussion. A
satisfactory
group member
who does what
is required.
2
Is only present
half the time.
1
Is seldom
present.
Rarely provides
useful ideas
when
participating in
group discussion.
May refuse to
participate and
does less than
what is required.
Never provides
useful ideas
when
participating in
group
discussion.
Refuses to
participate.
Provides work
that occasionally
needs to be
checked/redone
by other group
members to
ensure quality.
Tends to
procrastinate,
but always gets
things done by
the deadlines
Group does not
have to adjust
deadlines or
work
responsibilities
because of this
person’s
procrastination.
Provides work
that usually
needs to be
checked/redone
by other group
members to
ensure quality.
Rarely gets
things done by
the deadlines
AND group has
to adjust
deadlines or
work
responsibilities
because of this
person’s
inadequate time
management.
Doesn’t do
work.
Does not suggest
or refine
solutions, but is
willing to try out
solutions
suggested by
others.
Does not try to
solve problems
or help others
solve problems.
Lets others do
the work.
Does not try to
solve problems,
but complains
about them
instead.
Interferes with
the work.
Never gets
things done by
the deadlines
AND group has
to adjust
deadlines or
work
responsibilities
because of this
person’s
inadequate time
management.
5
CATEGORY
6. Attitude
5
Never is publicly
critical of the
project or the work
of others. Always
has a positive
attitude about the
task(s).
4
Rarely is publicly
critical of the
project or the work
of others. Often
has a positive
attitude about the
task(s).
3
Occasionally is
publicly critical of
the project or the
work of other
members of the
group. Usually has
a positive attitude
about the task(s).
2
Often is publicly
critical of the
project or the work
of other members
of the group. Often
has a positive
attitude about the
task(s).
7. Focus on the
task
Consistently stays
focused on the task
and what needs to
be done. Very selfdirected.
Focuses on the
task and what
needs to be done
most of the time.
Other group
members can
count on this
person.
Rarely focuses on
the task and what
needs to be done.
Lets others do the
work.
8. Preparedness
Brings needed
materials to
meetings and is
always ready to
work.
Almost always
brings needed
materials to
meetings and is
ready to work.
9. Pride
Work reflects this
student’s best
efforts.
Work reflects a
strong effort from
this student.
Focuses on the
task and what
needs to be done
some of the time.
Other group
members must
sometimes nag,
prod, and remind
to keep this person
on-task.
Almost always
brings needed
materials but
sometimes needs
to settle down and
get to work.
Work reflects
some effort from
this student.
10. Monitors
Group
Effectiveness
Routinely
monitors the
effectiveness of
the group, and
makes suggestions
to make it more
effective.
Almost always
listens to, shares
with, and supports
the efforts of
others. Tries to
keep people
working well
together.
Is punctual and
well-prepared.
Speaking parts are
rehearsed, visuals
are easily
displayed, all work
is complete and
checked.
Routinely
monitors the
effectiveness of
the group and
works to make the
group more
effective.
Usually listens to,
shares with, and
supports the
efforts of others.
Does not cause
“waves” in the
group.
Occasionally
monitors the
effectiveness of
the group and
works to make the
group more
effective.
Often listens to,
shares with, and
supports the
efforts of others,
but sometimes is
not a good team
player.
Is present, but
needs time to
prepare. Speaking
parts are
rehearsed, visuals
take some work to
display, work may
either be
incomplete or not
fully checked.
Is tardy or so unprepared that it
distracts from the
groups’ focus.
Speaking parts are
un-practiced,
visuals take some
work to display,
work is somewhat
incomplete and not
fully checked.
11. Working with
Others
12. Attends
Presentations
(ready to
participate/p
resent)
1
Often is publicly
critical of the
project or the work
of other members
of the group, and
in a rude way.
Often has a
negative attitude
about the task(s).
Never focuses on
the task and
distracts others
from the work.
Often forgets
needed materials
or is rarely ready
to get to work.
Often forgets
needed materials
AND is rarely
ready to get to
work.
Work reflects very
little effort on the
part of this
student.
Rarely monitors
the effectiveness
of the group, but
tries to work to
make the group
more effective.
Work reflects no
effort on the part
of this student.
Rarely listens to,
shares with, and
supports the
efforts of others.
Often is not a good
team player.
Never listens to,
shares with, and
supports the
efforts of others.
Often is not a good
team player.
Is absent during
part of the
presentations or
work is so
incomplete and so
unchecked that it
delays the entire
groups’
presentation.
Is absent during
the groups’
preparation and
presentation.
Rarely monitors
the effectiveness
of the group and
does not work to
make the group
more effective.
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Collaborative Work Skills : PEER Score FORM for Project Work - Olson - last revised: Spring, ;07
NAME:
Make one printout for each project assigned.
DO NOT SHOW THESE COMPLETED FORMS TO ANYONE except your instructor.
Please list all team members (put yourself in slot # 1.) and score each member (including
yourself) according to the scale and the Collaborative Work Skills: Group Scoring Rubrick.
Be honest in your scoring. Use the NUMERIC form of each grade and calculate the totals.
5. Excellent (A) 4. Good (B) 3. Satisfactory (C) 2. Needs Improvement (D) 1. Unsatisfactory (F)
ONLY students who were assigned to your group who you never saw during the entire process for a project
should receive a 0 (in every category). That is a non-attending F (NAF).
If there are more than five group members for a project, please use a separate score-sheet for any
additional members (staple it to this one).
Only complete # 12 for projects which are to be presented.
Disputed scores will be arbitrated by the instructor.
Caution:
Students turning in this form with all 5’s will receive an automatic 1 in categories 3 and 7.
Students turning in this form without reading the rubrick carefully will receive a 2 or 3 in categories 3 and 7.
Students who turn this form in late (or not at all) will receive a 1 in categories 4 and 8 (on all completed forms).
NAMES
1. (YOU)
2.
3.
4.
5.
Scores
Scores
Scores
Scores
Scores
First:
Last:
CATEGORY
1. Attends meetings
2. Contributions
3. Quality of Work
4. Time-management
5. Problem-solving
6. Attitude
7. Focus on the task
8. Preparedness
9. Pride
10. Monitors Group
Effectiveness
11. Working
With Others
12. Attends
Presentations
Total Score (each member):
Your final peer score
(completed by Instructor):
Your final project score
(completed by Instructor):
7
Team Projects - Oral Presentation Rubric (Use to Score Other Teams in-Class Presentations)
CATEGORY
Preparedness
4
The team is
completely prepared
and has obviously
rehearsed.
Enthusiasm
Facial expressions
and body language
generate a strong
interest and
enthusiasm about the
topic in others.
Speaks clearly and
distinctly all (10095%) the time, and
mispronounces no
words.
Student uses prop
that shows
considerable
work/creativity and
which makes the
presentation better.
Stays on topic all
(100%) of the time.
Speaks Clearly
Props
Stays on Topic
Content
Presentation on the
Whole
Shows a good
understanding of the
topic.
Overall, the
presentation was
excellent.
3
The team seems
pretty prepared but
might have needed a
couple more
rehearsals.
Facial expressions
and body language
sometimes generate
a strong interest and
enthusiasm about the
topic in others.
Speaks clearly and
distinctly all (10095%) the time, but
mispronounces one
word.
Student uses prop
that shows some
work/creativity and
which makes the
presentation better.
2
The team is
somewhat prepared,
but it is clear that
rehearsal was
lacking.
Facial expressions
and body language
are used to try to
generate enthusiasm,
but seem somewhat
faked.
Speaks clearly and
distinctly most (9485%) of the time.
Mispronounces no
more than one word.
Student uses prop
which makes the
presentation better.
1
The team does not
seem at all prepared
to present.
Stays on topic most
(99-90%) of the
time.
Shows a good
understanding of
most of the topic.
Overall, the
presentation was
well done.
Stays on topic some
(89-75%) of the
time.
Shows a good
understanding of
parts of the topic.
Overall, the
presentation was
average.
It was hard to tell
what the topic was.
Very little use of
facial expressions or
body language. Did
not generate much
interest in topic
being presented.
Often mumbles or
can not be
understood OR
mispronounces more
than one word.
Student uses no prop
OR the prop chosen
detracts from the
presentation.
Does not seem to
understand the topic
very well.
Overall, the
presentation was
poor.
Sample Form (will be provided to you in class during Presentation)
Team Projects - Oral Presentation Scoring FORM (Use to Score Other Teams in-Class Presentations)
Instructor: Ms. Olson
Team Presenting:
Make one copy of this form for each team presenting. Do not put your name on the form.
DO NOT SHOW THESE COMPLETED FORMS TO ANYONE except the instructor.
Please score the presentation according to the scale below and the Oral Presentation Rubric: Team Projects
sheet. Be honest in your scoring. Use the NUMERIC form of each grade and calculate the totals.
4. Excellent (A) 3. Good (B) 2. Satisfactory (C) 1. Needs Significant Improvement (D)
Teams which make a presentation cannot receive an F.
CATEGORY
1. Preparedness
2. Enthusiasm
3. Speaks Clearly
4. Prop
5. Stays on Topic
6. Content
7. Presentation on the Whole
Totals
AVERAGE
SCORE
COMMENTS
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Olson – Beginning Algebra – CAI – Teamwork Project – General Information - Last Revised Summer, 2007
KEEP THESE SHEETS with your SYLLABUS pages.
Cooperative Team Work: Regular participation in class and in small team activities is expected. One major longterm cooperative project will be graded based on the presentation and work collected from the team. THE longer
MAJOR TEAMWORK GRADE CAN NEITHER BE DROPPED NOR MADE UP. Each absence during classes
which have some time devoted to these projects drops your portion of your team’s total score by 2 points. Your
overall team project grade will be composed of the average score for all separate Teamwork Projects done
throughout the semester (each presentation date ends a current project).
Guidelines For Working Together
9. Agree on what your team must do and how you will get it done.
10. Be courteous and listen carefully to the other team members.
11. Create a team atmosphere that allows team members to be comfortable asking for help when needed.
12. Don’t assume the other members know more/less than you do. Your backgrounds are different and you all have
strengths to bring to the table.
13. Everyone has their own pace. Be patient. Offer your help. Receive help graciously.
14. Focus on the value of all contributions made.
15. Get help via the “order of three”: 1. Look it up, 2. Ask a team member, 3. Ask the instructor.
16. Help double-check the teams’ combined work. Can the team see a general rule about the process or describe a
real-world use for what you learned?
I will be assigning you to a specific team for the major project.
Once in your assigned team – get the other members phone numbers and email contacts. You may want to
create a team name. Also find a time in common you can meet outside class. For each separate activity, your
team members may want to adopt a specific team role:
Standard team roles are: Facilitator, Recorder, and Questioner.
These roles explained here:
Facilitator – leads the team, helping direct the activity.
Recorder – writes the information down that gets turned in for the team as a whole. This could also include creating
the visual aide for the team’s presentation.
Questioner – asks questions: during the process, to help the team clarify results, and the questioner is on the lookout
for errors.
The whole team stands together as their findings are presented to the whole class (for support), but not everyone
has to speak. Your team will need to decide how you want to do this.
Grading: Your grade will be composed from these parts (apart from attendance).
Again, note that each absence during classes which have some time devoted to these drops your portion of your
team’s total score by 10% of an individuals’ pts each absence.
Total possible for the Team = individual total possible * number of assigned team members.
4. 50%
The mathematics for the situation is correct (graded by the teacher).
5. 25%
All data collected and records are clear, neat, and complete (all required parts turned in)
– this includes proper use of the English language in a descriptive paragraph (see below)
(graded by the teacher).
6. 25%
The class report for the problem is well-presented
(graded by classmates not in your team and by the teacher).
4. Absence during teamwork times deducts from the above team total possible at a rate of
10%/individual/absence.
Your personal grade: Team Scoring: Individual accountability is the key to success of the whole team here.
Toward that end, to guard against “freeloading”, your participation will be decided by your fellow team members
and by your attendance in class. Your entire team will earn between 0% and 100% of the total points possible (20*
number of team members). I will allocate the total number of points earned by the entire team. Then, as a team, you
will help allocate how the points are divided among your members.
9
You do this by scoring each other via the rubric and score sheet. Here are some guidelines to keep in mind for this
part of the process:
1) No one person can get more than 100% of an individual score.
2) No one can get less than 0%.
3) In case of disputes, i.e., you can’t come to consensus as a team (not just majority), the instructor will act as
arbiter.
You need to grade yourself and each team member fairly based on the items listed when completing the rubric (also
see those pages for more details).
Beginning Algebra Projects – MODELING IN THE REAL WORLD via data collection and analysis and algebraic
methods.
This will be done in stages over the next few class periods and will take some individual and team time outside
class.
You will be allowed adequate time for report/results to come in before your team needs to report to the whole class.
6.
Preparation: All teams will work on a specific problem below as a team when (and if) it’s assigned over several
days and even weeks. You will need to do some field-work to collect real data, so some time outside class is
necessary.
Once the data is collected, your team should use the data and an algebraic process to try to find the
requested results. NOTE: one goal here is a hands-on and teamwork approach toward helping the entire team
toward a deeper understanding of some applications already studied or to be studied.
7.
Paragraph: For your team’s problem, you must write a paragraph discussing your work and any results in
words (at least three sentences). The paragraph must be in formal English (correct grammar and punctuation, no
abbreviations). Please feel free to visit the Writing Center for help with this component.
8.
Presentation: Your team will plan to present the data collected, the algebraic work, and the results to the whole
class once you’ve had a chance to prepare (typically one or two weeks). You will have the choice as a team on
format and who speaks. For your team’s presentation, you need to create some sort of
visual aide: a poster, an over-head (on film), a handout, or a power-point (with hand-outs). Don’t plan to just
write on the board, as this needs to be part of the over-all record turned in, but the board may be used in
addition to whatever you do create. (If using PowerPoint, the instructor must be notified well in advance to
reserve a computer and projector for that purpose.)
Note: This does not mean once your team has presented, it’s any less responsible for listening to the other
presentations. During presentations given by other teams, you will be responsible for grading them per a
presentation rubric. (Absence here counts off the same as any other teamwork activity time in class.) Also,
EVERYONE in the team needs to review the problems ALL teams worked, since any presented may be used or
referred to in some form on any quiz, test, or the final exam.
9.
What to turn in and when: For your team’s problem, the team must turn in
 all RAW data your team collects (that’s every rough draft from every team member). Include
EVERYTHING, no matter how messy, and label that with “field collection”
 all preparation work (including all scrap-work and any drafts and the algebraic process used, even ones
with errors),
 the organized, polished data and results
 be sure to include a paragraph discussing the work and results (see # 2 above),
 and any visual aides used in your presentation.
 These are all due when your problem is presented.
10
PROBLEMS: (You won’t do all these at once, and in fact, may not do them all this semester. This list is designed to
allow for variety of assignment but standardization of this form. Please note which ones are assigned when they are
assigned.)
1) Measures of central tendency problem (any time).
a) The team needs to create a survey asking something (or things) you want to know as a team. The questions
must ask for a numerical answer (how old, how many, what amount, what year, etc.). Avoid yes/no
questions (as the numeric equivalence is too limited). Your team must form 3 such questions. The questions
do not need to be related.
b) Create a common survey form to record responses easily when collecting the data. Make enough copies for
the team’s collection efforts.
c) Survey a total of 100 people with a common background (all students, all adults, all children age 10, etc.).
(Note, if there are 4 or 5 people in your team, that means survey 25 or 20 people each.)
d) Use EXCEL (I will help any team who needs it with this portion)
i) Enter all the data for each question (1 question per column is easiest).
ii) Use this to calculate the mean, the median, the mode, the maximum, the minimum, and the range, for
all data for each question (at the bottom of the column is easiest). Print a copy.
iii) Then make a full copy of all the data somewhere (another spreadsheet would work)
iv) and sort it.
v) Use this version to find the sum and the count.
vi) Print a copy of the sorted version with the sum and count, and then use this to find the mean, the
median, the mode, the maximum, the minimum, and the range by hand on the printout. The team needs
to turn in an electronic copy of the file created for this work (by email attachment with a clear,
descriptive memo or on CD).
2) Distance and Average Rage problem. (any time)
a) Each of you in the team needs to time yourself accurately during at least one commute from home to
class (write down departure and arrival times). Also write down the departure mileage and arrival
mileage (or use your trip-counter if available). Do this during a commute where you won’t make
any other stops.
Example Data Table:
Member
Name
Commute
Starting Odometer Reading
Distance
Time
Rate = ????????
Average Rate for each member
R=
Ending Odometer Reading
Name
Starting Odometer Reading
Ending Odometer Reading
Name
Starting Odometer Reading
Name
Starting Odometer Reading
Ending Odometer Reading
Ending Odometer Reading
b) Form a Data Table with the whole team’s data (see example above).
c) Now for a little bit of algebra: given the distance formula, distance = rate  time or D = R  T, it
will be easier to do the next task if the formula is solved for R. Solve it for R. Put that formula in
your Data Table.
d) Using the new form of the formula, calculate the average rate for each commute separately. Put all
these in the team table.
e) Discuss why averaging this entire list of results would or would not make sense.
f) Separately, work this problem (this last part is to be done during Ch 6 topics, if due before then,
you may stop with part e)): If one of you averages 5 mph faster than another teammate, and the first
of you can drive 150 miles in the same time that the second drives 135, find the (average) speed
(rate) of each of those two drivers.
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3) An object thrown/shot into the air (any time after 3.1).
The formula s = –16 t2 + v0t + s0 measures the height of an projectile where
s = height (in feet) at time t (in seconds), v0 is the initial velocity (in feet per second or ft/sec) and s0
is the initial height (in feet).
General Description: Using a tennis ball, one team member will throw it up into the air as hard as possible a few
times, while other team members find the release (initial) height and track the time the ball is airborne. The
team will use these to find the throwing (initial) velocity for each throw and then the average throwing velocity.
The graph of the team’s general formula will also be seen on a graphing calculator, and then roughly sketched
on graph paper.
Example Data Table:
Release Airborne
(initial)
Time = t
Height
(in seconds)
= s0
(in feet)
a)
Height when
projectile hits
the ground = s
(in feet)
Height formula
solved for throwing velocity (when
the projectile hits the ground):
Velocity formula
for each throwing
time (after
replacing t’s and
s0)
Throwing velocity for
each throwing time:
(once calculated)
Sum of
all 5 throwing velocities:
Average throwing velocity
= sum/count
(in ft/sec)
= v0
Using one practice throw, have the thrower keep their hand up as high as it was when they released
the ball, and the other team members quickly and carefully measure how high that is off the ground.
Only measure this and record it as the release height measurement once in a Data Table (see
example above). Be sure to record feet and inches carefully, and then convert the inches part to feet
form (as an exact, reduced, fraction or an exact decimal), before working on other calculations using
the formula.
b) Now, using a stop watch (borrow one from me if you don’t have one in the team), time 5 separate
throws. For each throw, start the watch when the thrower releases and stop it when the ball hits the
ground. This works best if the thrower says “start” and another team member watching the ball says
“stop” when it hits each time the ball is thrown. Record that airborne time (record any whole and
decimal parts) in your Data Table. Repeat this until 5 throwing times are recorded. Each of these
times is a separate t-value.
c)
Now for a little bit of algebra: given the height formula, when the ball hits the ground, what is that
height? (How far off the ground, think about it.) Replace s (on the left side) by that value in the
general formula:
s = –16 t2 + v0t + s0
It will be easier to work with if the new formula is solved for throwing velocity (v0). Solve it for v0. Put that
formula in your Data Table.
d) Now, use your first t and your s0 and place them into the new formula you found. Write that
complete expression in the Data Table. Repeat this for the second t, and so on until you’ve used all
five t’s.
e)
Calculate each separate v0 and write them in the Data Table. Remember to use correct
order-of-operations by keying in the entire expression (parentheses in place and all) carefully each
time.
To find the average throwing velocity for the thrower, add all 5 v 0’s and put that in the Sum box.
Then divide that sum by the count of throws (here that’s 5). Put the average throwing velocity in it’s
box.
g) Next, write your team’s general height formula by replacing s0 and v0 by the s0 and the average v0.
s = –16 t2 + v0t + s0 
s = –16 t2 +
t+
f)
To see the graph on a TI-82/83 graphing calculator, press
ON Y= (-) 1
6 XT x2
+
v0 XT +
s0
.
(Be sure to key in your average v0 and s0 numbers where those are written here.)
WINDOW ENTER 0 ENTER 8 ENTER ENTER 0 ENTER 5 0 ENTER 1 0 ENTER GRAPH
(Xmin = 0; Xmax = 8; Xscl = 1, Ymin = 0; Ymax = 50;
Yscl = 10)
h) Use TRACE or TABLE to get some points to plot between x = 0 and when the ball hits the ground
on average. Put the points in a hand-written t-table, plot them, and sketch the graph you see on the
TI-82/83/84.
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4) (Miller Manual Technology Connections
Chapter 3
Activity:
Investigating Graphs of Linear and Nonlinear Equations
Materials:
A computer with Internet Access or a Graphing Calculator
)
Part I:
A. A graphing calculator or computer graphing utility can be used to graph an equation in x and y by plotting
many points. Try accessing one of the graphing utilities on the Internet.
Part II:
B. In Chapter 3 we focused equations whose graphs are lines call linear equations. Some equations have graphs
that are not straight lines. We call these equations nonlinear. Use an on-line graphing utility to graph the
following equations. For each equation, state whether the equation is linear or nonlinear.
Equation
Enter as…
Example:
y=x
y=x
y = 2x + 3
y = 2x + 3
1
y = - 2 x –2
y = x2
Linear or Nonlinear
Sketch
linear
y = -(1/2)x – 2
y = x^2
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Enter as…
Equation
Linear or Nonlinear
y = x3
y = x^3
y = |x|
y = abs(x)
y=
1
x
y = -3x +
Sketch
y = 1/x
y = -3x + (5/2)
5
2
Applications:
Part II:
C. Use an on-line graphing utility or a graphing calculator to graph the following
of coordinate axes:
a.
y = 2x
y = 2x + 2
y = 2x + 4
How are these graphs related?
y = 2x – 2
y = 2x – 4
b.
D.
y=x+1
y = 2x + 1
y = 3x + 1
equations on the same set
How are these graphs related?
Use a graphing utility to graph the following pairs of equations. Then state
how each pair of lines is related.
a.
y = 3x + 2
y=
b.
 x–1
1
3
y= 5x+3
Hint: Enter as y = 3x + 2
Hint: Enter as: y = -(1/3)x – 1
Hint: Enter as y = (5/2)x + 3
2
y= 
c.
2
x–2
5
3
x+ 1
7
4
7
5
y= x
3
3
y =
Hint: Enter as –(2/5)x – 2
Hint: Enter as –(3/7)x + (1/4)
Hint: Enter as (7/3)x + (5/3)
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5) Using similar triangles (any time).
Use similar triangles to estimate the height of tall objects. Fact: similar triangles have the same angle
measures and their sides are proportional:
B
E
23mm
30 mm
D
F
A
C
26mm
34 mm
30 34
26 23
and
are just two of several appropriate ratios we can form.


23 26
34 30
In the following, it’s easier if you use one type of unit of measure (either all in feet or all in inches)
for the measurements (but the building’s measurement unit can be different than the person’s). You
will need to bring a long tape measure the day you do this (I recommend at least 50ft, but if
necessary, you may borrow my shorter one). Also, recall 1 ft = 12 in.
b) On a sunny day, measure one team-member’s height and the length of their shadow on the ground
carefully.
c) At that same time, measure the shadow of MAT or Burns Hall (state which you are using) or a tree
on the property where MAT is located (describe EXACTLY which tree) where a shadow’s corner or
peak is SHARP and easy to see.
Building or Tree
a)
Person
Shadow
Shadow
d) Use these three measurements and similar triangles (see the diagram above) to estimate the height of
the building at that point corner.
e) Compare your results with another team in the class. Comment on any similarities or differences in
your paragraph.
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6) (Miller Manual Activity 4.1D)
A.
Suppose you have $50,000 invested at 7% interest compounded annually for 4 years.
Complete the table below to determine the total amount in the account after two years.
Compound Period
B.
Annual Compound Interest
Interest Earned I = Prt
1
I = 50,000(0.07)(1) = __________
2
I = ________ (0.07)(1) = _________
3
I = ________
4
I = ________
Total Amount in the Account
50,000 + 3500 = __________
To verify your answer from Question 1, use A = P(1 + r) t, where
P is the amount of principal
r is the interest rate
t is the number of years
P = ________________
r = _________________
A = _________________
t = _________________
C.
How much total interest is earned in the 4 years? I = __________________
D.
Have a team member find out from their bank what the current interest rate is on a $5,000 CD that’s set up
for 4 years with annual compounding (as above). Repeat steps A – C for that account (you will need to
make a table similar to the one in part A, but remember to adjust the values to reflect $5,000 at your rate
instead of $50,000 at 7%).
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7) Geometry and factoring trinomials (during/after Ch 5). Factoring polynomials can be visualized
using areas of rectangles. To see this, let’s first find the areas of the following squares and rectangles.
(Recall that Area = Length  Width.)
x
area
= x2
1
area = 1x
1
x
area =
1
1
x
Use these same shapes and areas to visualize factoring the polynomial x2 + 3x + 2.
To do this, use the above shapes as many times as they’re listed (1 of the x 2’s, 3 of the 1x’s and 2 of the
1’s) and put them in the shape of a rectangle. The factored form is found by reading the length and the
width of the rectangle as shown below.
The only way they will form a rectangle is to put them in this format (up to just rotating).
x
1
1
=
x + 2 along the top edge
x
1
=x+1
along the left edge
Making the area product factors (x + 2)(x + 1)
Thus, x2 + 3x + 2 = (x + 2)(x + 1).
Try using this method to visualize the factored form of each polynomial below. Tiles can be made from
index cards.
1. x2 + 6x + 5
4. x2 + 4x + 3
2
2. x + 5x + 6
5. x2 + 6x + 9
3. x2 + 5x + 4
6. x2 + 4x + 3
Be sure to record each rectangle result and the factored forms.
Be sure to demonstrate how you did this for one of the problems (not the example) as part of your
classroom presentation.
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8)
Choosing Among Building Options (during/after Ch 5). You have just had a 10-ft-by-15-ft in-ground
swimming pool installed in your back yard. You have $3000 left from the project to spend to surround
the pool with a patio walkway of constant width (see the figure). You have talked to several local
suppliers about options for building this patio and must choose from among the following.
x
patio
10 ft
x
pool
15 ft
x
x
Option
A
B
C
Material
Price
Poured
Cement
Brick
$5 per square foot
Outdoor
Carpeting
Algebraic
Expression for
Total Cost
Maximum
Patio Width
$7.50 per square foot plus
$30 delivery fee
$4.50 per square foot plus
$10.86 per foot (of the
perimeter) to install an
edging
Use the following process to build a complete table like the one above and answer all the questions below.
1. Find the area of the swimming pool.
2. Write an algebraic expression for the total area of the region containing both pool and patio.
3. Find an algebraic expression for the area of just the patio (total area minus pool).
4. Find the perimeter of the pool.
5. For each patio material option, write an algebraic expression for the total cost of installing the patio
based on its area (see step 3) and the given price information.
6. If you plan to spend the entire $3000, how wide can the patio in option A be?
7. If you plan to spend the entire $3000, how wide can the patio in option B be?
8. If you plan to spend the entire $3000, how wide can the patio in option C be?
9. Which option should you choose? Why? Discuss the pros and cons of each option. (Be sure to include
that complete discussion in your paragraph.)
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9) Work problems (to be finished during Ch 6 topics).
Formulas: (rate-on-task)  (time-on-task) = 1
1
task completed, so rate  on  task 
. These types of rates will add up (working
time  on  task
together gets the job done faster than each working alone), so: rate1 + rate2 = (rates together).
Combining these two concepts gives us a standard work formula for calculating time when each person,
1
object, or machine is doing the same job  1  1 
. Commonly, the formula
time1 time2 time together
will take on this simpler form: 1  1  1 where a and b are time for each person or machine to do the
a
b
t
task separately and t is the time together (in both formulas). With this in mind, complete the following
three problems.
a) Data collection and comparison with the formula:
i) Determine a task at least two of your teammates can accomplish alone or together (work a
particular type of math problem or list of problems, mow a lawn with two separate mowers and
together, etc). ASK me if you are not sure your task will work (e.g., one example which won’t
work is to read a page in a book, since it doesn’t take less time for each to read it separately vs.
together).
ii) Time the two team members performing the entire task separately.
iii) Time them working on the task together.
iv) Use the work formula (above) to calculate what their time should be together based on their
separate times. Compare (and contrast) the two results your team gets from the actual timing
together vs. what the formula predicts their time should be together in your paragraph.
b) Solve: It takes two people 3 hr and 4 hr separately to do a task. Find how long it would take them to
do the same task together.
c) Solve: It takes two copiers 10 minutes and 25 minutes to copy a 500 page project separately. Find
how long it would take using both copiers to get one 500 page project copied.
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