Middle School Math

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Middle School Math

• Standard Based Projects and Rubrics
• Janet Bosche Deb Mosko

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Data Analysis

• Emergency at the Park
• Data Sheet
• Letter students receive to start project
• Rubric for project
• Rubric for group work
• Since this is a presentation students may use
  power point, posters, etc. to help convince the
  government officials present their proposal
  should be accepted.

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Measurement

• Larger than life project
• Rubric
• Index cards
• Web site of company

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Algebra

• Barbie Bungee Jump
• Barbie Bungee Activity Sheet
• Plans
• Bungee TV
• Bungee Jump Preview
• Line of Best Fit
• Barbie Bungee Jump Spread Sheet
• Questions for Students

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Graphing for 7th Grade

• Project Survey
• Rubric
• Example Grade 1,
• Data Analysis Awareness

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Metric Fun for 7th grade

• Metric Pretest
• Mission Metric
• Metric week ideas

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Ideas to pass along

• Interview questions
• Guidelines for math homework
• Math writing to inform, rubric
• PEMDAS Cheer
• Integer dance
• Quotient Conga line

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Bibliography

• Barbie Bungee jump NTCM
• Bay City Amusement park
• http//www.nottingham.ac.uk/education/MARS/tasks/
  g8_2/full.html
• Mission Metric
• http//library.thinkquest.org/J002831/missionmetri
  c.htm

http//illuminations.nctm.org/LessonDetail.aspx?id
L646
This lesson prepared by Samuel E. Zordak
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Emergency at the Park!

• Grade Level Middle
• The task asks students to compare two ambulance
  companies on the basis of their timely response
  to Emergency 911 dispatches. Students must use
  appropriate graphs or measures of center and
  spread or both to present a persuasive argument
  for choosing one of the ambulance companies over
  the other.
• Assumed Mathematical Background
• It is assumed that students have had some
  experiences with situations that involve
  selecting appropriate variables to sort data, to
  represent data in tabular and graphical forms,
  and to find measures of center and spread.
  Further, it is assumed that students will have
  had experiences drawing conclusions and making
  recommendations based on data analysis.
• Circumstances
• Grouping Partners or small groups, each group
  turns in one product
• Materials Graph paper
• Estimated time 1 week

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• The aim of this assessment is to provide the
  opportunity for you to
• select appropriate methods to analyze a data set,
  including appropriate graphs and calculations
• read and interpret a graph
• Use data analysis to make a recommendation.

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• Last week there was an accident at the Waterfront
  Amusement Park in Bay City. A seat on one of the
  rides broke loose resulting in the death of two
  teenagers. The owners of the amusement park have
  charged that if ambulances had responded more
  quickly, the two teens would have survived. They
  have threatened to sue the Bay City 911 emergency
  service for failing to dispatch ambulances
  efficiently.
• The Bay City Council has hired your firm to
  conduct an independent investigation of the
  City's 911 response. Upon completion of your
  investigation, you are to make a report to the
  City Council on your findings along with any
  recommendations for improving the 911 emergency
  services in the neighborhood of the amusement
  park.
• You start to work on this assignment. Your
  investigation has uncovered the following
  information.
• The 911 operators dispatch ambulances from two
  companies Arrow Ambulance Service and Metro
  Ambulances.
• The 911 operators aren't always sure which
  company to send when an emergency call is
  received.

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• Data on the response times of the two companies
  for an area of a one mile radius of the Amusement
  Park shows that it can take as little as 6
  minutes or as long as 19 minutes. (The response
  time is the length of time from when a 911
  operator receives an emergency call to when an
  ambulance arrives on the scene of the accident.)
• You need to continue your investigation by
  analyzing the response time data from the 911 log
  sheets for May. (The log sheets are shown on the
  next page.)
• Based on the information above and your analysis
  of the response time data, you conclude that the
  Bay City Council needs to establish a policy
  about which service to call.
• Write a report to the Bay City Council advising
  them of your recommendations about which service
  the 911 operators should dispatch in the area
  around the amusement park.
• You will need to prepare charts, graphs,
  calculations or other materials to include in
  your report to support your recommendations.
• Be sure to give clear reasons for the policy you
  are recommending.

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Emergency 911! Data sheet These log sheets show
all the emergency calls placed to 911 operators
in May for an area within a one-mile radius of
the Waterfront Amusement Park.
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City Government Janet Bosche, Mayor Date Student
s Company Name Your Schools Address City, State
Zip Dear Sir or Madam Thank you for agreeing to
conduct our internal evaluation of our EMS
response-time to the Waterfront Amusement Park.
We understand that you have agreed to provide us
with a report that accomplishes the following An
analysis of the 911 response times by the two
companies providing EMS services to the Bay City.
It is that this analysis will include graphs,
numerical summaries, narrative and suitable
visuals appropriate for distribution to our City
Council, Park personnel, news media and the
public at large. A recommendation complete with a
graphic that clearly states which of the
companies to dispatch to the Waterfront Amusement
Park during its hours of operation throughout the
week, this may vary day by day or the week and/or
time of day. A detailed explanation of your
rationale for your recommendations. As per our
written agreement, this evaluation must be
presented at our next council meeting on give
date due. Sincerely, Janet H Bosche Mayor
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INVOLVEMENT IN GROUP WORK
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Larger than LifeBuild a Scale Model 8th grade
Due date Mount Rushmore is an example of a scale
model that is larger than the objects on which it
is basedmuch larger! Other types of scale
models, such as some toys, are smaller than the
objects on which they are based. For your
project, you will build your own scale model.
First, you will choose an object to model. Use
your imagination. Your model can be larger or
smaller than the actual objectyou choose the
scale. Finally, you will select the building
materials and assemble the model.
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Research Decide which object you will
modelfind information about its history.
Measure the real-life dimensions of that object
and list all of those dimensions. Then decide on
the approximate size of your model. Writing
Choose the material from which you will construct
your model. The material can be wood, paper
mache, clay, or something else. Explain your
choice, stating advantages and disadvantages of
using various materials for the type of scale
model you are building. Explain what the actual
object is made from and its history. Calculating
Is your scale model an enlargement or a
reduction of the actual object? Give the scale
factor. Then, for each dimensions listed,
calculate the corresponding dimension of the
scale model.A spreadsheet may be
helpful. Analyzing Select at least 3
measurements on your scale model, and get the
corresponding real-life dimensions of the object
being modeled. Write a proportion using the
quantities. Even if all of your work is
accurate, the proportions may not be exactly
equalexplain. Reflect Is the model attractive?
Are the dimensions to scale? If necessary how
would you improve? Bibliography- 3-minute
presentation, with time after for questions.
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3 large index cards Card 1 history of object,
at least 4 interesting facts Card 2 dimensions
of original, picture of original, drawing of
dimensions, and your scale project Card 3
materials used benefits, problems, cost, etc
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Barbie Bungee Jump
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In this activity, you will simulate a bungee jump
using a Barbie doll and rubber bands. Before you
conduct the experiment, formulate a conjecture I
believe that _____ is the maximum number of
rubber bands that will allow Barbie to safely
jump from a height of 400 cm. Complete each
step below. As you complete each step, put a
check mark in the box to the left. ?? Tape a
large piece of paper to the wall from the floor
to a height of about six feet. ?? Draw a line
near the top to indicate the height from which
Barbie will make each jump. ?? Create a
double-loop to wrap around Barbies feet. A
double-loop is made by securing one rubber band
to another with a slip knot, as shown (below
left). ?? Wrap the open end of the double-loop
tightly around Barbies feet, as shown (below
right). ?? Attach a second rubber band to the
first one, again using a slip knot, as shown
below. ?? With two rubber bands now attached,
hold the end of the rubber bands at the jump line
with one hand, and drop Barbie from the line with
the other hand. Have a partner make a mark to the
lowest point that Barbie reaches on this jump. ??
Measure the jump distance in centimeters, and
record the value in the data table in Question 1.
You may wish to repeat this jump several times
and take the average, to ensure accuracy.
Accuracy is importantBarbies life could depend
on it! ?? Repeatedly attach two additional rubber
bands for each new jump, measure the
jump distance, and record the results in the data
table. ?? When youve completed the data table,
answer the following questions..
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1. Complete the data table below. NUMBER OFRUBBER
BANDS (X) JUMP DISTANCE IN CENTIMETERS
(Y) 2 4 6 8 10 12 2. Make a scatterplot of your
data. Indicate the scale on each axis. 3. On the
graph above, sketch a line of best fit. 4. What
is the relationship between the number of rubber
bands and jump distance? x Y 5. What is the
equation for your line of best fit? (You may wish
to use a graphing calculator for this part of the
lesson. Enter the rubber band data in L1, and
enter the jump distance data for L2.)
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6. What is the slope of your equation, and what
does it represent in this context? 7. What is
the y-intercept of your equation, and what does
it represent in this context? 8. Based on your
data, what would you predict is the maximum
number of rubber bands so that Barbie could still
safely jump from 400 cm? Using your Line of Best
Fit ________________________________ Using your
Regression Equation ____________________________
9. Are your predictions reliable? Justify your
answer. Be sure to consider your methods of
collecting, recording, and plotting data. 10.
How do your predictions from Question 8 compare
to the conjecture you made before doing
the experiment? What prior knowledge did you have
(or not have) that helped (or hindered) your
ability to make a good conjecture? 11. In what
ways did you contribute to the group while
working on this project? 12. List any
additional comments.
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• Get students' interest by asking, "Do you think
  the length of the cord and the size of the person
  matters when bungee jumping? Would it be smart to
  lie about your height or weight?" Allow students
  to offer suggestions as to why an accurate
  estimate of height and weight would be important
  to conduct a safe bungeee jump.
• You may also wish to show a short video about
  bungee jumping. Some bungee videos are available
  on the following web sites (note that the third
  video shows the tribal ritual of land diving, a
  precursor to bungee jumping, and may not be
  appropriate for all classrooms)
• (www.bungee.com)
• (www.extremeworld.com)
• (www.nationalgeographic.com)
• After a brief introduction, set up the lesson by
  telling students that they will be creating a
  bungee jump for a Barbie doll. Their objective
  is to give Barbie the greatest thrill while still
  ensuring that she is safe. This means that she
  should come as close as possible to the ground
  without hitting the floor.
• Explain that students will conduct an experiment,
  collect data, and then use the data to predict
  the maximum number of rubber bands that should be
  used to give Barbie a safe jump from a height of
  400 cm. (At the end of the lesson, students
  should test their conjectures by dropping Barbie
  from this height. If you school does not have a
  location that will allow such a drop, then you
  may wish to adjust the height for this
  prediction.)
• Distribute the Barbie Bungee activity packet to
  each student. In addition, give each group of
  3-4 students a Barbie doll, 15-20 rubber bands, a
  large piece of paper, some tape, and a measuring
  tool. Be sure that all rubber bands are the same
  size and thickness. Differences in rubber band
  elasticity will affect the results.

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Before students begin, demonstrate how to create
the double-loop that attaches to Barbies feet.
Also show how a slip knot can be used to add
additional rubber bands. Then, allow students
enough time to complete the experiment and record
the results in the data table for Question 2.
After all groups have completed the table, ask
them to check their data. They should look for
numerical irregularities. If any numbers in their
table do not seem to fit, they may need to re-do
the experiment for the number of rubber bands
where the data appears abnormal. (Common student
errors include measuring incorrectly and adding
too many or too few rubber bands. As students
conduct the experiment the first time, circulate
and attempt to spot these errors as they occur.
It will save time if students fix the errors
during the initial experiment instead of having
to re-do the experiment later.) Note that the
number of rubber bands in the first column
increases by 2. This is so students consider the
idea of slope during the experiment. If the
number of rubber bands increases by 1, then
students are not required to think about what the
slope means. When increased by 2, however,
students have to realize that the slope of the
line actually represents "centimeters per rubber
band" instead of "centimeters per two rubber
bands." To create a graph of the data, you may
wish to have students use the Illuminations Line
of Best Fit activity, or allow them to enter the
data in the Barbie Bungee Spreasheet (Excel).
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At the end of the lesson, take students to a
location where Barbie can be dropped from a
significant height. Possibilities include a
balcony, the top row of bleachers, or even
standing on a ladder in an area with a high
ceiling. Allow students to test their conjecture
about the maximum number of centimeters that can
be used for a jump of 400 centimeters
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• As a journal response, have students answer the
  Key Questions above. Then, require students to
  present their solutions to the class and
  demonstrate that their answers are correct. For
  instance, if a student says that Barbie can jump
  safely from a height of 400 cm with 12 rubber
  bands, then they should demonstrate that Barbie
  will not hit the ground when 12 rubber bands are
  used.
• The following rubric can be used to evaluate
  student work. You may wish to share this rubric
  with students prior to completing the lesson, so
  that they are aware of the criteria on which
  their performance will be measured.

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• Group Survey Project
• Your group will be expected to complete a group
  survey project.
• Your final display must include the following to
  receive the maximum number of points
• Name of group and all group members' full names.
• A paragraph explaining why you chose the survey
  questions and what makes them good questions.
• A paragraph explaining why your group thinks that
  your data are an accurate representation of the
  school's students. Remember you should consider
  equity of gender and age when conducting a survey
  so that it is a representative sample of the
  group you are polling.
• Frequency Tables
• Graph your data using a Microsoft Excel, or
  Create a Graph http//nces.ed.gov/nceskids/graphin
  g/ Each question must be graphed separately.
  If you are comparing two question you may graph
  them both on one graph - for example if you asked
  people what kind of shoes they buy and also ask
  them how much they spend on a pair of shoes.
• At least 4 different kinds of graphs.
• A paragraph explaining how your group rates
  itself in conducting the survey. Explain any
  problems that were encountered. Explain parts of
  the survey project that went well or did not work
  well.

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General Directions As a group member completes
each separate part of the project, make certain
that his/her NAME is on the work. Each member
must complete a minimum of 2 parts of the
project. Each group will be given glue,
scissors, rulers color printer will be available
to print graphs colored pencils will be available
for decorating time to work on laptops

• Suggested Time-line of Activities
• Monday/Tuesday
• make certain that all group members know what to
  ask and whom to ask
• decide how to make your survey accurate for
  gender,age
• assign tasks - decide who will write each
  paragraph
• start any tasks that can be done without data -
  any prints keep in group folder
• students who will be graphing the data
  should practice!
• Wednesday
• SURVEY organize data
• Thursday, Frequency tables and start to graph
• use computers to complete parts of the survey and
  assemble! - team work will be necessary
• Friday, Continue Frequency tables and graphs,
  work on paragraphs, and presentation
• Monday and Tuesday Fine tune project and
  presentation

Social Skill respect yourself
respect your classmates respect
the teachers
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Data Analysis Awareness

• Requirements
• 1. Daily Log of Graphs encountered
• Identify date, type of graph, topic of graph,
  source, use the   Graph Log
• Select a method of graph search
• 1. Daily search specific time per day to look
  in various sources for graphs.
• 2. Weekly Study one source type examined for
  the week.
• 2. Collection of Graph Examples
• In booklet, define Bar, Line, Circle, and
  Pictograph.
• Identify the source of the graph, describe the
  data displayed, and explain the purpose for the
  graph. Could a different type of graph be used
  for this data?
• Minimum of two graphs of each of the following
  types Bar, Line, Circle, Pictograph
• 3.    Create a Bar Graph from the Frequency Table
  developed using the data collected in the Daily
  Log of Graphs.     FREQUENCY TABLE
• 4.     Write a response to the following
  question
• What was the most often encountered graph?
• Explain how the graph search was conducted and
  the results of the search. If the search was
  conducted differently, would the results change -
  why or why not? 

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METRIC UNITS AND PREFIXES PRETEST    
             DO YOUR BEST  1)  What does the
prefix milli mean?  2)  What is the prefix for
0.01?  3)  What is the prefix for 100?  4) 
What is the abbreviation or symbol for centi?
 5)  What does the prefix mega mean?  6)  What
is the symbol for deka?  7)  What is the symbol
for micro?  8)  What is the prefix for the
symbol k?  9)  What is the abbreviation for
meter? 10)  How many grams in one hectogram?
11)  How many meters are there in one
centimeter? 12)  What is the prefix for 0.1?
13)  What is the symbol for liter? 14)  What
unit name has the symbol g? 15)  How many
milliliters are there in 5 liters?
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7th Grade Metric Week Benchmarks Selects and
computes with appropriate standard or metric unit
to measure length, area, volume, angles, weight,
capacity, time temperature, and money Converts
compares and computes with common units of
measure within the same measurement
system. Projects Create a poster with metric
(smiles, height, hand span, etc) List your
favorite foods. Record how much food is in the
package in both metric and standard units. Trace
the history of the meter. When and how the
length of the meter was first established.
Create a time line. Take a box mix of any food
and convert the ingredients to metric. Make a new
cover for the box with the new measurements and
instructions. Make a weather map and give the
forecast for the next five days in Celsius. Give
precipitation in centimeters. Design a bedroom
giving the details of measurement in SI. Include
door heights, windows, area, perimeter, length of
bed, furniture etc. Pick two of the above
projects. Be creative, colorful, appealing and
correct in all measurements
             
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• Topic (change with standard working on)
• How people use fractions, decimal, scientific
  notation or bases in their daily life?
• Name of person interviewed
• Job in which they use the above math topics
• Did they go to college?
• Where did they go to college?
• What was their major?
• How do they use the above topics in their job?
• What part of their job do they find most
  interesting?
• Do they use any special technology in their job?
• How long have they been doing or have done their
  job?
• Special insights

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Math Homework Guidelines Name, date,
assignment Standard paper (math notes, graph
paper, loose leaf) no fringe running down the
side If more than one paper attach with paper
clip, staple or tape Clearly indicate the problem
number. Write out problem. (Except word
problems) PENCIL ONLY Write legibly. Do not do
magic. Each step should be complete. Show all
work. Box answers. For tables and graphs if
not using graph paper use ruler to draw straight
lines.
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Mathematical Writing to Inform Checklist _______My
paragraphs have topic sentences. (STATE THE
PURPOSE) _______My writing clearly informs the
reader about the topic and uses at least three
sentences to support each topic
sentence. _______My writing includes specified
details. (Numerical and/or process
references) _______My sentences are well
organized. (SIGNAL WORDS first, next,
then,) _______My word choices are
appropriate. _______My writing includes words
that show knowledge of mathematical
terminology. _______My closing sentence includes
specific final results. (Strategical, numerical,
etc
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Mathematical Writing to Inform Rubric Name________
_______ Date________________
Score_____________