Mathematics Senior Level Capstone Course Unit Overview
Title of Unit: Campaign for Governor Unit Designers:
Rebecca Bienvenue-Stafford Co. Chris DuBois-Stafford Co.
Denise Glassford-Spotsylvania Co. Kim Riddle-Spotsylvania Co. Pam Bailey-Spotsylvania Co. Context:
Summary of the issue, challenge, investigation, or problem.
Student groups are given a set amount of money to determine the best way to use the funds when acting as a governor and his campaign committee.
Number of Class Hours:
18 hours Unit
Design: ___Task Based _X__Project Based Other Subject
Areas/Disciplines Addressed:
Political Science, Government, Geography, Accounting
Driving Question: What is the best distribution of funds that benefits the most individuals in your state? Mathematics Content
Addressed:
Line or curve of best fit, exponential and logarithmic functions, standard deviation, absolute mean value deviation, z-scores, probability, normal curve, five number summary
MPE Addressed:
Problem Solving, Decision Making and Integration
Understanding and Applying Functions Assumption of Prior
Knowledge:
Graphing, Linear equations, multiple representations, z-scores, probability, measures of spread, measures of central tendency
College and Career st
Skills to be taught (T) during this unit or expectation (E) for student use during this unit and assessed (A): BIE Page 35-37
Communication (Oral and/or Written) E, A Technology E, A
Critical Thinking/Decision Making E, A Other: (Describe)
Major Products and/or Performances:
Group: Presentation to constituents requesting their support to be elected to office.
Presentation Audience:
X Class
School Individual: Specific duties outlined in the timeline – action
plan.
X Expert
Community Other: Launch: Event or
experience used to engage the students interest and inquiry:
Prior to the first class students vote on five items (movies, food, best restaurants, etc) on a scale from 1 (like the least) to 5 (like the most). The one with the largest total number of points is the winner (Borda Count Method). Students are to determine the points for each item and discuss pros and cons for the method.
Evaluation: Formative Assessments (During the Unit)
Interview Practice Presentations
Mathematicians Journal X Notes
Preliminary
Plans/Outlines/Prototypes
X Checklists
Rough Drafts Concept maps
Field Tests Other:
Summative Assessment (End of Project)
Written Products, with a rubric X Peer Evaluation, with a rubric
Oral Presentation with a rubric X Self Evaluation, with a rubric
Other Product(s) or
Performance(s), with a rubric
Other:
Equipment/Technology: Internet, YouTube, computer lab with access to Word, Excel, and PowerPoint.
Materials: Chart paper, markers
Community Resources:
Reflection Methods: Individual, Group, and/or Whole Class
Mathematicians Journal X Small/Focus Groups
Whole Class Discussions Fishbowl Discussions
Survey Other:
Material Adapted From: (Provide credit for any materials or activities adapted from other sources.) http://www.regentsprep.org/ Tutorials and Assessments
http://www.khanacademy.org/ Tutorials and Assessments
Virginia’s Senior Level Capstone Course Instructional Plan
Unit Title: Campaign for Governor
Driving Question: How are statistics and the curve of best fit used to determine the best distribution of funds that benefits the most individuals in your state?
Task/Project/Problem: An individual running for governor, along with his/her staff, must determine how to distribute government funding that benefits the most individuals in the state and thereby win their vote.
ENGAGE How will
students’ interest be piqued so they want to engage in the inquiry in this unit?
20 minutes
Prior to class have students vote on five items (movies, food, best restaurants, etc) using a scale from 1 (like the least) to 5 (like the most).
Students are to determine the points for each item and discuss pros and cons for the method.
The one with the largest number of points is the winner (Borda Count Method).
Mathematician Journal Prompts Would you like to have a crucial election issue outcome based on this method?
EXPLORE Teacher provides
guidance for the explorations to prepare students with the
knowledge and skills to engage in the task. Students will self-assess on the prior knowledge and skills assumed for the unit
4 hours
Exploration 1: Regression Exploration
See HO #1a-c (student copy) and HO #2a-e (teacher key) Students, in groups, investigate four different sets of data to answer questions and determine the best fitting function that illustrate each.
Method A: Student groups rotate through each scenario
answering questions and determining the function. After all are completed students write and verbally share their comparisons and contrasts of the four outcomes.
Method B: A student group is given one scenario to complete. Each group presents their scenario, procedures, problem solving strategies, etc on chart paper to their classmates. Either through a whole class discussion or individually students compare and contrast the findings of all groups.
Teacher Note: It is possible to set Exploration 2 as the project and the elaborate part of this unit as a project.
Exploration 2: Using Excel in the NFL – A Statistical Exploration See HO #3 (student copy), HO #4a-b (NFL data), HO #5a-b (teacher key), and HO #6a-b. (Teachers may elect for students to find their own data on the internet.)
Student groups select four NFL teams to analyze using a five number summary, standard deviation, and box and whisker plots. Student groups determine the most consistent team and which team they would be more inclined to purchase according to data. The second part is for the student groups to select one team and answer questions given specific changes and/or situations that effect
Mathematician Journal Prompts How do you determine which type of function best models the data given? Can more than one model represent the given data? How does the median of a data set relate to the mean?
scores.
Groups make presentations and are expected to defend their answers using chart paper, PowerPoint, etc.
Exploration 3: The Better Score Exploration
See HO #7a-e (student copy) and HO #8a-e (teacher key).
Student HO #7a, section 1, requests students to determine answers using standard deviation, 5 number summary or regressions. HO #7b-d, sections 2-4, are additional sections on the z-score, location on the normal curve, and percentiles. HO #7e contains notes for students using the calculator and determining standard deviation. Students may work in pairs on section I.
**Self Assessments and Tutorials See HO #9a-b
The goal is for students to self assess and complete tutorials as needed to ensure mastery of prerequisite skills. Websites for the self assessments and tutorials are on the handout.
May use at the beginning of the “Explore” section or as needed as the class proceeds through Exploration 1-3.
See HO #9c for websites for assistance with Excel.
Why is it important to “standardize” scores or data? Give an example.
EXPLAIN Teacher introduces the main task of the unit and prepares students to in small group independent work...
20 minutes
The teacher introduces the Campaign For Governor:
Commonwealth Of Virginia project (See HO #10a-b) and the rubric (See HO #10c-d).
Student groups representing the candidate and his/her staff members have the task of determining how $35 billion dollars is best allotted in the state so that the most individuals are affected. There are several candidates so the team needs to do research. Presentations will be given to classes of students who will vote on who they believe made the best decisions with budget spending based on the data and presentation.
Expectations: 30 cities
Need to select a minimum of 4 topics to explore: o availability of water,
Determine how to spend $35 billion budget based on research using individual city data and comparison of cities.
Create a campaign timeline stating plan of action and which staff member is responsible for each task. Final Product:
Campaign Speech
5-7 minutes in length.
Present budget using statistics to justify decisions made. Justifications use diagrams and charts/graphs from Excel. Team presents a clear platform with detailed explanations. Question and answer period at the end of the presentation
where the team responds to voter concerns. Campaign Poster
Contain key points
Graphics with explanation
Displayed as a reminder of position the candidate and his/her staff have taken.
ELABORATE The student groups are working independently with teacher consultations. 9 hours
Candidate and his/her staff must turn in a timeline with plan of action and who is responsible for each specific task. The teacher monitors and checks in with each group as per their timeline during each class period.
(Teachers need to decide if all candidate teams are from Virginia, a state of their choice, or narrow the states students may select. Just need to be sure enough data is available for the state chosen.) Teacher may decide to provide specific websites given below or students may be responsible for finding their own.
City population: http://www.citypopulation.de/USA-Virginia.html
Demographics, Jobs, Education, Residential Status: http://profiles.nationalrelocation.com/Virginia/
Demographics, Income, Unemployment, Crimes, Occupations, Climate, Hospitals, Schools, Pollution, Drinking water: : http://www.city-data.com/city/Alexandria-Virginia.html Traffic Data for Virginia: http://www.virginiadot.org/info/ct-TrafficCounts.asp
Detailed Census Information, Race, Ethnicity breakdown, Business: http://quickfacts.census.gov/qfd/states/51000.html Gas Prices:
http://www.gasbuddy.com/gas_prices/Virginia/index.aspx
EVALUATE Working groups submit products or make
presentations 4 hours
Teacher monitors completion and pacing according to the timeline developed by the candidate and his/her staff.
Students give a formal presentation to the voters with a poster to illustrate and justify statements. Voters may be the class or additional classes of students if possible. Teacher may want to select a group of students to represent specific cities. These groups will ask the team questions and show concern for what their city will or will not receive under the proposed budget.
The teacher will use the Campaign for Governor Rubric (See HO #10c-d) to evaluate the students.
Mathematician Journal Prompts What could you have done better in your
Map the Unit
What do students need to know and be able to do to complete the task/project/problem
successfully? How and when will they assess their own necessary knowledge and skills? How will they remediate their own gaps or weaknesses in knowledge and skills? Look at each major task for the unit and analyze the tasks necessary to produce a high-quality product.
Task: An individual running for governor, along with his/her staff, must determine how to distribute government funding that will benefit the most individuals in the state and thereby win their vote.
KNOWLEDGE AND SKILLS NEEDED Assumed
already learned
Students will self-assess
Will be taught during the unit
1. Regression, Curve of Best Fit X X
2. 5 Number Summary X X
3. Standard Deviation, Absolute Mean Deviation
X X
4. z-scores X X
5. Percentiles and the Normal Curve X X
6. Excel – graphics and statistical analysis X X 7.
8.
9.
10.
11.
What project tools will student’s use? Know/need to know lists Daily goal sheet
Mathematician’s Journals Briefs/Memos
Task lists - timeline Planning Calendar
HO #1a
Regression Exploration
I. The table below shows the account balance for several years for money put into a bank account and left alone.
a. Use Excel to create a scatterplot of money vs. years for the data.
b. Using money vs time data calculate and graph the curve of best fit using Excel.
c. Estimate how much money should be in the account in 40 years.
d. Using the curve of best fit determine the amount of money in the account after 40 years and compare to your answer from c.
e. Are there any other models that may represent the data? If so, explain.
II. The data below shows the average growth rates of 12 Weeping Higan cherry trees planted in Washington, DC. At the time of planting each tree was 6 feet tall and 1 year old.
a. Use Excel to create a scatterplot of height vs. age for the data. Years Money
0 30
5 41.1
10 56.31 15 77.16 20 105.71 25 144.83 30 198.43
Age of Tree (in years)
Height (in feet)
1 6
2 9.5
3 13
4 15
5 16.5
6 17.5
7 18.5
8 19
9 19.5
HO #1b
b. Using height vs. age data calculate and graph the curve of best fit using Excel.
c. Estimate how tall a tree should be in 20 years.
d. Using the curve of best fit determine the height of the tree and compare to your answer from c.
e. Are there any other models that may represent the data? If so, explain.
III. The data represents the number of students who carried a virus. On day 1, one student had the virus. On the second day, the initial student shared the virus with one other student. On day three, a total of 4 people now carried the virus. The number of people with the virus each day is shown in the table.
a. Use your graphing calculator to create a scatterplot of number of students vs day for the data.
Day Number of
Students who carry the virus
1 1
2 2
3 4
4 8
5 13
6 20
7 24
8 25
b. Using number of students vs day data calculate and graph the curve of best fit using your graphing calculator.
c. Estimate how many students should carry the virus in 10 days.
d. Using the curve of best fit determine the number of students that carry the virus in 10 days and compare to your answer from c.
HO #1c
IV. The intensity of sunlight decreases as you descend into the ocean. The data in the table shows the percentage of sunlight found below sea level at various depths.
a. Use Excel to create a scatterplot of sunlight vs. feet for the data
Feet (Below Sea Level)
Percent of Sunlight
20 12
40 9.36
60 7.2
80 2.6
100 1.5
110 1.2
150 .8
200 .12
250 .035
b. Using sunlight vs. feet data calculate and graph the curve of best fit using Excel.
c. Estimate the percent of sunlight you should see when 300 feet below sea level.
d. Using the curve of best fit determine the amount of sunlight when 300 feet below sea level and compare to your answer from c.
HO #2a
Regression Exploration
I. The table below shows the account balance for several years for money put into a bank account and left alone.
a. Use Excel to create a scatterplot of money vs. years for the data.
b. Using money vs. time data calculate and graph the curve of best fit using Excel. y = 29.999e0.063x
c. Estimate how much money should be in the account in 40 years. 350 < x < 400
d. Using the curve of best fit determine the amount of money in the account after 40 years and compare to your answer from c.
$372.85
Years Money
0 30
5 41.1
HO #2b
e. Are there any other models that may represent the data? If so, explain. Possibly quadratic regression since the model is curved.
II. The data below shows the average growth rates of 12 Weeping Higan cherry trees planted in Washington, DC. At the time of planting each tree was 6 feet tall and 1 year old.
a. Use Excel to create a scatterplot of height vs. age for the data.
b. Using height vs age data calculate and graph the curve of best fit using Excel. y = 6.1082ln(x) + 6.0993
Age of Tree (in years)
Height (in feet)
1 6
2 9.5
3 13
4 15
5 16.5
6 17.5
7 18.5
8 19
9 19.5
10 19.7
HO #2c
c. Estimate how tall a tree should be in 20 years. ~20 feet
d. Using the curve of best fit determine the height of the tree and compare to your answer from c.
24.4 feet
e. Are there any other models that may represent the data? If so, explain. Possibly quadratic regression since the model is curved.
III. The data represents the number of students who carried a virus. On day 1, one student had the virus. On the second day, the initial student shared the virus with one other student. On day three, a total of 4 people now carried the virus. The number of people with the virus each day is shown in the table.
a. Use your graphing calculator to create a scatterplot of number of students vs day for the data.
Day Number of
Students who carry the virus
1 1
2 2
3 4
4 8
5 13
6 20
7 24
8 25
b. Using number of students vs day data calculate and graph the curve of best fit using your graphing calculator.
c. Estimate how many students should carry the virus in 10 days.
d. Using the curve of best fit determine the number of students that carry the virus in 10 days and compare to your answer from c.
e. Are there any other models that may represent the data? If so, explain.
This is a logistic function which is not prerequisite knowledge. Let students experiment with what they believe would be the best way to handle the representation.
HO #2d
IV. The intensity of sunlight decreases as you descend into the ocean. The data in the table shows the percentage of sunlight found below sea level at various depths.
a. Use Excel to create a scatterplot of sunlight vs. feet for the data
Feet (Below Sea Level)
Percent of Sunlight
20 12
40 9.36
60 7.2
80 2.6
100 1.5
110 1.2
150 .8
200 .12
HO #2e
b. Using sunlight vs. feet data calculate and graph the curve of best fit using Excel. y = 24.343e-0.026x
c. Estimate the percent of sunlight you should see when 300 feet below sea level. ~0% sunlight
d. Using the curve of best fit determine the amount of sunlight when 300 feet below sea level and compare to your answer from c.
0.01%
HO #3
Using Excel in the NFL – A Statistical Exploration
The National Football League is comprised of 32 teams. Your group must choose 4 teams to analyze. Offensive scores for each team’s 16 games during the 2010 season can be found in the file NFL2010.xls.
Record the teams selected and their scores in the table below.
TEAM/WEEK 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Using the data for the 4 teams selected, complete the following assignment:
Create an Excel spreadsheet. The spreadsheet must contain information for each team such as a count of the each team’s data values, the mean points scored, the standard deviation of points scored, and the five-number summary.
Create a box-and-whisker plot for each team using Excel.
Which team has more consistent scores? Why? Justify answers using data. Which team’s scores are most inconsistent? Why? Justify answers using data. If you wanted to become an owner of one of the teams, which team would it be and
why? Justify answers using data.
How does the mean compare to the median? Select one of the four teams.
o The team acquired a new offensive player through free agency. The new player helped the team improve their lowest score by 10 points. Write a conjecture about what will happen to the five-number summary and box-and-whisker plot.
o The team’s best player was injured during the season decreasing the team’s highest score by 10 points. Write a conjecture about what will happen to the five-number summary and box-and-whisker plot.
HO #4a NFL DATA TEAM WK 1 WK 2 WK 3 WK 4 WK 5 WK 6 WK 7 WK 8 WK 9 WK 10 WK 11 WK 12 WK 13 WK 14 WK 15 WK 16 WK 17
Atlanta Falcons 9 41 27 16 20 17 39 Bye 27 26 34 20 28 31 34 14 31
Baltimore Ravens 10 10 27 17 31 20 37 Bye 26 21 37 17 10 34 30 20 13
Buffalo Bills 10 7 30 14 26 Bye 34 10 19 14 49 16 14 13 17 3 7
Carolina Panthers 18 7 7 14 6 Bye 23 10 3 16 13 23 14 10 19 3 10
Chicago Bears 19 27 20 3 23 20 17 Bye 22 27 16 31 24 7 40 38 3
Cincinnati Bengals 24 15 20 20 21 Bye 32 14 21 17 31 10 30 7 19 34 7
Cleveland Browns 14 14 17 23 10 10 30 Bye 34 20 20 24 13 6 17 10 9
Dallas Cowboys 7 20 27 Bye 27 21 35 17 7 33 35 27 38 27 33 26 14
Denver Broncos 17 31 13 26 17 20 14 16 Bye 49 14 33 6 13 23 24 28
Detroit Lions 14 32 10 26 44 20 Bye 37 20 12 19 24 20 7 23 34 20
Green Bay Packers 27 34 17 28 13 20 28 9 45 Bye 31 17 34 3 27 45 10
Houston Texans 34 30 13 31 10 35 Bye 17 23 24 27 20 24 28 17 23 34
Indianapolis Colts 24 38 27 28 19 27 Bye 30 24 23 28 14 35 30 34 31 23
Jacksonville Jaguars 24 13 3 31 36 3 20 35 Bye 31 24 20 17 38 24 17 17
Kansas City Chiefs 21 16 31 Bye 9 31 42 13 20 29 31 42 10 0 27 34 10
Los Angeles Rams 13 14 30 20 6 20 17 20 Bye 20 17 36 19 13 13 25 6
Miami Dolphins 15 14 23 14 Bye 23 22 22 10 29 0 33 10 10 14 27 7
Minnesota Vikings 9 10 24 Bye 20 24 24 18 27 13 3 17 38 3 14 24 13
New England Patriots 38 14 38 41 Bye 23 23 28 14 39 31 45 35 36 31 24 38
New Orleans Saints 14 25 24 16 20 31 17 20 34 Bye 34 30 34 31 24 17 13
New York Giants 31 14 10 17 34 28 41 Bye 41 20 17 24 31 21 31 17 17
New York Jets 9 28 31 38 29 24 Bye 0 23 26 30 26 3 6 22 34 38
Oakland Raiders 13 16 23 24 35 9 59 33 23 Bye 3 17 28 31 39 26 31
HO #4b
Pittsburgh Steelers 15 19 38 14 Bye 28 23 10 27 26 35 19 13 23 17 27 41
San Diego Chargers 14 38 20 41 27 17 20 33 29 Bye 35 36 13 31 34 20 33
San Francisco 49ers 6 22 10 14 24 17 20 24 Bye 23 0 27 16 40 7 17 38
Seattle Seahawks 31 14 27 3 Bye 23 22 3 7 36 19 24 31 21 18 15 16
St. Louis Cardinals 17 7 24 10 30 Bye 10 35 24 18 13 6 6 43 12 27 7
Tampa Bay Buccaneers 17 20 13 Bye 24 6 18 38 21 31 21 10 24 17 20 38 23
Tennessee Titans 38 11 29 20 34 30 37 25 Bye 17 16 0 6 28 31 14 20
HO #5a
Using Excel in the NFL – A Statistical Exploration Teacher Notes
The National Football League is comprised of 32 teams. Your group must choose 4 teams to analyze. Offensive scores for each team’s 16 games during the 2010 season can be found in the file NFL2010.xls.
You can choose any number of teams. You may choose to have students examine an entire conference such as the NFC East. Data can also be changed so that this activity is applicable for any year.
Record the teams selected and their scores in the table below.
TEAM/WEEK 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Using the data for the 4 teams selected, complete the following assignment:
Create an Excel spreadsheet. The spreadsheet must contain information for each team such as a count of the each team’s data values, the mean points scored, the standard deviation of points scored, and the five-number summary.
Formulas for one team are given in the Excel answer file. The process needs to be repeated for every team. In addition, the answer file has team data set up in rows in the spreadsheet which does NOT allow you to copy and paste the formulas. In order to copy formulas, the data must be set up in columns. If you choose to have students set team data up in columns, please note that the formulas will change to reflect a
summation of the column instead of the row.
HO #5b
Create a box-and-whisker plot for each team using Excel.
Step-by-step instructions for creating box-and-whisker plots can be found at
http://peltiertech.com/WordPress/excel-box-and-whisker-diagrams-box-plots/ Which team has more consistent scores? Why? Justify answers using data. Which team’s scores are most inconsistent? Why? Justify answers using data. If you wanted to become an owner of one of the teams, which team would it be and
why? Justify answers using data.
How does the mean compare to the median?
Answers will vary depending on teams selected. However, students should realize smaller data spreads mean teams are more consistent with points scored per game. Int addition, a higher mean indicates more points scored per game on average.
Select one of the four teams.
o The team acquired a new offensive player through free agency. The new player helped the team improve their lowest score by 10 points. Write a conjecture about what will happen to the five-number summary and box-and-whisker plot.
o The team’s best player was injured during the season decreasing the team’s highest score by 10 points. Write a conjecture about what will happen to the five-number summary and box-and-whisker plot.
o Justify conjectures by creating new five-number summaries and box-and-whisker plots.
HO #6a
EXCEL ANSWERS AND NOTES
Ravens Redskins Steelers Packers
Count 16 16 16 16
Mean 22.5 18.875 23.4375 24.25
SD 9.479803 6.344289 9.084556 12.32071
Min 10 7 10 3
Q1 16 15.5 16.5 16
Median 20.5 17 23 27
Q3 30.25 24.25 27.25 31.75
Max 37 30 41 45
Bottom 16 15.5 16.5 16
2Q Box 4.5 1.5 6.5 11
3Q Box 9.75 7.25 4.25 4.75
Whisker- 6 8.5 6.5 13
Whisker+ 6.75 5.75 13.75 13.25
Offset 0.5 1.5 2.5 3.5
Column B Formulas "=COUNT(B20:R20)" "=AVERAGE(B20:R20)" "=STDEV(B20:R20)" "=MIN(B20:R20)" "=QUARTILE(B20:R20,1)" "=MEDIAN(B20:R20)" "=QUARTILE(B20:R20,3)" "=MAX(B20:R20)" "=B6" "=B7-B6" "=B8-B7" "=B6-B5" "=B9-B8"
TEAM WK 1 WK 2 WK 3 WK 4 WK 5 WK 6 WK 7 WK 8 WK 9
WK 10 WK 11 WK 12 WK 13 WK 14 WK 15 WK 16 WK 17
Baltimore Ravens 10 10 27 17 31 20 37 26 21 37 17 10 34 30 20 13
Washington
Redskins 13 27 16 17 16 24 17 25 28 19 13 7 16 30 20 14
Pittsburgh
Steelers 15 19 38 14 28 23 10 27 26 35 19 13 23 17 27 41
Green Bay
HO #6b
HO #7a
The Better Score Exploration
I.
Using the internet (or other resource), find the mean height and standard deviation of individuals (male, female, or combined) in a country around the world.
Anyone that is more than two standard deviations from the mean is considered unusual, and 3 standard deviations are extremely unusual. Use the normal table, calculator, or computer program along with the information about average ______ heights to find the following:
a. What heights are within 1 standard deviation? _______to _______
b. What heights are within 2 standard deviations? _______to _______
Now, select your height, a height of a classmate, or the mean height of the entire class.
c. Determine the z-score of your selection.
d. The selected height is taller than ______% of the population
HO #7b
II. Calculating z-scores
Calculating z-scores is critical in statistical studies. The z-score tells us how many standard deviations from the mean an observation falls. Observations larger than the mean have positive z-scores; observations smaller than the mean have negative z-scores.
To ensure mastery of calculating z-scores, complete the following situations.
(1) A certain brand of automobile tire has a mean life span of 35,000 miles and a standard deviation of 2250 miles. If the life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 31,000 miles. Find the z-scores that correspond with each of these mileages. Would the life spans of any of the tires be considered unusual? Explain your response.
a) 34,000 = b) 37,000 =
c) 31,000 =
HO #7c
(3) On a statistic test the class mean was 63 and the standard deviation was 7 and for the biology
test the mean was 23 and has a standard deviation of 3.9.
Find the z-score for each grade. And determine on which test the student had a better score.
i. A student received a 73 on the statistics test and a 26 on the biology test.
ii. A student gets a 60 on the statistics tests and a 20 on the biology test.
iii. A student gets a 78 on the statistics test and a 29 on the biology test.
iv. A student gets a 63 on the statistics test and a 23 on the biology test.
(4) A pharmaceutical company wants to test a new cholesterol drug. The average cholesterol of the target population is 200 mg and they have a standard deviation of 25 mg. The company wished to test a sample of people who fall between 1.5 and 3 z-scores above the mean. Into what range must a candidate’s cholesterol level be in order for the candidate to be included in the study? Explain your response.
HO #7d
III. Measuring location on the Normal Distribution Curve
A. There are two major tests of readiness for college, the ACT and the SAT.
B. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores in recent years has been roughly normal with a mean of 20.9 and a standard deviation of 4.8.
C. SAT scores (prior to 2005) were reported on a scale from 400 to 1600. SAT scores have been roughly normal with a mean of 1026 and a standard deviation of 209.
(6) Jose scores 1287 on the SAT. Assuming that both tests measure the same thing, what score on the ACT is equivalent to Jose’s score? Explain your logic.
(7) Which score, SAT = 1444 or ACT = 30, shows the greatest distance from the mean, and therefore, the better score? Show your calculations and explain your response.
For the following problems, refer to the Algebra II SOL formula sheet for the Standard Normal Distribution charts.
(8) Someone gets an ACT score of 16.
a) Calculate the z-score. ____________
b) Determine the percent of people who scored lower? _____________
c) Determine the percent of people who scored higher? _____________
(9) When a college requires an SAT score of 1250 for admission, then only the top
HO #7e
IV. Calculating Percentiles and Quartiles
(10) Reports on a student’s ACT and SAT usually give the percentile as well as the actual score. Tonya scores 1318 on the SAT. What is her percentile? Show your method.
HO #8a
The Better Score Exploration
I.
Using the internet (or other resource), find the mean height and standard deviation of individuals (male, female, or combined) in a country around the world.
Anyone that is more than two standard deviations from the mean is considered unusual, and 3 standard deviations are extremely unusual. Use the normal table, calculator, or computer program along with the information about average ______ heights to find the following:
a. What heights are within 1 standard deviation? _______to _______
b. What heights are within 2 standard deviations? _______to _______
Now, select your height, a height of a classmate, or the mean height of the entire class.
c. Determine the z-score of your selection.
d. The selected height is taller than ______% of the population
HO #8b
II. Calculating z-scores
Calculating z-scores is critical in statistical studies. The z-score tells us how many standard deviations from the mean an observation falls. Observations larger than the mean have positive z-scores; observations smaller than the mean have negative z-scores.
To ensure mastery of calculating z-scores, complete the following situations.
(1) A certain brand of automobile tire has a mean life span of 35,000 miles and a standard deviation of 2250 miles. If the life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 31,000 miles. Find the z-scores that correspond with each of these mileages. Would the life spans of any of the tires be considered unusual? Explain your reasoning.
a) 34,000 = b) 37,000 =
c) 31,000 =
(2) The average for the statistics exam was 75 and the standard deviation was 8. André was told by the instructor that he scored 1.5 standard deviations below the mean. What was André’s exam score and what can you conclude? Explain your reasoning.
HO #8c
(3) On a statistic test the class mean was 63 and the standard deviation was 7 and for the biology test the mean was 23 and has a standard deviation of 3.9.
Find the z-score for each score. And determine on which test the student had a better score.
i. A student received a 73 on the statistics test and a 26 on the biology test.
Statistics test is better.
ii. A student gets a 60 on the statistics tests and a 20 on the biology test.
Statistics test is better.
iii. A student gets a 78 on the statistics test and a 29 on the biology test.
Statistics test is better.
iv. A student gets a 63 on the statistics test and a 23 on the biology test.
Both are at the mean – equally good.
(4) A pharmaceutical company wants to test a new cholesterol drug. The average cholesterol of the target population is 200 mg and they have a standard deviation of 25 mg. The company wished to test a sample of people who fall between 1.5 and 3 z-scores above the mean. Into what range must a candidate’s cholesterol level be in order for the candidate to be included in the study?
HO #8d
(5) A manufacturer of bolts has a quality control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. The quality control engineer knows that the bolts coming off the assembly line have a mean length of 8 cm with a standard deviation of 0.05 cm. For what length will a bolt be destroyed?
Any bolt less than 7.9 cm or more than 8.1 cm is destroyed.
III. Measuring location on the Normal Distribution Curve
A. There are two major tests of readiness for college, the ACT and the SAT.
B. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores in recent years has been roughly normal with a mean of 20.9 and a standard deviation of 4.8.
C. SAT scores (prior to 2005) were reported on a scale from 400 to 1600. SAT scores have been roughly normal with a mean of 1026 and a standard deviation of 209.
(6) Jose scores 1287 on the SAT. Assuming that both tests measure the same thing, what score on the ACT is equivalent to Jose’s score? Explain your logic.
(7) Which score, SAT = 1444 or ACT = 30, shows the greatest distance from the mean, and therefore, the better score? Show your calculations.
HO #8e
For the following problems, refer to the Algebra II SOL formula sheet for the Standard Normal Distribution charts.
TEACHER NOTE: attached are the steps to find the area under the curve using the TI-84 and a YouTube video link: http://www.youtube.com/watch?v=ee5vfSOSG6E
(8) Someone gets an ACT score of 16.
a. Calculate the z-score.
b. Determine the percent of people who scored lower? 15.4%
c. Determine the percent of people who scored higher? 84.61%
(9) When a college requires an SAT score of 1250 for admission, then only the top
14.23% of test takers will be considered for admission.
IV. Calculating Percentiles and Quartiles
(10) Reports on a student’s ACT and SAT usually give the percentile as well as the actual score. Tonya scores 1318 on the SAT. What is her percentile? Show your method.
Tonya’s SAT is in the 92nd
percentile.
(11) The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75. What are the quartiles of the distribution of ACT scores? Show your method.
HO #9a
Self Assessments and Tutorials
Khan Academy www.khanacademy.org
Statistics: The Average
http://www.khanacademy.org/video/statistics--the-average?playlist=Statistics Statistics: Sample vs. Population Mean
http://www.khanacademy.org/video/statistics--sample-vs--population-mean?playlist=Statistics Statistics: Variance of a Population
http://www.khanacademy.org/video/statistics--variance-of-a-population?playlist=Statistics Statistics: Standard Deviation
http://www.khanacademy.org/video/statistics--standard-deviation?playlist=Statistics
Normal Distribution Excel Exercise
http://www.khanacademy.org/video/normal-distribution-excel-exercise?playlist=Statistics Introduction to the Normal Distribution
http://www.khanacademy.org/video/introduction-to-the-normal-distribution?playlist=Statistics Normal Distribution Problem – Qualitative sense
http://www.khanacademy.org/video/ck12-org-normal-distribution-problems--qualitative-sense-of-normal-distributions?playlist=Statistics
Normal Distribution Problem – z-score
http://www.khanacademy.org/video/ck12-org-normal-distribution-problems--z-score?playlist=Statistics
Normal Distribution Problem – Empirical Rule
http://www.khanacademy.org/video/ck12-org-normal-distribution-problems--empirical-rule?playlist=Statistics
Standard Normal Distribution and the Empirical Rule
http://www.khanacademy.org/video/ck12-org-exercise--standard-normal-distribution-and-the-empirical-rule?playlist=Statistics
More Empirical Rule and z-score
http://www.khanacademy.org/video/ck12-org--more-empirical-rule-and-z-score-practice?playlist=Statistics
Algebra II: Mean and Standard Deviation
HO #9b
Mean, Median, and Mode
http://www.khanacademy.org/video/mean-median-and-mode?playlist=Developmental+Math+2 Average or Central Tendency: Arithmetic Mean, Median, Mode
http://www.khanacademy.org/video/average-or-central-tendency--arithmetic-mean--median--and-mode?playlist=ck12.org+Algebra+1+Examples
Range, Variance and Standard Deviation as Measures of Dispersion
http://www.khanacademy.org/video/range--variance-and-standard-deviation-as-measures-of-dispersion?playlist=ck12.org+Algebra+1+Examples
Measures of Center
http://www.khanacademy.org/video/measures-of-center?playlist=Developmental+Math+2
Box-and-Whisker Plot
http://www.khanacademy.org/video/box-and-whisker-plot?playlist=ck12.org+Algebra+1+Examples
Box-and-whisker Plot
http://www.khanacademy.org/video/box-and-whisker-plots?playlist=Developmental+Math+2 Reading Box-and-Whisker Plots
http://www.khanacademy.org/video/reading-box-and-whisker-plots?playlist=Developmental+Math+2
Regression Line Example
http://www.khanacademy.org/video/regression-line-example?playlist=Statistics Second Regression Example
http://www.khanacademy.org/video/second-regression-example?playlist=Statistics
Regents Exam Prep Center www.regentsprep.org
Central Tendency: Mean, Median, and Mode
http://www.regentsprep.org/Regents/math/ALGEBRA/AD2/indexAD2.htm Displaying Data
http://www.regentsprep.org/Regents/math/ALGEBRA/AD3/indexAD3.htm Scatter Plots, Correlation, Line of Best Fit, Prediction
http://www.regentsprep.org/Regents/math/ALGEBRA/AD4/indexAD4.htm Percentiles and More Quartiles
HO #9c
Excel Assistance
Basic Excel Information
HO #10a
CAMPAIGN FOR GOVERNOR: COMMONWEALTH OF VIRGINIA
In today’s economy voters are constantly concerned with how government funds will be budgeted. Your task, as a team of the Candidate and staff members, will be to take a $35 trillion budget and determine how it should be spent based off of your state’s concerns and needs.
Your team will be running against other candidate teams in our class. On Election Day, voters (your classmates) will be afforded the opportunity to vote for the candidate team they believe made the best decisions with budget spending based off of the mathematics researched and presented.
To guide you with the project expectations a rubric is attached. You will have ____ days to prepare your campaign presentation for Election Day on ____________________.
Project Expectations:
Research data on a minimum of 30 cities within the Commonwealth of Virginia. Locate statistics on availability of water, good sanitation, transportation, public safety, education, employment, poverty, healthcare, etc. Population is to be recorded for each city. A minimum of 4 areas of concern must be researched and addressed in the campaign.
Use Excel as a tool for finding statistical summaries, regressions, and charts to assist with justifications in how your budget is spent.
Determine how the team will spend the $35 trillion budget based of the research and
calculations in hopes of gaining votes from the community. Decisions will be made based on comparisons between the cities as well as the needs of the state as a whole.
Final Products:
Candidate Speech/Presentation
o On Election Day each candidate, with the assistance of their staff members, will present their budget and how decisions are made about how money will be spent.
o The presentation will include diagrams, charts/graphs (Excel), and mathematical justifications.
o The team will have a clear platform and detailed explanations for their budget.
o At the end of the presentation the team will answer questions from the voters about the choices made concerning their budget.
o The presentation will be 5-7 minutes. Campaign Poster
o Create a campaign poster that coincides with the team’s speech/presentation. Posters will be displayed at the voting station as a reminder to voters of the mathematics used to create their budget.
HO #10b
Teacher Notes
It is up to you if you have every group research the same state or have a bigger ballot and have 2-3 groups researching the same state. We were concerned if the students would be able to find data for specific cites (and enough cities) to get good data that they could apply statistical knowledge to. We did some research and found that the Commonwealth of Virginia had plenty of research to be found for specific cities.
Resources (to assist with getting research started): It was pretty easy to find just by using Google. It is up to you if you divulge this information to your students; maybe just inform them if they are struggling with finding data.
City Population Information: http://www.citypopulation.de/USA-Virginia.html
Two Suggested Sites: Pick a city and get plenty of information and data about that particular city.
Demographics/Jobs/Education/Residential Status: http://profiles.nationalrelocation.com/Virginia/
Demographics/Income/Unemployment/Crimes/Occupations/Climate/Hospitals/Schools/Polut ion/Drinking water: http://www.city-data.com/city/Alexandria-Virginia.html
Other Helpful Sites:
Traffic Data for Virginia: http://www.virginiadot.org/info/ct-TrafficCounts.asp Detailed Census Info/Race/Ethnicity Breakdown/Business:
http://quickfacts.census.gov/qfd/states/51000.html
HO #10c
Campaign for Governor Project Rubric
Categories 4 3 2 1
Understanding Campaign Poster and Presentation shows a deep understanding of the mathematics needed to obtain their conclusion.
Campaign Poster and Presentation are complete but understanding needed to obtain their conclusion is missing or lacking in explanation.
Campaign Poster and Presentation are attempted. Some of the mathematics applied is the correct concept but lacking
completion.
Campaign Poster and Presentation are not completed or not meeting the expectation.
Reasoning Justifications of their budget are appropriate and mathematical sound.
Some of the justifications of their budget are appropriate and mathematical sound.
Justification of the budget is given but lacking in
mathematical understanding.
No justification of the budget is given for the
mathematics.
Communication All necessary concepts are presented in the speech as well as the presentation
All necessary concepts are presented in the speech but the presentation was missing explanation. Speech and presentation are missing concepts and explanations. Speech OR presentation is missing.
Presentation of the budget to the voters in an appropriate manner
(professionalism).
Presentation of the budget to the voters was done but some may be in an unprofessional manner.
Presentation of the budget to the voters was unprofessional.
No presentation of the budget to the voters given.
Connections Connections were made between the mathematics and the problem to reach a conclusion.
Connections between the
mathematics and the problem were not clear in all explanations.
HO #10d
Representations All mathematical representations and symbols in the presentation and campaign poster were complete and correct.
Some of the mathematical representations and symbols in the presentation and campaign poster were complete but incorrect.
Mathematical representations in the presentation and the campaign poster were complete and incorrect. Mathematical representations in the presentation and campaign poster were incomplete and incorrect. Mathematical Skills and Procedures Execution of algorithms and computations are complete and accurate. Execution of algorithms is complete with minor errors in computations. Execution of algorithms and computations contain major errors.
No attempt of algorithms and computations are attempted.
Technology All use of PowerPoint and Excel was complete and accurate.
Some of the use of PowerPoint and Excel was complete and accurate.
Use of PowerPoint and Excel is incomplete and inaccurate.
No use of PowerPoint or Excel was demonstrated. Collaboration All team members
participated equally in the project.
Team members need encouragement to participate equally in the project.
Team members did not equally share the work of the project.
One or two team members
