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Data Analysis

 

Objectives:  Students will collect and analyze data and create a model to solve a problem.

 

                    Download as Microsoft Word Documents or Inspiration File:

Instructional Plan

Unit Outline – requires Inspiration

Data Sheet

Frayer Model

Graphing Instruction

Information Worksheet

Information Worksheet Answer Key

M cubed Worksheet

Measurement Instructions

MMM

Radius Bone Collection Data

Rubric

 

Instructional Plan Template

Mathematics Governor’s Institute 2005

 

 

Names of group members: Jennifer Heidlebaugh, Lucille Pritchard, Doug Murdoch

 

Topic/Theme: Data Analysis

 

Level: 9th grade Algebra I

 

Time Element: 2 days (45 minutes) – 1 block

 

NCTM Standards Addressed:

·        Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

·        Select and use appropriate statistical methods to analyze data

·        Develop and evaluate inferences and predictions that are based on data

·        Understand and apply basic concepts of probability

 

PA Math Standards Addressed:

·        Design and conduct an experiment using random sampling

·        Use appropriate technology to organize and analyze data

·        Determine the regression equation of best fit (e.g., linear, quadratic, exponential).

·        Make predictions using regression and estimation using technology to verify them.

 

 

Math Assessment Anchors Addressed: 

M11.E.1- Formulate or answer questions that can be addressed with data and/or organize, display, interpret or analyze data.

M11.E.2- Select and/or use appropriate statistical methods to analyze data.

M11.E.3- Understand and/or apply basic concepts of probability or outcomes.

M11.E.4- Develop and/or evaluate inferences and predictions or draw conclusions based on data or data displays.

 

Reading Assessment Anchors Addressed:

R.11.A.2 - Demonstrate the ability to understand and interpret fiction text, including short story, appropriate to grade level.

Objectives:  Students will collect and analyze data and create a model to solve a problem.

 

Instructional Strategies and Plan (include strategies used to help different types of learners, i.e. auditory, visual, etc):

1.      Pre-teach vocabulary (Frayer Model)

2.      Collect data

3.      Enter data into calculator

4.      Generalize results both graphically and algebraically

5.      Solve an open ended problem to solve a murder mystery

 

Materials/Resources:

            Overhead

Calculator TI 83, TI 84

            Measuring tape

            Notebook

            Pencil

            Data Sheet

            Student data

 

Interdisciplinary Connections:

·         Reading – CSI story that brings in forensic science and mathematics

 

 

·         Technology-Graphing calculator TI 83, TI 84

 

 

·         Other- Real world applications, science and art

 

Assessment Strategies:

·         Formative Evaluation (checking student understanding during the lesson):

Teacher observes the student measurement and recording of data

      Teacher asks questions to broaden the understanding of the concept

 

·         Summative Evaluation (How will it be determined that the objectives were achieved?):

Homework assignments will be reviewed

Corrections and questions answered

Open ended problem solved and explained

Quiz

 

Correctives/Remediation:

Calculator directions will be repeated if necessary with different data

 

 

Extensions/Enrichment:

            Students can investigate forensic science

            Students can investigate other body measurements for predicting height.

 

 

 

             Definitions                               Facts/Characteristics

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                                              Main Idea

 

 

 

 


Examples                                        Nonexamples

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DATA SHEET

 

Initials

Height

Radius

Shoe Size

Index finger

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Graphing and Lines of Best Fit

 

                The following steps can be used to quantify the data collected from the measurements collected by your students.

 

  1. Hit the STAT key on the calculator.
  2. Select EDIT.  If there is data in the lists, move the cursor up and highlight the list name, then hit CLEAR then ENTER to erase the data in the lists.
  3. Enter the data in the lists.  Enter the data in the lists in the same order it is in on the data sheet.
  4. When you have finished entering the data, calculate the lines of best fit for the following sets of data using the instructions below.  The following instructions are specific to the first set of data. 

Ř       Height versus Shoe Size

Ř       Height versus Index Finger Length

Ř       Height versus Radius Length

Ř       Index Finger versus Radius Length

Your calculator screen should look similar to the screen shown below.

  

 

Now that the data has been entered, we must calculate the line of best fit.  For this line, we will make a plot and graph the line inside of the plot.  To find the information for height versus shoe size, follow the following steps:

  1. Hit the STAT button
  2. Select CALC
  3. Select choice number 4, LinReg(ax+b).  Your screen will look like the screen at the top of the next page.

 

  1. After selecting the linear regression line, we must specify which lists to use for our X and Y values, and where we would like to paste the equation for the line of best fit after we calculate it.  Height, in list L1 will be our X value and Shoe Size, in list L2 will be our Y value.  We will paste the equation into the first slot on our Y= editor.  Hit the following sequence of keys:  2ND, 1, (the comma key), 2ND, 2, (the comma key), VARS, select Y-VARS, ENTER, ENTER.  Your Screen will look as follows:

 

  1. Now hit ENTER your screen will show the following display.  Your numbers will be substantially different, since your data set is different.  Do not worry about the r and r2 squared values since will not use them at this time.

 

  1. This display shows us a line with a slope of .1384415489 and a y intercept of .8235579387.  This line has been added to our editor, and will be displayed with a dot plot of our data set.  To create a scatter plot hit the following keys 2ND, Y=.  Your screen will look like

  1. Once we have entered the STAT PLOT menu we must set up our plots.  Select plot 1.  Turn the plot on, and select the appropriate graph type, and be sure to select the proper lists for our X and Y values.  Your screen will look as follows:

 

  1. We must next set up the proper window to display our graph.  Your minimum X and Y values must be smaller than the smallest X and Y values you have collected.  Your maximum X and Y values should be greater than the largest X and Y values you have collected.  Hit the WINDOW key, and change the window settings as necessary.  My window was as follows:

  1. At this point we are ready to display our graph by hitting the graph key

 

 

 The procedure to find the other lines of best fit is the same, only the lists used will change.

 

 

 Information Worksheet

 

  1. Record the equation for the line of best fit for Height versus shoe size below.

 

 

 

  1. What does a represent?  What does b represent?

 

 

 

  1. Record the equation for the line of best fit for Height versus Index Finger Length below.

 

 

 

  1. Record the equation for the line of best fit for Height versus Radius length below.

 

 

 

  1. Record the equation for the line of best fit for Index finger length versus radius length below.

 

 

 

  1. Find the height of a person with a 3 inch index finger.

 

 

 

  1. Find the shoe size of a person who is 73 inches tall.

 

 

 

 

  1. Find the height of a person whose radius is 12.75 inches long.

 

 

  1. Find the index finger length of a person who is 67 inches tall.

 

 

 

  1. If a person wears a size 11 shoe, how tall is he?

 

 

 

  1. Reread the murder mystery.  Can we help Dr. Schroeder solve this case? How?

 

 

 

 

Information Worksheet

 

  1. Record the equation for the line of best fit for Height versus shoe size below.

Not available (will vary with class data)

 

  1. What does a represent?  What does b represent?

a = will represent slope

b = will represent the y-intercept

 

  1. Record the equation for the line of best fit for Height versus Index Finger Length below.

Not available (will vary with class data)

 

  1. Record the equation for the line of best fit for Height versus Radius length below.

 (will vary with class data)

 

  1. Record the equation for the line of best fit for Index finger length versus radius length below.

Not available (will vary with class data)

 

  1. Find the height of a person with a 3 inch index finger.

Not available (will vary with class data)

 

  1. Find the shoe size of a person who is 73 inches tall.

Not available (will vary with class data)

 

  1. Find the height of a person whose radius is 12.75 inches long.

                 Answer is He is about 84.25” tall

 

 

 

  1. Find the index finger length of a person who is 67 inches tall.

Not available (will vary with class data)

 

  1. If a person wears a size 11 shoe, how tall is he?

Not available (will vary with class data)

 

  1. Reread the murder mystery.  Can we help Dr. Schroeder solve this case? How?

Start discussion with the class about how we can make predictions using the lines we created with the data we collected.

***** Introduces the open-ended question*****

 

 

Measurement Instructions

 

Use the following guidelines to collect your measurements.

  1. Write down your height in feet and inches.  Convert the measurement to all inches.  Be sure to convert any fractions to a decimal.
  2. Measure the length of you index finger from where it meets your hand next to your middle finger, to the tip of your index finger.  Round your measurement to the nearest 1/8th inch.  Convert this measurement to a decimal. 
  3. Write down your shoe size.  Male and female shoe sizes are measured differently.  We must adjust the shoe sizes of the females to compensate for this difference.  Therefore, if you are a female, add 1.5 sizes to your shoe size to make it a male shoe size. 
  4. Measure the radius bone of your right arm.  The radius is the bone on the outside of your arm that runs from the bump on the outside of the wrist to the point on your elbow.  Round your measurement to the nearest 1/8th inch.  Convert this measurement to a decimal.

 

 

M3 Project

 

          Project Question: How can we help Dr. Schroeder?

 

 

 

 

Can we use the equations we have calculated to analyze the body parts and shoes found on The Campus of Millersville University?  Determine which measurements can be used to possibly identify the victims of our gruesome discovery?  Determine the possible identity of the remains based on your investigation.  Support your conclusion and defend your position. 

 

 

MILLERSVILLE MURDER MYSTERY!!!

 

OR M3

 

 

In a bizarre series of events, construction workers at Millersville University uncovered several skeletal remains. Following the demolition of some walls in McComsey, Mercer, Mifflin, Monroe and Montgomery Houses, on campus, the workers were shocked to find what CSI Chief Bernie Schroeder determined were human remains.

 

When asked by this reporter, Dr. Schroeder said, “ We are considering all of these locations as crime scenes”. When asked further questions, Dr. Schroeder explained that a radius bone, which is the bone that runs from the elbow to the wrist, was found at the Montgomery House. A small shoe was found at McComsey and a mummified index finger was found at Mercer. It is unclear, at this time, if all the remains are from one body or many. Dr. Schroeder has determined the age of the radius bone to be approximately 60 years old.

 

Several local disappearances were reported in 1945, according to Police Chief Monaghan. Dr. Schroeder is now trying to determine how the human remains could be identified since DNA was not collected 60 years ago.

Among the missing was the Murphy family, which consisted of Mary and Mike, the parents, along with 10 year old Matthew and 4 year old Megan. Also missing that winter was Mighty Mark Morgan, the star basketball player for Millersville University who disappeared after practice one night.

Also reported as missing, was pretty coed Margaret Murdock, who was reported missing by her family in March.

 

Dr. Schroeder indicated that Mathematics would play a large part in solving this 60 year old case.

 

 

DATA SHEET

 

Initials

Height

Shoe Size

Index finger

Radius

1

65

 

 

10

2

68

 

 

9.75

3

64

 

 

10.375

4

66

 

 

9

5

71

 

 

10.25

6

70

 

 

10.5

7

61

 

 

9.25

8

67

 

 

10.75

9

60

 

 

9

10

67

 

 

10.25

11

62

 

 

8.75

12

71

 

 

10

13

62

 

 

9.5

14

66

 

 

9.5

15

73

 

 

11.875

16

62

 

 

9.875

17

68

 

 

10.125

18

62

 

 

9.5

19

69

 

 

10.625

20

62

 

 

9..625

21

70

 

 

10.5

22

65

 

 

10

23

64

 

 

9.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

GRADING RUBRIC

 

FOR

 

“ MILLERSVILLE MURDER MYSTERY”

 

4                    The student demonstrates complete, correct and thorough understanding of the concept being presented

The problem is labeled, well-organized and represented correctly and easily understood

The axes and drawings are labeled and the data is displayed correctly

The regression equation is correct

The student uses the equation to predict the correct outcome

 

3                 The student demonstrates a general understanding of the concept being presented

The problem is labeled and organized.

The axes and drawings are labeled, but may be incorrect

The regression equation is correct

There is a minor calculation problem or an item from above may be missing

The student makes an incorrect prediction

 

2                   The student demonstrates a partial understanding of the concept

The data is displayed incorrectly or disorganized

The axes and/or drawings are not labeled correctly

The student is unable to find the regression equation

The student is unable to make a prediction or the prediction is missing

 

1                 The student demonstrates minimal understanding of the concept

The student attempts the initial steps to organize and display the data

No other work is evident

 

0          The student omits the problem, there is no attempt made or the response is off-task

 

 

 

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