| Title: |
Unit 4: Descriptive Statistics |
| Author & Email: |
Holly Plunkett hplunket@access.k12.wv.us
Nathan Sams nsams73@hotmail.com |
| Grade Level: |
High School Math I |
Unit Overview:
|
Students summarize, represent and interpret data on both 1- and 2-variable measurements. They will fit mostly linear, but also exponential functions to data. They will interpret linear models to solve problems. |
Unit Calendar
| http://wveis.k12.wv.us/teach21/cso/upload/UP92CAL.doc |
Next Generation Content Standards and Objectives:
|
Objectives Directly Taught or Learned
Through Inquiry/Discovery | Evidence of Student Mastery of Content | M.1HS.DST.1
represent data with plots on the real number line (dot plots, histograms, and box plots). | Lesson 2 Activities, Extra Practice Marketing Plan | M.1HS.DST.2
use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | Lesson 1 Activities Lesson 3: Show Me Marketing Plan | M.1HS.DST.3
interpret differences in shape, center and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | Lesson 2 Activities Marketing Plan | M.1HS.DST.4
summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | Lesson 4: It’s a 2-Way Street Lesson 4 Homework: Nuclear Data Analysis Marketing Plan | M.1HS.DST.5
represent data on two quantitative variables on a scatter plot and describe how the variables are related. - fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models.
- informally assess the fit of a function by plotting and analyzing residuals. (Focus should be on situations for which linear models are appropriate.)
- fit a linear function for scatter plots that suggest a linear association.
| Lesson 5: Exponential Growth and Decay: M&M’s Lesson 6 Activity Sheets (A, B, C or D) Lesson 7: Square It Up! Homework | M.1HS.DST.6
interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. (Build on students’ work with linear relationships in eighth grade and introduce the correlation coefficient. The focus here is on the computation and interpretation of the correlation coefficient as a measure of how well the data fit the relationship.) | Lesson 6 Activity Sheets After Lesson 8: “How Tall is That Criminal?” | M.1HS.DST.7
compute (using technology) and interpret the correlation coefficient of a linear fit. | Lesson 8: Lab Activity: Correlation Coefficients | M.1HS.DST.8
distinguish between correlation and causation. (The important distinction between a statistical relationship and a cause-and-effect relationship arises here.) | Lesson 7: Exit slips on causation versus correlation Lesson 8: Group responses to summary | |
Mathematical Practices::
|
| Mathematical Practices | Evidence of Student Engagement in Mathematical Practices | | MP.2 Reason abstractly and quantitatively. | Lessons 2, 3, 4, 6 | | MP.4 Model with mathematics. | Lessons 4, 5, 6 | | MP.5 Use appropriate tools strategically. | Lessons 1, 2, 3, 4, 5, 7, 8 | | MP.6 Attend to precision. | Lessons 1, 2, 3, 7 | | MP.7 Look for and make use of structure. | Lesson 4 | |
Focus/Driving Question:
|
In what ways can data be organized and presented so that the information is clear and concise?
Is there a best way to represent data?
What types of conclusions can be made about data? |
Student will Know:
|
Graphs and tables are used to display data
Appropriate usage of regression equations, correlation coefficients
Measures of central tendency: median, mode, mean, and how to calculate
Proper usage of vocabulary of data analysis |
Student will Do:
|
Gather data and construct appropriate graphs to represent data.
Use the regression equations to make predictions
Use technology to calculate measures and represent data |
Materials/Resources/Websites:
|
Golden Ratio - http://www.geom.uiuc.edu/~demo5337/s97b/art.htm "Anscombe?s Quartet." . Wikipedia, 27 Feb 2012. Web. 4 May 2012. http://en.wikipedia.org/wiki/Anscombe?s_quartet. "Calculate Correlation Coefficient - Maths Calculator." easycalculation.com. 4 May 2012. http://www.easycalculation.com/statistics/correlation.php. Lemmon, Alan R.. "EVO Tutor: Simple Linear Correlation." EVO Tutor: Statistics. 3 Feb 2007 . Web Inquiry 120." Curriculum Pathways. SAS In Schools. 3 Feb 2007 . “Classroom Activities with TI Graphing Technology by Texas Instruments” Texas Instruments. 4 May 2012, http://education.ti.com/educationportal/sites/US/sectionHome/classroomactivities.html
DeVeaux, Richard D, and Velleman Paul F. Intro Stats: Preliminary Edition. Boston: Addison Wesley, 2003. Interactivate: Normal Distribution. Shodor Education Foundation Inc.. Jan 31, 2007 http://www.shodor.org/interactivate/activities/NormalDistribution/ IFA Services: Statistics, Correlation coefficient." Statistical Tests. Institute of Phonetic Sciences, Amsterdam. 3 Feb 2007 http://fonsg3.let.uva.nl/Service/Statistics/Correlation_coefficient.html
West, R. Webster. "Regression Applet." 09 Sep 1996. University of South Carolina. 3 Feb 2007 .. |
Assessment Plan:
|
The students will create the products listed in the following section. |
Major Products:
|
How Tall is That Criminal? (Group - Lesson 8) Complete the TI Activity based on a Numb3rs TV show. Marketing Plan (Individual or in pairs– Lesson 9) You are the marketing director for a local store. You have a budget to buy commercials on one prime-time TV show. Collect data to do a marketing study on which show to choose. Present your conclusion in a letter to the president of the company with proper graphics and statistics. Square It Up (Individual – homework after lesson 7) |
Unit Reflection:
|
Students will have the opportunity to summarize the major skills in this unit by completing the Marketing Project and How Tall is that Criminal Activity. The students may reflect on how useful statistics can be, but also how misleading. Teachers may reflect after each lesson on whether or not the students grasped the objectives presented. There are many Texas Instruments activities available for extra explorations of the Descriptive Statistics objectives studied in Math I. That may be a good starting point if extra work or enrichment is needed. |
| Tagged Next Generation Content Standards and Objectives |
| NxG ID |
NxG Objectives |
| M.1HS.DST.1 |
represent data with plots on the real number line (dot plots, histograms, and box plots). (CCSS.Math.Content.HSS-ID.A.1) |
| M.1HS.DST.2 |
use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. (CCSS.Math.Content.HSS-ID.A.2) |
| M.1HS.DST.3 |
interpret differences in shape, center and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). (CCSS.Math.Content.HSS-ID.A.3) |
| M.1HS.DST.4 |
summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. (CCSS.Math.Content.HSS-ID.B.5) |
| M.1HS.DST.5 |
represent data on two quantitative variables on a scatter plot and describe how the variables are related.
- fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models.
- informally assess the fit of a function by plotting and analyzing residuals. (Focus should be on situations for which linear models are appropriate.)
- fit a linear function for scatter plots that suggest a linear association.
(CCSS.Math.Content.HSS-ID.B.6) |
| M.1HS.DST.6 |
interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. (Build on students’ work with linear relationships in eighth grade and introduce the correlation coefficient. The focus here is on the computation and interpretation of the correlation coefficient as a measure of how well the data fit the relationship.) (CCSS.Math.Content.HSS-ID.C.7) |
| M.1HS.DST.7 |
compute (using technology) and interpret the correlation coefficient of a linear fit. (CCSS.Math.Content.HSS-ID.C.8) |
| M.1HS.DST.8 |
distinguish between correlation and causation. (The important distinction between a statistical relationship and a cause-and-effect relationship arises here.) (CCSS.Math.Content.HSS-ID.C.9) |
|
| Files Uploaded |
|
| Date Created: |
May 31, 2012 |
| Date Modified: |
August 06, 2012 |
Unit Plan Outline
(Lesson Plans) |
Lesson 1: Measures of Center
Lesson 2: Graphic Representations
Lesson 3: Normal Distribution
Lesson 4: Categorical Data – 2-Way Frequency Tables
Lesson 5: Exponential Modeling
Lesson 6: Does That Data Fit? (Regressions)
Lesson 7: Square It Up! (Residuals on Linear Regressions)
Lesson 8: Is That a Good Fit? (Correlation Coefficients)
Lesson 9: Unit Project – Marketing Plan
|
Career Connections:
|
statisticians, sports analysts, scientists, actuaries, consumers, criminologists, marketing analysts |
| Key Word Search Fields |
statistics, data analysis, exponential functions
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