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TRANSCRIPT
Session 127Strategic Use of Technology Tools for Statistics of High School Math Courses
● Measure your armspan in inches (and height, if necessary).
● Take the survey at http://tinyurl.com/Session127 to provide the following data: name, height, armspan, gender, and email (so we can send you link to digital resources).
● Place a sticky dot on the dot plot (height) and another on the scatter plot (armspan vs. height).
@SFUSDMath http://tinyurl.com/NCTM127Slides
Overview of Statistics Topics● Univariate Statistics
○ Median-based (median, IQR, box plots, histograms)○ Mean-based (mean, standard deviation, normal curve)
● Bivariate Statistics○ Numerical (line of best fit, residuals, LSRL)○ Categorical (two-way tables, association)
● Digital tools: Google Sheets, Tuva, Desmos, PhET
Agenda1. Median-based Statistics: Height Data
● Acting out the 5-Number Summary● Histograms and Box Plots using Google Sheets and Tuva
2. Data Experiments: Shape of Data● Gather data for Penny Toss, Five Seconds, Roll a Die● Represent data using Google Sheets and Tuva
3. Card Sort: Matching Histograms and Box Plots4. Mean-based Statistics: Five Second Data
● Normal Curve5. Bivariate Data: Height versus Armspan Data
● Linear regression using Desmos and PhET Simulation6. Average Monthly Temperature Data
● San Francisco, New York, Philadelphia, and San Antonio
Median-based Statistics: Height Data
● Determining median and quartiles
● Making a box plot○ Quartiles: include or exclude median?○ Whiskers: entire range or last data point within 1.5 • IQR?
● Technology○ Google Sheet: Histogram○ Import into Tuva from Google Sheet○ Tuva: Histogram, Box Plot, and 5-Number Summary
Data Experiments: Shape of Data
● Collect data at each station.
● Enter your data (take each survey 5 times):○ http://tinyurl.com/NCTM127Penny○ http://tinyurl.com/NCTM127Stop○ http://tinyurl.com/NCTM127Roll
● Predict (sketch) what the graphs of the data from each experiment will look like.
Card Sort: Matching Histograms and Box Plots● Group Activity
● Relating histograms and box plots (demo)
Mean-based Statistics: Five Second Data
● Calculating standard deviation with a Google Sheet
● Transforming a normal curve in Desmos
● Area under a normal curve
Normal Curve: The Empirical Rule
Bivariate Statistics: Height versus Armspan
● From univariate to bivariate representations in Tuva
● Line of best fit (spaghetti method and LSRL)
● Linear regression using Desmos
● Least squares in PhET Simulation
● Least Squares demo in Desmos
Average Monthly Temperature Data
● Temperature data in a Google Sheet● Predict what graph of San Antonio will look like
Month San Francisco New York Philadelphia San AntonioJanuary 57 39 40 62
February 60 42 44 67
March 62 50 53 74
April 64 60 64 80
May 66 71 74 86
June 66 79 83 91
July 66 85 87 95
August 67 83 85 95
September 70 76 78 90
October 69 64 67 82
November 64 54 56 71
December 57 44 45 64
From 6–8 Statistics and Probability Progression (page 7):It must be understood that the connection between relative frequency and probability goes two ways. If you know the structure of the generating mechanism (e.g., a bag with known numbers of red and white chips), you can anticipate the relative frequencies of a series of random selections (with replacement) from the bag. If you do not know the structure (e.g., the bag has unknown numbers of red and white chips), you can approximate it by making a series of random selections and recording the relative frequencies. This simple idea, obvious to the experienced, is essential and not obvious at all to the novice. The first type of situation, in which the structure is known, leads to “probability”; the second, in which the structure is unknown, leads to “statistics.”
Digital Tools● Desmos (http://www.desmos.com)
● Tuva (https://tuvalabs.com)
● Relating Histograms and Box Plots Demo
● Least Squares Desmos Demo
● Least Squares PhET Demo
● Transforming a Normal Curve Desmos Demo
● Google spreadsheets (standard deviation example)
Thank you!Elizabeth DeCarliHS Math Content [email protected]
Andres MartiHS Math Content [email protected]
www.sfusdmath.org
@SFUSDMath