Session 535Strategic Use of Technology Tools for Statistics in Algebra 1

● Measure your armspan in inches (and height, if necessary).

● Take the survey at bit.ly/AsilomarStatsSurvey to provide the following data: first name, height, armspan, gender, and email (to receive a link to resources).

● Place a sticky dot on the dot plot (height) and another on the scatter plot (armspan vs. height).

@SFUSDMath bit.ly/535AsilomarSlides

Overview of Statistics Topics● Univariate Statistics

○ Median-based (median, IQR, box plots, histograms)○ Mean-based (mean, standard deviation, normal curve)

● Bivariate Statistics○ Numerical (residuals, LSRL, correlation coefficient)○ Categorical (two-way tables, association)

● Statistics and Probability Progression

● Digital tools: Google Sheets, Tuva, Desmos, PhET Demo

Agenda1. Median-based Statistics

● Acting out the 5-Number Summary: Height data● Histograms and Box Plots: Google Sheets, Tuva

2. The Shape of Data● Data Experiments: Penny Toss, Five Seconds, Roll a Die● Represent Data: Google Sheets, Tuva, online resources

3. Mean-based Statistics● Standard Deviation: Five Seconds data in Google Sheets● Normal Curve: Desmos demo, Average Monthly Temperature data

4. Comparing Data Sets● Work in pairs with Tuva: Pixar vs. Dreamworks

5. Bivariate Data● Numerical Data: Scatter Plots and Linear Regression● Categorical Data: Two-way Tables in Tuva

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

The Shape of Data: Data Experiments

● Collect data at each station. (SFUSD student pages)

● Enter your data (take each survey 5 times):○ bit.ly/AsilomarPennyToss○ bit.ly/AsilomarFiveSeconds○ bit.ly/AsilomarRollADie

● Predict (sketch) what the graphs of the data from each experiment will look like.

Matching Histograms and Box Plots

● Relating Histograms and Box Plots (online activity)

● Distribution Card Sort (group activity)

Mean-based Statistics: Five Second Data

● Calculate standard deviation using a Google Sheet (SFUSD student pages)

● Transform a normal curve in a Desmos demo

● Area under a normal curve: The Empirical Rule

Normal Curve: The Empirical Rule

Average Monthly Temperature Data

● Estimate mean and standard deviation of temperature data.● Predict the shape of each graph.

Month San Francisco New York PhiladelphiaJanuary 57 39 40February 60 42 44March 62 50 53April 64 60 64May 66 71 74June 66 79 83July 66 85 87August 67 83 85September 70 76 78October 69 64 67November 64 54 56December 57 44 45

● Compare Pixar versus Dreamworks using Tuva.

● Register for a free Tuva Premium license:

○ Go to tuvalabs.com and sign up as a teacher.

○ Choose the organization:California Mathematics Council - North

○ Free license for Tuva Premium until June 30, 2018.

Comparing Data Sets

Bivariate Statistics● Numerical Data: Height versus Armspan

○ Scatter Plots in Tuva and Desmos○ Moveable Lines and Least Squares Regression Lines

● Linear Regression:○ Desmos (Height versus Armspan example)○ Least Squares demo (CPM Desmos demo)○ PhET Simulation

● Categorical Data: Passengers of the Titanic○ Two-way Tables in Tuva

Bivariate Graph of Univariate Statistics

From 6–8 Statistics and Probability Progression (page 7):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.”

● 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 Sheets (standard deviation example)

Digital Tools

Thank you!

Andres MartiHS Math Content Specialistmartia@sfusd.edu

Christine SierraHS Math and CS Teachersierrac@sfusd.edu

www.sfusdmath.org

@SFUSDMath