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South Carolina ETV
1101 George Rogers Boulevard
Columbia, SC 29201-4761
Phone: 803-737-3545

What’s Your Average? What Do You Mean? I’m More Than Just Average (Grades 5-7)

Master Teacher

Sherri K. Boone

Time Allotment

Two to three 55-minute class periods (based on modifications)

Overview

In this lesson students will discover how to find the mean, median, mode, and range of a set of data through a series of exercises, streaming video, and Internet activities. Students will begin with basic lessons and extend their knowledge into higher mathematical concepts by collecting, analyzing and interpreting results based on the Measures of Central Tendencies and the range of the data. Students will be introduced to the concept of Statistics and Mean, Median, and Mode in the Mathematical Eye streaming video mini-lessons. Students will practice these skills on various Web sites.

Subject Matter

Mathematics (Data Analysis)

Learning Objectives

Students will be able to:

• Formulate questions that will facilitate the collection of data;
• Collect data about a characteristic shared by two groups or different characteristics within the same group;
• Compute and analyze collected data; and
• Interpret the data.

South Carolina Standards

The 5 th and 6 th grade South Carolina math standards are available online at http://www.myscschools.com/offices/cso/standards/math/

Data Analysis and Probability – 7th Grade SC Math Standards

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

A. Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.

1. Given a problem situation involving two populations, collect, analyze, and interpret data.

Media Components

Video

Mathematical Eye: Statistics , "Collecting Information and Using Statistics" and "Finding Mean, Median and Mode." To access these video clips, log on to your account at ETV's StreamlineSC Web page ( http://etv.streamlinesc.org ). In the search by keyword box, type Mathematical Eye: Statistics and hit go. Click on the program title and then down the two video clips to your computer and preview them. "Collecting Traffic Accident Statistics" runs four minute and 27 seconds and "Finding Mean, Median and Mode" runs five minute and 23 seconds.

(Note to Teacher: If you don't have an account with ETV's StreamlineSC, check with your media specialist or Instructional Technologist about signing up for your own account.)

Web sites

Introduction to Descriptive Statistics at http://www.mste.uiuc.edu/hill/dstat/dstat.html

This site contains statistics in a variety of situations and shows students the relevance of such in their own lives. This page allows students to go through further study of the Measures of Central Tendency and actually using mean, median, and mode in on-line examples. It also introduces range. The mode in this section is shown in a stem-and-leaf plot which is a 6 th and 7 th grade standard. The mode for the cost of ice cream is $1.20 it is the one that shows up the most.

BBC ReviseWise Maths at http://www.bbc.co.uk/schools/revisewise/maths/data/12_act.shtml

This site provides data handling in a fun interactive way. This page will allow students to use temperature to find the mean, median, mode, and range of a set of numbers. They will also be able to look at a fact sheet and take a fun on-line quiz using a set of data.

National Center for Education Statistics at http://nces.ed.gov/NCESKids/graphing/

This page allows students to create graphs with all of its labels and data to create an array of visual interpretations.

Agriculture and Math Fun at http://www.usda.gov/nass/nasskids/nasskids.htm

NASS – National Agricultural Statistics Service – Provides accurate, timely statistical information.

Materials

• Transparency - 1
• Activity Sheets1, 2 and 3 (1 each child)
• Milliken Math Champs! Tables, Charts & Graphs
• Sample Graphs
• Whiteboard
• Magazine
• Newspapers

Equipment

• LCD Projector
• Computer
• Overhead

Prep for Teachers

• Bookmark your Web sites used in this lesson on each laptop/desktop computer that will be used by students or on the computer you will use with a projector.
• Load plug-ins if needed. You may also use TrackStar at www.trackstar.com for a wide variety of online lessons and activities. (You may choose to collect Web sites, enter them into TrackStar, add annotations for your students, then you have an interactive, online lesson called a Track. You may create your own Track or use others already made by educators.)
• When using media, provide students with a Focus for Media Interaction, a specific task to complete and/or information to identify during or after viewing of video segments, Web sites, or other multimedia elements.

Introductory Activity

Step1: Distribute Activity Sheet 1: Collecting Data: Favorite Numbers. Tell your students that you will be collecting data about their favorite numbers less than 10. Tell them we are collecting data to learn about statistics, the collection, analysis, and representation of data.

Step 2: Tell your students that you will now collect the favorite number data from the class by putting a tally mark under each number at the time it is selected.

Step 3: Ask the students to record the data on their sheets as you record it on the overhead.

Step 4: Ask students to count each tally mark to find the number of students selecting each number. Tell the students to find the fraction of the class selection of a particular number. For example, if a class of 25 students has 8 people select #4, then the fraction of the class selecting #4 is 8/25. Tell them to organize all of the information with a table, name the table, list headings, and fill in the data. Check to see if students are correctly progressing with their tables.

Step 5: Tell the students to use the table of favorite numbers to answer the following questions: What number was selected most? Which number was selected least? What fraction of the class selected the three most popular numbers? How many more times was the most popular number selected that the least popular number? What is the sum of all the fractions representing the part of the class selecting each number?

Step 6: Tell your students to interpret the data and tell you their findings. (Students should be able to point out the favorite number and how many people chose it, the least favorite number, the difference in the amount of people choosing the least and most favorite number. They should also be able to tell which number was chosen the most.)

Step 7: Tell students to write a brief explanation of how the data was collected and what the data tells them.

Step 8: Ask the students to tell you some reasons for collecting data.

Learning Activities

Step 1: Tell students they will watch streaming video clips from Mathematical Eye which will further introduce them to statistics and the Measures of Central Tendency, a fancy name for mean, median, and mode. Tell them they will learn about range in some of their other activities.

Step 2: Tell your students that the first part of the video shows them about data collection. Remind them that they just collected data on their favorite numbers. Provide them with a Focus for Media Interaction by telling them to identify what kind of data is being collected in the clip.

Step 3: As a second Focus for Media Interaction, ask them to devise a way of how they would determine the number of people in attendance in the second part of the clip.

Step 4: PLAY the "Collecting Information and Using Statistics" video clip. Start the video when you hear….Have you ever wondered…(What data is being collected? 1) How many people are riding bus, where they want to go, etc? 2) How many fish with blue dots? 3) What styles are most popular? 4) How do you collect statistics on popular music?)

Step 5: After the clip, allow the students to reflect on the questions above. Ask them to brainstorm other ways to collect data. (What different ways can you think of to count huge crowds like the one in the clip?)

Step 6: Tell students that they will now see a clip that will show them how to work with the statistical skill of finding the mean, median, and mode of a set of data. Provide them with a Focus for Media Interaction by telling them to identify the three different kinds of averages and the steps to find as the video goes along.

Step 7: PLAY the video clip "Finding Mean, Median and Mode." Start the video when you hear “Car # 12 is doing an average of…” PAUSE when you hear “What is an average and how do you find it?” Let students brainstorm. Resume PLAY when you hear “The average height of this class…”

Step 8: PAUSE the video when you hear…“What do you think the average will be?” Ask a child to go to the whiteboard and mark the average height of the fungi, based on his understanding.

Step 9: RESUME video when you hear “Remember there are three kinds of averages.” PAUSE the video when you hear… “Which average do you think is best?” Ask students which type of average do they think is best and explain their reasoning (verbally or written).

Step 10: Resume PLAY when you hear “which average do you think is best.” PAUSE when you hear “What good are averages in real life?” (Allow students to respond to real life situations where averages may be used.) PAUSE when you hear “What kind of averages would tell you which shoes are best? How would you work them out?” (Allow students to respond.)

Step 11: Resume PLAY. Stop the video when you see a Picture of an Eye – Look at this to see whether your class is average.) PAUSE after you hear “In your class, how many of you can see a numbers in the left side and /or right side of the circle?” Ask students to raise their hands if they see the number in the circle and to identify it by writing it down on their papers. Tell them to tally how many boys and girls see both numbers. (Allow students to use tally marks of boys to girls. Ask them which kind of average would be best to use in this situation. Tell students they need to explain their answer in terms of mean, median, or mode.

Step 12: Tell students they will go to TrackStar and find use sites that are related to mean, median, mode, and range. Provide them a Focus for Media Interaction by telling them that the purpose in the TrackStar activities is to help them to master using mean, median, mode and range.

Tell students to type in TrackStar in the Search Engine. Then tell them to enter Track #78328, a track annotated by Hollie Thompson (http://trackstar.4teachers.org ). Tell them they have three tasks that they should complete. Provide them with Activity Sheet 2: Calculating Mean, Median, Mode, and Range.

Step 13: Ask the Students to 1) calculate the mean, median, mode, and range for career homerun for Cal Ripkin from 1981 to 2001. Tell them they should show all of the data in the sections provided for each task. Tell them to next 2) find the m ean, median, mode and range for starts Dale Jarrett had from 1984 - 2003. 3) Calculate the mean, median, and mode for Michael Jordan for career games played.

Step 14: Ask students to go to the favorites folder and find ReviseWise Maths Web site (Teacher must save site to favorites or other program that keeps bookmarks.). Provide them a Focus for Media Interaction by a sking them to use this site to use the computer more interactively as they continue to perfect their skills with mean, median, mode, and range. Tell them that they will click on the data handling activity and work through the tutorial http://www.bbc.co.uk/schools/revisewise/maths/data/ . (If they do not master using this interactive tutorial, they may try as many times as they like.)

Step 15: Tell students once they have completed the ReviseWise Maths Web site Activity to click on the Data Handling Tab. Provide them a Focus for Media Interaction by letting them know that they will be taken through another interactive tutorial about graphs http://www.bbc.co.uk/schools/revisewise/maths/data/ , parts of graphs (labeling) bar graphs.

Step 16: Tell them to use Worksheet “On Yer Bike!” http://www.bbc.co.uk/schools/revisewise/maths/ to practice reading and making bar graphs.

Culminating Activity

Step 1: Tell students they will now take the “tests” on both the ReviseWise Maths Web site activities. Then they will receive Activity Sheet 3: Weathering the Heat. Tell them to think back to the on-line activity where they worked with temperatures. Tell them they will use temperatures to practice using data.

Step 2: They will make a tally and frequency table to show their data, then, they will answer the questions about temperatures, based on the data as it relates to mean, median, mode, and range.

Step 3: Tell them to brainstorm some topics that they can use in a survey – the kind of music that their peers like, the most favorite foods or TV shows, etc. Then they will compile their data and make a bar graph or line graph to show their data. Tell them that they will need to analyze their data and present their finding to the class. The graph must be properly labeled, the intervals must be equal, etc.

Step 4: Tell students that they can use any software program or internet resource to help them with the final product. Demonstrate how to use paint and import graphic from MSPaint. Demonstrate how to use Create-A-Graph at the site of the National Center for Educational Statistics http://nces.ed.gov/NCESKids/graphing/.

Assessment

The on-line tests on the ReviseWisehttp://www.bbc.co.uk/schools/revisewise/maths/data/ Web site on mean, median, mode, & range, and graphing can be used as assessment. They will also be assessed on how well they used their knowledge to collect data, analyze, visually display, and orally interpret the data that they collected.

Picking Data at http://www.bbc.co.uk/education/mathsfile/shockwave/games/datapick.html

Tell students to pick each student in the 8H class photo to collect data to make a frequency table. Tell them to them pick a graph that matches their data. (Observation)

TrainRace - Data Handling at http://www.bbc.co.uk/education/mathsfile/shockwave/games/train.html

Tell students to compare, mean, median, mode, and range to see if Hypatia and Pythagoras’ train will make it to an event on time. (Observation)

Cross-Curricular Extension

Agriculture And Math Fun (http://www.usda.gov/nass/nasskids/nasskids.htm This is a site that students can use to connect math, science, health, geography and agriculture. Students can use this site to see trends in data, they can investigate different charts and graphs, play games that tell about different types of foods, find which states have the highest inventory of certain types of livestock, play word games that tell how different crops are used, etc.

Students can select information that they think is important and write a short report to share with the class. They can choose to display their information creatively.

Community Connections

• Bring in a representative from a local grocery chain or Wal-Mart to discuss how they use statistics in business.

Student Materials

• Calculators (optional)
• Laptops
• Paper
• Pencils
• Work Sheets