## 6th grade Statistics, Data Analysis, and Probability

**Note: the type of resource is bolded in the descriptive text.**

*Tested on The CAHSEE*– Compute the range, mean, median, and mode of data sets.

Statistics: Power from Data! This site can assist readers in **getting the most from statistics**. Each chapter is intended to be complete in itself.

Mean, Median & Mode – **Video and auditory tutorial** from the Tampa Educational Channel. One of over 30 topics specifically covering problem areas of middle school math. (You may need to set up a free user account to access this site and see all topics). Designed as a homework help site, this makes an excellent link for teachers to include on their own web pages. Students can pause and replay the videos as needed. Requires Flash 6.

Introduction to Mean, Median and Mode – **Interactivate lesson and activity.** Designed as a lesson outline for teachers on how to teach the topic. Includes ideas for guided and independent practice, sample problems and activities for students.

Measures Activity – This **Interactivate activity** allows students to input various types of data and request mean, median, mode and range information. The java applet allows students to collect or make up their own data on any subject they wish to study and measure any characteristic they wish. Section includes exploration questions and a discussion.

Mrs. Glosser’s Math Goodies Introduction to statistics is a series of **interactive lessons** that provides detailed examples, diagrams, summaries and exercises.

Measures of Central Tendency: Mean-Mode-Median **Explanation and Practices exercises **using a calculator – from Oswega City Schools.

Data Handling: Mean, Median & Mode –** interactive tutorial** from the BBC that uses weather data as an opportunity for students to develop an understanding of concepts.

Plop It! – A free resource from the Concord Consortium’s “Seeing Math” Project. Plop It! **lets students experiment with the concepts of mean, median, and mode**. Users see the differences among them on a bar graph, as they add or remove blocks to an axis with a given range. Can be downloaded for offline use. A user’s guide, warm-up and sample activities are included.

Train Race Game – Help Pythagoras and Hypatia make their connecting trains. This **shockwave game** from BBC Education can be used to extend a basic understanding of the median, mean and range. Data about particular trains is given from which estimates of the arrival time are calculated. The reliability of a particular train is assessed by the size of its range: a train is judged to be more reliable than another if it has a smaller range. Teacher support and print-offs are provided.

Rags to Riches – learn the four basic definitions (mean, mode, median and range) in a **“Millionaire” style game** from Quia.

School Sports Day – In this **shockwave game** from the BBC on data handling, teams compete for trophies and need to have the best competitors entered for each track event. Students pick a winning team by working out the median, mean and range. Teacher support and print-offs are provided.

Mean, Median and Mode – This **Microsoft Word template example** reinforces the concepts of mean, median, mode, range, maximum, and minimum. Once you have done this with your students, have them think of different ways to practice new concepts. You can use other programs such as Microsoft PowerPoint to have your students animate objects or add slide transitions to demonstrate concepts.

SDP 1.2 Understand how additional data added to data sets may affect these computations of measures of central tendency.

Create Custom Data Reports – This “Kids Count” web site, from the Annie E. Casey Foundation, tracks health information about children in the United States. Use the Online Databook 2002 for resources displayed in profiles, line graphs, rankings, and r**aw data in delimited files that you can manipulate** to create your own graphs and charts.

Exploring Measures of Central Tendency – A** video from the Junior High Math Interactives** series (learnalberta.ca) illustrates how math is used by emergency response planners to save lives. Using an interactive component, students explore and predict changes as new emergency response times are added to a set of times with known means and medians. A central tendency print activity is included.

Central Tendency/Outliers – Students build a data set and find the mean, median, and mode. They explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. This **activity is part of Explore Learning, a subscription-based site** but five minutes of free usage of any gizmo are allowed per day. A 30-day free trial is also available for teachers.

Central Tendency: Comparing Properties of Mean & Median – **Students use a java applet to experiment with seven data points** in a line plot which represent the distances a paper airplane traveled after it was thrown. They can compare and contrast properties of measures of central tendency, specifically the influence of changes in data values on the mean and median. The student’s task is to explore how changing one (or more) of the data points affects the mean and the median of the data set. As students change the data values, the interactive figure immediately displays the mean and median of the new data set. This electronic sample was created by NCTM and includes teacher support for using this activity in the classroom.

Video Gamer – in this activity from Microsoft Education, **students assume the role of video game developers** to learn about central tendency and to understand how data can be used to make decisions. They conduct a survey, interpret the data that they collect, and determine the appropriate audience for a new video game. Business skills are used as students write a memo to the CEO of a hypothetical company explaining their choice of audience for the game, and create a presentation for the board of directors of the company. For extra credit, **they write and produce a commercial for their game.** Uses Microsoft Word, Excel and PowerPoint.

Data – Statistics This site is from the Annie E. Casey Foundation, tracking health information about children in the United States. Use the Online Databook 2002 for resources displayed in profiles, line graphs, rankings, and **raw data in delimited files that you can manipulate to crate your own graphs and charts**.

Lesson Plan-Does More Wins Mean More Fans At The Ballpark? **Determine an attendance-to-win ratio** for each of the 28 major league teams and then study the results to see if winning always leads to good attendance. Project uses a four-function calculator, rounding to the nearest number.

SDP 2.2 Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.

Sampling & Probability: Discovery & Practice – **Video on Demand lesson from Annenberg Media on sampling and probability that engages students in their own learning**. Emphasis is on instructional techniques. Includes discussion of the concept of sampling as a way of making predictions on a larger populations, sample sizes, and the importance of random sampling to eliminate biases. Select Lesson 7. In the follow-up lesson (#8), the teachers discuss how they taught the sampling lessons in their classrooms and learn to evaluate whether or not student work meets standards.

SDP 2.3 Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached.

Probability by Surprise – This resource, from Susan P. Holmes at Stanford University, features **a collection of applets demonstrating probability. **

Probability Tutorial and Counting Cards Game – BBC Education web site** game and tutorial**. Students learn about using the probability scale, and work out probabilities using fractions and percentages.

Data Picking – A **shockwave game from BBC Education** with three levels of difficulty. Students click on students to collect data and produce a frequency table. At the advanced level, they collect pairs of data. Students are challenged to tally results and choose a graph which reflects the tally. Level 1 shows simple pie charts, Level 2 a selection of line graphs, histograms and pie charts and Level 3 simple scatter charts.

SDP 2.4 Identify data that represent sampling errors and explain why the sample (and the display) might be biased.

Exploring Data – This collection has numerous resources for data exploration. This page has l**inks to standards, data sets, lessons, and more web sites for the K-12 classroom.**

Polling the Neighborhood –** Using interactive tools, students conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question**. They use the results to estimate the sentiment of the entire population and investigate how the error of this estimate becomes smaller as more people are polled. They also compare random versus non-random sampling. Explore Learning is a subscription-based site but allows five minutes of free usage for each gizmo.

Class Activities – Census at School is an **international online project **that can be used to teach students about handling and interpreting data.

Shampoo Claims – Truth or Lies? A hair shampoo advertiser’s claim to make hair 10% stronger has been banned by the Advertising Standards Authority. There was, says the ASA, insufficient scientific evidence to support the claim. This activity asks students to **evaluate data** from hair strength trials, and to decide what the data shows (if anything!). They then examine other advertisers’ claims.

SDP 3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events:

Discrete Mathematics – **A collection of discrete mathematics activities** geared towards a young audience

Teaching Discrete Mathematics in Grades 7-12 – Hart, Maltas, Rich; Eisenhower National Clearinghouse

A paper that **discusses various ways to introduce discrete** math into the junior high and high school curriculum.

Fair Game??? Dilemma – This exemplar offering differentiated, classroom-tested, **standards-based assessment and instructional materials on a dice problem **where students must explain all the possible outcomes to determine the probability for winning a game of dice in which the number 1 is missing.

Dice Game Probabilities – Determine **probability outcomes **when a red die and green die are rolled. Includes visuals and feedback.

SDP 3.2 Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven).

Discrete Mathematics – A **collection of discrete mathematics activities geared towards a young audience.**

Teaching Discrete Mathematics in Grades 7-12 – Hart, Maltas, Rich; Eisenhower National Clearinghouse

A paper that **discusses various ways to introduce discrete math** into the junior high and high school curriculum.

Fish Tank – In this **shockwave game** from BBC Learning, the student must guess the probability of a fisherman catching a red fish in a tank of red and yellow fish. There are three levels of difficulty, the easiest beginning with the student guessing the probability of the fisherman catching a red fish and ending with the student having to drag the fish in the tank to get the correct probability. Not as easy as it looks!

What Are the Chances? – **Math TV problem-solving video**. Students must solve a probability problem involving multiple events and sequence of colors in drawing marbles from a bag. Onscreen audio and visual help is provided in setting up the problem and solving it. Once it is solved, students are given another problem to solve and can make use of the practice video, a scratch pad and calculator.

*Tested on the CAHSEE*– Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1-P is the probability of an event not occurring.

Probability by Surprise – This resource, from Susan P. Holmes at Stanford University, features a **collection of applets demonstrating probability. **

Probability Tutorial and Counting Cards Game – BBC web site. **Students learn about using the probability scale, and work out probabilities using fractions and percentages.**

Experimenting with Probability using a Digital Spinner –** this coaching article for teachers **explains the value of using Shodor.org’s digital spinner, which gives students the opportunity to explore concepts of probability. Includes actual classroom examples.

Experimental Probability – This** digital spinner activity** from Shodor.org (described above) allows the user to conduct probability experiments with traditional probability devices such as a spinner and dice. Studying random events with such devices and computer simulations allows students to gain familiarity with the connection between experimental and theoretical probability.

A Cereal Box Problem: A lesson in Expected Value – This **online simulation and lesson** allows students to go on a simulated shopping trip and collect animal cards in boxes of cereal. You have the option to modify the number of possible prizes available and log your different trials. Includes teacher notes and info on how to model the problem in your classroom.

Ken White’s Coin Flipping Page – T**his site will show you the experimental results of flipping as many pennies or dimes as you would like.**

SDP 3.4 Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.

Introduction to Statistics – This site with **lesson plan ideas and activities** is above grade level but some of the activities might be able to be modified for 6th grade or might work as extension for more advanced students.

Probability – **Video and auditory tutorial **from the Tampa Educational Channel. One of over 30 topics specifically covering problem areas of middle school math. (You may need to set up a free user account to access this site and see all topics). Designed as a homework help site, this makes an excellent link for teachers to include on their own web pages. Students can pause and replay the videos as needed. Requires Flash 6. 6.

Spy Guys Probability. **Video** – Click on Lesson 19. Covers probability expressed as a fraction, decimal or percent. This video and auditory tutorial from http://www.learnalberta.ca allows teachers and students to explore math concepts, pause and replay. Learn how to show fractions and mixed numbers on a number line. Includes interactive exercises that provide immediate feedback. Printable worksheets, parent notes, and a glossary are included for each lesson. In addition to the lessons, there are sections on problem-solving strategies.

SDP 3.5 *Tested on the CAHSEE* – Understand the difference between independent and dependent events.

Independent & Dependent Events – This **Explore Learning gizmo for fee** allows students to compare the theoretical and experimental probabilities of a compound independent event by drawing colored marbles from a bag. They record the results of successive draws with or without replacement of marbles to calculate the experimental probability. Subscription fee but 5 minutes of free usage for each gizmo is allowed.

Compound Independent Events – the focus of this **gizmo **is the probability of a compound independent event P(A, then B) is equal to the product P(A) • P(B). allowed. Subscription fee but 5 minutes of free usage for each gizmo is allowed.

Does More Wins Mean More Fans At The Ballpark? **Lesson Plan/Activity** to use when working with various Statistics, Data Analysis and Probability standards.

Last Updated (Tuesday, 02 March 2010 16:49)