> molM +bjbj== .nWW'l2222222F^^^^<F2r2!2!2!2!2!2!2$`4 6E22E2622Z2666222626z6,22.f0ܾF^*-.|p202-767.6FF2222Grade 7 - Statistics and Probability (Data Analysis)
PRESCRIBED LEARNING OUTCOMES
It is expected that students will develop and implement a plan for the collection, display, and analysis of data, using measures of variability and central tendency.
It is expected that students will:
formulate questions that explore whether or not a relationship exists in a real-world context
select and justify appropriate methods of collecting data (designing and using questionnaires, HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appdmai.htm" \l "interview" interviews, experiments, research)
display data by hand or by computer in a variety of ways, including circle graphs
read and interpret graphs that are provided
determine measures of central tendency for a set of data:
HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appfk_o.htm" \l "mode" mode
HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appfk_o.htm" \l "median" median
HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appfk_o.htm" \l "mean" mean
determine measures of the distribution of a set of data:
HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appfp_r.htm" \l "range" range
extremes, gaps, and HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appfa_e.htm" \l "cluster" clusters
HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appfp_r.htm" \l "quartile" quartiles
HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appff_j.htm" \l "interpolate" interpolate from data to make predictions
SUGGESTED INSTRUCTIONAL STRATEGIES
Statistics allow us to make a summary of what we know of the world and to make inferences about things we do not know. Young students pose questions based on their immediate environment. Students' investigations expand to include community and global issues. Often the questions they wish to investigate are raised in social studies and science contexts. Statistics are also used frequently in the world of sports.
Have students formulate and implement a plan to pursue a question of interest to them, such as:
How does height relate to jumping ability?
Does your pet prefer dry or moist food?
Discuss appropriate ways to collect and display data for different kinds of questions. Their plan must include a method for collecting data (e.g., experimental measurement, library research, survey forms), for organizing and graphing the data, and for drawing conclusions or raising further questions from the investigation.
Using students' graphs, discuss with the class what information can be derived from them such as mean, median, mode, and range.
Grade 7 - Statistics and Probability (Data Analysis)
SUGGESTED ASSESSMENT STRATEGIES
When students gather their own data, they are familiar with and interested in the information. They develop a greater understanding of what it means to organize and summarize data and are then better able to draw conclusions and to make predictions for new contexts.
Collect
After a whole-class discussion, ask students to write to reflect on their reasoning, including information about revisions they may have made. Look for evidence of logical reasoning. For example, how does the student explain why the average is between the highest and lowest values?
After students have had opportunities to display information in a variety of ways, ask them to make a list of the decisions that need to be made when summarizing and displaying data.
Work with the class to develop task specifications and a HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appdmai.htm" \l "checklist" checklist or rating scale that specifies criteria for scoring their investigations.
Box Cars & One-Eyed Jacks
Constructing Ideas About Fractions, Decimals & Percents
Electrical Connections
Interactions 7
Junior High Probability Jobcards
Machine Shop
Mathematics From Many Cultures
Mathpower Seven
Maths Workshop
Minds on Math 7
Nelson Canadian School Mathematics Dictionary
Out of this World
The Sky's The Limit
Video
Mathematics: What Are You Teaching My Child?
INCLUDEPICTURE "http://www.bced.gov.bc.ca/irp/mathk7/icons/software.gif" \* MERGEFORMATINET Software
The Cruncher
Statistics Workshop
INCLUDEPICTURE "http://www.bced.gov.bc.ca/irp/mathk7/icons/games.gif" \* MERGEFORMATINET Games/Manipulatives
D.I.M.E. Probability Pack A
D.I.M.E. Probability Pack B
Heads or Tails
Designed by: Tammy Hester School: Gibbes Middle
Grade Level: 7 Subject: Mathematics
Core Curriculum Objective: Find and compare experimental and theoretical probabilities. HYPERLINK "http://www.richlandclicks.org/ASP/Prescriptions.asp?ObjectiveCode=7SP2-1" (7SP2-1)
South Carolina Curriculum Standards: VI. Probability and Statistics C. 3.
Overview: Students will experience hands-on how the number of trials of an experiment affects the relationship between theoretical and experimental probabilities. Students will understand the difference between theoretical and experimental probabilities.
Focus Question: If you were calling a toss in a football game, would you call heads or tails? Why?
Time Frame: Two 50 minute periods
Resources:
Enough pennies for each student to have one
Website: HYPERLINK "http://shazam.econ.ubc.ca/flip/" shazam.econ.ubc.ca/flip/
Assessment: Students will design their own problem and determine the theoretical probability and perform an experiment to determine the experimental probability. Students will write a report about their findings and share with the class.
Day One
Activity One
The teacher should as the following question: "Suppose I flip this coin. Will it turn up heads or tails?" Then, the teacher should toss a coin to see the result. Repeat the scenario. Next ask the students what is the probability the next coin will be heads? Have students give explanations for their answers.
Then pose this question to the students. "Suppose I flip all 10 coins, how many will land on heads and how many will land on tails?" Allow several students to give their answers and reasons for their answers.
Explain that the situation they have described is an example of a theoretical probability. Have students add this term to their notebooks. Guide the students to see that a theoretical probability is found by applying a formula.
Example: P(H)=1/2 1 is the number of ways to toss heads 2 is the number of possible outcomes
*****note****** tables for the following activities are provided
Activity Two
Conduct a simulation to find the experimental probability of a similar problem.
1. Go to website HYPERLINK "http://shazam.econ.ubc.ca/flip/" http://shazam.econ.ubc.ca/flip/
2. Flip the coin 25 times and fill in the table with the results.
3. Combine the results from your simulation with those from the other members of your class and fill in the class data table.
After the tables are completed, compare the results from individual internet simulation with the results obtained by the entire class. Explain why they are different through class discussion.
Add the term experimental probability to the vocabulary section of your notebook. Guide student to the understanding that experimental probability is given by collecting data.
Activity Three
Now conduct the experiment using a penny. Flip the penny 25 times. Record the results in the table. Then collect the results of the class and fill in the class table. Again, discuss the results.
Activity Four
In the journal section of the student's notebook have them explain how the theoretical, Internet simulation, and actual coin toss probabilities compare with each other. Allow time for some students to read their explanations.
Assessment:
1. Students are to make up a problem similar to the one in done in class.
2. Determine the theoretical probability.
3. Perform an experiment and determine the experimental probability.
4. Write a report about the experiment and the results.
5. Give an oral report to the class.
Rubric for the assessment provided in the lesson plan.
Name_______________________________ Date___________ Period_________
Tables for Internet Simulation Coin Toss
Website: HYPERLINK "http://shazam.econ.ubc.ca/flip/" shazam.econ.ubc.ca/flip/
Individual Internet Coin Toss SimulationNumber of HeadsNumber of TailsTotal Number of FlipsProbability HeadsProbability Tails
Class Data Internet Coin Toss SimulationNumber of HeadsNumber of TailsTotal Number of FlipsProbability HeadsProbability Tails
Name_______________________________Date____________ Period________
Tables for Actual Coin Toss Experiments
Individual Coin TossNumber of HeadsNumber of TailsTotal Number of FlipsProbability HeadsProbability Tails
Class Data From Coin TossNumber of HeadsNumber of TailsTotal Number of FlipsProbability HeadsProbability Tails
Rubric for Assessment of Individual Probability Problem
Rubric for Probability ProblemName_________________________ Date _____________ Period _____Required Item20 points15 points10 points5 pointsProblem statedCorrectly written, free of errorsCorrectly written, one errorProblem is not a probability problemProblem is not clear, but attemptedTheoretical probabilityCorrectly given with explanation and formulaCorrectly given, missing explanation or formulaIncorrect, but explanation or formula attemptedIncorrect, no explanation or formula givenExperimental ProbabilityCorrectly given with evidence and explanation of experimentCorrectly given , missing evidence or explanationIncorrect, but evidence or explanation attemptedIncorrect, no evidence or explanation or experimentWritten reportTitle, and all 3 parts included w/ through explanation and evidenceAll 3 parts included, but support lacking in one areaAll 3 parts included, but evidence poor in more than one areaOne or more parts are left out of the report.Oral reportOverview of report clear and all parts presented.3 to 5 minutes.Overview of report clear and all parts presented. Time frame not met.Report is not clear and one component is left out.Report is not clear, components left out, less than 3 minutes.SubtotalTotal pointsFinal Grade
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