Unit 5: Statistics and Probability (7.SP)

Big Ideas:
Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences. (CCSC Grade 7 p.46)

In Grade 7, students move from concentrating on analysis of data to production of data, understanding that good answers to statistical questions depend upon a good plan for collecting data relevant to the questions of interest. Because statistically sound data production is based on random sampling, a probabilistic concept, students must develop some knowledge of probability before launching into sampling. Their introduction to probability is based on seeing probabilities of chance events as long-run relative frequencies of their occurrence, and many opportunities to develop the connection between theoretical probability models and empirical probability approximations. This connection forms the basis of statistical inference. With random sampling as the key to collecting good data, students begin to differentiate between the variability in a sample and the variability inherent in a statistic computed from a sample when samples are repeatedly selected from the same population. This understanding of variability allows them to make rational decisions, say, about how different a proportion of “successes” in a sample is likely to be from the proportion of “successes” in the population or whether medians of samples from two populations provide convincing evidence that the medians of the two populations also differ. (CCSC writing team p. 2 (December 2011) www.commoncoretools.wordpress.com)

Overview (Big Ideas), Enduring Understandings, Essential Questions, Common Misconceptions:


Unit 5 Starting Points: *New*


McCallum Web Resource:
Statistics and Probability Progressions Document

Maryland State Department of Education Resources: *New*
Grade 7 Statistics and Probability

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Common Core Content Standards:

Use random sampling to draw inferences about a population.
7.SP.A.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

HCPSS Math Task:
Verbose Words (This task also addresses 7.SP.2)


HCPSS UDL Lesson:
Cloning




PARCC Assessment Limit/Clarification:
This standard is part of supporting content cluster assessed on PARCC. This content cluster supports the work in the Ratios and Proportional Relationships domain. The standards in this cluster represent opportunities to apply percentages and proportional reasoning. To make inferences about a population, one needs to apply such reasoning to the sample and the entire population.
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Web Resources:
http://www.learnnc.org/lessons/
Learn North Carolina lesson plans and ideas: Lessons from this website may apply to all domains.

http://www.ilovemath.org/index.php?option=com_docman&Itemid=31
I Love Math lesson supplements or homework ideas created and posted by other teachers.

http://www.amstat.org/censusatschool/index.cfm
Census at School: Students can fill out their own version of the census and compare their results with the class or even with other students in the U.S.


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Use random sampling to draw inferences about a population.
7.SP.A.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

HCPSS Math Task:
Ping Pong


PARCC Assessment Limit/Clarification:
This standard is part of supporting content cluster assessed on PARCC. This content cluster supports the work in the Ratios and Proportional Relationships domain. The standards in this cluster represent opportunities to apply percentages and proportional reasoning. To make inferences about a population, one needs to apply such reasoning to the sample and the entire population.
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Web Resources:
http://www.learner.org/courses/learningmath/data/session2/part_b/index.html
Counting Raisins: This applet allows students to examine a small box of raisins to make predictions about larger boxes.

http://serc.carleton.edu/sp/cause/datasim/examples/reeses.html
Reese's Pieces Activity on Sampling: This is a simple lesson plan on sample size and sample distributions. If you click on other parts of the website, you can find teaching tips, resources, and instructional ideas (such as a gallery walk, game-based learning, teaching with simulations, etc.).

http://fcit.usf.edu/math/lessons/activities/GoFishT.htm
Florida Center for Instructional Technology: Go Fish Lesson. This is a simple lesson plan on representative samples. There is a link for Math Portal Home which has links for math templates and clipart for use in the classroom.


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Draw informal comparative inferences about two populations.
7.SP.B.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

HCPSS Math Tasks:
Team USA




A (Ear)Budding Problem. (This task may also be used for 6.SP.4, 6.SP.5, and 7.SP.4).



PARCC Assessment Limit/Clarification:
This standard is considered additional content assessed on PARCC.
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Web Resources:
http://www.keycurriculum.com/resources/tinkerplots-resources/free-activities-and-resources/data-analysis-and-modeling-activities
TinkerPlots®Dynamic Data Exploration is a technological resource for teachers to create visual representations of data. It can be used to create graphs, analyze data, model probability, and simulate data. This particular link has a list of middle school math lesson plans that already incorporate TinkerPlots®. Each link is a zip file that will open a folder with a lesson plan and additional supplements you might need for that lesson. Sketching Distributions and Fish Length Distributions are two specific lessons that address 7.RP.3.

http://ittc-web.astate.edu/lessonportal/viewLesson.php?lid=20
SMART Portal (Science and Mathematics Accessible Resource Tool developed by Arkansas State University). "We're in the Money" Lesson includes teacher preparation notes, a 5E lesson plan, and student work samples.


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Draw informal comparative inferences about two populations.
7.SP.B.4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

HCPSS Math Task:
The Great Debate


PARCC Assessment Limit/Clarification:
This standard is considered additional content assessed on PARCC.
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Web Resources:
http://www2.edc.org/mathpartners/pdfs/6-8%20Statistics%20and%20Probability.pdf
This site contains activities for various probability and data analysis topics.

http://www.prb.org/Educators/LessonPlans/200/PyramidBuilding.aspx
Pyramid Building Lesson (created by the Population Reference Bureau). Materials and website links are included in the plan.


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Investigate chance processes and develop, use, and evaluate probability models.
7.SP.C.5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Note: Introduce concepts of sample space, independent and dependent events.

HCPSS UDL Lesson:
Deal or No Deal





PARCC Assessment Limit/Clarification:
This standard is part of supporting content cluster assessed on PARCC. This content cluster supports the work in the Ratio and Proportional Relationships domain. Probability models draw on proportional reasoning and should be connected to the major work in those standards.
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Web Resources:
http://classroom.jc-schools.net/basic/math-prob.html
This site includes games and activities involving probability.

http://xpmath.com/forums/arcade.php?do=play&gameid=70
http://www.nbc.com/Deal_or_No_Deal/
Each of these sites allow the user to play the game Deal or No Deal. Teachers can use these sites for the Deal or No Deal lesson and can encourage students to calculate probabilities as they play.

http://www.xpmath.com/forums/arcade.php?do=play&gameid=98
This link is for the game Plinko: The Probability is Right. Students can play this game to practice finding probabilities. If you go to the top of the page, under the tab "Data Analysis and Probability", you can find more games for students to play and practice various standards.


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Investigate chance processes and develop, use, and evaluate probability models.
7.SP.C.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

HCPSS Math Task:
Conquering SKUNK (for 7.SP.5 & 7.SP.6)


PARCC Assessment Limit/Clarification:
This standard is part of supporting content cluster assessed on PARCC. This content cluster supports the work in the Ratio and Proportional Relationships domain. Probability models draw on proportional reasoning and should be connected to the major work in those standards.
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Web Resources:
http://www.shodor.org/interactivate/activities
This site includes online probability simulations.

http://www.stagecast.com/cgi-bin/templator.cgi?PAGE=School/worlds/simhost/COINFLIP_SIM
This site includes coin flip simulations.

http://education.ti.com/calculators/downloads/US/Activities/Detail?id=13726
"Probability Not!" Lesson: This TI lesson plan utilizes graphing calculators. Teachers notes and student work samples are included.


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Investigate chance processes and develop, use, and evaluate probability models.
7.SP.C.7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

7a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

HCPSS UDL Lesson:
Candy Colors





PARCC Assessment Limit/Clarification:
This standard is part of supporting content cluster assessed on PARCC. This content cluster supports the work in the Ratio and Proportional Relationships domain. Probability models draw on proportional reasoning and should be connected to the major work in those standards.
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Web Resources:
http://alex.state.al.us/lesson_view.php?id=29784
"Flipping out over Probability!" Lesson: This lesson plan includes specific teacher instructions, student worksheets, online self-check quizzes, and links to related extension activities.


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Investigate chance processes and develop, use, and evaluate probability models.
7.SP.C.7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

7b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

HCPSS Math Tasks:
Deli Dilemma (This task also corresponds to 7.SP.8b.)



PARCC Assessment Limit/Clarification:
This standard is part of supporting content cluster assessed on PARCC. This content cluster supports the work in the Ratio and Proportional Relationships domain. Probability models draw on proportional reasoning and should be connected to the major work in those standards.
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Web Resources:
http://joshmadison.com/2007/12/02/mms-color-distribution-analysis/
Josh Madison Blog post on M&M sampling.

http://www.mathlanding.org/content/data-analysis-two-dice-toss
Math Landing: This site includes resources and tools for elementary math teachers, but the lessons may be adapted for middle school grades.

http://www.mathwire.com/data/dicetoss2.html
Two Dice Toss Games: Directions for various dice games as well as other student resources needed for the games are included.

http://www.mathlanding.org/content/probability-and-law-large-numbers
http://www.pbslearningmedia.org/content/vt107.math.data.col.lplawlarge/
Probability and the Law of Large Numbers: Each of the sites above link to a PBS lesson plan that includes media resources, materials, and answer keys.

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Investigate chance processes and develop, use, and evaluate probability models.
7.SP.C.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

8a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

HCPSS Math Task:
The Kingdom Problem (for 7.SP.8a and 7.SP.8c)


PARCC Assessment Limit/Clarification:
This standard is part of supporting content cluster assessed on PARCC. This content cluster supports the work in the Ratio and Proportional Relationships domain. Probability models draw on proportional reasoning and should be connected to the major work in those standards.
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Web Resources:
http://www.crctlessons.com/probability-of-compound-events.html
This site includes online videos, games, and quizzes about compound probability.

http://alex.state.al.us/lesson_view.php?id=24042
"Probability with Tree Diagrams" This Alabama Learning Exchange Lesson focuses on finding probability and total outcomes using tree diagrams. Extension and remediation ideas are included, as well as all materials, PowerPoints and supplemental resources.

http://www.webquest.hawaii.edu/kahini/webquests/math/grade6/MA6.14.1Junkenpo/index.php
"What should I show?" Webquest: This online webquest is designed for students to follow and complete a task exploring probability. On the side you can easily access background information, outcomes, evaluation, steps, reflection, feedback, and additional resources.

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Investigate chance processes and develop, use, and evaluate probability models.
7.SP.C.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

8b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

HCPSS Math Task:
Cafe 240


PARCC Assessment Limit/Clarification:
This standard is part of supporting content cluster assessed on PARCC. This content cluster supports the work in the Ratio and Proportional Relationships domain. Probability models draw on proportional reasoning and should be connected to the major work in those standards.
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Web Resources:
http://mathforum.org/workshops/usi/pascal/pizza_pascal.html
Pascal's Triangle - Antonio's Pizza Palace: Use organized lists, tables, or tree diagrams to find how many pizza topping combinations you can order with a variety of toppings. The resource relates this standard to Pascal's Triangle.


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Investigate chance processes and develop, use, and evaluate probability models.
7.SP.C.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

8c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

HCPSS Math Task:
How Many Field Goals Will You Make?


PARCC Assessment Limit/Clarification:
This standard is part of supporting content cluster assessed on PARCC. This content cluster supports the work in the Ratio and Proportional Relationships domain. Probability models draw on proportional reasoning and should be connected to the major work in those standards.
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Web Resources:
http://www.scholastic.com/browse/lessonplan.isp?id=461
Scholastic Teachers: Branching Out with Tree Diagrams: This is a lesson plan on using tree diagrams to find probabilities in a real-world scenario about natural disasters.