Download Unit 7-Probability and Statistical Displays

Unit Overview
Content Area: Math
Unit Title: Probability and Statistical Displays
Target Course/Grade Level: Seventh Grade
Unit: 7
Timeline: 4 weeks
Unit Summary: Students will explore theoretical and experimental probabilities and determine whether
particular events are likely or unlikely. Students will understand the distinction between independent and
dependent events.
Primary interdisciplinary connections: Language Arts and Technology
9.1 21st-Centuries Life & Career Skills
Standard 9.1 All students will demonstrate the creative, critical thinking, collaboration, and
problem-solving skills needed to function successfully as both global citizens and workers in
diverse ethnic and organizational cultures.
Strand: A. Critical Thinking and Problem Solving
B. Creativity and Innovation
C. Collaboration, Teamwork and Leadership
Content Statement:
9.1.8: A The ability to recognize a problem and apply critical thinking skills and problem
solving skills to solve the problem is a lifelong skill that develops over time.
9.1.8: B Gathering and Evaluating knowledge and information from a variety of sources,
including global perspective, fosters creativity and innovative thinking.
9.1.8: C Collaboration and team work enable individuals or groups to achieve common goals
with greater efficiency.
Leadership abilities develop over time through participation in group and or teams that
that are engaged in challenging or competitive activities.
21st Century themes and skills: Critical Thinking and Problem Solving, Collaboration, Teamwork and
Leadership, Creativity and Innovation
Mathematical Practices:
7.MP.1 Make sense of problems and persevere in solving them.
7.MP.2 Reason abstractly and quantitatively.
7.MP.3 Construct viable arguments and critique the reasoning of others.
7.MP.4 Model with mathematics.
7.MP.6 Attend to precision.
7.MP.7 Look for and make use of structure.
7.MP.8 Look for and express regularity in repeated reasoning.
Learning Targets
Domain: Statistics and Probability
Cluster: Probability and Predictions / Statistical Display
Standard #
Standards
7.SP.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.
7.SP.2
Use data from a random sample to draw inferences about a population with an unknown
characteristic of interest. Generate multiple samples of the same size to gauge the variation
in estimates or predictions.
7.SP.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 measure of variability.
7.SP.4
Use measures of central and measures of variability for numerical data from random
samples to draw informal comparative inferences about two populations.
7.SP.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, and a probability around ½
indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a
likely event.
7.SP.7
Develop a probability model and use it to find probabilities of events. Compare
probabilities from a model to observe frequencies; if the agreement is not good, explain
possible sources of the discrepancy.
7.SP.7a
7.SP.7b
a. Develop a uniform probability model by assigning equal probability to all outcomes,
and use the model to determine probabilities of events.
b. Develop a probability model (which may not be uniform) by observing frequencies in
data generated from a chance process.
7.SP.8
Find probabilities of compound events using organized lists, tables, tree diagrams, and
simulations.
7.SP.8a
8.SP.8b
a. Understand that, just as with simple events, the probability of a compound event is the
fractions of outcomes in the sample space for which the compound occurs.
b. Represent sample spaces for compound events using methods such as organized lists,
tables and tree diagrams. For an event described in everyday language, identify the
outcomes in the sample space which compose the event.
9.1.8.A.1
Develop strategies to reinforce positive attitudes and productive behaviors that impact
critical thinking and problem-solving skills.
9.1.8.A.2
Implement problem-solving strategies to solve a problem in school or the community.
9.1.8.B.2
Assess data gathered to solve problems for which there are varying perspective (e.g., cross
cultural, gender specific, generational, etc.) and determine how the data can best be used to
design the multiple solutions.
9.1.8.C.1
Determine an individual’s responsibility for personal actions and contributions to group
activities.
9.1.8.C.2
Demonstrate the use of compromise, consensus and community building strategies for
carrying out different task, assignments and projects.
9.1.8.C.3
Model leadership skills during classroom and extracurricular activities.
Unit Essential Questions
 What are some real-world situations in which
you can use probability to make predictions?
 How is the sample space related to the
probability of an event?
 How are compound events related to simple
events?
 How can experimental probability be used to
make predictions?
 How are statistical displays helpful to us in our
everyday life?
Unit Enduring Understandings
 The chance of an event happening is called its
probability. The sample space consists of all
possible outcomes of a probability experiment and
to find the number of outcomes, you can use a tree
diagram or The Fundamental Counting Principle.
 Compound events consist of two or more simple
events and are either considered independent or
dependent.
 Probability can be determined either theoretically
or experimentally.
Unit Learning Targets
Students will ...
 Find the probability of a simple event.
 Find sample spaces and probabilities.
 Use multiplication to count outcomes and find probabilities.
 Find the number of permutations of a set of objects.
 Predict actions of a larger group by using a sample.
 Explore the probability of independent and dependent events.
 Find the probability of independent and dependent events.
 Predict actions of a larger group by a using a sample.
Evidence of Learning
Summative Assessment
 Determine the outcomes of an experiment, predict whether events are likely or unlikely, and if the
experiment is fair or unfair.
 Determine, compare, and make predictions based on experimental or theoretical probability of
independent or dependent events.
 Evaluate the reasonableness of a sample to determine the appropriateness of generalization made about
the population.
Equipment needed: Smart Board, white boards, calculators, Elm
Teacher Instructional Resources: Textbook (To be determined)
Study Island
Khan Academy Videos
Formative Assessments
 Skill sheets
 Quizzes/Tests
 Student workbook
Integration of Technology:
 Homework
 Math games
 Study Island
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Smart Board to play online games, utilize online resources, generate models with Smart Software.
Kahn Academy Videos
Elmo – for demonstration
Study Island
Technology Resources:
http://www.purplemath.com
http://www.khanacademy.org – Interactive 2.0 instructional and practice site. Students can view
instructional videos and complete practice modules for additional practice/remediation.
http://www.studyisland.com/ - Web-based instruction, practice, assessment and reporting built from NJ
standards.
http://www.ixl.com/math/grade-7 - IXL 7th grade online interactive activities for the students to
complete
http://www.aaamath.com/grade7.html - AAA math 7th grade – online interactive activities and
problems for the student to complete.
http://www.adaptedmind.com/Math-Worksheets.html?type=hstb – Grade level material for practice,
lessons, games, etc.
Opportunities for Differentiation:
Decelerate:
Scaffold the experience of drawing a tree diagram by providing an incomplete diagram that the students
can fill in the blanks.
Place the students’ names in a hat then draw a name, before each pick have them predict the outcome and
have them write the remaining probability. Ask them how the probability changes after each selection,
probability of boy versus girl (sum should equal 1).
Accelerated:
Have students write a short story that could be represented by a tree diagram.
Tell students there are certain number of combinations and then have them work backward to find the
possibilities – EX: 45 different lunch combinations, you may choose a sandwich, drink and dessert.
Have students work in groups to create a survey (yes or no, MC). Conduct the survey to the class and use
the results to predict the entire grade and/or school.
Teacher Notes:
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