7.5.3Ma


 * Grade: 7 Unit: 5 Week: 3**
 * Content: Populations and Samples**
 * Generating Multiple Samples**
 * Dates: 3/25/2013 – 3/28/2013 (4 days)**

How are sampling of a populations used to make valid inferences and/or predictions about their respective general populations?
 * __ Theme Essential Question __****__ : __**


 * __ Essential Questions: __**
 * How can you use a sample to gain information about a population?
 * How can you use a sample to make and compare predictions about a population?


 * __ 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. Understand that random sampling tends to produce representative samples and support valid inferences.
 * ** 7. SP.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.


 * __ Objectives __**** : **
 * The student will use a sample to gain information about a population.
 * The student will use a sample to make and compare predictions about a population.
 * The student will critique the selection process or other possible discrepancies that could affect the outcome of valid predictions.

(Taken from [|Ohio Dept of Education Mathematics Model Curriculum 6-28-2011] ** ) ** In Grade 6, students used measures of center and variability to describe data. Students continue to use this knowledge in Grade 7 as they use random samples to make predictions about an entire population and judge the possible discrepancies of the predictions. Providing opportunities for students to use real-life situations from science and social studies shows the purpose for using random sampling to make inferences about a population. Make available to students the tools needed to develop the skills and understandings required to produce a representative sample of the general population. One key element of a representative sample is understanding that a random sampling guarantees that each element of the population has an equal opportunity to be selected in the sample. Have students compare the random sample to population, asking questions like ü “Are all the elements of the entire population represented in the sample?” and ü “Are the elements represented proportionally?” Students can then continue the process of analysis by determining the measures of center and variability to make inferences about the general population based on the analysis. Provide students with random samples from a population, including the statistical measures. Ask students guiding questions to help them make inferences from the sample.
 * __ Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team __**


 * Recommended: For a quick overview of the standard(s) to be addressed in this Unit, see Arizona’s Content Standards Reference Materials at ** @http://www.azed.gov/educator-certification/

Part I: Explain the procedure used in the project Part II: Display all chart and graphs used in the project Part III: Using the information provided in the report, draw conclusions @http://www.pbs.org/teachers/mathline/lessonplans/pdf/msmp/somethingfishy.pdf Students will estimate the size of a large population by applying the concepts of ratio and proportion through the capture-recapture statistical procedure. or @http://illuminations.nctm.org/LessonDetail.aspx?id=L721 In this lesson, students experience an application of proportion that scientists actually use to solve real-life problems. Students learn how to estimate the size of a total population by taking samples and using proportions. The ratio of “tagged” items to the number of items in a sample is the same as the ratio of tagged items to the total population. or
 * __ Assessment __**** : **
 * Product: **
 * Working with a partner, students will complete one of the following projects and prepare a report:
 * ** PBS Activity: Something Fishy **
 * ** Capture-Recapture **
 * Use the **Gizmo** Activities noted below


 * Key Questions **
 * How is statistics used to gain information about a population by examining a sample of the population?
 * What must be considered in order to assure the random sample is valid?
 * How is data used from a random sample draw inferences about the population?
 * How is the variation in estimations and predictions gauged?


 * Observable Student Behaviors (Performance) **
 * The student will conduct their own experiment using a sample population in order to make inferences about the general population.

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||
 * ** Mathematical Practices **


 * __ Vocabulary __**** : **


 * ** Math ** ||
 * Population Sample Random Sample Biased Sample Prediction ||

@http://www.learner.org/courses/learningmath/data/session9/index.html In this session, you will learn how to use results from a random sample to estimate characteristics of an entire population. To predict the accuracy of your estimates, you will investigate the variation in estimates based on repeated random samples from that population. **Highly Recommended:** (7.SP.1-2) @http://illustrativemathematics.org/illustrations/235, Election Poll, Variation 1 @http://illustrativemathematics.org/illustrations/559, Election Poll, Variation 2 @http://illustrativemathematics.org/illustrations/558, Election Poll, Variation 3 @http://illustrativemathematics.org/illustrations/260, Estimate the mean state area The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
 * __ Suggested Activities __** :
 * // Houghton Mifflin On Core Mathematics Middle School // Grade 7
 * Unit 6-1, p. 139-142
 * Unit 6-2, p. 143-144
 * ABC //Mastering the Common Core in Mathematics//
 * Chapter 14.8, Simple Random Sampling, p. 185
 * Chapter 14.9, Representative Sampling, p. 186
 * // Teaching the Common Core Math Standards with Hands-On Activities //
 * Examining Samples (7.SP.1), p. 129-130
 * How many cubes? (7.SP.2), p. 131-132
 * Independent computerized lesson
 * JBHM 8th, GP 3, p. 183-210
 * Glencoe 7th Grade //Mathematics Application and Concepts Course 2//,
 * Chapter 7-3b, p. 301
 * Chapter 8-3a, p. 344
 * Chapter 8-3, p. 345-347
 * Glencoe //PreAlgebra//, Chapter 6, p. 275
 * Glencoe Algebra I, Chapter 13-1, p. 708-713
 * Gizmo Correlation
 * 7.SP.1
 * Polling: City
 * Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
 * Polling: Neighborhood
 * Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling.
 * 7.SP.2
 * Populations and Samples
 * Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population.


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Algebra’s Cool Mod 19.5 and 20


 * __ Homework __**** : ** (Teacher Discretion)
 * @http://www.kutasoftware.com/free.html To print assignment on a variety of topics.
 * See appropriate Glencoe On Core, JBHM and ABC Materials under Suggested Activities
 * Exit Slip (Question or problem to answer before leaving class that will help guide instruction for the following day.)


 * __ Terminology for Teachers __**** : **

** E ** thnicity/**C**ulture | **I**mmigration/**M**igration | **I**ntercultural **C**ompetence | **S**ocialization | **R**acism/**D**iscrimination ** High Yield Strategies ** ** S ** imilarities/**D**ifferences | **S**ummarizing/**N**otetaking | **R**einforcing/**R**ecognition | **H**omework/**P**ractice | ** N ** on-**L**inguistic representation | **C**ooperative **L**earning | **O**bjectives/**F**eedback | ** G ** enerating-**T**esting **H**ypothesis | **C**ues, **Q**uestions, **O**rganizers || Lesson Plan in Word Format (Click Cancel if asked to Log In)
 * ** Multicultural Concepts **


 * __ Resources __**** : **
 * __ Professional Texts: __**

Click on the following link, @http://libguides.nl.edu/mathinchildrenslit, and then look under __Math and Literature Bibliographies__. Many books include websites with __lesson ideas__. @http://sci.tamucc.edu/~eyoung/middle_school_literature.html @http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html
 * __ Literary Texts __**
 * ** Mathematics in Children's Literature: ** Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
 * ** Middle & High School: Literature in Mathematics **
 * ** Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine) **

@http://sci.tamucc.edu/~eyoung/literature.html
 * ** Miscellaneous Math and Children's Literature **


 * __ Informational Texts __**


 * __ Art, Music, and Media __**


 * __ Manipulatives __**


 * __ Games __**


 * @http://www.mathchimp.com/7thGrade.php
 * @http://www.sumdog.com/ A variety of games covering many math topics
 * @http://www.mathplayground.com/SMP_index.html


 * __Videos__**
 * Discovery Learning @http://www.discoveryeducation.com/
 * The Teaching Channel
 * The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
 * https://www.teachingchannel.org/videos?categories=topics common-core


 * __ SMART Board Lessons, Promethean Lessons __**
 * __ Smartboard Resource Website __ Smartboard lesson search engine

__ @http://www.shodor.org/interactivate/guide/ __
 * __ Other Activities, etc. __**
 * @http://www.mathgoodies.com/lessons/vol5/division.html
 * @http://www.math.com/school/subject1/lessons/S1U1L12GL.html
 * // Interactivate // is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.

@http://www.shodor.org/interactivate/activities/
 * __ Activities and tools: __**


 * Thinkfinity Links: Search by Common Core Standards/Seventh Grade/Math Often students are confused about ‘where to start’ when solving a multi-step equation. In this lesson the equation is labeled as a ‘party’. The 'host' is labeled (x) with remaining operations being labeled according to their relationship to the host (friends, family, acquaintances, etc...). Technology assignments are used as one method to assess student understanding.//This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.//

@http://www.ixl.com/math/grade-5/radius-diameter-circumference-and-area-of-a-circle @http://curvebank.calstatela.edu/circle/circle.htm
 * Thinkfinity Links: Search by Common Core Standards/Seventh Grade/Math @http://www.thinkfinity.org/state-standards-search
 * Website tool: @http://curvebank.calstatela.edu/circle/circle.htm
 * The Area of a Circle-The method of rearranging @http://www.themathpage.com/aTrig/area.htm
 * Website tools:

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