{"id":4381,"date":"2022-04-09T15:43:33","date_gmt":"2022-04-09T15:43:33","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=4381"},"modified":"2022-04-10T01:44:49","modified_gmt":"2022-04-10T01:44:49","slug":"instructor-guide-2a-forming-connections","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/instructor-guide-2a-forming-connections\/","title":{"raw":"Instructor Guide 2A: Forming Connections","rendered":"Instructor Guide 2A: Forming Connections"},"content":{"raw":"<h2>Overview<\/h2>\r\n<ul>\r\n \t<li>This in-class activity guides students through the process of selecting a random sample\u00a0using a biased method and the process of selecting a simple random sample using an\u00a0unbiased method (random number generator),<\/li>\r\n \t<li>Students will perform both methods of selecting a sample then compare the results.<\/li>\r\n \t<li>The population\u00a0from which students will sample is an excerpt from a 2001\u00a0speech by Justice Sonia Sotomayor[footnote]<a href=\"https:\/\/www.law.berkeley.edu\/article\/supreme-court-nominee-sonia-sotomayors-speech-at-berkeley-law-in-2001\/\">https:\/\/www.law.berkeley.edu\/article\/supreme-court-nominee-sonia-sotomayors-speech-at-berkeley-law-in-2001\/<\/a>[\/footnote], which they were asked to select a \"representative\" sample of 10 words from the excerpt by eye.<\/li>\r\n \t<li>This activity connects back to <em>Forming Connectons [1C]<\/em>, where students explored data collection and types of variables. It introduces the following vocabulary terms: population, sample,\u00a0parameter, statistic, unbiased, biased, simple random sample, and sampling frame.<\/li>\r\n \t<li><span style=\"background-color: #ffff99;\">S2, S4, C2, C4, C6, V1, V4, 01, 03 \u2190 Link to EBTP descriptions\u00a0<\/span><\/li>\r\n<\/ul>\r\n<h3>Prerequisite assumptions<\/h3>\r\nStudents should be able to do each of the following after completing the <em>What to Know<\/em> assignment.\r\n<ul>\r\n \t<li>Identify the population for a given study.<\/li>\r\n \t<li>Identify the parameter of interest for a given study.<\/li>\r\n \t<li>Determine whether a sampling method is biased and explain why.<\/li>\r\n<\/ul>\r\n<h3>Intended goals for this activity<\/h3>\r\nAfter completing this activity, students should understand that collecting a sample \u201cby eye\u201d will, in general, be a biased sampling method. They will also understand that a simple random sample is an unbiased sampling method. They should be able to select\u00a0a simple random sample from a finite population using a random number\u00a0generator and explain why a sampling method is unbiased or biased.\r\n<h2>Synchronous Delivery and Activity Flow<\/h2>\r\nThe sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.\r\n<h3>Frame the activity (3 minutes)<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Technology\r\n<ul>\r\n \t<li aria-level=\"1\">Note that students will need access to a web browser to use the Data\u00a0Analysis Tools, either individually or in\u00a0 groups. If only the instructor\u00a0has access to a computer, skip Questions 7\u20139, demonstrate\u00a0Question 12 for the class, and then have students answer Questions\u00a010 and 11 using the plot from Question 12 rather than the plot that\u00a0would have been generated in Question 9.<\/li>\r\n \t<li aria-level=\"1\">A method for collecting student data and displaying in a dotplot should be set up ahead of time to facilitate Questions 5 and 9. This could be as low-tech as drawing a horizontal axis on a whiteboard and having students place a dot at the location of their sample mean.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li aria-level=\"1\">Question 1 -- think-pair-share\u00a0<span style=\"background-color: #ffff99;\">S2, C4, V1, V4, O3<\/span>\r\n<ul>\r\n \t<li aria-level=\"1\">Allow 30 seconds for students to think about Question 1 then discuss their answers with a partner for two minutes. Ask some of the pairs to share their ideas.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Transition to the in-class activity by briefly discussing the Objectives\u00a0for the activity.<\/li>\r\n<\/ul>\r\n<h3>Activity Flow (17 minutes)<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Questions 2-4 -- working individually, then moving into groups\u00a0<span style=\"background-color: #ffff99;\">C6, V1, O1, O3, S2, S4<\/span>\r\n<ul>\r\n \t<li aria-level=\"1\">Guiding questions: \"\u201cWhat makes a sample representative of a population?\u201d and\u00a0\u201cDo you feel your method of sampling led to a representative\u00a0sample?\u201d<\/li>\r\n \t<li aria-level=\"1\">After students have answered Questions 2 - 4 individually, have them come together in small groups and come to a consensus of what \"representative\" means.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Question 5 -- working in groups <span style=\"background-color: #ffff99;\">S4<\/span>\r\n<ul>\r\n \t<li aria-level=\"1\">Display a dotplot of student sample means. Students are not\u00a0introduced to visual displays of quantitative data until In-Class\u00a0Activity 3.C, but students should be familiar enough with dotplots\u00a0from previous K\u201312 work in order for them to understand the plots. To save time as needed, an example appears in the text.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li aria-level=\"1\">Question 6 -- working in groups <span style=\"background-color: #ffff99;\">S4<\/span>\r\n<ul>\r\n \t<li aria-level=\"1\">Students will not yet be familiar with descriptive characteristics like shape, center, spread, and variability. Ask instead about what value they think might represent a \"typical\" sample and if they can describe the distribution visually.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li aria-level=\"1\">Questions 7 - 10 -- think-pair-share or small groups <span style=\"background-color: #ffff99;\">C4, V1, O3<\/span>\r\n<ul>\r\n \t<li aria-level=\"1\">Have students complete Questions 7 and 8 individually before working in pairs. Assist with the random number generator as needed.<\/li>\r\n \t<li aria-level=\"1\">In Question 9, collect student data to display a dotplot of the distribution of student-generated sample means. To save time as needed, an example appears in the text.<\/li>\r\n \t<li aria-level=\"1\">In Question 10, provide the population mean for this excerpt before students continue. The population mean is 4.68.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li aria-level=\"1\">Questions 11-13 -- small groups <span style=\"background-color: #ffff99;\">C4, V1, O3, O1<\/span>\r\n<ul>\r\n \t<li aria-level=\"1\">Throughout these questions, have students compare their answers\u00a0from their collected data to get a sense of sampling variability.<\/li>\r\n \t<li aria-level=\"1\">To save time, you may want to either skip Question 12 or do\u00a0Question 12 on your computer and display for the class using a\u00a0projector.<\/li>\r\n \t<li aria-level=\"1\">Students may struggle with the concept that it's the sampling method that is unbiased\/biased, not an individual sample.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h3>Wrap-up\/transition (5 minutes)<\/h3>\r\n<ul>\r\n \t<li>Exit tickets can be used to check student understanding at the end\u00a0of the activity.\r\n<ul>\r\n \t<li>Have each student write on a piece of paper one key\u00a0concept they learned from the activity and one concept they have\u00a0questions about.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Have students refer back to the Objectives for the activity and\u00a0check the ones they recognize. Alternatively, they may check the\u00a0objectives throughout the activity.<\/li>\r\n \t<li>Let students know that the next activity will continue these ideas by discussing sampling methods and sampling bias.<\/li>\r\n \t<li>Assign the homework or\u00a0<em>Practice<\/em>\u00a0and any <em>What to Know<\/em> pages for the <em>Forming Connections<\/em> activities you plan to complete in the next class meeting. <span style=\"background-color: #ffff99;\">C2<\/span><\/li>\r\n<\/ul>","rendered":"<h2>Overview<\/h2>\n<ul>\n<li>This in-class activity guides students through the process of selecting a random sample\u00a0using a biased method and the process of selecting a simple random sample using an\u00a0unbiased method (random number generator),<\/li>\n<li>Students will perform both methods of selecting a sample then compare the results.<\/li>\n<li>The population\u00a0from which students will sample is an excerpt from a 2001\u00a0speech by Justice Sonia Sotomayor<a class=\"footnote\" title=\"https:\/\/www.law.berkeley.edu\/article\/supreme-court-nominee-sonia-sotomayors-speech-at-berkeley-law-in-2001\/\" id=\"return-footnote-4381-1\" href=\"#footnote-4381-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>, which they were asked to select a &#8220;representative&#8221; sample of 10 words from the excerpt by eye.<\/li>\n<li>This activity connects back to <em>Forming Connectons [1C]<\/em>, where students explored data collection and types of variables. It introduces the following vocabulary terms: population, sample,\u00a0parameter, statistic, unbiased, biased, simple random sample, and sampling frame.<\/li>\n<li><span style=\"background-color: #ffff99;\">S2, S4, C2, C4, C6, V1, V4, 01, 03 \u2190 Link to EBTP descriptions\u00a0<\/span><\/li>\n<\/ul>\n<h3>Prerequisite assumptions<\/h3>\n<p>Students should be able to do each of the following after completing the <em>What to Know<\/em> assignment.<\/p>\n<ul>\n<li>Identify the population for a given study.<\/li>\n<li>Identify the parameter of interest for a given study.<\/li>\n<li>Determine whether a sampling method is biased and explain why.<\/li>\n<\/ul>\n<h3>Intended goals for this activity<\/h3>\n<p>After completing this activity, students should understand that collecting a sample \u201cby eye\u201d will, in general, be a biased sampling method. They will also understand that a simple random sample is an unbiased sampling method. They should be able to select\u00a0a simple random sample from a finite population using a random number\u00a0generator and explain why a sampling method is unbiased or biased.<\/p>\n<h2>Synchronous Delivery and Activity Flow<\/h2>\n<p>The sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.<\/p>\n<h3>Frame the activity (3 minutes)<\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Technology\n<ul>\n<li aria-level=\"1\">Note that students will need access to a web browser to use the Data\u00a0Analysis Tools, either individually or in\u00a0 groups. If only the instructor\u00a0has access to a computer, skip Questions 7\u20139, demonstrate\u00a0Question 12 for the class, and then have students answer Questions\u00a010 and 11 using the plot from Question 12 rather than the plot that\u00a0would have been generated in Question 9.<\/li>\n<li aria-level=\"1\">A method for collecting student data and displaying in a dotplot should be set up ahead of time to facilitate Questions 5 and 9. This could be as low-tech as drawing a horizontal axis on a whiteboard and having students place a dot at the location of their sample mean.<\/li>\n<\/ul>\n<\/li>\n<li aria-level=\"1\">Question 1 &#8212; think-pair-share\u00a0<span style=\"background-color: #ffff99;\">S2, C4, V1, V4, O3<\/span>\n<ul>\n<li aria-level=\"1\">Allow 30 seconds for students to think about Question 1 then discuss their answers with a partner for two minutes. Ask some of the pairs to share their ideas.<\/li>\n<\/ul>\n<\/li>\n<li>Transition to the in-class activity by briefly discussing the Objectives\u00a0for the activity.<\/li>\n<\/ul>\n<h3>Activity Flow (17 minutes)<\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Questions 2-4 &#8212; working individually, then moving into groups\u00a0<span style=\"background-color: #ffff99;\">C6, V1, O1, O3, S2, S4<\/span>\n<ul>\n<li aria-level=\"1\">Guiding questions: &#8220;\u201cWhat makes a sample representative of a population?\u201d and\u00a0\u201cDo you feel your method of sampling led to a representative\u00a0sample?\u201d<\/li>\n<li aria-level=\"1\">After students have answered Questions 2 &#8211; 4 individually, have them come together in small groups and come to a consensus of what &#8220;representative&#8221; means.<\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Question 5 &#8212; working in groups <span style=\"background-color: #ffff99;\">S4<\/span>\n<ul>\n<li aria-level=\"1\">Display a dotplot of student sample means. Students are not\u00a0introduced to visual displays of quantitative data until In-Class\u00a0Activity 3.C, but students should be familiar enough with dotplots\u00a0from previous K\u201312 work in order for them to understand the plots. To save time as needed, an example appears in the text.<\/li>\n<\/ul>\n<\/li>\n<li aria-level=\"1\">Question 6 &#8212; working in groups <span style=\"background-color: #ffff99;\">S4<\/span>\n<ul>\n<li aria-level=\"1\">Students will not yet be familiar with descriptive characteristics like shape, center, spread, and variability. Ask instead about what value they think might represent a &#8220;typical&#8221; sample and if they can describe the distribution visually.<\/li>\n<\/ul>\n<\/li>\n<li aria-level=\"1\">Questions 7 &#8211; 10 &#8212; think-pair-share or small groups <span style=\"background-color: #ffff99;\">C4, V1, O3<\/span>\n<ul>\n<li aria-level=\"1\">Have students complete Questions 7 and 8 individually before working in pairs. Assist with the random number generator as needed.<\/li>\n<li aria-level=\"1\">In Question 9, collect student data to display a dotplot of the distribution of student-generated sample means. To save time as needed, an example appears in the text.<\/li>\n<li aria-level=\"1\">In Question 10, provide the population mean for this excerpt before students continue. The population mean is 4.68.<\/li>\n<\/ul>\n<\/li>\n<li aria-level=\"1\">Questions 11-13 &#8212; small groups <span style=\"background-color: #ffff99;\">C4, V1, O3, O1<\/span>\n<ul>\n<li aria-level=\"1\">Throughout these questions, have students compare their answers\u00a0from their collected data to get a sense of sampling variability.<\/li>\n<li aria-level=\"1\">To save time, you may want to either skip Question 12 or do\u00a0Question 12 on your computer and display for the class using a\u00a0projector.<\/li>\n<li aria-level=\"1\">Students may struggle with the concept that it&#8217;s the sampling method that is unbiased\/biased, not an individual sample.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>Wrap-up\/transition (5 minutes)<\/h3>\n<ul>\n<li>Exit tickets can be used to check student understanding at the end\u00a0of the activity.\n<ul>\n<li>Have each student write on a piece of paper one key\u00a0concept they learned from the activity and one concept they have\u00a0questions about.<\/li>\n<\/ul>\n<\/li>\n<li>Have students refer back to the Objectives for the activity and\u00a0check the ones they recognize. Alternatively, they may check the\u00a0objectives throughout the activity.<\/li>\n<li>Let students know that the next activity will continue these ideas by discussing sampling methods and sampling bias.<\/li>\n<li>Assign the homework or\u00a0<em>Practice<\/em>\u00a0and any <em>What to Know<\/em> pages for the <em>Forming Connections<\/em> activities you plan to complete in the next class meeting. <span style=\"background-color: #ffff99;\">C2<\/span><\/li>\n<\/ul>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-4381-1\"><a href=\"https:\/\/www.law.berkeley.edu\/article\/supreme-court-nominee-sonia-sotomayors-speech-at-berkeley-law-in-2001\/\">https:\/\/www.law.berkeley.edu\/article\/supreme-court-nominee-sonia-sotomayors-speech-at-berkeley-law-in-2001\/<\/a> <a href=\"#return-footnote-4381-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":25777,"menu_order":11,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4381","chapter","type-chapter","status-publish","hentry"],"part":4126,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4381","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":8,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4381\/revisions"}],"predecessor-version":[{"id":4433,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4381\/revisions\/4433"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/4126"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4381\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=4381"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=4381"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=4381"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=4381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}