{"id":748,"date":"2017-07-07T09:19:03","date_gmt":"2017-07-07T13:19:03","guid":{"rendered":"http:\/\/sites.miamioh.edu\/edt222-2017\/?p=748"},"modified":"2018-05-24T22:12:46","modified_gmt":"2018-05-25T02:12:46","slug":"knurek-pbl","status":"publish","type":"post","link":"https:\/\/sites.miamioh.edu\/edt222-2017\/2017\/07\/knurek-pbl\/","title":{"rendered":"Knurek &#8211; PBL"},"content":{"rendered":"<p><strong><u>PBL Lesson: \u201cHeight vs. Shoe Size\u201d<\/u><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-751\" src=\"http:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/07\/Screen-Shot-2017-07-07-at-9.17.48-AM-297x300.png\" alt=\"\" width=\"297\" height=\"300\" srcset=\"https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/07\/Screen-Shot-2017-07-07-at-9.17.48-AM-297x300.png 297w, https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/07\/Screen-Shot-2017-07-07-at-9.17.48-AM.png 474w\" sizes=\"auto, (max-width: 297px) 100vw, 297px\" \/><\/p>\n<p><strong>Standards:<\/strong><\/p>\n<p><strong>8.SP.1:<\/strong> Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.<\/p>\n<p><strong>8.SP.2:<\/strong> Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.<\/p>\n<p><strong>8.SP.3:<\/strong> Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm\/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.<\/p>\n<p><strong>Objectives:<\/strong><\/p>\n<ul>\n<li>Students will be able to construct a scatter plot.<\/li>\n<li>Students will be able to identify outliers in data.<\/li>\n<li>Students will be able to draw a line of best fit.<\/li>\n<li>Students will be able to come up with the equation for the line of best fit.<\/li>\n<li>Students will be able to use linear regression.<\/li>\n<\/ul>\n<p><strong>Student Learning Goals:<\/strong><\/p>\n<p>This project requires students to collect and analyze data to see if there is a strong relationship between a person\u2019s height and their shoe size. Students are challenged with a task as a lawyer for a person being charged with a crime. They are required to use statistical reasoning to justify whether or not the person is innocent.<\/p>\n<p>This lesson requires students to perform the following:<\/p>\n<ul>\n<li>Collect meaningful data<\/li>\n<li>Create a scatter plot of data<\/li>\n<li>Identify outliers in a set of data<\/li>\n<li>Come up with an equation to represent the line of best fit for a set of data<\/li>\n<li>Come up with and analyze linear regression<\/li>\n<\/ul>\n<p><strong>Challenging Problem:<\/strong><\/p>\n<p>You are a lawyer hired by a man being charged with robbery. The man who hired you was one of several men spotted near a bank right after it had been broken into. The man swears that he did not rob the bank, saying that he was just in the wrong place at the wrong time. The man was arrested after the one sole witness identified him as the robber. However, her statement about the man\u2019s height and shoe size doesn\u2019t seem to be accurate:<\/p>\n<p>\u201cThe man was over 6-feet tall! However, he seemed to have very small feet. I would have to say he probably wears a size 8, maybe size 7\u201d<\/p>\n<p><strong>Project Outline:<\/strong><\/p>\n<p>If you can prove that the sole witness\u2019s statement is invalid, the man will be set free (proven innocent). Your goal is to prove that this man is innocent by falsifying the witness\u2019s statement using statistical reasoning. You must collect and analyze data on people\u2019s heights and shoe sizes. You can collect the data however you\u2019d like, but you must be able to justify your final sample size.<\/p>\n<p>(Students will have time in class to work on this project, but are encouraged to collect data outside of the classroom. The goal is to have the students collect data from people of all heights and sizes. If they only collect data in their class, the sample will be restricted to 8th grade students.)<\/p>\n<p><strong>Assessment:<\/strong><\/p>\n<p>Upon completion of the data collection process, put together a presentation of the data to justify to your classmates that the witness\u2019s statement is false. Your presentation should include a scatterplot of the data you collected, along with the line of best fit and linear regression.<\/p>\n<p><strong>Authenticity:<\/strong><\/p>\n<p>This is the part that I&#8217;m struggling with. I think that this lesson is in part &#8216;real-world&#8217;, however the statement that the witness gave would never be enough to put a suspect in jail. However, I do think the process of using data to justify a decision is very &#8216;real-world&#8217;. This lesson could shed light on how statistics can be used to not only justify your own decisions, but also to persuade the decisions of others.<\/p>\n<p><strong>Reflection:<\/strong><\/p>\n<p>The reflection process of this project will take two different forms:<\/p>\n<ol>\n<li>Class Discussion: After all of the students have presented, the teacher will lead a class discussion on the similarities and differences between the data presentations. Were some people more thorough than others? How can we determine if a sample size accurately represents a population? There are a lot of statistical connections that can be made during this discussion.<\/li>\n<li>Personal Reflection: The teacher will fill out a rubric with feedback for the students. The feedback will provide the students with strengths and weaknesses for their statistical argument. The student will reflect on their presentation and data collection process using this feedback.<\/li>\n<\/ol>\n<p><strong>Media:<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/www.statcrunch.com\/5.0\/viewreport.php?reportid=35115\">Height vs. Shoe Size<\/a><\/li>\n<li><a href=\"https:\/\/www.mathsisfun.com\/data\/correlation.html\">Correlation<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>PBL Lesson: \u201cHeight vs. Shoe Size\u201d Standards: 8.SP.1: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. &hellip; <a href=\"https:\/\/sites.miamioh.edu\/edt222-2017\/2017\/07\/knurek-pbl\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2104,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[1,2],"tags":[162,163,63,148,70],"class_list":["post-748","post","type-post","status-publish","format-standard","hentry","category-misc","category-pbl","tag-correlation","tag-height-vs-shoe-size","tag-math","tag-pbl","tag-statistics"],"_links":{"self":[{"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/posts\/748","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/users\/2104"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/comments?post=748"}],"version-history":[{"count":3,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/posts\/748\/revisions"}],"predecessor-version":[{"id":752,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/posts\/748\/revisions\/752"}],"wp:attachment":[{"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/media?parent=748"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/categories?post=748"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/tags?post=748"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}