{"id":378,"date":"2017-06-25T22:27:19","date_gmt":"2017-06-26T02:27:19","guid":{"rendered":"http:\/\/sites.miamioh.edu\/edt222-2017\/?p=378"},"modified":"2018-05-24T22:13:13","modified_gmt":"2018-05-25T02:13:13","slug":"walters-concept-based-unit","status":"publish","type":"post","link":"https:\/\/sites.miamioh.edu\/edt222-2017\/2017\/06\/walters-concept-based-unit\/","title":{"rendered":"Walters-Concept Based Unit"},"content":{"rendered":"<p><b>Unit Title<\/b><span style=\"font-weight: 400\">: \u00a0Stretching and Shrinking (title from CMP3 curriculum)<\/span><\/p>\n<p><b>Conceptual Lens<\/b><span style=\"font-weight: 400\">: \u00a0Relationships and Change<\/span><\/p>\n<p><b>Unit Strands<\/b><span style=\"font-weight: 400\">: \u00a0Perimeter and Scale Factor, Area and Scale Factor<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-381\" src=\"http:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/3371055cdf2a8d3fff4e2767b8c81a30-math-charts-middle-school-math-anchor-charts-300x225.jpg\" alt=\"\" width=\"300\" height=\"225\" srcset=\"https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/3371055cdf2a8d3fff4e2767b8c81a30-math-charts-middle-school-math-anchor-charts-300x225.jpg 300w, https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/3371055cdf2a8d3fff4e2767b8c81a30-math-charts-middle-school-math-anchor-charts.jpg 736w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><b>Web out Unit\u2019s topics and concepts<\/b><span style=\"font-weight: 400\">:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-379 size-large\" src=\"http:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/web-791x1024.jpg\" width=\"640\" height=\"829\" srcset=\"https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/web-791x1024.jpg 791w, https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/web-232x300.jpg 232w, https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/web-768x994.jpg 768w, https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/web.jpg 1275w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><b>Generalizations:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">The scale factor of a polygon has a relationship towards how the perimeter and area of the new figure changes.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Scale factor is how much larger or smaller a figure is getting in all dimensions.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">The perimeter change will be the scale factor<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">The area change will be the scale factor squared<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">The changes of perimeter and area only apply if the 2 figures are similar.<\/span><\/li>\n<\/ul>\n<p><b>Develop the guiding questions<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">How do you find the area of a polygon? (F)<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">How do you find the perimeter of a polygon? (F)<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">How do you find scale factor? (C)<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">How do you see the perimeter is affected by a scale factor? (C) <\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">How do you see the area is affected by the scale factor? (C)<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">What would happen if you are looking at volume changes with a scale factor? (D)<\/span><\/li>\n<\/ul>\n<p><b> Identify the Critical Content<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Perimeter is the outside distance around a figure<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Area is the inside space of a figure<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Scale factor affects all dimensions of a figure and is the number I multiplied each of the sides of the original figure to get to my new figure<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Similar shapes have a scale factor, same angles and same shape.<\/span><\/li>\n<\/ul>\n<p><b>Identify the Key Skills<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">How to calculate area and perimeter<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">How to build a figure based on a certain scale factor<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Using multiplication and division skills to find a pattern<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Be familiar with and be able to calculate problems involving an exponent of 2<\/span><\/li>\n<\/ul>\n<p><strong>Standards:<\/strong><\/p>\n<p class=\"g-eight-text\">7.RP.2: \u00a0Recognize and represent proportional relationships between quantities.<\/p>\n<p class=\"g-eight-text\">7.RP.3: \u00a0Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.<\/p>\n<p><span class=\"fa fa-circle-o undergrad-text-dk-yellow\">\u00a0<\/span>\u00a07.G.1: \u00a0Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.<\/p>\n<p>7.G.2: \u00a0Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.<\/p>\n<p><b>Day 1: \u00a0<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400\">Students will watch this you tube video to refresh their thinking on scale factor before we begin our activity:<\/li>\n<\/ul>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=8HNsG6qhl60\">https:\/\/www.youtube.com\/watch?v=8HNsG6qhl60<\/a><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Students are given centimeter cubes in their groups and a piece of white paper. \u00a0They are to create a rectangle of any number of cubes long (from 4-20) and any number of cubes wide (from 4-20).<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-382\" src=\"http:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/61z9Vt11ybL._SY355_-300x300.jpg\" alt=\"\" width=\"213\" height=\"213\" srcset=\"https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/61z9Vt11ybL._SY355_-300x300.jpg 300w, https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/61z9Vt11ybL._SY355_-150x150.jpg 150w, https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/61z9Vt11ybL._SY355_.jpg 355w\" sizes=\"auto, (max-width: 213px) 100vw, 213px\" \/><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Using a ruler, they draw their created rectangle and remove the cubes.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Each group is given a die and they will roll to see what scale factor they will have to draw of their figure (excluding 1). \u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Using the centimeter cubes, they will create their new rectangle based on the scale factor. Then, they will draw the new rectangle on their paper.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">They will find the area and perimeter of each rectangle and write down\u00a0those answers on a new piece of paper<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">All the student groups will then hang up their work around the classroom and we will do a gallery walk where they have to go look at 3 other groups work. \u00a0As they are walking around they need to write down their original area and perimeters, the scale factor, and the new areas and perimeters while trying to come up with a pattern.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">At the end of the day, students will write down their predictions after day 1 as to how scale factor affects area and perimeter changes. \u00a0It could be helpful to ask the question, &#8220;How could I get from the original perimeter to the new perimeter?&#8221;<\/span><\/li>\n<\/ul>\n<p><b>Day 2<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400\">The day will begin with students bringing out their observations from yesterday and looking over them to see what their predictions are so far with scale factor relationships.<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Students today will be using a program on <a href=\"https:\/\/phet.colorado.edu\/en\/simulation\/area-builder\">phet.colorado.edu<\/a> to compare perimeter and area of similar shapes.<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-383\" src=\"http:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/Capture-300x212.jpg\" alt=\"\" width=\"300\" height=\"212\" srcset=\"https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/Capture-300x212.jpg 300w, https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/Capture.jpg 342w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">They will begin by starting with a non-traditional shape (no squares, rectangles, etc.) and the computer will calculate the area and perimeter for them. I tell students to think about Tetris pieces if they are stuck with what shape to make.\u00a0<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-384 alignright\" src=\"http:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/Capture-2-277x300.jpg\" alt=\"\" width=\"201\" height=\"218\" srcset=\"https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/Capture-2-277x300.jpg 277w, https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/Capture-2.jpg 379w\" sizes=\"auto, (max-width: 201px) 100vw, 201px\" \/><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Then, they will have to recreate their original picture with a scale factor of 2. \u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">They will do the same for scale factor of 3. \u00a0Without the program they will try to do the same activity on paper for a scale factor of 4. \u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">At the end of this lesson, students will again write down their observations and predictions for what they see happening. \u00a0As a teacher I would ask the question, how do you see the scale factor changing the perimeter? \u00a0the area?<\/span><\/li>\n<\/ul>\n<p><b>Day 3<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Students will get into their groups and each will share their predictions from the past two days of how scale factor relates to area and perimeter. <\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">They will then use the MTV strategy of headlines and create a headline for what they believe is happening.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">We will discuss the headlines as a class, making observations and establish as a group what is happening.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">I would then have us get out white boards and practice this concept as well as doing some practice at our seat to get them ready for the assessment day tomorrow<\/span><\/li>\n<\/ul>\n<p><b>Day 4: \u00a0Assessment Day<\/b><\/p>\n<p><b>Assessment and scoring guide\/rubric<\/b><\/p>\n<p><b>What:<\/b><span style=\"font-weight: 400\"> \u00a0Investigate the relationship with scale factor affecting changes in area and perimeter<\/span><\/p>\n<p><b>Why<\/b><span style=\"font-weight: 400\">: In order to understand that the scale factor times perimeter will give me my new perimeter among similar figures and the scale factor squared times area will give my new area among similar figures.<\/span><\/p>\n<p><b>How:<\/b><span style=\"font-weight: 400\"> \u00a0In our textbook that we use, we introduce the \u201cWump Family\u201d to teach the students about similar figures. \u00a0This is not in our textbook but I bring the Wump Family back through the sad new of a murder. \u00a0I have the classroom marked up like a crime scene and tape a \u201cdead\u201d Wump cartoon character on the floor. \u00a0Students are given a scale drawing of the murdered Wump. \u00a0<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-386\" src=\"http:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/wump-300x224.jpg\" alt=\"\" width=\"300\" height=\"224\" srcset=\"https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/wump-300x224.jpg 300w, https:\/\/sites.miamioh.edu\/edt222-2017\/files\/2017\/06\/wump.jpg 330w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><span style=\"font-weight: 400\">They are then given a list of clues of who killed him. \u00a0<a href=\"https:\/\/docs.google.com\/document\/d\/1Oi4O_1TUy0oHZDkwfuYQUgezBE_yQcxTJfsF21Tk4JE\/edit?usp=sharing\">Clues<\/a><\/span><\/p>\n<p><span style=\"font-weight: 400\"> It is their job as detectives to draw to scale the murderer based on the clues. \u00a0All of the clues deal with scale factors of the \u201cdead\u201d wump. \u00a0Some questions are phrased as changes in perimeter and some are asking about changes in area. \u00a0When they are completed with their drawing, they will turn it in for me to grade. \u00a0Here is the grading rubric that their grade will be based on:<\/span><\/p>\n<p><span style=\"font-weight: 400\">Correct Body<\/span> <span style=\"font-weight: 400\">___\/3<\/span><\/p>\n<p><span style=\"font-weight: 400\">Correct Hat<\/span> <span style=\"font-weight: 400\">___\/3<\/span><\/p>\n<p><span style=\"font-weight: 400\">Correct Legs<\/span> <span style=\"font-weight: 400\">___\/3<\/span><\/p>\n<p><span style=\"font-weight: 400\">Correct Arms<\/span> <span style=\"font-weight: 400\">___\/3<\/span><\/p>\n<p><span style=\"font-weight: 400\">Correct Face<\/span> <span style=\"font-weight: 400\">___\/3<\/span><\/p>\n<p><strong>TOTAL ___\/15<\/strong><\/p>\n<p><b>Unit overview<\/b><\/p>\n<p>What happens to the perimeter when a similar figure is double in size? What happens to the area when the similar figure is scaled down? \u00a0Who killed Mug Wump? \u00a0All of these questions will be answered and more as we jump into our new unit of Stretching and Shrinking. Through this unit, we will be looking at the relationship scale factor has on both area and perimeter of a similar figure. \u00a0So get ready to explore and become detectives on this great mystery we are about ready to embark on.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Unit Title: \u00a0Stretching and Shrinking (title from CMP3 curriculum) Conceptual Lens: \u00a0Relationships and Change Unit Strands: \u00a0Perimeter and Scale Factor, Area and Scale Factor Web out Unit\u2019s topics and concepts: Generalizations: The scale factor of a polygon has a relationship &hellip; <a href=\"https:\/\/sites.miamioh.edu\/edt222-2017\/2017\/06\/walters-concept-based-unit\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2109,"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":[4],"tags":[],"class_list":["post-378","post","type-post","status-publish","format-standard","hentry","category-cbci"],"_links":{"self":[{"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/posts\/378","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\/2109"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/comments?post=378"}],"version-history":[{"count":5,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/posts\/378\/revisions"}],"predecessor-version":[{"id":428,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/posts\/378\/revisions\/428"}],"wp:attachment":[{"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/media?parent=378"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/categories?post=378"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/tags?post=378"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}