{"id":520,"date":"2017-06-26T23:59:50","date_gmt":"2017-06-27T03:59:50","guid":{"rendered":"http:\/\/sites.miamioh.edu\/edt222-2017\/?p=520"},"modified":"2018-05-24T22:13:13","modified_gmt":"2018-05-25T02:13:13","slug":"cbci-unit-plan-markham","status":"publish","type":"post","link":"https:\/\/sites.miamioh.edu\/edt222-2017\/2017\/06\/cbci-unit-plan-markham\/","title":{"rendered":"CBCI Unit Plan &#8211; Markham"},"content":{"rendered":"<p>The following reflects an outline for an Algebra unit on factoring that was developed using CBCI philosophies as outlined in Concept-Based Curriculum and Instruction for the Thinking Classroom by Lynn Erickson, Lois Lanning, and Rachel French.<\/p>\n<p>&nbsp;<\/p>\n<p><em>Unit Title:<\/em> Factoring: aka &#8211; Expression Makeovers<\/p>\n<p><em>Conceptual Lens:<\/em> Transformations<\/p>\n<p><em>Time Allocation:<\/em> Approximately 8 days in a high school Algebra course<\/p>\n<p><em>Unit Strands:<\/em><\/p>\n<ul>\n<li>Identifying and using Greatest Common Factor<\/li>\n<li>Factoring Trinomials<\/li>\n<li>Factoring Difference of Squares<\/li>\n<li>Using Factoring to Solve Equations<\/li>\n<\/ul>\n<p><em>Unit Overview:<\/em>\u00a0 There are many ways to transform an expression into an equivalent expression that looks different.\u00a0 How many ways can you think of to rewrite 10?\u00a0 What about 3(x+2)?\u00a0 Factoring is a common method for rewriting a sum of terms as a product of polynomials, which can be useful in solving quadratic equations.<\/p>\n<p><em>What we would like students to&#8230;<\/em><\/p>\n<ul>\n<li><strong>Know: <\/strong>How to identify the greatest common factor (GCF) (where GCF is a number, a variable, or a binomial); the definitions of factor, greatest common factor, perfect square trinomial, and difference of squares; zero factor theorem; standard form a quadratic equation.<\/li>\n<li><strong>Do: <\/strong>Factor out a GCF; factor a trinomial; factor a difference of squares; solve a quadratic equation by factoring.<\/li>\n<li><strong>Understand:<\/strong> Factoring is writing an equivalent expression; factoring is the reverse process of multiplying polynomials; factoring can be used to solve equations.<\/li>\n<\/ul>\n<table style=\"height: 282px\" width=\"841\">\n<tbody>\n<tr>\n<td>\n<table style=\"height: 58px\" width=\"363\">\n<tbody>\n<tr>\n<td><strong>Generalizations (Students understand that\u2026)<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td><strong>Guiding Questions<\/strong><\/td>\n<\/tr>\n<tr>\n<td>1. Factoring is writing an equivalent expression, transforming the expression from a sum of terms to a product of polynomials<\/td>\n<td><span style=\"text-decoration: underline\">Factual Questions<\/span>:<\/p>\n<p>What is a factor?<\/p>\n<p>What is a greatest common factor (GCF)?<\/p>\n<p>What is factoring by grouping?<br \/>\n<span style=\"text-decoration: underline\">Conceptual Questions<\/span>:<\/p>\n<p>How can identifying the GCF help us transform an expression into an equivalent expression?<\/p>\n<p>How are your two equivalent expressions similar? How are they different?<\/td>\n<\/tr>\n<tr>\n<td>2. Factoring is the reverse process of multiplying polynomials<\/td>\n<td>\n<table>\n<tbody>\n<tr>\n<td><span style=\"text-decoration: underline\">Factual Questions<\/span>:<\/p>\n<p>What are the methods for factoring a trinomial?<\/p>\n<p><span style=\"text-decoration: underline\">Conceptual Questions<\/span>:<\/p>\n<p>How is factoring related to the Distributive Property? To \u201cFOILing\u201d?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<tr>\n<td>3. Transforming an expression on one side of an equation may help in solving the equation<\/td>\n<td>\n<table>\n<tbody>\n<tr>\n<td><span style=\"text-decoration: underline\">Factual Questions<\/span>:<\/p>\n<p>What is the standard form of a quadratic equation?<\/p>\n<p>What is the zero product property?<br \/>\n<span style=\"text-decoration: underline\">Conceptual Questions<\/span>:<\/p>\n<p>Why is factoring useful in solving quadratic equations?<\/p>\n<p>How does transforming one side of the equation allow us to find potential solutions?<\/p>\n<p>Why are there two solutions to some quadratic equations?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">\n<table>\n<tbody>\n<tr>\n<td colspan=\"2\">Debatable Unit Questions: \u00a0Is there one method for factoring trinomials that is best?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p><em>Two suggested Learning Experiences:<\/em><\/p>\n<p><span style=\"text-decoration: underline\"><strong>Lesson 1:<\/strong><\/span><\/p>\n<p style=\"padding-left: 30px\">This would be the first day of the unit. \u00a0This lesson introduces students to greatest common factor, as well as reminds students of previous experiences that involved transformations of expressions, setting the foundation for the transferable macro-concept of transformations.<\/p>\n<p><strong>Objectives<\/strong>:<\/p>\n<ul>\n<li>Students will make connections to previous experiences in writing equivalent expressions.<\/li>\n<li>Students will identify common factors, and the greatest common factor, of expressions and write the factored form of these expressions.<\/li>\n<\/ul>\n<p><strong>Standards<\/strong>:<\/p>\n<ul>\n<li><a href=\"http:\/\/www.corestandards.org\/Math\/Content\/HSA\/SSE\/A\/1\/a\/\">CCSS.Math.Content.HSA.SSE.A.1.a<\/a> &#8211; Interpret parts of an expression, such as terms, factors, and coefficients.<\/li>\n<li><a href=\"http:\/\/www.corestandards.org\/Math\/Content\/HSA\/SSE\/A\/2\/\">CCSS.Math.Content.HSA.SSE.A.2<\/a> &#8211; \u00a0Use the structure of an expression to identify ways to rewrite it.<\/li>\n<li><a href=\"http:\/\/www.corestandards.org\/Math\/Practice\/MP7\/\">CCSS.Math.Practice.MP7<\/a> &#8211; \u00a0Look for and make use of structure.<\/li>\n<\/ul>\n<p><strong>Resources and Materials<\/strong>:<\/p>\n<p style=\"padding-left: 30px\">Teacher &#8211; White board (or poster paper) and marker<\/p>\n<p style=\"padding-left: 30px\">Student &#8211; Pencil and paper<\/p>\n<p><strong>Learning Tasks<\/strong>:<\/p>\n<ol>\n<li>Warm-up Discussion: When students enter the room, have the following task on the board\/projector, \u201cWrite at least two different expressions that are equivalent to 10 but look different.\u201d \u00a0Students may work individually or with a neighbor. (Potential answers: 2*5, 3+7, 11-1, 3*2+4, etc.) \u00a0After a minute, ask students to share some of their expressions and record them beside \u201c10\u201d on the board\/projector. \u00a0Repeat the process with 3(x+4), which will likely trigger students to apply the familiar distributive property, giving 3x+12.<\/li>\n<li>Review of key features\/terms: Using the lists of equivalent expressions from the warm-up, have students identify expressions that display a sum vs. a product, recall the definition of factor, and identify the factors in the product expressions. \u00a0Ask students to speculate about (greatest) common factors in variable expressions based off their understanding of (greatest) common factors in numbers.<\/li>\n<li>GCF Maze: For practice, have students do a GCF maze, like this one available on Pintrest, <a href=\"https:\/\/www.pinterest.com\/pin\/415034921893301951\/\">https:\/\/www.pinterest.com\/pin\/415034921893301951\/<\/a>.<\/li>\n<li>The Transformation: Now that we have the GCF, let\u2019s actually transform the expression to an equivalent, but different looking, one. \u00a0This Khan Academy video, <a href=\"https:\/\/www.youtube.com\/watch?v=FvS7v6KM1ig\">https:\/\/www.youtube.com\/watch?v=FvS7v6KM1ig<\/a>, has a good explanation of \u201cundistributing\u201d this GCF, starting around the 2.5 minute mark.<\/li>\n<\/ol>\n<p><strong>Assessment<\/strong>:<\/p>\n<p style=\"padding-left: 30px\">Teacher will informally assess prior knowledge and understanding based off discussions. \u00a0The warm-up for Day 2\u2019s lesson will be a sum of terms where students are asked to identify the GCF and rewrite the expression as a product of the GCF and the remaining factor(s).<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"text-decoration: underline\"><strong>Lesson 2:<\/strong><\/span><\/p>\n<p style=\"padding-left: 30px\">This will be day 3 of the unit. \u00a0Students will have discussed factoring by grouping in the context of polynomials that are already set into 4 terms. \u00a0Today\u2019s lesson will center around rewriting trinomials into 4 terms as a precursor to factoring by grouping.<\/p>\n<p><strong>Objectives<\/strong>:<\/p>\n<ul>\n<li>Students will transform trinomials into expressions with 4 terms using both a \u201ctrial and error\u201d method and an area method.<\/li>\n<\/ul>\n<p><strong>Standards<\/strong>:<\/p>\n<ul>\n<li><a href=\"http:\/\/www.corestandards.org\/Math\/Content\/HSA\/SSE\/A\/2\/\">CCSS.Math.Content.HSA.SSE.A.2<\/a> &#8211; \u00a0Use the structure of an expression to identify ways to rewrite it.<\/li>\n<\/ul>\n<p><strong>Resources<\/strong>:<\/p>\n<p style=\"padding-left: 30px\">Teacher: Computer with projector, term tiles and practice problems for area activity (see explanation below)<\/p>\n<p style=\"padding-left: 30px\">Students: pencil and paper<\/p>\n<p><strong>Learning Tasks<\/strong>:<\/p>\n<ol>\n<li>Warm-up: Review factoring by grouping from an expression with four terms. \u00a0i.e. &#8211; \u201cUse the information on GCF from last class to rewrite this expression as a product of two binomials: xy + 2x + 3y + 6.\u201d (Answer: (x+3)(y+2))<\/li>\n<li>Discussion: Ask students to discuss with a neighbor or two the following question, \u201cHow might someone say that FOIL connects the two expressions in the warm-up?\u201d \u00a0If necessary, guide students toward the idea that the four terms of the initial expression are the F, O, I, and L if you \u201cFOIL\u201d the product.<\/li>\n<li>Rewriting trinomials. \u00a0Using an example like (x + 7)(x &#8211; 4), remind students that in binomials with only one variable, after we \u201cFOIL,\u201d we can collect like terms, giving us a trinomial instead of an expression with 4 terms. Let this discussion lead to the idea of transforming \u00a0trinomials into expressions with 4 terms, and then attempting factoring by grouping. \u00a0Students should quickly see that this trial and error method is not always effective and, therefore, not the most efficient.<\/li>\n<li>Use the area activity at <a href=\"http:\/\/courses.wccnet.edu\/~rwhatcher\/VAT\/Factorin\">http:\/\/courses.wccnet.edu\/~rwhatcher\/VAT\/Factorin<\/a> to demonstrate an alternative to \u201ctrial and error.\u201d \u00a0This activity also serves the purpose of helping students to visualize the connection between product and sum via the concept of area. \u00a0Note: This app is clunky and not very user friendly. \u00a0To save time (and avoid the need for a class set of computers), create several sets of terms tiles. \u00a0Have students work in small groups on problems together, using the same method and process as the app but at their desk with the paper tiles.<\/li>\n<li>Exit ticket: \u201cSummarize a key finding from the area activity just completed. \u00a0Is there a pattern or process you can summarize that would help a fellow student quickly split a trinomial into a set of four terms that would allow factoring by grouping?\u201d<\/li>\n<\/ol>\n<p><strong>Assessment:<\/strong><\/p>\n<p style=\"padding-left: 30px\">Teacher will informally assess knowledge and understanding based off discussions, as well as the information students provided on the exit tickets. \u00a0For the warm-up the next day, project a couple of the exit ticket ideas (or an amalgamation of ideas). \u00a0Ask students to apply it to a practice problem, and then answer \u201cwas the method(s) helpful? \u00a0Would you like to tweak the process\/hint in any way?\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The following reflects an outline for an Algebra unit on factoring that was developed using CBCI philosophies as outlined in Concept-Based Curriculum and Instruction for the Thinking Classroom by Lynn Erickson, Lois Lanning, and Rachel French. &nbsp; Unit Title: Factoring: &hellip; <a href=\"https:\/\/sites.miamioh.edu\/edt222-2017\/2017\/06\/cbci-unit-plan-markham\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2105,"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":[13,114,63,23],"class_list":["post-520","post","type-post","status-publish","format-standard","hentry","category-cbci","tag-algebra","tag-factoring","tag-math","tag-transformations"],"_links":{"self":[{"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/posts\/520","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\/2105"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/comments?post=520"}],"version-history":[{"count":5,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/posts\/520\/revisions"}],"predecessor-version":[{"id":529,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/posts\/520\/revisions\/529"}],"wp:attachment":[{"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/media?parent=520"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/categories?post=520"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.miamioh.edu\/edt222-2017\/wp-json\/wp\/v2\/tags?post=520"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}