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Lesson Objective:\u00a0Students will use prior knowledge of quadratic functions from pre-algebra as well as linear equations to identify mathematical properties of the images presented. Students will begin to explore properties of quadratic functions as well as any other mathematical ideas and concepts as they appear in the image. \u00a0Students will make connections to the mathematics they already know, what they want to know and the phenomena they observe through a mathematical lens. This activity is designed to be an open-ended activity. There is not one specific property of a quadratic function that should be discovered through the activity, but rather a starting point for students forming meaningful connections to quadratic functions, their properties and graphs.<\/span><\/b><\/p>\n Lesson Outline:\u00a0<\/b>This lesson is intended to get Algebra I students thinking about what a parabola looks like outside of the mathematics classroom. Ideally, this lesson would be used to introduce quadratic functions and their properties so students can associate properties of quadratic functions and graphs of quadratic functions with concrete examples that exist outside of the classroom. <\/span><\/p>\n Timing:\u00a0<\/strong>This lesson is designed for a 45 minute class period and will only take one day. However, if good conversations are occurring, the conversation and extensions may run over into a second day.<\/p>\n Prior knowledge<\/strong>:<\/strong> Students do not necessarily need prior knowledge of quadratic functions to be successful in this activity. There are other mathematical aspects of the images that students may pick up on and wish to discuss.<\/span><\/p>\n Standards:\u00a0<\/strong><\/p>\n Set up<\/strong>:<\/strong> Class begins with three images on the board <\/span><\/p>\n See<\/strong>:<\/strong> \u201cAre these images mathematical?\u201d<\/span><\/p>\n Think<\/strong>:<\/strong> Think about how these images are connected to the mathematics you already know. Think about the mathematics you <\/span>want<\/span><\/i> to know about these images.<\/span><\/p>\n Wonder<\/strong>:<\/strong> Why are these images mathematical? What other structures or images are mathematical? Where else do you see mathematical images such as these outside of the classroom? <\/span><\/p>\n Discussion: <\/strong>A class discussion follows the activity to explore what mathematics students saw, what they thought about that mathematics and where else they see similar mathematics. * If the discussion strays from these topics, that is okay. Discuss any appropriate mathematics students want to explore in the activity.<\/span><\/p>\n Video<\/strong>: After the discussion, this video can be used to show students other parabola examples outside of the classroom: \u00a0Quadratic Functions and Parabolas in the Real World<\/a><\/p>\n Assessment:<\/strong><\/p>\n Materials:<\/strong><\/p>\n Teacher Notes: \u00a0<\/b>Be sure to allow enough time for students to examine each image through a mathematical lens. This may be tough at first, but don\u2019t guide them to specific properties of quadratics or parts of the image, such as the vertex. Students will draw on their prior knowledge of parabolas, which will take longer for some students to recall than others. <\/span>The discussion will be the most insightful part of this activity; allow and encourage students to build on each other\u2019s discoveries and thoughts. Avoid pointing out mathematical features of the images and asking students leading questions that point to various aspects of quadratics functions.<\/span><\/p>\n Lesson Two: <\/b>Transformations – Circle of Viewpoints<\/span><\/p>\n Lesson Objective:\u00a0<\/b>Students will be exploring the various representations of quadratic transformations as they relate to one another as well as the parent function. Students will be provided a graph, equation and table for a quadratic function and will be asked to describe the function using mathematical language. Students will then engage in justifying that each of the mathematical representations are representing the same quadratic transformation. They will communicate using mathematical language and problem solving in order to justify their conclusions. This activity is designed to be a connection creating activity. Students have knowledge of quadratic transformations, tables, graphs, equations and are well versed in communicating mathematically. Thinking is made visible in this activity through proving posing and problem solving. <\/span><\/p>\n Lesson Outline:\u00a0This lesson focuses on examining quadratic transformations of functions from different representational perspectives. Quadratic transformations can be expressed verbally, graphically, by an equation and by a table (this is not an extensive list, but the ones I would focus on for this activity).<\/span><\/b><\/p>\n Timing:\u00a0This lesson is designed for a 45 minute class period and will take two days. Day one is designed to identify the viewpoints, and for students to explore the different representations with their group. Day two will be finishing up those discussions and exploring the different groups\u2019 perspectives as a whole class.<\/span><\/strong><\/p>\n Prior Knowledge:\u00a0Students are beginning this lesson after having been exposed to linear transformation, properties of quadratic functions and base knowledge of parent functions. <\/span><\/strong><\/p>\n Standards:\u00a0<\/strong><\/p>\n Set Up:<\/strong> Multiple representations of a quadratic function that has been transformed is given to students who will be working in small groups) <\/span><\/p>\n Identify viewpoints:<\/strong> The representations will be apparent to students as they will physically see a table, a graph and an equation and will be given directions to describe the transformation from the parent function verbally (orally within the group and written on paper)<\/span><\/p>\n Select a Viewpoint to Explore: <\/strong>Students will be given topics to explore for the various representations such as:<\/span><\/p>\n Respond to the \u201cI think\u2026.\u201d<\/i> Prompt: <\/strong>Students will explore how each individual representation is representing the quadratic transformation and how the representation relates to the parent function. Students will be asked to provide concrete evidence \u00a0that each of the representations in fact do represent the same quadratic transformation and justify their evidence. <\/span><\/p>\n Respond to the \u201cA question I have from this viewpoint\u2026.\u201d<\/i> Prompt: <\/strong>This step will happen naturally throughout the activity as students discuss the multiple representations of the quadratic transformation and justify whether or not they all represent the same quadratic transformation. Questions will arise regarding the connections between different representations as well as the representations themselves and groups will address these questions as they arise.<\/span><\/p>\n Share the Thinking<\/strong>:<\/strong> Student groups will share their findings and discuss these findings with their classmates in an open-idea environment. This allows for all students to ask questions, clarify confusion, expand upon discoveries, reflect upon the process and revise their findings if necessary\/desired. In this discussion, common misconceptions regarding transformations (that were most likely noticed during the activity) should be addressed.<\/span><\/p>\n Assessment<\/strong>:<\/strong> Groups will be assessed based upon their justifications provided for whether or not each mathematical representation describes the same quadratic function. Students will be provided a rubric for their justifications. Participation in the discussion will also be included as part of the assessment.<\/span><\/p>\n Materials<\/b>:\u00a0<\/span><\/p>\n Teacher Notes:\u00a0The purpose of this activity is to let students create connections and justify their thinking while connecting knowledge. Allow students to participate in this activity by not telling them if they are on the right or wrong track with their justifications. Students seek approval and will want to know if they are on the right track. Instead of saying yes or no, try to pose an open question that keeps students thinking in terms of their task and where they are at in justifying their conclusions. <\/span><\/strong><\/p>\n Extension:<\/strong> After students have been successful thought the graphing transformations unit, Marble slides<\/a>, a Dan Meyers Desmos activity, \u00a0can be used to formally or informally\u00a0student’s\u00a0knowledge and application of domain, range and transformations.<\/p>\n Check out @HollyClarkEdu<\/a>\u00a0for some great ideas on making thinking visible in classrooms with technology! Here’s a link to her blog<\/a> too!<\/p>\n","protected":false},"excerpt":{"rendered":" This blog post contains two lesson plans intended for Algebra I classrooms. The lessons can be adapted for similar topics in pre-algebra or Algebra II with moderate alterations. The two thinking strategies that I chose to highlight are the See-Think-Wonder … Continue reading \n
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