#SELFIE THE GRAPHING IMAGES PROJECT

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1 #SELFIE THE GRAPHING IMAGES PROJECT Key Learning Area: Mathematics Topic: Coordinate Geometry (Year 7-10+) Syllabus Outcome(s): Possible interdisciplinary links to Visual Arts, English, TAS, Programming NUMBER AND ALGEBRA - MA4-11NA creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane - MA5.1-6NA determines the midpoint, gradient and length of an interval, and graphs linear relationships - MA5.1-7NA graphs simple non-linear relationships - MA5.2-8NA solves linear and simple quadratic equations, linear inequalities and linear simultaneous equations, using analytical and graphical techniques - MA5.2-9NA uses the gradient-intercept form to interpret and graph linear relationships - MA5.2-10NA connects algebraic and graphical representations of simple non-linear relationships - MA5.3-7NA solves complex linear, quadratic, simple cubic and simultaneous equations, and rearranges literal equations - MA5.3-8NA uses formulas to find midpoint, gradient and distance on the Cartesian plane, and applies standard forms of the equation of a straight line - MA5.3-9NA sketches and interprets a variety of non-linear relationships - MA5.3-12NA uses function notation to describe and sketch functions William J. Plaskett (2015) Page 1 of 12 #SELFIE THE GRAPHING IMAGES PROJECT

2 Working Mathematically Outcomes: STAGE 4 STAGE 5.1 STAGE 5.2 STAGE 5.3 Communicating MA4-1WM communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols Problem Solving MA4-2WM applies appropriate mathematical techniques to solve problems Reasoning MA4-3WM recognises and explains mathematical relationships using reasoning Problem Solving MA5.1-2WM selects and uses appropriate strategies to solve problems Reasoning MA5.1-3WM provides reasoning to support conclusions that are appropriate to the context Problem Solving MA5.2-2WM interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems Reasoning MA5.2-3WM constructs arguments to prove and justify results Assessments: - Homework and formative/summative assessment task, as normal - Graphing Images: Robot - Graphing Images: House - Checking for Understanding #1 (Kahoot!) - Practice assessment tasks - Rough draft of their project - Final Project (using the co-constructed rubric) - Informal check-in with students during class - Optional Tasks: Plaskett Ball Investigation (Quadratics) and the Mickey Mouse Activity (Quadratics and Circles) William J. Plaskett (2015) Page 2 of 12 #SELFIE THE GRAPHING IMAGES PROJECT

3 THE HOLOGRAM PROJECT: TABLE OF CONTENTS Page 4 Lesson 0: Project Planning Project Design (Page 4) Page 6 Page 8 Page 9 Page 10 Page 12 Page 13 Page 14 Page 14 Page 15 Page 15 Page 17 Page 17 Page 18 Page 18 Page 19 Lesson 1: Introduction To Holograms And Projections Lesson 2: Procedural Fluency Lesson 3: Procedural Fluency And Checking For Understanding Lesson 4: Modeling And Pepper s Box Lesson 5: Project Reveal Rubric Develeopment Lesson 6: Project Time Lesson 6: Project Time Lesson 8: Project Time And Checking For Understanding Lesson 9: Project Time Lesson 10: Critique And Project Time Lesson 11: Project Time Lesson 12: Exhibition Prep Exhibition Night Lesson 13: Reflection, Clean Up/Curate, Connections Lesson 14: Assessment William J. Plaskett (2015) Page 3 of 12 #SELFIE THE GRAPHING IMAGES PROJECT

4 THE GRAPHING IMAGES PROJECT: SAMPLE UNIT OUTLINE LESSON CONTENT TEACHING STRATEGIES LEARNING EXPERIENCES RESOURCES LESSON 0: PROJECT PLANNING PROJECT DESIGN The following project plan addresses the lowest level of coordinate geometry (Year 7) but can be naturally adapted or extended to achieve higher-level outcomes in Mathematics. There will be sections for adjustments and recommendations to be made for including or targeting more complex or difficult linear modelling and non-linear modelling at the end of this document. CRITICAL: YOU MUST DO THIS WEEKS BEFORE YOU START THE UNIT! Before starting this unit, you must consider the context, resources, and feasibility of this project at your school or institution. That being said, you should have a general idea of what your final project will be, what you need to accomplish that, how you will exhibit it, and where you will curate it. You must do the project yourself! You must do the project yourself! You must do the project yourself! As you do the project, you will realize where students may struggle or need more support, where the significant teaching moments are, when would it be appropriate to do a critique session on student work, what the success criteria or rubric may be, what experts or adults you could invite into your classroom or go visit, etc. Complete the project and make a complete plan before you present the project to students. Also, retain all of your old planning documents, notes, staff and student feedback, and reflections. You will review these at the end of this unit. Ensure that you include your head of department and, where applicable, head of innovation or head of curriculum as much as possible. Propose exhibition ideas and plans to all necessary staff within your school (Principal, Head of Curriculum, Facilities, Community Relations, etc.) NOTE: This project can cover coordinate geometry and functions outcomes in years Determine what the baseline expectation for your project is (perhaps its plotting coordinate points in Year 7 or graphing quadratics in vertex for in Year 10) and communicate that clearly with students. Allow for opportunities for students to extend beyond the baseline expectation but focus the rubrics and instructional content on the outcomes you are aiming to achieve in this project. William J. Plaskett (2015) Page 4 of 12 #SELFIE THE GRAPHING IMAGES PROJECT

5 LESSON 1: INTRODUCTION TO COORDINATE GEOMETRY Demonstrate, very simply through only one example, how to plot a coordinate point. Define the x-axis and y-axis in your demonstration and write the coordinate pair on the board near the graphed example. Worksheet: Graphing Images (Robot) - Graphing Images: Robot (BLANK) - Graphing Images: Robot (SOLVED) Complete the accompanying Graphing Images: Robot sheet. - MA4-11NA creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane Before moving onto the next lesson, have students co-construct a list of the key terms and concepts from the worksheet. Ask for a student to volunteer to be a scribe. On the board (or large paper), have the student scribe as other students list (and define) key terms. Assign introductory homework as normal relating to your scope and sequence document. Allow remaining class time for students to begin homework and to copy the lists of terms and into books. LESSON 2: TRACING AND LINEAR MODELLING WITH COORDINATE POINTS Have a student summarise the procedure for plotting coordinate points from lesson 1 at the board. Worksheet: Graphing Images (House) - Graphing Images.docx - 2D House.jpg - Graph Paper.jpg - GraphingImagesHouse.pdf Complete the accompanying Graphing Images sheet, using the 2D House image and Graph Paper as seen in the Graphing Images House (PDF) - MA4-11NA creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane NOTE: The tracing will be easier if there are light boards or glass windows to use. Tape or Blue Tack could be used to attach the graph paper to the 2D house image. William J. Plaskett (2015) Page 5 of 12 #SELFIE THE GRAPHING IMAGES PROJECT

6 The coordinates provided for the roof are not exact, use this as a conversation starter about the error in tracing/estimating coordinate points or why to intentionally plot points differently to the image for simplicity. The intent for providing the roof coordinates is to establish the two axis and provide an opportunity for extension (determining slope and distance of line segments) regardless of the student s tracing. Assign homework as normal relating to your scope and sequence document. Allow remaining class time for students to begin homework. LESSON 3: PROJECT REVEAL RUBRIC DEVELEOPMENT DURING THIS LESSON: Pre-arrange the seats into a circular formation where every student is a part of the circle as well as the teacher. Introduce the project to the students by telling them that they will be taking a selfie and tracing their portrait onto the Cartesian Coordinate Plane. Be excited and encouraging. Whiteboard for the rubric co-construction Graph Paper (Blank) Microsoft Excel OPTIONAL: Show the students other student samples or your project sample from when you did the project yourself. Instruct students that they will be co-constructing the rubric for the project with you. Inform students that they will be assessed formally and informally, individually. Ask students to propose themes or elements that they think should be assessed they will need to be prepared to justify their proposition and describe it. Create the individual assessment criteria and the group assessment criteria. Allow students to contribute openly and without fear of dismissal. Feel free to contribute ideas as well, but allow students to adapt to or add to them. Non-Negotiable Rubric Item (Instruction/Mathematics Outcome): For minimum marks, students must provide the coordinate points for their portrait in table format (Microsoft Excel); one column for x-values and the next column for y-values. For improved marks, students must provide the coordinate points for their portrait as instructions in table format; coordinate points in order of how they should be plotted with start and stop indicators and descriptions of what the points create. William J. Plaskett (2015) Page 6 of 12 #SELFIE THE GRAPHING IMAGES PROJECT

7 For maximum marks, students must provide a completed geogebra file with their portrait graphed in addition to the Microsoft Excel file in instruction format. Allow remaining class time for students to begin their project by taking their photo, printing their photo, and tracing their photo. AFTER THIS LESSON: As you complete this lesson and have taken note of student feedback and the co-constructed rubric, you must make amendments to your project plan. It is important for students to have choice and voice in their project so ensure that you make reasonable changes (this gives the students ownership, advocacy, and relevance). Immediately after making changes, meet with your head of department and, where applicable, head of innovation or head of curriculum. Finalize the exhibition and the plans to curate the project within the school. LESSON 4: PROJECT TIME Students will continue working on their projects. Allow students the entire lesson, if possible, to work. During this time, students may need constructing their product or acquiring new math skills or procedural fluencies; make yourself readily available to help your students for the entirety of your class time. Working on the project in class, under your supervision and support, is the focus of this lesson; any additional homework is supplementary. Students should complete the initial trace of their portrait as homework and be prepared to start grid-locking their tracing to coordinate points in the next lesson. William J. Plaskett (2015) Page 7 of 12 #SELFIE THE GRAPHING IMAGES PROJECT

8 LESSON 5: PROJECT TIME Students will continue working on their projects. Allow students the entire lesson, if possible, to work. During this time, students may need constructing their product or acquiring new math skills or procedural fluencies; make yourself readily available to help your students for the entirety of your class time. Working on the project in class, under your supervision and support, is the focus of this lesson; any additional homework is supplementary. Students must have completed their first draft of their portrait (colouring optional) and be prepared for a critique in the next lesson. LESSON 6: CRITIQUE AND PROJECT TIME With the exception of a critique, allow students the entire lesson, if possible, to work. Before starting this lesson, watch Austin s Butterfly video by Ron Berger: Optional documents: Peer Critique Form.doc Project Action Plan.doc Think of the butterfly example. The artist was able to make refinements and improvements because their feedback was: Kind Specific Helpful William J. Plaskett (2015) Page 8 of 12 #SELFIE THE GRAPHING IMAGES PROJECT

9 The other reasons why these were effective feedback sessions is because: There was a culture of welcoming feedback and criticism. The feedback and refinement cycle was repeated until the creator was satisfied. You will design a critique session for your students. - First, you should show Austin s Butterfly to your students in this lesson and have them acknowledge the reasons that the feedback was helpful. - Second, you should use your project (from when you did the project yourself!) and have the class critique your project. Emphasise being kind, specific, and helpful. Also, set the following norm: hard on content, soft on people. - Lastly, have students critique each other s work. I prefer silent gallery critiques using the attached peer critique form and project action plan documents; however, this may take form in a variety of ways and must be catered to your classroom culture and the nature of your project/product. Students are expected to make amendments to their portrait given their feedback and create their final drafts as homework. LESSON 7: EXHIBITION PREP Student Projects must be completed! Students must prepare for and create the exhibition. This may require more than one lesson and it is recommended that you inquire about the possibility of having your students for at least half of the day, if not the entire day. William J. Plaskett (2015) Page 9 of 12 #SELFIE THE GRAPHING IMAGES PROJECT

10 As students are setting up, you should begin preparing for parent s and the school community. - This may be their first educational exhibition so prepare some sort of welcome (a video, students greeting, students in costumes, an opening speech, etc.). - Consider having catering or food. - If you ve worked with experts or adults outside of the school, make time and effort to thank them meaningfully. - Background music can be competing stimulus or it can be complementing; consider having students perform live or play recorded tracks. - Allow all students the capacity to share their work, complete or incomplete, and be proud of what they have accomplished. - Prepare a list of questions that parents can ask students to start the conversation. My personal suggestion would be to have a practice exhibition during the day with another class, other faculty members, etc. so you and the students know what things need to be adjusted before the real exhibition begins. Praise your students! Congratulate them on what they have accomplished, regardless of what their final product looks like. Students are not professionals and sometimes their best work may not present as beautifully as we hoped; do not make the mistake of protecting your ego or reputation at the cost of a student s sense of pride and accomplishment. Similarly, parents will be proud of their child and will see the range of quality projects and products at your exhibition so there is no need to defend yourself or your student s work. Want to read some research and anecdotal evidence about Happiness? Shawn Achor, The Happiness Advantage: TED Talk: EXHIBITION NIGHT Take photos. Smile. Enjoy yourself. Continue to motivate and praise the students throughout the exhibition as they may be nervous, anxious, or self-conscious. Take pride in your student s work. William J. Plaskett (2015) Page 10 of 12 #SELFIE THE GRAPHING IMAGES PROJECT

11 LESSON 8: REFLECTION, CLEAN UP/CURATE, CONNECTIONS Allow for 5 minutes of classroom discussion about the exhibition. Provide students with positive feedback and congratulate them on completing the project. Ask students to silently reflect in a letter, non-graded, that you will collect and read for 5 minutes. Extend this time if reflection is meaningful and the students are engaged in this process. Have students clean up the exhibition space and classroom. If possible, curate the student work within the school immediately (take advantage of the hype and buzz about the exhibition and showcase your student s work as soon as possible). Connections: Connections is a Quaker tradition used as a reflective practice. Have everyone sit in a circle facing inward. You will facilitate the activity. Read the following instructions: Welcome to Connections. Connections is an opportunity for us to openly reflect on what we have done over the last few weeks. If you feel the quake, or an impulse to speak, then speak. You may only speak once and cannot respond to something that someone else has said. You may reflect on a personal learning experience, a struggle, something significant that occurred, a fun memory, etc. I will not call on you, just begin speaking when you feel the impulse to speak. There will be periods of silence. Once silence has become prolonged, I will say Connections will end in 1 minute as a warning. If no one speaks within that minute I will say Connections has now closed. When you are ready, say connections has begun. After connections, allow students time to revise for their assessment or to celebrate their accomplishment. LESSON 9: ASSESSMENT William J. Plaskett (2015) Page 11 of 12 #SELFIE THE GRAPHING IMAGES PROJECT

12 Have students complete your assessment task as normal relating to your scope and sequence document. While students are completing the assessment task, begin writing comments and scoring students on their projects. If possible, aggregate their report outcomes and marks to reflect the rubric and curriculum outcomes. William J. Plaskett (2015) Page 12 of 12 #SELFIE THE GRAPHING IMAGES PROJECT

Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice

Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice Title: Considering Coordinate Geometry Common Core State Standards