Unit Planning Assignment: Math Project and Unit Write-Up

Grade 11 Math: Circle Properties Unit Project

For this unit’s project, students will be given the following 2 options:

1. Create a Board-Game
• Students would be expected to work in groups of no more than 3 to come up with a board game that incorporates the material covered in this unit

Ø      The game should be given an interesting title

• Examples of props that would be used when playing this game would be expected to be included (ie, dice, playing cards, geometric shapes, etc)
• Clear written instructions and rules to the game should be written-up

Ø      This should include how many players allowed, solutions to any questions asked, etc

• Each group will give a short presentation to the class explaining how the game is played

Ø      Presentation must have equal participation from all group members

• A short 1 page explanation would also be required from each group describing the mathematical concepts involved in the game and how this game will help students gain a better understanding of these concepts

2. Create a Poster Display

·         Students would be expected to work in groups of no more than 3 to create a poster display about a real life application of a topic or concept covered in this unit

Ø      An interesting title should be given to chosen topic

·         The poster should explain the how the chosen application is related to and/or involves the mathematical concepts that have been discussed in this unit

·         Relevant mathematical illustrations and/or formula must be included on the poster

·         Each group will give a short presentation to the class explaining the topic they’ve chosen, the interesting facts they’ve found out about the topic and how the topic relates to this unit

Ø      Presentation must have equal participation from all group members

Evaluation:  Students will be evaluated on the following for this project (out of 20 marks):

·         Mathematical Content (10 marks)

Ø      how much and how well does the project focus on math

Ø      are relevant mathematical diagrams and equations included

Ø      is the information provided accurate

·         Creativity (3 marks)

Ø      is there an interesting title

Ø      how original and innovative is the project

·         Presentation (5 marks)

Ø      is it well-planned and organized

Ø      is there minimal use of cue cards

Ø      is there equal participation from all group members

·        Overall Appearance (2 marks)

Ø      is it neat and visually appealing

Ø      does it have correct grammar and appropriate use of language

Unit Planning Assignment Write-Up for Math 11 Circle Properties Unit

1. The topic of the unit:

      The topic of this unit is circle properties.  This topic is included in the curriculum because it is an essential lead-in to other topics of geometry including coordinate geometry.  The properties that are discussed in this unit build the foundation for the following units in the course.  This topic also allows students to develop deductive reasoning skills that can be used to solve problems involving circle geometry.  This is an important skill for students to learn as it is used in various real-life situations including in landscape architecture, civil engineering and meteorology.

2. The breakdown of the big topic into lessons and projects:

      In teaching this unit I will make use of several resource materials.  One will of course be the textbook as it provides a very practical breakdown of the unit into separate sections; however, I feel that in order to give students exposure to a wide variety of questions I will need to supplement the textbook with my own handouts and worksheets.  From my personal experience, I remember it was more through my teacher’s own worksheet problems than through those in the textbook that I was able to apply the material I learnt in class.  If there aren’t enough exercises in the textbook and/or the ones presented are not challenging enough, then I think it’s very important for me as a teacher to supplement the textbook with my own material.  I also think that this unit will give a great opportunity to introduce students to the computer program geogebra.  This program will provide students with an interactive way to ‘test’ the circle properties they learn in class and help to reinforce the concepts that are being taught.

3. The pedagogy of the unit:

      To encourage and motivate students’ active participation in this unit I will make participation in class discussions a requirement, something for which the students will receive marks (see evaluation rubric below); however, I want to make sure students are comfortable and engaged in class and not simply participating because they’re receiving marks for it.  To accomplish this I will try to incorporate into my lessons various activities that will allow students to interact with each other and at the same time take part in class discussions (ie, think-pair-share).  Having games like math style ‘Jeopardy” will not only help reinforce the material being covered in class but also help to keep students engaged and interested and at the same time, force all the students to participate without putting one student on the spot.

      I will also try to make connections with other school subjects and other areas of life to show the students how relevant and important the material they’re learning actually is.  Relating mathematical concepts to applications in real life will be a major theme for this unit and to accomplish this, I will try to tie in every lesson to another subject or area of life (ie, explore science subjects like eclipses when discussing tangents to a circle or discuss how angle properties are important for orthodontists when putting braces on a patient.)  I think this strategy will help to keep students interested in the topic they’re learning and at the same time get them actively involved in the learning.

4. Assessment and evaluation:

            For this unit, the following evaluation rubric will be followed:

                        Participation (in-class)                                       5%

                        Homework (completion)                                    10%

                        Assignments (exit-slips, warm-up Qs)                15%

                        Quizzes                                                           15%

                        Project                                                             25%

                        Unit Test                                                          30%

                        Total                                                                100%

            I think this assessment breakdown will encourage students to complete their

            homework, participate in the class discussions and prepare for their quizzes and

            test.

Unit Planning Assignment-Unit Plan

EDCP 342A: UNIT PLAN

Math 11 Unit: Circle Properties

Lesson No.	Topic	Learning and Teaching Objectives	Connections Made	Activities of Students and Teacher	Materials Needed	Assessment and Evaluation
1.	Introduction to Circle Concepts	-to learn about terminology relating to circles -to teach and relate new terms to concepts and applications in real life	-the existence of circles and these concepts in real life	-lesson notes and student exercises	-prepared lesson notes -prepared exercises for students along with solutions	-think, pair, share at the end of class with discussion of answers
2.	Properties of Chords	-to learn the chord properties -to have students conjecture these properties based on findings from examples	-use of technology in math	-student activity using geogebra -lesson notes	-prepared lesson notes -booked computer lab with geogebra program	-exit slip Q
3.	Proving Chord Properties	-to introduce concept of proofs -to learn how to prove the properties of a chord -to understand how and why these properties hold true	-the use of inductive reasoning in proofs	-class discussion on proofs through examples with student participation	-prepared student example questions with solutions	-group work with teacher monitoring students’ progress by walking around class
4.	Angles of a Circle Properties	-to learn the properties of angles in a circle -to have students conjecture these properties based on their findings from examples	-use of technology in math -how important of an impact differing angles can have (ie, in a photograph or building a structure)	-lesson notes and student activity using geogebra	-prepared lesson notes -booked computer lab with geogebra program	-partner quiz
5.	Proving Angle Properties	-to further practice doing proofs -to understand how angle properties were developed -to understand why these properties are true	-the use of logic in completing a proof	-jigsaw activity with students -lessons notes summarizing concepts learnt	-prepared jigsaw activity handouts and questions (with solutions) -prepared notes	-warmup Q
6.	Properties of Cyclic Quadrilaterals	-to learn the properties of cyclic quadrilaterals -to relate these properties to those learnt about chords and angles	-the applications of cyclic quadrilaterals in real life (ie, a walkway around a hemispherical dome)	-lessons notes and student exercises -unit math project will be assigned	-prepared lesson notes -prepared student exercises with solutions -prepared math project handout	-review quiz
7.	Proving Cyclic Quadrilateral Properties	-to develop ability at proving theorems using indirect proofs -to understand why the properties of cyclic quadrilaterals hold true	-completing a proof by incorporating earlier learnt properties of circles	-lesson notes then review of concepts learnt so far with student activity game-Jeopardy style	-prepared lesson notes -prepared Jeopardy-styled activity	-assess performance and ability during Jeopardy game
8.	Tangents to a Circle	-to learn what is a tangent and the properties a tangent to a circle has -to have students conjecture these properties by working on examples	-relating tangents to solar and lunar eclipses	-group problem solving activity -lesson notes	-solar and lunar eclipse diagrams -prepared group questions with solutions -prepared lesson notes	-exit Q
9.	Proving Tangent Properties	-to learn and understand how and why the tangent properties are true -for students to be able to now construct a proof on their own	-completing a proof using what was learnt from earlier proofs -develop mathematical reasoning and understanding	-class discussion on proofs through examples with students working on boards -work on math project	-prepared discussion questions with solutions	- think, pair, share at the end of class with discussion of answers
10.	Tangent-Chord Theorem	-to learn the tangent-chord theorem -to understand how all the earlier learnt properties cause this theorem to hold true	-incorporating earlier learnt material on circles, chords and angles	-lesson notes and student exercises -work on math project	-prepared lesson notes -prepared student exercises with solutions	-pop quiz

Flatland Math Project

Group Members: Vincent, Donna & Mandeep

Part 1:  Trying Out the Project

Donna and Vincent were both very interested in trying out this project.  Both of them probably ended up spending more time than Susan suggested they do.  It was interesting to see how visually and conceptually different their end products were from each other. 

Vincent found that it was necessary to read the first half of Flatland in order to understand the general concepts behind the story (such as how Flatlanders “see”).  But he found this first half of the book very dry and not very entertaining to read.  He enjoyed the second part of the book, which told the story.  He found that watching the 30 minute Flatland movie partway through reading the first half of the book helped re-energize his interest in finishing the book.  Vincent thought mostly about how to draw the comic in a way that would convey the story of Flatland to the audience as efficiently as possible.  He concentrated on telling a story in a minimal way that would visually convey the concept of dimensions.  He had a few false starts before he starting drawing a comic that he found satisfying.  He settled on simple black and white line drawings with minimal words.

Donna thought that watching a math movie and reading a math story was in itself a very interesting task.  She was very curious and did not know what to expect.  The book, the film and the movie each had slight variations that became topics of discussion.  Creating a comic strip forced her to really think about the concepts, often going back to the book for reference.  She really enjoyed using colors and shapes, and if anything, spent too much time on the production since it was addicting.  Her comic was created on a computer and she spent a significant amount of time on the visual details of her comic. 

The fact that these two comics turned out so differently demonstrate that students will focus on the different parts that are of interest to them.  We both felt this was an educational experience that students will enjoy.

Vincent's comic is located here: 

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B_WqVw36Np6_ZWUwYjYzNTgtNmY4OS00MGE2LWEyYWUtODQ2YzlkNmQ0OWE3&hl=en&authkey=CIfHqNkO

Donna's comic is located here: 

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B_WqVw36Np6_ZDJhZDJiNDktYzZlZi00NmIxLTg5ZjItYjk0ZmJjODM5Y2U1&hl=en&authkey=CMbM6dcD

Part 2: Looking at the Project with “Teachers’ Eyes”

The strengths of this project are that this is an enrichment assignment which allows students to develop a deeper understanding of geometric shapes and projections.  Having to create a comic telling the story of Flatland gives students the opportunity to apply their understanding of the book and the mathematical concepts discussed in it in a creative manner.  This project also enables students to take part in an inventive hands-on activity that the visual and artistically inclined students in the class will appreciate.   Reading the story of Flatland is also beneficial because it illustrates to students how fascinating and intriguing mathematics can be and encourages them to be imaginative and enquiring about the world and the math around us (ie, could there exist a fourth dimension and if it does, what would it look like?)  It also provides students with an alternative way of looking and comprehending geometric shapes (ie, a circle as a polygon with an infinite number of sides.)

The weaknesses of the project include having the possibility that students may spend too much time coming up with a comic strip and not concentrate enough on the mathematical aspect of this project.  Some constraints within the context of the classroom include there being is a lot of reading required for this assignment and some students may not have strong reading skills and thus may require a lot of time to finish the readings.  This may put pressure on the time constraints for this project.  The first half of Flatland is also very heavy with explanations which may make it difficult for some students (especially ESL and some LD students) to understand the novel and if they’re unable to comprehend the math topics discussed in the book, they will not gain anything from this activity.  Another issue with this project may be that some people (the girls in particular) may take offense at the sexism presented in the novel.  Getting a class set of the books may also be a problem in some schools.

The ways to adapt this project to try to overcome these weaknesses include having emphasis placed on the fact that this is a math (and not an art) project, so it will be mathematical content and understanding (not drawing skills) that will be assessed with this project.  Some strategies to deal with the time constraints of this project include having students read only Flatland for this assignment and, only if necessary, specific parts of Flatterland, Sphereland and/or the Scientific American article on the “planisphere,” with the teacher specifying which parts to read.  There is enough new mathematical material and concepts for students to learn and absorb just from reading Flatland; however, the projects that follow up with readings from these other books could be given bonus marks though.  To deal with the explanation-heavy first half of Flatland, there could be class/group discussions of the readings in class.  Also the project could be adapted to include the viewing of the Flatland movie and film (either during or outside of class) to help reinforce students’ understanding of the mathematical concepts (like dimensions) that are presented in the book.  There could also be a disclaimer before beginning the book and/or discussions while reading the book about the sexism presented in the novel so that students are prepared for it and not taken by surprise.  The teacher could also contact public libraries to try to obtain copies of Flatland if there is not a class set available.

Some ways to modify the project include:

•   Getting the class to write out and then perform a play and/or small skit about the story of Flatland
• Having the class divided into small groups and then having each group make their own movie about Flatland
• Allowing students to use computer graphics and/or photographs of common items and props to come up their comic strip about Flatland
• Having students use a simple, free programming environment of Scratch to create the 2D characters described in the story

Part 3: New Project Idea

Flatland Project – Personifying Shapes

Published by Edwin A. Abbott in 1884, Flatland:  A Romance of Many Dimensions is a satirical novella that tells the story of a world with only two dimensions. The inhabitants of Flatland are shapes, all with interesting characteristics and personalities.  Several films have been created from this original book, including a short film entitled Flatland: The Movie.

For this project, you will need to read the book and we will view the short movie in class.  We will then have a discussion about the concepts in the book.  Following this discussion, you will work in pairs to personify the shape of your choice with the result being a poster to be presented to the class.  You will have 1 full class period to work in pairs on this project.

1.     Read Flatland, available on line via Google Books (cut and paste link below).

http://books.google.ca/books?id=s2Tdsgf1KTwC&printsec=frontcover&dq=flatland&hl=en&ei=NADfTI_bH5OgsQOlmPnrCg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCsQ6AEwAA#v=onepage&q&f=false

2.     On Friday, February 11, we will watch Flatland: The Movie in class.  Following the movie, each pair will be assigned to one of the two discussion groups that map to the two parts of the book: PART I: THIS WORLD and PART II: OTHER WORLDS.

3.     You and your partner will then chose a geometric shape (not restricted to those in the movie) and create a poster that expresses/advertises the shape, including but not limited to the following:

·      Accurately drawn shape

·      Origin of the name of the shape (eg pentagon => penta is 5)

·      Description of how to draw the shape and what tools were used (protractor, compass, ruler, etc)

·      3 mathematical facts about the shape (eg angles, lengths, area calculation)

·      3 places where the shape can be found in natural and/or man-made settings

·      2 thoughts/ideas about where the shape could be used

4.     You and your partner will then present your poster and ideas to the class on February 23.  Presentations should be approximately 5 minutes.

Marking Rubric

Criteria	Marks Allocated	Marks Assigned
Completeness of Assignment	Contains all the required parts: shape, name origin, 3 facts, 3 places and 2 thoughts/ideas where shape can be used.	/5
Mathematical Correctness	Angles, lengths and geometric relationships are depicted correctly and accurately.	/5
Creativity/Originality	Poster and presentation demonstrates unique and innovative ideas.	/5
Presentation	Presentation was well organized. Delivery was clear and effective.  Duties were shared amongst the pair.	/5
Bonus	Poster explains more than one method of drawing the shape.	/1
Total		/20

Other Project Information not included in worksheet above:

Grade Level: 10.

Essentials of Math 10: In the Section on Shape and Space, there is a Geometry Project with the following elements:

·       C3 measure lengths in both SI and Imperial units

·       C4 estimate measurements of objects in SI and Imperial systems, including length, area, volume, mass

·       C5 interpret drawings and use the information to solve problems

·       C6 draw top, front, and side views for both 3-D rod or block objects and their sketches

·       C7 sketch 3-D designs using isometric dot paper

·       C8 enlarge or reduce a dimensioned object according to a specified scale

·       C9 solve problems involving linear dimensions, area, and volume

·       C10 complete a project that includes a 2-D plan and a 3-D model of some physical structure

Applications of Math 10: Under Shape and Space, there is a Measurement Section:

·       C5 calculate the volume and surface area of a sphere, using formulas that are provided

·       C6 determine the relationships among linear scale factors, areas, the surface areas, and the volumes of similar figures and objects

·       C7 solve problems involving length, area, volume, time, mass, and rates derived from these

·       C8 interpret drawings, and use the information to solve problems

Purpose:

The purpose of this project is to raise the curiosity and understanding of geometric shapes.  The Flatland story gets them thinking about all the implications of living in a 0, 1, 2, and 3 dimensional lands.  It also raises their awareness of how to communicate such concepts based on what the audience already knows.

Total Length of Time:

The total time for this project is 3 class periods (1 for movie and discussion, 1 for group work time and 1 for presentations).  Outside the class would be for reading the book or further project time. The actual time students will have to work is 1.5 weeks.

Materials/Resources:

Materials needed for this project include poster board, compass, protractor, pencil crayons and markers.

Thoughts on 'Creativity, Flexibility, Adaptivity, and Strategy Use In Mathematics' Article

Reading this article took me back to my math classes in elementary and secondary school.  I tried to think back and remember if there was ever any emphasis placed on the creativity, flexibility and adaptivity when learning how to solve problems and I realized that there never was any importance placed the these three abilities.  Instead, I can specifically recall instances (right up until senior level high school math classes) where the teacher insisted we solve problems in a particular manner, using a particular method and/or formula, just so that marking the question would be easier for the teacher.  I believe this was an attitude I encountered a lot from my math teachers and as a result, I became one of the students who could learn how to solve a problem really well but in only one specific manner.  I found this was not the case once I came to university hence I struggled to be creative and come up with new and/or modify known strategies of solving problems.  Concepts like flexibility and adaptivity seemed strange to me because that wasn't how I'd been taught how to solve math problems.  I always felt there was one method and/or strategy that had to be more correct than the others because I'd always been taught there can only really be one "right" way to solve a problem.

Reflecting back on this experience and now reading through this article, it illustrates to me how important it is for students to have a good grasp on all three strategies of creativity, flexibility, and adaptivity.  Math shouldn't be about robotic routines to solve problems but should involve thinking and conceptual understanding.

Practicum Stories

One of my favourite experience during this practicum was when I finally had a chance to interact with a class of junior science students as they worked on a class worksheet.  Up until this point, though I had observed many classes and been introduced in many of these classes, I found none of the students really had any interaction with me.  Since I sat in the back of the room, none of them spoke to me as they came in to the class and ignored me throughout the actual lesson.  I was quite worried at first that perhaps these students hadn't taken a liking towards me and did not want me as their student teacher; however, during my observations of one junior science course, I found that much of the class was confused about the material they learning and did not know how to get started on a worksheet they had been given.  Since it was a large class and the teacher was busy trying to help some of these kids with their questions, I tried to help out and see if I could answer the questions of anyone waiting to see the teacher.  Not only were the students openly appreciative of the help I gave them, but soon many of the kids had formed a group around me as they all wanted to hear about the explanations to solve the science questions.  Up until this point I hadn't had any chance to interact with any of the students, I had begun to feel that the students found me unapproacheable; however, I found once students know you are there to help them, they were more than happy to come up and talk to you and ask you for help.

Another part of the practicum that had an influence on me was the first lesson plan I came up with and the first lesson I actually taught.  I was so proud of myself when I finished my first lesson plan and was printing it off at my home computer.  I was surprised at how long it took me to come up with it though, as I'd expected it would have been simple enough to come up with the lesson as it was for a Math 8 class.  It actually ended up taking me hours to decide how to teach the lesson, make up my notes, etc.  The teaching of this lesson was also a big moment for me, as it was the first time I was actually teaching.  It felt somewhat surreal when I was up there in front of the class and whenever the students called me Ms. Sidhu, I felt like smiling.  I was extremely nervous before starting the lesson but ended up quite happy with how the lesson went.  I felt quite comfortable in front of the class and look forward to teaching more classes during my long practicum!

Reflection On Chapters 2 & 3 of "Thinking Mathematically"

          I found the reading from chapters 2 and 3 of “Thinking Mathematically” to be quite interesting.  I agree with the argument that too often in mathematics, students are more focused on getting the “right” answer and this often is the their drive behind solving a problem as opposed to truly understanding and reflecting on a problem before answering it.  I think this relates back to the discussion we had in class earlier in the term regarding relational versus instrumental understanding of mathematics.  Do we want students to just be able to come up with the correct answers or do we want them to be able to understand the fundamentals behind the question they’re solving?  I’m sure if you were to ask me when I was in high school, I would’ve thought reflecting on math problems was not only crazy but also a waste of time because the goal for me at that time would be to just come up with a (correct) answer; however, after completing my degree and now as a teacher candidate, I recognize the importance in getting students to think instead of simply just solve mathematical problems and I hope this will be something I am able to show my high school students through my teaching.