Unit Planning Assignment-Lesson 8

Lesson 8: Tangents to a Circle

Bridge (5 min)	·        Bring diagrams of solar and lunar eclipses to class and ask students if they how such eclipses occur Ø      Show the students diagrams that illustrate how tangents drawn from the sun help explain the shadow that will appear on Earth during a solar eclipse
Learning Objectives	·        To have students learn what is a tangent and the properties a tangent to a circle has ·        To have students conjecture these properties after working through given examples
Teaching Objectives	·        To have students gain an appreciation for how and why these tangent properties are important in real life ·        To have students relate these properties to what they have already learnt about for chords and angles
Pre-Test (5 min)	·        Teacher will review verbally the concepts covered so far in the unit Ø      Will draw-out example problems on the board and have students volunteer to answer on how to solve the question
Participatory Learning (25 min)	·        Have students work together in small groups on a set of problems that will involve tangents to circles Ø      Have groups predetermined by teacher Ø      Have students try to come up with tangent properties by following instructions given on provided problems
Post-Test (20 min)	·        As a class go over what each group found based on their answers to the problems (10 min) Ø      On board write up the similar/differing properties that the groups conjectured ·        Lesson notes on the properties of tangents to a circle        (10 min) Ø      Refer back to the class conjectured in their groups and comment on the ones that are true and the ones that aren’t o       For the ones found not to be true, go over where the groups were mistaken to clear up any confusion students may have
Summary (10 min)	·        End class with an exit slip question for students Ø      Have students answer on slip of paper the question written on board relating to tangents to a circle and have the students hand in this paper before leaving

Unit Planning Assignment-Lesson 4

Lesson 4: Angles in a Circle Properties

Bridge (5 min)	·        Ask students if any of them have had or currently have braces Ø      Ask these students how their orthodontist knew where to place their braces such that their teeth will be pulled in exactly how they want them to be ·        Show students various photographs taken of the same object/region but from a different angle each time Ø      Have students consider and discuss outloud the importance differing angles can play in even the simplest event like taking a picture Ø      Have students consider how would one determine what angle one should stand in order to have a photograph turn out a certain way
Learning Objectives	·        To have students learn about the properties of angles in a circle ·        To have students conjecture these properties based on their finding from examples they do using geogebra
Teaching Objectives	·        To give students further exposure to using computer programs like geogebra for doing mathematics ·        To have students recognize the importance differing angles can play in real life (ie, in a photograph, building a structure, for orthodontists determining where and what size braces a patient should wear)
Pre-Test (10 min)	·        Start the class with a partner quiz that reviews everything they have learnt so far in the unit Ø      Partners assigned according to seating plan
Participatory Learning (35 min)	·        Lesson notes on the properties of angles and how they can be used to solve problems involving angles in a circle       (10 min) ·        Have students verify these properties using geogebra       (10 min) ·        Have students work individually or with the students around them on practice questions on angle properties (15 min) Ø      Students allowed to use geogebra to help solve these questions Ø      Practice questions will incorporate material learnt in previous classes (ie, chord properties)
Post-Test (10 min)	·        Go over each practice question by having a different student come up to front board and show/explain how they solved the question (peer-teaching)
Summary (5 min)	·        Teacher recaps the major concepts learnt that day and briefly goes over topic for next day-proving angle properties

Unit Planning Assignment-Lesson 1

Lesson 1: Introduction to Circle Concepts

Bridge (5 min)	·        Show students a CD and have them point out the center, radius, diameter, etc on them Ø      Explain how a CD runs from one track to another by rotating around the center
Learning Objectives	·        To learn about the terminology relating to circles including: Ø      Center Ø      Radius Ø      Diameter Ø      Chord Ø      Minor/Major arc Ø      Sector Ø      segment
Teaching Objectives	·        To have students understand how these terms are related and real life examples of where they’re used ·        To have students gain an appreciation for why circle concepts are important in real life
Pre-Test (5 min)	·        Review of terms students have learnt about in previous math courses (ie, radius and diameter) ·        Have diagram of circle on board and have students volunteer to come up and identify on the circle where is the center, radius and diameter Ø      Have students identify these parts on a dartboard
Participatory Learning (40 min)	·        Lesson notes on new terminology of chord, minor/major arc, sector and segment (10 min) ·        Relate new terminology to radius, diameter and circumference (10 min) Ø      Add illustration of new terms onto diagram of circle on board (different colour for each term) ·        Have students work on exercise problems relating to material covered in lesson notes (20 min) Ø      Teacher will walk around class to monitor students’ progress
Post-Test (10 min)	·        Go over the solutions to the exercise problems as a class with students volunteering their answers
Summary (5 min)	·        Think-Pair-Share Ø      Have students turn to a partner and tell them one thing they learnt in class today Ø      Have students volunteer to share their partner’s answers with the class to summarize the material covered in the day’s lesson

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