Storyboard for Geometry(1)

STORYBOARDMATH 111 - GEOMETRY

INSTITUTION: COSTAATT LECTURER: Anthea Clarke

COURSE: MATH 111- Geometry

COURSE DAY/TIME: Wednesdays; 5:00p.m. - 7:50p.m. ROOM: 310

COURSE SUMMARY: (from Course Outline, to be displayed in top left corner)

Geometry is designed to explore topics in an organized, logical way, with an emphasis on proof. The course

covers topics in Euclidean geometry and will include: inductive and deductive reasoning, proof, points, lines,

planes, angles, two and three dimensional geometric figures, triangle congruence and similarity, right-

triangle trigonometry; area and volume calculations, straight edge and compass constructions.

INSTRUCTIONAL STRATEGIES: (from Course Outline; displayed in Block 1)

A Blended Learning approach will be used which combines face-to-face instruction with computer-mediated

instruction. Course content will be presented through online sessions via MOODLE and other web-based

tools; teacher-directed exploration and demonstration via lecture, lecture-discussion, discovery learning,

PowerPoint and video presentations.

Learners and lecturers will work together to improve the quality of learning and teaching, the ultimate aim of

blended learning being to provide realistic practical opportunities for learners and teachers to make learning

independent, useful, sustainable and ever growing.

Students will work independently and in groups to complete course topics.

COMPOSITION:

Face to face – 60%: Sessions will last between 90 min. and 120 min. to facilitate student use of

labs to participate in online activities.

Online learning – 40%: All constructions to be learned using online applet. Online assessment

will be mainly formative.

TLTL 6206 –ePedagogy Anthea Clarke -93738943

ASSESSMENT

Quizzes (Review)Quizzes (Assessment)

Assignments- Concept maps, graphic organizers

QuestionnairesChoices

GlossaryWiki

ASSESSMENT

Quizzes (2)Coursework Tests

Concept mapsGraphic organizers

Portfolio

Final exam

STRATEGIES

PowerPointVideo (YouTube, TMW media group DVDs)Links to webpages-appletsText pages-Lecture Notes

News ForumJournals

Discussion Forums

Jeopardy Games

STRATEGIES

Lecture - Interactive lecturePowerPoint

Video(TMW media DVDs)Manipulatives (pentominoes, tangrams, polygons, solids)

Collaborative LearningThink-Pair- Share

Fomulate-Share-Listen-CreateDiscussion (group, plenary)

Jeopardy GamesMatching Games

Crossword Puzzles

OnlineComponents

Face to FaceComponents

MATH 111 GEOMETRY

BLENDED LEARNING - OUTLINE OF COMPONENTS


STORYBOARD

BLOCK #

SESSION #LESSON TITLE

OBJECTIVES:At the end of this session students will be able to:

FACE TO FACERESOURCES /ACTIVITIES

ONLINE RESOURCES/ACTIVITIES

ASSESSMENT

Block 1 Gather details about the course.

Welcome Course Outline Online text (pdf) Schedule of Classes News- Student Announcements Glossary –Geometry terms and

concepts Wiki – Famous Geometers

þ Working knowledge of Course outline by second class

þ Glossary – each student enters 3 terms by end of course.

þ Wiki - each student enters 1 biography by end of course.

Block 2

Session 1

Introduction to Geometry

Outline the historical development of geometry

List geometric terms and symbols.

List Euclid’s 5 postulates

describe the tools and rules of Euclidean Construction

Introductions Ice breaker – Pass the geometry

ball Ppt – A short history of geometry

leading up to Euclid Handouts - Terms & Symbols Discussion of schedule Discussion of assessments Pair activity - Complete a

timeline of history of Geometry.

Video (YouTube) – History of Geometry Ppt – Euclid’s 5 Postulates Link to online text:http://www.ck12.org/flexr/flexbook/805/ Link to Webpage for Constructionshttp://www.mathopenref.com/tocs/constructionstoc.html Journal entry 1 – First impressions Graphic organizer – famous geometer to

be placed in portfolio

þ Participation in f2f activities

þ Fill out Timeline þ Participation in online

journal.þ GO completed and

submitted in portfolio

Block 3

Session 2

Basic Geometric Concepts

Describe the undefined terms of Points, Lines and Planes

Define an angle and distinguish between angle pairs

Classify Triangles/Polygons

Select appropriate problem solving strategies

Ppt – Points, lines and Planes Interactive lecture Handout – lecture notes Individual activity - Complete a

concept map for the undefined terms

Jeopardy game to review concepts

Ppt - Points, lines and Planes Video – Fundamental Geometric concepts

Jeopardy game Construction website - Complete the

following constructions Copy a line segment

Copy an angle

Bisect an angle Construct 30°, 45 and 60° angles

Concept Quiz 1 – Review


þ Attempts at 2+ questions in jeopardy game

þ 3 attempts at concept quiz 1


http://www.mathopenref.com/tocs/constructionstoc.html

http://www.mathopenref.com/tocs/constructionstoc.html

http://www.ck12.org/flexr/flexbook/805/

Block 4

Session 3

Reasoning and Proof

Differentiate between inductive and deductive reasoning

Analyze conditional statements

State the algebraic properties used in proofs

Draw diagrams for proofs Create a two column proof

Video – Inductive and deductive reasoning

Think-pair-share activity – Reasoning and number patterns

Interactive lecture Individual Activity – diagrams for

proofs

Ppt –Logic and reasoning Video –Planning proofs in geometry Link to Webpage – Lecture notes Link to worksheetshttp://www.kutasoftware.com/freeige.html Journal entry 2 – Logic, reasoning and

proof


þ 4 Diagrams correctly interpreted.

þ Participation in online journal

Block 5

Session 4

Parallel and Perpendicular lines

Investigate the relationships between angle pairs formed by Parallel lines and Transversals

Create proofs for parallel lines and related angles

Lecturer available for individual consultation

Ppt – Parallel & perpendicular lines Video – Parallel Lines and transversals Link to Webpage Construction website - Complete the

following constructions Perpendicular bisector of a line segment Perpendicular to a line at a point on the

line Perpendicular to a line from an external

point Perpendicular to a ray at its endpoint A parallel to a line through a point

Construct a 90° angle (right angle) Concept Quiz 2- Review


Block 6

Session 5

Symmetry and Tessellations

Apply concepts using transformational geometry and laws of symmetry

Develop properties of tessellating figures and use those properties to tessellate the plane.

Pair Activity – Pentominoes Ppt – Symmetry & Tessellations Activity -

http://mathforum.org/sum95/suzanne/tess.intro.html

Ppt – The Golden Spiral – Introduction to group project

Quiz 1

Ppt – Symmetry Video – Escher’s Art Link to Webpage -

http://www.haelmedia.com/OnlineActivities_txh/mc_txh4_001.html

Construction website - Complete the following constructions

Divide a line segment into n equal segments

Constructing 75° 105° 120° 135° 150° angles and more

Discussion : Geometry and Art

þ Participation in f2f activity

þ Participation in discussion

þ Group project on The golden mean submitted in week 14

þ Quiz 1 –MCQ -5%




http://www.kutasoftware.com/freeige.html

Block 7

Session 6

Congruent Triangles

Define congruent figures Prove triangle congruence

using SSS Prove triangle congruence

using ASA and AAS Prove triangle congruence

using SAS

Pair Activity – Tangrams Ppt – Triangle Congruence Interactive lecture Formulate-Share-Listen-Create –

Two column Proofs Pair activity – Two column proofs

-Matching game Individual Activity –Two Column

proofs (continued for homework) Discussion of portfolio activity -

tangrams

Ppt – Congruent Triangle Proofs Video – link

http://www.onlinemathlearning.com/triangle-congruence.html

Construction website - Complete the following constructions Triangle, given all 3 sides (SSS) Triangle, given one side and adjacent

angles (ASA) Triangle, given two sides and included

angle (SAS) Copy a triangle Equilateral Triangle Isosceles Triangle, given base and one

side; given base and altitude Link to Webpage- Online tangram

http://www.gieson.com/Library/projects/games/matter/

Questionnaire – readiness for tangrams -Space and shape


þ Homework activity on Proofs completed by next f2f class

þ Tangram activity completed and submitted in portfolio

Block 8

Session 7

Relationships within Triangles

construct a triangle’s medians, altitudes, angle and perpendicular bisectors using various methods

Develop logical concepts about their relationships to be used in solving real-world problems.


Ppt – Triangle Inequality Ppt – In Triangles Video – Construction website - Complete the

following constructions Medians of a Triangle Incenter of a Triangle Circumcenter of a Triangle Centroid of a triangle Orthocenter of a Triangle Incircle (inscribed circle) of a Triangle Circumcircle (circumscribed circle) of

a Triangle Concept Quiz 3 – review Choices – Proof (two column vs. paragraph)


þ Participation in choice activity






Block 9

Session 8

Right Triangle Trigonometry

apply the Pythagorean Theorem and its converse to solve real-world problems

Derive the special right triangle relationships (i.e. 30-60-90, 45-45-90).

Ppt – Right Triangles Interactive lecture Formulate-Share-Listen-Create –

Problem solving –real word problems

Portfolio Activity discussed –Pythagorean Spiral

Test #1

Video – Right triangles and Proof Text page – Construction website - Complete the

following constructions 30-60-90 right triangle given the

hypotenuseJournal entry 3 – Triangles, Congruence and Proof.



þ Test # 1 – 10%þ Tangram activity

completed and submitted in portfolio

Block 10

Session 9

Quadrilaterals

identify general properties of parallelograms, rectangles, rhombuses, squares, trapezoids, kites

compare and contrast the properties of convex and concave quadrilaterals


Ppt – Quadrilaterals and Proof Video – Quadrilaterals Online Activity -Link to Webpagehttp://www.google.tt/#hl=en&source=hp&biw=1117&bih=561&q=quadrilaterals+activity&aq=7&aqi=g10&aql=&oq=quadrilaterals&fp=5d78efcc54534c94 Concept Quiz 4 – review


Block 11

Session 10

Ratio, Proportion and Similarity

Use proportions to identify similar polygons.

Apply AA, SAS, and SSS similarity statements.

Find and use relationships in similar right triangles.

Apply self-similarity concepts (Fractals)

Activity – Crossword puzzle Ppt – Triangle Similarity Interactive lecture Pair Activity –Similar Triangles

proofs (continued for individual homework)

Group work Time – discussion of project

Ppt – Triangle Similarity Link to Webpage -

http://www.nos.org/Secmathcour/eng/ch-17.pdf

Discussion : Real world applications of Geometry


þ Homework activity completed by next f2f class

þ Participation in online discussion




http://www.google.tt/#hl=en&source=hp&biw=1117&bih=561&q=quadrilaterals+activity&aq=7&aqi=g10&aql=&oq=quadrilaterals&fp=5d78efcc54534c94



Block 12

Session 11 Circles

use the relationship between radii and a tangents

use congruent chords, arcs, and central angles

Recognize properties of lines through the center of a circle.

Calculate the measure of an inscribed angle and angles formed by a tangent and a chord.


Ppt – Circle Proofs Video – The Circle Link to Webpage

http://mathforum.org/alejandre/circles.html

Construction website - Complete the following constructions Finding the center of a circle Tangents to a circle through an external

point Tangent to a circle through a point on

the circle Circle through three points

Ppt – Mandalay (activity for portfolio) Circle Proofs (offline activity)

þ Offline activity completed by next f2f class

þ Mandela activity completed and submitted in portfolio

Block 13

Session 12

Perimeter and Area

Derive and justify formulas for area, perimeter of plane shapes and apply them to solve real-world problems.


Ppt –Perimeter and Area Link to Webpage –Lecture Notes Construction website - Complete the

following constructions Hexagon given one side Hexagon inscribed in a circle Pentagon inscribed in a circle

Jeopardy game Assessment - Online Quiz

þ Online quiz: 1 attempt -5%

Block 14

Session 13

Solid Geometry

Recognize the parts of a polyhedron (i.e. faces, edges, vertices)

Describe properties of prisms, cylinders, pyramids, cones, spheres.

Construct nets of solids

Pair Activity – Solid shapes Ppt – Polyhedra Interactive lecture Test #2

Ppt – Solids and their nets Video – Three dimensional geometry Link to Webpage

http://illuminations.nctm.org/activitydetail.aspx?id=70

Construction website - Complete the following constructions Nets of solids

Discussion – Sacred Geometry Choices – Which is a net?

þ Test # 2 – 10%þ Participation in online

discussionþ Participation in choice

activity






Block 15Session 14

Surface Area and Volume

Derive and justify formulas for surface area and volume using nets of solids and apply them to solve real-world problems.

Think –Pair –Share Activity Interactive lecture Individual activity – Word

problems Group work - project

Ppt –Surface Area & Volume Video - Textpage–Lecture Notes

Online activityhttp://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/

Journal entry – Reflection on course

þ Submission of Group project


Block 16

Session 15

Review

Review coursework. Jeopardy game Group activity -Past exam

questions

Past exam papers Concept quiz þ Submission of Individual

portfolioþ Multiple attempts at quiz

Block 17

Session 16

Final exam

FINAL EXAM – 2HRS 45 MINS Additional Readings Assessment Rubric for Group project Assessment Rubric for Portfolio

þ Final exam

1. All constructions in green will be handed in (worksheets) as part of the portfolio.


http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/

http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/

Documents

Storyboard for Geometry(1)