SKEMA TLO

RANCANGAN PENGAJARAN DAN PEMBELAJARAN

PROGRAM: Program Ijazah Sarjana Muda Perguruan (PISMP)SEMESTER: 2TAHUN: 1

KURSUS: GeometriKOD: MTE3033KREDIT: 3(2+1)

MingguTajuk dan KandunganHasil PembelajaranInteraksi BersemukaInteraksi Bukan BersemukaCatatan

KuliahAmaliTutorialPentaksiranPembelajaran Kendiri (sebelum/ selepas kuliah)Lain-lain (Tugasan, ulangkaji dll)

1 Jam2 Jam1 JamJam2 JamJam

M1

Teselasi Satah Jenis-jenis teselasi Menggunakan satu bentuk Menggunakan dua atau lebih bentukTeselasi dan seni Jenis teselasi Escher

Pelajar dapat:

Memilih teselasi yang sesuai dan relevan untuk matematik

Menggunakan satu bentukteselasi

Menggunakan dua atau lebih bentuk Mengintegrasi teselasi dalam pdp matematik Menyelidik kerja teselasi Escher1. Teselasi Satah

Jenis-jenis teselasi

Teselasi dan seni

Geometer Sketchpad (GSP)

meneroka dan mencipta teselasi

melazimkan diri dengan arahan asas GSP

melazimkan diri dengan arahan asas GSP

membina titik,

segmen dan garisan(selari dan bersudut tegak

(parallel and perpendicular)

Membina bentuk asas

poligon (polygons)

Membincangkan ide-ide utama dalam geometri

:interseksi,mengukur jarak, sudut, parallelism,

perpendicularity,kongruen,similariti dan simetri(garisan dan putaran) dan jenis-jenis transformasi

Mencari dalam laman sesawang contoh teselasi yang melibatkan

a. satu bentuk

b.dua bentuk

c.jenis Escher

Taklimat tentang kandungan kursus,log reflektif,projek dan penilaian

Log reflektif individu hendaklah dihantar kpd pensyarah

Resources:

Coxford, (1996)

Geometry from Multiple perspectives. pp 1-11

Galtrey & Pool .(1995). Shape, space and measures I. pp 31-38, 41-54

M2

Plane tessellations

Tessellation and art

Escher type tessellation

Fractal geometry

Introduction to fractals

Fractal trees

Produce creative manipulative materials to support and learning in mathematics

Create potato stamping and produce potato printing tessellation Describe the properties of fractal geometry, their dimension and calculation1. Teselasi Satah

Geometri fraktal Geometer Sketchpad (GSP)

meneroka dan mencipta teselasi

melazimkan diri dengan arahan asas GSP

Hands-on activity:

Using potato printing to create Escher type tessellations (potato stamps)

Hands-on activity:

Using potato printing to create Escher type tessellations (potato stamps)

Read the articles stated below:

1. Geometry Fractals by Bass,Charles,Johnson & Kennedy (2002) . pp 525-539

2. GSP Learning Guide (Version 4.06) Tour 8: Constructing a snowflake Iteration; Understanding the Koch Curve

Reader article:

1. Groves S. (2006). The work of M.C. Escher pp 63-80

2. Ernst(1994).The Magic Mirror of M. C. Escher

Activity 4.7 and 4.8 pp 81-84

Addendum:

Ernst (1994).Potato-printing, A game for winter Evenings. pp 9-11

Resource Materials:

1. Bass L.E, Charles R.I, Johnson A. & Kennedy D. (2002). Geometry -Fractals. Pearson,Prentice Hall. pp 525-539

2. GSP Learning Guide (Version 4.06) Tour 8: Constructing a snowflake Iteration; Understanding the Koch Curve

M3

Plane tessellations

Fractal geometry

Plane symmetries and transformations

Isometry of the plane

Rotation

Reflection

Translation

Glide reflection

Investigate isometry and symmetry Create and explore the use of single and combine transformation

Analyze the properties of tessellation and glide reflection

construct simple glide tessellation rotational, reflection, translation2. Simetri Satah dan Transformasi

Satah isometri

putaran

pantulan

translasi

pantulan geluncuran (glide reflection)

Geometer Sketchpad (GSP)

menerokai dan mencipta transformasi asas

Exploring fractals using GSP: Folder Fractal Gallery/ Sketches/ samples

Exploring fractals using GSP: Folder Fractal Gallery/ Sketches/ samples

In groups, search for examples of patterns that involve rotation, reflection, translation and glide reflection in your institution. Take pictures and comment on the patterns Resource:

GSP 4.06

Resource materials:

1. Groves S. (2006). Symmetries and transformations in the plane. pp 72-107

M4

Plane symmetries and transformations

Plane symmetry

Use GSP to develop a tool kit for tessellation and isometry of the plane

using rotation, reflection, translation and glide reflection2. Simetri Satah dan Transformasi

Simetri satah

Geometer Sketchpad (GSP)

membina kit alat untuk teselasi, isometri satah dan konik.

Do Exercise 4.1, 4.2 and Activity 4.6 in Groves S. (2006) pp 76-80Do Exercise 4.1, 4.2 and Activity 4.6 in Groves S. (2006) pp 76-80Individual planning of Exercise 4.1, 4.2 and Activity 4.6 in Groves S. (2006) pp 76-80Resource materials:

1. Groves S. (2006). Symmetries and transformations in the plane. pp 76-80

M5

Plane symmetries and transformations

Finite symmetry groups and the seven Frieze patterns

develop a tool kit for tessellation and isometry of the plane

Discuss and present the finite symmetry of seven Frieze patterns2. Simetri Satah dan Transformasi

Kumpulan simetri finit and tujuh pola Frieze

Pameran

Kit alat bantu GSP untuk teselasi dan isometri

Cetakan kentang

In groups, present exercise 4.12 from Groves S. (2006) pp 93

In groups, present exercise 4.12 from Groves S. (2006) pp 93

Discuss and plan presentation of exercise 4.12 from Groves S. (2006) pp 93

Reader articles:

1. Ranucci & Teeters (1977). Plane Symmetry

2. Groves S. (2006). Patterns in the plane pp 93

M6

Plane symmetries and transformations

Finite symmetry groups and the seven Frieze patterns

Regular and semi-regular solids

Five platonic solids

Construct paper construction of the five platonic solids

Construct the five platonic solids and submit for assessment

Create as many nets as possible for the five platonic solids

3. Pepejal Sekata dan Separa Sekata

Lima pepejal platonik

Pembinaan Pepejal Platonik

pembinaan lima pepejal platonik menggunakan kertas

Create as many nets as possible for the five platonic solids.

Create as many nets as possible for the five platonic solids.

Complete Activity 5.1 on pp 113-114 from Groves S. (2006)

Resource materials:

1. Groves S. (2006). Patterns in the plane pp 95 104

Ex. 4.15 , Activity 4.9

2. Groves S. (2006). Regular and semi-regular solids. Topic 5

Reader articles:

1. Kepler and the platonic solids by A . Adler (1967)

2. Polygons & Polyhedra by J.Simpson (1975)

3. Nets with polyhedron by J. Russell, (1996)

Briefing and commencement of project

M7

Regular and semi-regular solids

Vertices, faces and edges

Archimedean solids

Describe the properties of regular, semi-regular of Archimedean solids

Construct a truncated tetrahedron, a truncated cube and a truncated

icosahedron from the nets and template

compare and contrast Platonic solids and Achimedean polyhedra

3. Pepejal Sekata dan Separa Sekata

Bucu, muka dan sisi

Pepejal Archimedes

Pembinaan Pepejal Platonik

pembinaan pepejal Archimedes menggunakan kertas

Do Activity 5.3, 5.4, 5.5 and 5.6 from Groves S. (2006) pp 115-119

Do Activity 5.3, 5.4, 5.5 and 5.6 from Groves S. (2006) pp 115-119

Classify the polyhedra using codes as stated in the article Polygons and polyhedra by J. Simpson (1975)

Resource materials:

1. Groves S. (2006). Regular and semi-regular solids. pp 115-119

Reader articles:

1. Polyhedra: A visual approach by A.Pugh (1976)

2. Polygons & polyhedra by J. Simpson (1975)

M8

Regular and semi-regular solids

Kepler-Poinsot solids

List the characteristic of Kepler-Poinsot solids

construct selected kepler-pointsot solids3. Pepejal Sekata dan Separa Sekata

Pepejal Kepler-Poinsot

Pembinaan Pepejal Platonik

pembinaan pepejal Kepler-Poinsot

gambar-gambar pepejal yang dibinaCompare and contrast Platonic solids and Archimedean polyhedra

Read the article Polyhedron models by M.J. Wenninger (1971)Resource materials:

1. Groves S. (2006). Regular and semi-regular solids. pp 119-121

Reader article:

1.Polyhedron models by M.J. Wenninger

(1971)

M9

Geometric modeling

Paper engineering

Making pop-up models

Getting started

pop-up techniques

Produce a pop-up card using basic paper folding techniques

Make pop-up models by using basic paper folding techniques such as Hill fold, valley fold, parallel fold and angled fold4. Pembinaan Model Geometri

Paper engineering

model pop-up

Projek Paper Engineering

meneroka dan menganalisis elemen matematik dalam teknik asas lipatan kertas

Present the samples collected and explain the paper folding techniques used to produce the samplesCollect samples of paper engineering productsResource materials:

1. Groves S. (2006). Paper Engineering. pp 125-129

2. Shell Centre for Mathematical Education: Be a Paper Engineer-Teachers Guide

M10

Geometric modeling

Paper engineering

Creating your own original designs

Paper engineering in the classroom

Develop an idea of a pop up engineering project using three different technique

4. Pembinaan Model Geometri

Paper engineering

teknik pop-up

Projek Paper Engineering

menganalisis koleksi paper engineeringberbentuk kad, buku dan bungkusan

Plan your pop-up paper engineering projectPlan exhibition

of GSP toolkit for tessellation & isometry, potato printing and

the paper engineering projectResource materials:

1. Groves S. (2006). Paper Engineering. pp 129-133

2. Shell Centre for Mathematical Education: Be a Paper Engineer-Teachers Guide

M11

Geometric modeling

Paper engineering

Art and design

produce a high quality pop-up project using at least 3 different techniques

4. Pembinaan Model Geometri

Paper engineering

Seni dan reka bentuk

Projek Paper Engineering

menghasilkan kad pop-upPlan and do your pop-up paper engineering projectPlan exhibition

of GSP toolkit for tessellation & isometry, potato printing and

the paper engineering projectResource materials:

1.Shell Centre for Mathematical Education: Be a Paper Engineer-Teachers Guide

2. Groves S. (2006). Developing the mathematics. Some sample ideas.

pp 49-66

Submission of project

M12

Conics

Locus

explore conics using GSP such as locus

plan for project presentation

5. Konik

Lokus Meneroka Konik Menggunakan TMK Seperti GSP

Explore GSP 4.06\GSP 4.06\set up & samples GSP 4.06\sketchpad\samples\sketches\conics

Explore

GSP 4.06 M

Folder: samples/sketches/

geometry.gsp and do a printoutPlan exhibition

of GSP toolkit for tessellation & isometry, potato printing and

the paper engineering projectGSP 4.06 M

Folder: samples/sketches.conics/unified conics.gsp

GSP 4.06\GSP 4.06\set up & samples GSP 4.06\sketchpad\samples\sketches\conics

M13

Conics

Parabola

explore conics using GSP such as parabola

Present and display toolkit of the project proposed by groups

5. Konik

Parabola

Meneroka Konik Menggunakan TMK Seperti GSP

Explore GSP 4.06\GSP 4.06\set up & samples GSP 4.06\sketchpad\samples\custom tools\sample tools

Explore GSP 4.06\GSP\sketch 3\samples\sketch\analytic\Parabtan

Explore

GSP 4.06 M

Folder: samples/sketches/

geometry.gsp and do a printout

Plan exhibition

of GSP toolkit for tessellation & isometry, potato printing and

the paper engineering projectGSP 4.06\GSP 4.06\set up & samples GSP 4.06\sketchpad\samples\custom tools\sample tools

GSP 4.06\GSP\sketch 3\samples\sketch\analytic\Parabtan

GSP 4.06 M

Folder: samples/sketches.conics/unified conics.gsp

M14

Conics

Ellipse and

Hyperbola

explore conics using GSP such as Ellipse and Hyperbola

5. Konik

Elips

hiperbola

Meneroka Konik Menggunakan TMK Seperti GSP

Explore GSP 4.06\GSP\sketch 3\samples\sketches\Trigconi\3conics

Explore

GSP 4.06 M

Folder: samples/sketches/

geometry.gsp and do a printoutPlan exhibition

of GSP toolkit for tessellation & isometry, potato printing and

the paper engineering projectGSP 4.06\GSP\sketch 3\samples\sketches\Trigconi\3conics

GSP 4.06 M

Folder: samples\sketches.conics\unified conics.gsp

M15

Conics

Parabola

Ellipse

Hyperbola

explore conics using GSP such as parabola, ellipse and hyperbola.

Present and display toolkit of the project proposed by groups

5. Konik

Elips

hiperbola

Meneroka Konik Menggunakan TMK Seperti GSP

Explore

GSP 4.06 M

Folder: samples\sketches\

geometry.gsp and do a printout Plan exhibition

of GSP toolkit for tessellation & isometry, potato printing and

the paper engineering projectGSP 4.06 M

Folder: samples\sketches.conics\unified conics.gsp

Kerja Kursus/Amali2525

Ulangkaji Peperiksaan17.517.5

Peperiksaan2.52.5

Jumlah1530152.53042.5120

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