topic 10 two dimensional shapes (2d)

7/28/2019 Topic 10 Two Dimensional Shapes (2D)

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X INTRODUCTIONLook at things around you. How do they appear or look like? Almost everythingaround you is in the form of solids or in three-dimensional form, but topologically,they can be described as two dimensional shapes. What does an apple, an ice-cream cone, a star fruit and a ball look like to small children? Are children able toname and relate logically between three dimensional solids and two dimensionalshapes?

SHAPE AND SPACE IN DAILY LIFE

Understanding the environment we live in is very important as we live in anenvironment made up of shape and space. Take a look at the things around you many objects around are either in the form of two dimensional shapes or threedimensional solids. Some pertinent questions come to mind. How do youngchildren see things surrounding them? How do they develop geometric thinkingand mental reasoning about shapes? How does the human mind, or thinking,change and make connections between 3D solids and 2D shapes? Things likecauliflower, cabbage and broccoli are usually spherical in shape like that of a ball,

10.1

TTooppiicc

1100X Two

DimensionalShapes (2D)

By the end of this topic, you should be able to:

1. Explain the shape and space in daily life;

2. Identify shapes using the correct vocabulary related to 2D shapes;

3. Classify two dimensional (2D) shapes; and

4. Describe the teaching and learning of shape activities.

LEARNING OUTCOMES


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TOPIC 10 TWO DIMENSIONAL SHAPES (2D) W 213

see Figure 10.1 (i.e. 3D in shape) but at certain angles, they may look like the faceof a clock (i.e. 2D in shape)!

Figure 10.1: Spherical 3D solids can be viewed as circular 2D shapes

SPATIAL SENSE

How do we deal with the space around us? To understand more about spatialsense, let us consider a few situations. How are bags and luggage arranged in thecompartments of an aeroplane to accommodate all baggage checked in? How dowe ensure that we can walk into a laboratory or classroom without stumblingover instruments and furniture? Why do drivers position their cars on the rightlane of the road in order to avoid tragic accidents? Why is it we cannot simplydrive on the road without getting a driving licence first? One has to apply spatialsense to be safe on the roads. To acquire a driving licence, we have to undergoseveral tests and practise driving for hours under the supervision of experts

before we can drive independently and safely on the roads.

Spatial sense is defined as an intuition about shape and the relationshipamong shapes, including our ability to mentally visualise objects and spatialrelationships by turning things around in our minds. It is about our feeling ofgeometric aspects of objects and shapes that appear within our surroundingsor our living environment. (Walle and Lovin, 2006)

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1. What is meant by geometric spatial sense?2. Why is geometric spatial sense important for understanding our

environment?

SELF-CHECK 10.1


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X TOPIC 10 TWO DIMENSIONAL SHAPES (2D)" " " " "214

Geometry has several applications in real life. Spatial sense is spatial visualisationor spatial perception that helps children in understanding their world.

Furthermore, spatial sense is an imaginary visualisation of object orientation inour minds. People with good spatial sense are able to analyse, using theirgeometric reasoning and ideas to appreciate nature, space exploration, homedecoration, architecture, art and design. It promotes creativity in art and design.

One is also able to imitate and transfer a bouquet of flowers into 2D shapes.See Figure 10.2.

Figure 10.2: Bouquet of flowers

Next, carry out the following task. Take a look at the pictures shown inFigure 10.3.

Spatial sense is spatial perception or spatial visualisation that helps studentsto understand the relationship between objects and their locations in threedimensional worlds.

(Kennedy and Tipps, 2006)

Do your pupils/young children have spatial sense? Is spatial sense innatein children or do we have to teach spatial sense in the classroom? Discuss.

ACTIVITY 10.1


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Figure 10.3: Pictures of objects

GEOMETRIC THINKING

Geometry recognition is part of the primary mathematics curriculum. The aim ofintroducing two dimensional shapes in the primary school curriculum is todevelop the pupils reasoning and spatial sense with respect to geometry sincegeometric practical applications are very useful in everyday life. Most of themathematics primary curriculum incorporates number systems and numericalthinking as a foundation into the teaching of geometry. The development of thehuman mind on geometric concepts and reasoning of solids and shapesencompasses two basic areas (see Table 10.1).

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Show these pictures to your pupils. Ask them to arrange the pictures inascending order according to their size in real life. Discuss and look out foryour pupils spatial reasoning when doing the arranging.

The answer: (picture frame < door < Eiffel Tower)If their arrangement is as such, how did they know that Eiffel Tower is the

biggest/ tallest among the three things?

x Have they ever visited Eiffel Tower?

x Did they use their spatial sense when arranging the pictures in ascendingorder?

x Get your children to look closely at the picture of the rabbit and ask themwhether it is possible that the size of the rose (flower) can be bigger thanthe rabbit in reality.


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Table 10.1: Two Basic Areas of Human Mind on Geometric ConceptBasic Area Description

Visual spatialthinking This happens on the right hemisphere of the brain that is associatedwith literature and can occur unconsciously without one being awareof it. It can operate holistically and intuitively, with more than onething at a time and is literally called simultaneous processing.

Verbal logicalthinking

This lies on the left hemisphere of the brain consisting of continuousprocessing and one is always aware of it. It operates sequentially andlogically and is related to language or symbols and numbers.

Gardner proposed that the multiple intelligence of spatial ability can bedeveloped through experience. Children are able to explain and demonstrate

their discoveries after seeing how things work and observing their properties.The levels of thought, or childrens thinking, is the basis for the instructionalactivities at the primary school level.

The Van Hiele Theory: Levels of Geometric ThinkingFigure 10.4 explains the level of geometric thinking according to Van Hiele.

Figure 10.4: Van Hieles levels of geometric thinkingAccording to Pablo Picasso, Observation is the most significant element of mylife, but not just any kind of observation. This means that certain observations orthe way we look at things will form a visual image that can be used in the studyof mathematics and its applications.


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GEOMETRIC SYSTEMS

Children learn geometry at the primary level which can be divided into fourseparate geometrical systems as suggested by many mathematicians (Kennedyand Tipps, 2000), as described in Table 10.2.

Table 10.2: Four Separate Geometrical SystemsGeometricalSystem Description

Euclideangeometry

Euclidean geometry is the geometry of shapes and objects in a plane (2D)or in space (3D). It is about the properties or the characteristics of objects,points and lines, circles and spheres, triangles, polygons, pyramids,

cylinders, cones and other solids. Shapes have properties includingsimilarities and congruence, length of sides, number of parallel sides,lines or rotational symmetry.

Coordinategeometry

It is about the location of shapes on coordinate or grid systems.Coordinate geometry ranges from simple to complex uses that define thelocation of an object on plane coordinates of the vertical and horizontalaxes for 2D shapes or the positioning of objects on grid systems for threedimensional spaces. Complex uses of coordinate geometry include thelocation of vessels in the Pacific Ocean or the location of a travellerscamp at the Antarctic or the grid location of Mount Everest.

Transformationgeometry

Transformation geometry is about geometry in motion. It describes themovement of shapes or objects in a plane or in space. Objects or shapes inmotion can be transformed by flipping (reflection), sliding or gliding(translation), and turning (rotation) or a combination of thesetransformations in many different ways. For example, during anaircrafts landing or departing, it slides on the runway, flips and turns inthe sky or exhibits a combination of movements in different ways.

Topologicalgeometry

Topological geometry describes the locations of objects and theirrelations in space or the recognition of objects in the environment.Children view everything and their perceptions relative to their standing

positions or locations in space. It focuses on the development of thechildrens mental understanding, the use of extensive vocabulary, givingdescriptions of objects in space, as well as the size and position of objectswithin their perspectives. The use of vocabulary to describe the locationsof objects in space include words such as: far-near, high-low, big-small,above-below, inside-outside or in front, in between, front and behind, etc.

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GEOMETRIC CONTENT

The Primary Mathematics curriculum touches on the simple concept of geometric

systems. The geometric content for primary schools focuses more onVisualisation and Euclidean Geometry, as well as Van Hieles theory of childrensthinking. The sequence of teaching geometric content and the teaching ofconcepts at the primary school level is as illustrated in Figure 10.5.

Figure 10.5: Sequence of teaching geometry in primary schools

10.5

Group discussion:

The teaching of geometry covers four areas of geometric systems andmust be aligned to the Van Hieles theory of levels of thought. In groups,discuss how to integrate the teaching of the concept of geometry with anytwo areas underlined.

ACTIVITY 10.2


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Visualisation covers the recognition of shapes in the environment, classification,sorting and naming of shapes. Euclidean geometry is the study of shapes andtheir properties. Advance concepts of topological geometry, Euclidean Geometry,

coordinate and transformation geometry will be taught at secondary school or athigher levels.

The geometric content includes:

(a) Identifying shapes sorting, classification and grouping;

(b) Knowing and naming shapes (vocabulary):

(i) Triangle (types of triangles);

(ii) Rectangle (quadrilaterals);

(iii) Polygon; and

(iv) Circle and ellipse.

(c) Identifying geometric properties of shapes;

(d) Classification and grouping; and

(e) Shapes in the environment.

THE TEACHING AND LEARNING OFSHAPES

The learning of shapes is the second stage for children learning about geometry.The teaching and learning of geometry should be associated with the childrenslevels of thinking and the four areas of geometric systems described earlier. As ateacher, we have to understand our pupils levels of thinking and mentalreasoning before teaching them the concept of two dimensional shapes. Bothhemispheres of our pupils minds must be stimulated. Exposure and experiencethrough investigation and discovery will promote pupils learning.

Some suggested teaching-learning activities for helping children to develop orconsolidate ideas and further understanding of geometrical concepts arehighlighted. There should be a progressive development of activities and aproper sequence for introducing concepts, starting from basic geometric conceptsto the highest level of geometric problem solving.

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Learning ActivitiesThe following are some suitable learning activities:

(a) Contextual learning children look around and observe the environmentplus describe in words what they have seen.

(b) Explore and experiment with shapes (visual images) in order to gain insightinto the properties and their uses.

(c) Analyse shapes informally, observe size and position in order to makeinferences; then refine and extend knowledge that develops from variouslearning activities.

Introduction of three dimensional shapes must be done earlier or before the

teaching of 2D shapes. The concept of two dimensional shapes can be developedfrom three dimensional shapes. Shapes that can be introduced to pre-school orearly primary level include those easier concepts that are commonly foundwithin their environment.

Figure 10.6: Different views of the surface area of faces of a cuboidA teacher should always guide young children on how to relate solids of three

dimensions (3D) to shapes of two dimensions (2D). As described previously inTopic 9, for the visualisation of cuboids, pencil boxes can be used to representcuboids. Pupils can be encouraged to rotate, visualise and trace the shapes fromdifferent perspectives by looking at them from different orientations or fromdifferent sides or elevations (see Figure 10.6).


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TEACHING AND LEARNING ACTIVITIES

Geometric thinking and spatial reasoning can be developed through formal orinformal activities. A good instructional activity includes good planning,appropriate activities and a variety of selection of effective teaching materials.The learning of geometric concepts can be incorporated into the childrensactivities such as playing activities, discussion, role play, music activities, dramasas well as art and design activities while they are actively involved. Teaching andlearning activities suggested here cover the four areas mentioned earlier and can

be modified to teach 2D shapes to pre-school and early primary school children.

Part I: Euclidean Geometry

10.7.1 Identifying Shapes Sorting, Classification andGrouping

Shape is generally defined as space within an enclosed boundary.

Shapes are drawn on a flat surface called a plane. Two dimensional planegeometry is about shapes like lines, circles and triangles. As such, shapes can beenclosed by straight or curved lines. Shapes enclosed by only straight lines are

called polygons. Other shapes are known as non-polygons.

The activities described here are geared towards achieving the following learningoutcomes with respect to 2D shapes:

(a) Identify 2D shapes, i.e. figures with closed boundaries;

(b) Sort and classify 2D shapes;

(c) Discover features and properties of 2D shapes;

(d) Identify similarities and differences of shapes between groups; and

(e) Use correct vocabulary and language while doing activities.

Activity 1.1: Identifying 2D ShapesLearning Outcomes:By the end of this activity, pupils should be able to:

(a) Identify and colour 2D shapes i.e. figures with closed boundaries; and

(b) Count how many figures there are with closed and open boundaries.

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Materials:x Exercise sheet: Set of shapes (open and closed figures); and

x

Colour pencils.

Procedure:(i) Distribute the exercise sheet (see Figure 10.7), containing examples of

various shapes to the pupils.

(ii) Ask pupils to colour the shapes with closed boundaries and count howmany shapes there are with closed boundaries and how many there arewithout.

Figure 10.7: Set of shapesThis activity is an early introduction to the concept of shapes whereby shapes areidentified as figures that have closed boundaries. Children have to colour all theshapes with closed boundaries and leave out those with open boundaries. This

activity serves to give a clear picture to young children about 2D shapes.

Play the game ofLook Around.Children who can spot the most number of 2D shapes will be the winner.

ACTIVITY 10.3


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Activity 1.2: Sort and Group 2D ShapesLearning Outcomes:By the end of this activity, pupils should be able to:

(a) Sort, group and classify shapes to discover their features and properties.

Materials:x Set of 2D shapes/cut-outs of 2D shapes;

x A4 paper/manila cards; and

x Vocabulary (word cards).

Procedure:(i) Sort and group the shapes. Place the sorted shapes under the respective

categories on the pieces of A4 paper/manila cards provided. Use commonfeatures for grouping the shapes into various categories: Triangles,Quadrilaterals/Rectangles, Polygons and Non-polygons/Enclosed

boundaries (see Figure 10.8).

(ii) Discuss what is interesting about each group.

Figure 10.8: Examples of 2D shapes(iii) Ask simple questions and guide pupils to describe in simple words the

common features used for sorting and grouping shapes:

x How many groups of shapes are there?

x What are the special features of the figures or shapes in each group?

x What are the common features within each group?

x Is there any difference between the groups?


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(iv) Say in simple sentences or describe clearly the special features of eachgroup.

(v) Encourage the children to say in simple words what they understand aboutthe interesting features of the shapes.

(vi) Ask pupils to look for similarities and differences within and between thegroups.

(vii) Introduce simple geometric words and correct vocabulary to help pupils todescribe the features and propertries of the shapes.

(viii) Check the answers for the grouping of 2D shapes: For example as shown inFigure 10.9:

Figure 10.9: Grouping of shapes under different categories(ix) Distribute worksheet to reinforce the concept learnt.

10.7.2 Knowing and Naming Shapes (Vocabulary)

Introduce different types of shapes and let pupils look for features and propertiesto identify the various groups of shapes. At this level, only simple geometry isused and the shapes shown here are to be considered as extra knowledge forteachers.


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Activity 2.1: Identifying PolygonsPolygons are two dimensional flat surfaces with length and breadth or width.Polygons have special names based on the number of angles and the number ofsides (straight edges) that enclose them. A triangle is a polygon with the leastnumber of points and sides to form a closed boundary, followed by quadrilaterals,pentagons, hexagons, heptagons, octagons, nonagons, decagons, dodecagons, etc.Other figures known as non-polygons also have enclosed boundaries but withsides that are circular and elliptical. Here, various examples of polygons and a fewnon-polygons are illustrated in Table 10.3 (to be used as teachers notes).

Table 10.3: Examples of Polygons and Non-PolygonsTriangle3 points3 sides

Quadrilateral4 points4 sides

Pentagon5 points5 sides

Hexagon6 points6 sides

Heptagon7 points7 sides

Octagon8 points8 sides

Nonagon9 points, 9sides

Decagon10 points, 10sides

Hendecagon/Undecagon11 points, 11 sidesDodecagon12 points

Non-polygons:Circle, Ellipseand othershapesEnclosed

boundaries


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Most of the polygons shown in Table 10.3 are irregular plane figures or polygonswhere all the sides and angles are not of equal measure. Regular polygons havesides that are all equal in length and angles that are all equal in measure. Figure

10.10 shows an example of a regular and irregular hexagon.

Figure 10.10: Regular and irregular hexagons

Stop and Have Fun! Activity: Shapes of games

Take your pupils outside and play these games:

(a) Shape jumping

(b) Track to the moon

(c) Play ting-ting

ACTIVITY 10.4


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1. Shape jumping

x Lay out a few sets ofshapes (coloured,hard cardboard) on

the floor.x Call out the shapes

and jump to land onthe shape called oute.g. triangles,quadrilaterals,polygons, curvedshapes.

2. Track to the moon

x Lay out a few sets ofplane figures(coloured, hard

cardboard) on thefloor.

x Call out the shapesand Jump and singthe Jumping song:Names of shapes.

3. Play ting-ting

x Number and shapes

x Jump in steps.

x Count the number ofsides, corners andangles.

x Discuss specialfeatures of regularrectangles (squares).

Activity 3: Vocabulary for Naming ShapesThis activity is to enhance childrens understanding of different types of shapesfor each group and the differences between various classes of shapes. Provide theopportunity for pupils to look for special features and properties as well as learnthe names of shapes.

Learning Outcomes:By the end of this activity, pupils should be able to:

(a) Identify different types of shapes (triangle, quadrilateral, polygon, etc.);

(b) Name shapes;(c) Discover features and properties of shapes;

(d) Identify special features and properties of each group of shapes;

(e) Identify similarities and differences of shapes between groups; and

(f) Use correct vocabulary and language while doing activities.


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Materials:x Geoboard (safety nail pegs), see Figure 10.11;

x

Coloured rubber bands (see Figure 10.11); andx Vocabulary cards: (Names of shapes; properties of shapes).

Figure 10.11: Geoboard and rubber bandsProcedure:(i) Take a rubber band and form shapes using the pegs on the geoboard.

(ii) Name and label the shapes made using appropriate vocabulary cards.

(iii) Identify the features or properties of the shapes labelled.

Activity 3.1: TrianglesLearning Outcomes:By the end of this activity, pupils should be able to:

(a) Discover features and properties of triangles;

(b) Identify special features and properties of triangles; and

(c) Use correct vocabulary and language to describe triangles.

Materials:x Rubber bands;

x Geoboard;

x Grid paper; and

x Vocabulary cards: (names of shapes, labels of properties).


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Procedure:(i) Ask pupils to use three points and a rubber band to form a triangle.

(ii) Then, ask them to form different types of triangles see Figure 10.12 (a) -and draw the shapes on grid paper.

(iii) Guide them to look for properties of triangles, classify and describe thetriangles made.

Figure 10.12 (a): Examples of trianglesA. Teachers Instructions:A triangle is a shape with three points (see Figure 10.12 (b)), three corners andthree straight sides.


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Figure 10.12 (b): Examples of trianglesB. Teachers notes: Extra information on types of triangles.Types of TrianglesThese are triangles, each of them has three straight sides, three corners or threevertices but they are all different. There are many types of triangles such asequilateral, right angle, isosceles, acute, obtuse or scalene triangles (see Figure10.12 (c)).

At this level of visualisation, we want young children to be able to use theirsenses to observe differences and similarities between the shapes within a group.It may seem difficult to explain the different types of triangles but at this level,children only have to understand that there exists special properties for trianglesand that there are many different types of triangles (see Figure 10.12 (d)).


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Figure 10.12 (c): Types of triangles

Figure 10.12 (d): Classification of trianglesActivity 3.2: Matching TrianglesLearning Outcomes:By the end of this activity, pupils should be able to:

(a) Identify special features and properties of different types of triangles; and

(b) Use correct vocabulary and language to describe the types of triangles.

Materials:x Exercise sheet Matching activity; and

x Vocabulary cards (Names of shapes, labels of properties).


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Procedure:(i) Can you see any differences between those four triangles in the upper row?

Look at them closely look for similarities and differences between them.

(ii) Try to match those on the upper row by drawing arrows to those shown inFigure 10.13.

Figure 10.13: Matching activity: Types of trianglesActivity 3.3: QuadrilateralsLearning Outcomes:By the end of this activity, pupils should be able to:

(a) Discover features and properties of quadrilaterals;

(b) Identify special features and properties of quadrilaterals; and

(c) Use correct vocabulary and language to describe quadrilaterals.


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x

Geoboard;x Grid paper; and

x Vocabulary cards: (names of shapes, labels of properties).

Procedure:(i) Ask pupils to use 4 points and a rubber band to form a quadrilateral.

(ii) Then, ask them to form different types of quadrilaterals see Figure 10.14(a) - and draw the shapes on grid paper.

(iii) Guide them to look for properties of quadrilaterals, name and describe thequadrilaterals made, (see Figure 10.14 (b) and Figure 10.14 (c)).

Figure 10.14 (a): Examples of quadrilaterals


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A. Teachers Instructions:

Figure 10.14 (b): How to make the quadrilaterals

Figure 10.14 (c): Examples of quadrilaterals shapesActivity 3.4: PolygonsLearning outcomes:By the end of this activity, pupils should be able to:

(a) Discover this features and properties of polygons;

(b) Identify special features and properties of polygons; and

(c) Use correct vocabulary and language to describe polygons.


x Geoboard;

x Grid paper; and

x Vocabulary cards (names of shapes, labels of properties).


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Procedure:(i) Ask pupils to use five points and a rubber band to form a pentagon.

(ii) Then, ask them to form different types of polygons using six pegs andmore, see Figure 10.15 and draw the shapes on grid paper.

(iii) Guide them to look for properties of polygons, name and describe thepolygons made.

Figure 10.15: Examples of polygonsActivity 3.5: Curved Shapes: Circle and EllipseLearning Outcomes:By the end of this activity, pupils should be able to:

(a) Discover features and properties of non-polygons or curved shapes such ascircle and ellipse;

(b) Identify special features and properties of non-polygons or curved shapes;and

(c) Use correct vocabulary and language to describe non-polygons or curvedshapes.

Materials:x Picture card: Set of pictures of curved shapes;

x Vocabulary cards: Names of shapes (circle, semicircle, ellipse); and

x Vocabulary cards: Features/properties (crescent/lunar/cloud/heart shape).


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Procedure:(i) Ask pupils to look at the set of curved shapes in the picture card

distributed. Explore and observe shapes through visual images to gaininsight into their properties. Look for similarities and differences (seeFigure 10.16).

(ii) Guide them to look for properties of non-polygons, name and describe thenon-polygons shown. Introduce names, vocabulary or the language ofgeometry for describing non-polygons or curved shapes shown.

(iii) Count the total number of faces, the number of similar faces and slowlyintroduce the names and properties of the curved shapes.

Figure 10.16: Examples of non-polygons or curved shapesShapes in the Environment

The learning of geometric concepts will be easier if pupils are actively involved inthe fun learning process using appropriate teaching materials from theenvironment, such as the use of common materials from the childrensenvironment like potatoes, star fruits, pears or banana stems as materials fordrawing and painting shapes (see Figure 10.17).

Colour and print shapes of the environmentUse any 3D solids or objects from the environment. Cut and colour thecross-sections or longitudinal sections of objects (e.g. star fruits, pears,

banana stems, potatoes, leaves). Then, print them on to a piece of drawingpaper. Use your creativity. Are they shapes of the environment?

ACTIVITY 10.5


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Cross-sectional or longitudinal cuttings of:

Figure 10.17: Cross-sectional or longitudinal cuttings of objectsPart II: Transformation Geometry

The following activity allows children to have some fun with shapes, with respectto motion geometry, where the learning of geometric concepts is incorporatedinto childrens play.

Activity 4.1: Fun with Shapes: The Most Powerful Spinning Propeller (MotionGeometry)Learning Outcomes:By the end of this activity, pupils should be able to:

(a) Construct propellers of different shapes: semi-circular shape, crescent(lunar) shape, heart shape and arrow shape; and

(b) Discover which shape forms the most powerful spinning propellers.

Materials:x Instruction cards for making different shaped propellers;

x Plastic glass;

x Manila card;

x Coloured paper/Fancy cards;

x

Straws;x Pencils;

x Pins; and

x Plasticine.


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Procedure:(i) Divide the children into four groups of five.

(ii) Ask each group to prepare different shapes of propellers as follows:

x Group 1 : semi circular shaped propellers;

x Group 2 : lunar shaped propellers;

x Group 3 : heart shaped propellers; and

x Group 4 : arrow shaped propellers.

(iii) Using their finished products, ask pupils to blow on to the propellers to seewhich propellers will spin the fastest.

Group 1Figure 10.18 (a), Figure 10.18 (b), Figure 10.18 (c) and Figure 10.18 (d) explain thesteps in making the semi-circular, lunar, heart and arrow shaped propellers foreach of the four groups.

Figure 10.18 (a): The making of semi-circular propellers


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Group 2

Figure 10.18 (b): The making of lunar-shaped propellersGroup 3

Figure 10.18 (c): The making of heart-shaped propellersGroup 4

Figure 10.18 (d): The making of arrow-shaped propellers


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Finished ProductsFigure 10.18 (e) shows the finished products of the different shaped propellersfrom each group.

Figure 10.18 (e): Different shaped propellersPart III: Coordinate Geometry

An activity about coordinate geometry dealing with the location of places or

destinations is described next.

Activity 5.1: Location of PlacesLearning Outcomes:By the end of this activity, pupils should be able to:

(a) Explain the location and state the direction of places from a picture map.

Materials:x Picture map; andx A4 paper.

Procedure:(i) Distribute the picture map (see Figure 10.19) to your pupils.

(ii) Ask them to study the map and explain the location of the places stated inthe map to a tourist who lands at KLIA.


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(iii) Discuss in detail the location and direction of those places.

Figure 10.19: Picture mapPart IV: Topological Geometry

The last area of geometric concept to be discussed concerns topology and touches

on the location of objects according to a relative standing position in space.

Activity 6.1: Location of ShapesLearning Outcomes:By the end of this activity, pupils should be able to:

(a) Describe the locations and state the positions of objects with respect to arelative standing position from the picture provided.

Materials:x Picture card;

x A4 paper; and

x Vocabulary cards: (positional words e.g. behind in front, left right, far near, beside adjacent, etc.).


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Procedure:(i) Ask pupils to colour the shapes according to the colour scheme given i.e.

(triangles green, quadrilaterals red, polygons light blue, circles darkblue, and ellipses yellow) or any scheme of their choice in the picture cardas shown in Figure 10.20.

(ii) Count the number of figures for every group of shapes that appears in thepicture.

(iii) Topology concept: Discuss the site or the location of objects in the picturefrom the girls standing position i.e. behind in front, left right, far near,

beside adjacent, etc.

(iv) Ask pupils to describe and state the positions of objects using appropriatevocabulary.

Figure 10.20: Picture card

x This topic of two dimensional shapes discusses spatial sense in detail, how weunderstand our world, childrens level of thinking and the teaching ofgeometry concepts within four geometric systems, which are:

(a) Euclidean Geometry;

(b) Transformation Geometry;


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(c) Coordinate Geometry; and

(d) Topological Geometry.

x Examples and activities suggested are within the primary school curriculumprescribed especially for pre-school and early primary school levels.

x Teachers are encouraged to develop good lesson plans, creative and effectiveteaching activities to suit pupils interest and their ability to understand thegeometric aspects of their surrounding and the environment.

Acute angle

Apex

Base

Boundary

Circle

Cone

Corner

Edge

Equilateral triangle

Hexagon

Isosceles triangle

Rectangle

Scalene triangle

Sphere

Square

Symmetry

Tessellate

Triangle

Two dimensional

Vertex (Vertices (p))

As an early childhood mathematics school teacher, you have to plan teaching andlearning activities that cover the teaching of geometric concepts for the fourgeometric systems. Suggest suitable teaching and learning activities that can becarried out to enable the children to acquire the geometric concepts discussed.Teaching activities and teaching materials should be creative and effective basedon respective learning outcomes.


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The teaching of geometric concepts has to be aligned to childrens levels of

thought, pupils experience and their geometric reasoning ability. List threelearning activities that can suit the criteria mentioned.

APPENDIX

WORKSHEET

1. Count the shapes. Fill in the blanks with the correct numbers:

(a) There are _____ circles.

(b) There are _____ rectangles.

(c) There are _____ squares.

(d) There are _____ triangles.

(e) There are _____ stars.

topic 10 two dimensional shapes (2d)

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