Shape & Space

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TEACHING OF TEACHING OF SHAPE & SPACE SHAPE & SPACE

Transcript of Shape & Space

Page 1: Shape & Space

TEACHING OF TEACHING OF SHAPE & SPACESHAPE & SPACE

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YEAR 4YEAR 4Curriculum Specifications:Curriculum Specifications:9.0 Shape and Space9.0 Shape and Space9.1 Two dimensional shapes9.1 Two dimensional shapes9.1.1 Understand the perimeter of a two-dimensional 9.1.1 Understand the perimeter of a two-dimensional shape. (square, rectangle and triangle)shape. (square, rectangle and triangle)9.1.2 Understand the areas of a two-dimensional shape9.1.2 Understand the areas of a two-dimensional shape (square and rectangle)(square and rectangle)9.1.3 Find the area and perimeter.9.2 Three-dimensional shapes9.2.1 Understand the volume for cubes and cuboids.9.2.2 Find the volume for cubes and cuboids.

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Two- dimensional geometric formsTwo- dimensional geometric forms

rectangle

square

rhombus triangle

hexagon

circle

Examples:

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Two- dimensional geometric formsTwo- dimensional geometric forms

These geometric figures have only two These geometric figures have only two dimensional dimensional plane surfacesplane surfaces

- - lengthlength

- - breadthbreadth

length

breadth

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Three- dimensional geometric formsThree- dimensional geometric formsExamples:

cylinder

cubes

cuboids

pyramid

prism

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Three- dimensional geometric formsThree- dimensional geometric forms

These geometric figures are These geometric figures are solid formssolid forms which have three dimensionswhich have three dimensions

- - lengthlength

- - breadthbreadth

- - heightheight

lengthbreadth

height

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PerimeterPerimeterPerimeter is measurement of length of a boundary which encompasses a closed plane surface. It is the distance around the outside edge of a figure.

In Mathematics, perimeter is the total length of the sides enclosing a certain geometrical shape.

10cm

10cm

4cm4cm

Perimeter = 10cm + 4cm + 10cm + 4cm

= 28cm

OR

Perimeter = 10cm × 2 + 4cm × 2

= 20cm + 8cm

= 28cm

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Try out the questions below.Try out the questions below.Important steps should be shown in your Important steps should be shown in your task sheet given.task sheet given.

1)

75cm

182cm

163 cm

What is the perimeter of the triangle above?

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2)

68cm

154cm

What is the perimeter of the rectangle above?

3)

What is the perimeter of the equilateral triangle above?

57cm

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4)

The perimeter of the square above is 148cm. What is the length of its side?

5)

195cm

The perimeter of the rectangle above is 534cm. What is the length of BC?

B

C

A

D

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AreaAreaArea is the amount of space or surface which occupies a two-dimensional closed plane figure.

NamesNames Two-dimensional geometric Two-dimensional geometric figuresfigures

Area FormulaeArea Formulae

squaresquare

A = length A = length ××

lengthlength

rectanglerectangle A = length A = length ××

breadthbreadth

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simple concept about areasimple concept about area

C

B

A

D

The rectangular board is divided with squares of unit size each.

We can find the area of any part by counting the number of squares as its unit measure.

Thus,Area of A = 2 square units or 2 unit²Area of B = 3 square units or 3 unit²Area of C = 4 square units or 4 unit²Area of D = 5 square units or 5 unit²

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Try out the questions below.Try out the questions below.Important steps should be shown in the task sheet Important steps should be shown in the task sheet given.given.

1)

a) What is the length of the square above? _____cm

b) What is the perimeter of the square above? _____ cm

c) What is the area of the square above? ______ cm²

2cm

2cm

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2)

3cm

3cm

a) What is the length of the rectangular above? _____cm

b) What is the perimeter of the rectangular above? _____cm

c) What is the area of the rectangular above? _____cm²

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3) The area of a rectangle is 120cm². If the breadth is 5cm, what is the length?

4) The length of a carpet is 12m. Its breadth is less than the length by 4m. What is the area of the carpet?

5) The area of Ahmad’s school field is 6000m². If the length is 100m, what is the breadth of the field?

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VolumeVolumeThe real world is actually a three-dimensional space. All things in this world, whether solid, liquid or gaseous, exist in three dimensions. As such, the amount of three-dimensional space which an object occupies is called its volume.

To calculate the volume of an object or solid, we have to use a specific unit of measure. The most suitable shape for the unit of volume is a unit cube with dimensions 1cm × 1cm × 1cm.

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A unit cube is a cube whose edges are of unit length. The volume of a unit cube with edges 1cm each is 1cm × 1cm × 1cm = 1cm³This unit cube is the unit of measure usually used for measuring volume of a solid.

1cm

1cm1cm

Example:

If = 1cm³, find the volume of the solid below.

Solution:

Volume = 1cm³ × 4 = 4cm³

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Volume of cube = length × 3 = l ³

Volume of cuboid = length × breadth × height

OR

Volume of cuboid = Area of base × height

l

ll

lb

h

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Try out these questions.Try out these questions.Important steps should be shown in the task Important steps should be shown in the task sheet given.sheet given.

1) Siti has a shoe box. Find the volume of the shoe box if its length is 40cm, its breadth is 20cm and its height is 10cm.

2) The volume of a cuboid is 1120cm ³. Its breadth is 8cm. Its height is 7cm. What is its length?

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3) The milk container is a cube. What is the length of its side?

Milk1000cm ³

4) The volume of the pencil case is 720cm ³. What is its length?

Pencil case

5cm

8cm

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5) The length of the cube is 4cm. The area of the cuboid is 27cm² What is the total volume of the cube and cuboid?

5cm

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What did we learnt here?

2D Shapes

3D Shapes

Perimeter

Area

Volume

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