Class 09 Number system To construct a square-root spiral.

 Activity 1

 OBJECTIVE       

                                                             

To construct a square-root spiral.

MATERIAL REQUIRED

Coloured threads, adhesive, drawing pins, nails, geometry box, sketch pens, marker, a piece of plywood

 METHOD OF CONSTRUCTION

Coloured threads, adhesive, drawing pins, nails, geometry box, sketch pens, marker, a piece of plywood.

 1.   Take a piece of plywood with dimensions 30 cm × 30 cm.

 2.   Taking 2 cm = 1 unit, draw a line segment AB of length one unit.

 3.   Construct a perpendicular BX at the line segment AB using set squares (or compasses).

 4.   From BX, cut off BC = 1 unit. Join AC.

5.   Using blue coloured thread (of length equal to AC) and adhesive, fix the thread along AC.

 6.   With AC as base and using set squares (or compasses), draw CY perpendicular to AC.

7.  From CY, cut-off CD = 1 unit and join AD

8.    Fix orange coloured thread (of length equal to AD) along AD with adhesive.

 9.   With AD as base and using set squares (or compasses), draw DZ perpendicular to AD.

 10.  From DZ, cut off DE = 1 unit and join AE.

 11.  Fix green coloured thread (of length equal to AE) along AE with adhesive [see Fig. 1].

12. Repeat the above process for a sufficient number of times. This is called “a square root spiral”.

 DEMONSTRATION

 1. From the figure, AC² = AB² + BC² = 12 + 12 = 2 or AC =   √ 2 .

 AD² = AC² + CD² = 2 + 1 = 3 or AD =   √3 .

2. Similarly, we get the other lengths AE, AF, AG, ... as   √₄ or 2,  √₅ ,  √₆ ....

 OBSERVATION

 On actual measurement

 AC = ..... ,   AD = ...... ,   AE =...... ,     AF =....... ,  AG = ......

 _√2 = AC = ............... (approx.),_√3 = AD = ............... (approx.),

_√4 = AE = ............... (approx.),_√5 = AF = ............... (approx.)

 APPLICATION

 Through this activity, existence of irrational numbers can be illustrated.

Class 07 Visualizing solid shapes solids from nets

 

VISUALIZING SOLID SHAPES

 

ACTIVITY –2. Solids from nets

DATE:

 

AIM / Objective:

To make 3d model

 

MATERIALS REQUIRED:

Pencil, scale, eraser

 

PREREQUISITE KNOWLEDGE:

Concept of solid shapes

 

PROCEDURE:

 

Prepare net of cube, cuboid, cylinder, cone using cardboard and then make solids using them, of different dimensions.

Paste sheets and cardboard may also be used for making  solids.

 

LEARNING ASSESSMENT:

 

Make 3 d shapes model

SOLUTION:

 

Class 07 Visualizing solid shapes play with dice

 

VISUALIZING SOLID SHAPES

 

ACTIVITY –1. Play with Dice

DATE:

 

AIM / Objective:

To make solid cubes

 

MATERIALS REQUIRED:

Pencil, scale, eraser

 

PREREQUISITE KNOWLEDGE:

Concept of solid shapes

 

PROCEDURE:

 

Description:

1. Make two solid cubes using cards.

2. From the two cubes, make two dice with conditions :

(i) Top face number 6 and number 2 is adjacent to 4.

(ii) Bottom face has number 3 and number 4 is adjacent to 5.

 

LEARNING ASSESSMENT:

 

Make 2 dices

SOLUTION:

Class 07 Symmetry symmetry on roads

 

SYMMETRY

 

ACTIVITY –3. Symmetry on roads

DATE:

 

AIM / Objective:

To draw line of symmetry

 

MATERIALS REQUIRED:

Pencil, scale, eraser

 

PREREQUISITE KNOWLEDGE:

Concept of symmetry

 

PROCEDURE:

 

Description:

The students will be given some road signs. They will draw the line of symmetry if any. If there is no line of symmetry then they will mention that the  figure is non -

symmetric. They will name the road sign and explain in a sentence, its meaning.

 

LEARNING ASSESSMENT:

 

draw the line of symmetry if any. If there is no line of symmetry then mention it.

SOLUTION:

 

Class 07 Symmetry album of symmetrical shapes

 

SYMMETRY

 

ACTIVITY –2. Album of symmetrical shapes

DATE:

 

AIM / Objective:

To identify the symmetrical figures in nature

 

MATERIALS REQUIRED:

Pencil, scale, eraser

 

PREREQUISITE KNOWLEDGE:

Concept of Angles

 

PROCEDURE:

 

Description:

Line of symmetry is found in abundance everywhere around us. Collect samples of symmetrical figures found in nature, in your house, school etc. and prepare an album.

 

LEARNING ASSESSMENT:

 

 

How many angles you can identify? Mark them using coloured pencil.

 

 

SOLUTION:

Class 07 Symmetry garden of flower

 

SYMMETRY

 

ACTIVITY –1. Garden of Flower

DATE:

 

AIM / Objective:

To draw lines of symmetry

 

MATERIALS REQUIRED:

Pencil, scale, eraser

 

PREREQUISITE KNOWLEDGE:

Concept of  Symmetry

 

PROCEDURE:

 

Description:

Out of a swarm of bees, one fifth settled on a blossom of Rose, and one third on a flower of Sun flower, and three times the difference of those numbers flew to the bloom of a marigold. One bee, which remained hovered and flew about in the air, allured at the same moment by the pleasing fragrance of a jasmine and pandanus. What are the number of bees?

 

LEARNING ASSESSMENT:

 

a) Paste a petal of each of the above said flowers and draw the line of symmetry (if any)

b) Give one useful product made from each of the three flowers for our daily needs.

 

 SOLUTION:

Class 07 Exponents and powers paper folding activity

 

EXPONENTS AND POWERS

 

ACTIVITY –2. Paper Folding Activity

DATE:

 

AIM / Objective:

to represent the exponential function

 

MATERIALS REQUIRED:

Pencil, scale, eraser

 

PREREQUISITE KNOWLEDGE:

Concept of exponents and powers

 

PROCEDURE:

 

Demonstration:

Draw four rectangles in a row, exactly identical to represent the exponential function with two parts of the rectangles as shown below:

Cut each rectangle and fold them along the lines marked and number of small rectangles that are formed.

In rectangle (a) 0 fold of 2 parts. or 2^0   = 1

In rectangle (b) one fold of 2 parts or 2^1   = 2

In rectangle (c) two folds of 2 parts or  2^2= 4

In rectangle (d) three folds of 2 parts or 2^3 = 8

 

LEARNING ASSESSMENT:

 

Represent the exponential function

 

SOLUTION:

Class 07 Exponents and powers magic square

 

EXPONENTS AND POWERS

ACTIVITY –1. Magic Square

DATE:

AIM / Objective:

To complete the magic square

 

MATERIALS REQUIRED:

Pencil, scale, eraser

 

PREREQUISITE KNOWLEDGE:

Concept of exponents and powers

PROCEDURE:

Description:

Complete the following magic square filling in the empty boxes with numbers in exponential rotations with a prime number as the base. The numbers when simplified and added should give you the same sum row wise, column wise or

diagonally.

 

LEARNING ASSESSMENT:

 

Complete the following magic square

 

 

SOLUTION:

 

Algebraic expressions – 1 construct new algebraic expressions

 

ALGEBRAIC EXPRESSION

 

ACTIVITY –1. Construct New Algebraic Expressions

DATE:

 

AIM / Objective:

To  identify terms and factors from the given algebraic expression

 

MATERIALS REQUIRED:

Pencil, scale, eraser

 

PREREQUISITE KNOWLEDGE:

Concept of algebra

 

PROCEDURE:

Description: Fill in the gaps.

Algebraic Expression:

 

LEARNING ASSESSMENT:

 

Fill in the gaps.

 

SOLUTION: