Class 09 To represent some irrational numbers on the number line.

 

Activity 2

OBJECTIVE                  

To represent some irrational numbers on the number line.                                                  

MATERIAL REQUIRED

Two cuboidal wooden strips, thread, nails, hammer, two photo copies of a scale, a screw with nut, glue, cutter.

 METHOD OF CONSTRUCTION

Two cuboidal wooden strips, thread, nails, hammer, two photo copies of a scale, a screw with nut, glue, cutter.

 1.   Make a straight slit on the top of one of the wooden strips. Fix another wooden strip on the slit perpendicular to the former strip with a screw at the bottom so that it can move freely along the slit [see Fig.1].

 2.   Paste one photocopy of the scale on each of these two strips as shown in Fig. 1.

 3.   Fix nails at a distance of 1 unit each, starting from 0, on both the strips as shown in the figure.

 4.   Tie a thread at the nail at 0 on the horizontal strip.

DEMONSTRATION

 11.   Take 1 unit on the horizontal scale and fix the perpendicular wooden strip at 1 by the screw at the bottom.

2.   Tie the other end of the thread to unit ‘1’ on the perpendicular strip. 

the horizontal strip to represent			√2 on the horizontal strip [see Fig. 1].
Similarly, to represent		√3 , fix the perpendicular wooden strip at  √2 and
repeat the process as above. To represent				√a , a > 1, fix the perpendicular
scale at	√a – 1 and proceed as above to get					√a .
OBSERVATION
On actual measurement:
a – 1 = ...........			√a =  ...........
APPLICATION
The activity may help in representing some irrational numbers  such as √2, √3, √4, √5, √6,√7.

. on the number line.

3.   Remove the thread from unit ‘1’ on the perpendicular strip and place it on

NOTE

You may also find   √a such as  √13 by fixing the perpendicular      strip at 3 on the horizontal strip       and tying the other end of thread               at 2 on the vertical strip.

CLASS 09 NCERT ACTIVITIES

CLASS 09 NCERT ACTIVITIES & PROJECTS

1. To construct a square-root spiral.

2. To represent some irrational numbers on the number line.

3. To verify the algebraic identity : (a + b)² = a² + 2ab + b²

4.To verify the algebraic identity :(a – b)² = a² – 2ab + b²

5. To verify the algebraic identity :a² – b² = (a + b)(a – b)

6. To verify the algebraic identity :(a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

7.To verify the algebraic identity :(a+b)³ = a³ + b³ + 3a²b + 3ab²

8. To verify the algebraic identity (a – b)3 = a3 – b3 – 3(a – b)ab

9. To verify the algebraic identity : a³ + b³ = (a + b) (a² – ab + b²)

10.Class 09 To verify the algebraic identity :a3 – b3 = (a – b)(a2 + ab + b2)

11. To find the values of abscissae and ordinates of various points given in a cartesian plane.

12. To find a hidden picture by plotting and joining the various points with given coordinates in a plane.

13. (i)       the vertically opposite angles are equal (ii)        the sum of two adjacent angles is 180º (iii)      the sum of all the four angles is 360º.

14. To verify experimentally the different criteria for congruency of triangles using triangle cut-outs.

15. To verify that the sum of the angles of a triangle is 180º.

16. To verify exterior angle property of a triangle.

17. To verify experimentally that the sum of the angles of a quadrilateral is 360º.

 18. To verify experimentally that in a triangle, the longer side has the greater angle opposite to it.

19. To verify experimentally that the parallelograms on the same base and between same parallels are equal in area.

20. To verify that the triangles on the same base and between the same parallels are equal in area.

21. To verify that the ratio of the areas of a parallelogram and a triangle on the same base and between the same parallels is 2:1.

22.To verify that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

23. To verify that the angles in the same segment of a circle are equal.

24.To verify that the opposite angles of a cyclic quadrilateral are supplementary.

25. To find the formula for the area of a trapezium experimentally.

26.To form a cube and find the formula for its surface area experimentally.

27. To form a cuboid and find the formula for its surface area experimentally.

28. To form a cone from a sector of a circle and to find the formula for its curved surface area

29. To find the relationship among the volumes of a right circular cone, a hemisphere and a right circular cylinder of equal radii and equal heights.

30. To find a formula for the curved surface area  of  a  right  circular  cylinder,experimentally.

31. To obtain the formula for the surface area of a sphere.

32. To draw histograms for classes of equal widths and varying widths.

33. To find experimental probability of unit’s digits of telephone numbers listed on a page selected at random of a telephone directory.

34.To find experimental probability of each outcome of a die when it is thrown a large number of times.

Class 09 PROJECT 1  ARYABHAT— THE MATHEMATICIAN AND ASTRONOMER

Class 09 PROJECT 02  SURFACE AREAS AND VOLUMES OF CUBOIDS

Class 09  PROJECT 03   GOLDEN RECTANGLE AND GOLDEN RATIO

Class 09  PROJECT 04  π - WORLD'S MOST MYSTERIOUS NUMBER

List of Projects

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: