**NCERT Secondary Mathematics kit Manual, One of the most significant recommendations of the National Curriculum Framework (NCF)-2005 is the mathematisation of the child’s thought processes. In achieving this goal, concrete mathematical experiences play a major role. **

A child is motivated to learn mathematics by getting involved in handling various concrete manipulatives in various activities. In addition to activities, games in mathematics also help the child’s involvement in learning by strategizing and reasoning.

For learning mathematical concepts through the above- mentioned approach, a child-centred Mathematics kit has been developed for the students of Secondary stage based on some of the concepts from the newly developed NCERT mathematics textbooks. NCERT Secondary Mathematics kit Manual.

The Maths Activities Kit kit includes various kit items along with a manual for performing activities. The kit broadly covers the activities in the areas of geometry, algebra, trigonometry and mensuration.

**Advantages of Maths Kit: **

**The kit has the following advantages:**

• Availability of necessary materials at one place

• Multipurpose use of items

• The economy of time in doing the activities

• Portability from one place to another

• Provision for teacher’s innovation

• Low-cost material and use of indigenous resources

- special features of the Maths kit items:
- Here are some of the special features of the kit items: Two variety of plastic strips with slots and markings have been provided. They help in creating angles, triangles, quadrilaterals and determination of values of trigonometric ratios. The full or half protractor can be fixed on the strips for measuring the angles in the activities related to angles, triangles, and quadrilaterals.
- Circular Board: A Circular Board is designed in such a manner that it can be used to verify results related to a circle as well as trigonometric ratios.
- Geoboard: A Geoboard is a board of dimensions 19cmx19cmx1cm having holes drilled on side A of it at a distance of 1cm each. Geoboard pins can be fitted in the holes and with the help of rubber bands, different geometrical shapes can be formed.
- Cutouts of corrugated sheet: Cutouts of corrugated sheets in the form of a parallelogram, triangle, trapezium and circle help in learning concepts related to areas.
- cube: A cube with adjusting cut-outs of cuboid, cylinder, cone and hemisphere have been given to construct the concept of surface area and volume.
- Cut-outs of plastic cardboard: Cut-outs of plastic cardboard in the form of triangles, quadrilaterals and rectangle etc. have been given to verify Pythagoras theorem and algebraic identities like a2b2abab.
- Algebraic Tiles: Another interesting item, Algebraic Tiles has also been provided. They are provided in two different colours and three different sizes. They can be used for the concretisation of the concept of factorisation of quadratic equations.

The kit items, apart from being academically useful, are also designed in an attractive manner. It is hoped that this kit will generate enough interest in learning mathematics at the secondary stage. It will prove to be an important part of the mathematics resource room in schools across the country.

**Maths Activities**:

ACTIVITY 1: To form different angles and measure 1 them.

ACTIVITY 2: To verify the relation of different pairs 5 of angles formed by a transversal with two parallel lines.

ACTIVITY 3: To explore the properties of a triangle. 9

ACTIVITY 4: To verify the mid-point theorem “A-line 15 joining the midpoints of a triangle is parallel to the third side and half of it”

ACTIVITY 5: To verify that a line drawn through 17 the mid-point of one side and parallel to the second side bisects the third side.

ACTIVITY 6: To verify the basic proportionality 19 theorem.

ACTIVITY 7: To verify that a line dividing two sides 21 of a triangle in the same ratio is parallel to the third side.

ACTIVITY 8: To explore various properties of 23 different types of quadrilaterals.

ACTIVITY 9: To verify that a quadrilateral formed 29 by joining the mid-points of the sides of a quadrilateral taken in order, is a parallelogram.

ACTIVITY 10: To form different shapes on 31 geoboards and explore their areas.

ACTIVITY 11: To verify that the ratio of areas of two 35 similar triangles is equal to the ratio of squares of their corresponding sides.

ACTIVITY 12: To verify that the median of a triangle 37 divides it in two triangles of equal area.

ACTIVITY 13: To form different figures in a 39 Geobaord satisfying the following conditions:

(a) lying on the same base.

(b) lying between the same parallels but not on the same base.

(c) lying on the same base & between the same parallels

ACTIVITY 14: To verify that triangles on the same 42 base and between the same parallels are equal in area.

ACTIVITY 15: To verify parallelograms on the same 44 bases and between the same parallels are equal in area.

ACTIVITY 16: To verify that for a triangle and a 46 parallelogram on the same base and between the same parallels, the area of a triangle is half the area of a parallelogram.

ACTIVITY 17: To explore the area of a triangle , 48 parallelograms and trapezium.

ACTIVITY 18: To verify Pythagoras theorem. 41

ACTIVITY 19: To verify the algebraic identities. 53

(i) (ii)

a b 2 a 2 2ab b 2

a b 2 a 2 2ab b 2

ACTIVITY 20: To verify the algebraic identity 57

a2 b2 a ba b

ACTIVITY 21: To factorise expression of the type 60 A x 2 B x C ,

f o r e x a c t ly

(i) (ii) (iii)

x2 5x 6

x2 x 6

2 x2 7 x 6

ACTIVITY 22: To explore the area of a circle. 64

ACTIVITY 23: To verify that the longer chord 68 subtends a larger angle at the centre of a circle.

ACTIVITY 24: To verify that equal chords subtend 70 equal angles at the centre of a circle.

ACTIVITY 25: To verify that chords subtending equal 72 angles at the centre of a circle are equal.

ACTIVITY 26: To verify that the perpendicular from 74 the centre of a circle to a chord bisects the chord.

ACTIVITY 27: To verify that the line is drawn through 76 the centre of a circle to bisect a chord is perpendicular to the chord.

ACTIVITY 28: To verify that equal chords of a circle 78 are equidistant from the centre of the circle.

ACTIVITY 29: To verify that the chords equidistant 81 from the centre of a circle are equal in lengths.

ACTIVITY 30: To verify that equal arcs of a circle 83 subtend equal angles at the centre.

ACTIVITY 31: To verify that the angle subtended by 85 an arc of a circle at the centre, is double the angle subtended by it on any point in the remaining part of the circle.

ACTIVITY 32: To verify that the angles in the same 88 segment of a circle are equal.

ACTIVITY 33: To verify that an angle in a semi-circle 90 is a right angle.

ACTIVITY 34: To verify that the sum of either pair 92 of opposite angles of a cyclic quadrilateral is 180°

ACTIVITY 35: To verify that the sum of a pair of 94 opposite angles of a noncyclic quadrilateral is not equal to 180°

ACTIVITY 36: To verify that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

ACTIVITY 37: To verify that the lengths of the two tangents drawn from an external point to a circle are equal.

ACTIVITY 38: To understand the meaning of different trigonometric ratios using the circular board.

ACTIVITY 39: To estimate the trigonometric ratios of some special angles such as 0°, 30°, 45°, 60° and 90°

ACTIVITY 40: To verify that the values of trigonometric ratios of an angle do not vary with the lengths of the sides of the triangle.

ACTIVITY 41: To verify standard trigonometric identities.

Activity 42 : (i) To understand the concept of surface area and volume of solids.

( ii ) To verify the fact that increase decrease in the volume of a solid may not result in the same change in its surface area.

**NCERT Secondary Mathematics kit Manual Book for Maths Activities performing**

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