## Topic outline

• • ### 01 Integers

We have learnt about whole numbers and integers in Class VI. We know that integers form a bigger collection of numbers

which contains whole numbers and negative numbers. What other differences do you find between whole numbers and

integers? In this chapter, we will study more about integers, their properties and operations. First of all, we will review and

revise what we have done about integers in our previous class.

• ### 02 Fractions and Decimals

You have learnt fractions and decimals in earlier classes. The study of fractions included proper, improper and mixed fractions as well as their addition and subtraction. We also studied comparison of fractions, equivalent fractions, representation of fractions on the number line and ordering of fractions. Our study of decimals included, their comparison, their representation on the number

line and their addition and subtraction. We shall now learn multiplication and division of fractions as well as of decimals.

• This topic ### 03 Data Handling

In your previous classes, you have dealt with various types of data. You have learnt tocollect data, tabulate and put it in the form of bar graphs. The collection, recording and presentation of data help us organise our experiences and draw inferences from them.

In this Chapter, we will take one more step towards learning how to do this. You will come across some more kinds of data and graphs. You have seen several kinds of data through newspapers, magazines, television and other sources. You also know that all

data give us some sort of information. Let us look at some common forms of data that you come across:

• ### 04 Simple Equations

In short, an equation is a condition on a variable. The condition is that two expressions should have equal value. Note that at least one of the two expressions must contain the variable.

• ### 05 Lines and Angles

You already know how to identify different lines, line segments and angles in a given shape. In this chapter you can identify the different line segments and angles formed.

• ### 06 The Triangle and its Properties

1.The six elements of a triangle are its three angles and the three sides.

2. The line segment joining a vertex of a triangle to the mid point of its opposite side is called a median of the triangle. A triangle has 3 medians.

3. The perpendicular line segment from a vertex of a triangle to its opposite side is called an altitude of the triangle. A triangle has 3 altitudes.

4. An exterior angle of a triangle is formed, when a side of a triangle is produced. At each vertex, you have two ways of forming an exterior angle.

5. A property of exterior angles: The measure of any exterior angle of a triangle is equal to the sum of the measures of its interior opposite angles.

6. The angle sum property of a triangle: The total measure of the three angles of a triangle is 180°.

7. A triangle is said to be equilateral, if each one of its sides has the same length. In an equilateral triangle, each angle has measure 60°.

8. A triangle is said to be isosceles, if atleast any two of its sides are of same length. The non-equal side of an isosceles triangle is called its base; the base angles of an isosceles triangle have equal measure.

• ### 07 Congruence of Triangles

You are now ready to learn a very important geometrical idea, Congruence. In particular, you will study a lot about congruence of triangles. The relation of two objects being congruent is called congruence. For the present, we will deal with plane figures only, although congruence is a general idea applicable to three-dimensional shapes also. We will try to learn a precise meaning of the congruence of plane figures already known.

• ### 08 Comparing Quantities

In our daily life, there are many occasions when we compare two quantities.

• ### 09 Rational Numbers

You began your study of numbers by counting objects around you.The numbers used for this purpose were called counting numbers or natural numbers. They are 1, 2, 3, 4, ... By including 0 to natural numbers, we got the whole numbers, i.e., 0, 1, 2, 3, ... The negatives

of natural numbers were then put together with whole numbers to make up integers. Integers are ..., –3, –2, –1, 0, 1, 2, 3, .... We, thus, extended the number system, from natural numbers to whole numbers and from

whole numbers to integers. You were also introduced to fractions. These are numbers of the form numerator denominator,

where the numerator is either 0 or a positive integer and the denominator, a positive integer. You compared two fractions, found their equivalent forms and studied all the four basic operations of addition, subtraction, multiplication and division on them.

In this Chapter, we shall extend the number system further. We shall introduce the concept of rational numbers along with their addition, subtraction, multiplication and division operations.

• ### 10 Practical Geometry

You are familiar with a number of shapes. You learnt how to draw some of them in the earlier classes. For example, you can draw a line segment of given length, a line perpendicular to a given line segment, an angle, an angle bisector, a circle etc.

Now, you will learn how to draw parallel lines and some types of triangles.

• ### 11 Perimeter and Area

In Class VI, you have already learnt perimeters of plane figures and areas of squares and rectangles. Perimeter is the distance around a closed figure while area is the part of plane or region occupied by the closed figure.In this class, you will learn about perimeters and areas of a few more plane figures.

• ### 12 Algebraic Expressions

We have already come across simple algebraic expressions like x + 3, y – 5, 4x + 5, 10y – 5 and so on. In Class VI, we have seen how these expressions are useful in formulating puzzles and problems. We have also seen examples of several expressions in the chapter on

simple equations.

Expressions are a central concept in algebra. This Chapter is devoted to algebraic expressions. When you have studied this Chapter, you will know how algebraic expressions are formed, how they can be combined, how we can find their values and how they can be used.

• ### 13 Exponents and Powers

Do you know what the mass of earth is? It is 5,970,000,000,000,000,000,000,000 kg! Can you read this number? Mass of Uranus is 86,800,000,000,000,000,000,000,000 kg. Which has greater mass, Earth or Uranus? Distance between Sun and Saturn is 1,433,500,000,000 m and distance between Saturn and Uranus is 1,439,000,000,000 m. Can you read these numbers? Which distance is less? These very large numbers are difficult to read, understand and compare. To make these numbers easy to read, understand and compare, we use

• ### 14 Symmetry

Symmetry is an important geometrical concept, commonly exhibited in nature and is used

almost in every field of activity. Artists, professionals, designers of clothing or jewellery, car

manufacturers, architects and many others make use of the idea of symmetry. The beehives,

the flowers, the tree-leaves, religious symbols, rugs, and handkerchiefs — everywhere you

find symmetrical designs.

• ### 15 Visualising Solid Shapes

In this chapter, you will classify figures you have seen in terms of what is known as dimension.

In our day to day life, we see several objects like books, balls, ice-cream cones etc.,

around us which have different shapes. One thing common about most of these objects is that

they all have some length, breadth and height or depth.

That is, they all occupy space and have three dimensions.

Hence, they are called three dimensional shapes.