| NCERT Exemplar Solutions | ||||||
|---|---|---|---|---|---|---|
| 6th | 7th | 8th | 9th | 10th | 11th | 12th |
| Class 6th Chapters | ||
|---|---|---|
| 1. Number System | 2. Geometry | 3. Integers |
| 4. Fractions & Decimals | 5. Data Handling | 6. Mensuration |
| 7. Algebra | 8. Ratio & Proportion | 9. Symmetry & Practical Geometry |
Class 6 Mathematics NCERT Exemplar Solutions
Chapter 1: Number System
This chapter introduces students to the concept of natural numbers, whole numbers, and place value. Learn how to represent large numbers using the Indian and International Number Systems. Explore patterns, rounding off numbers, and estimation in real-life contexts. Understand how to write numbers in expanded form and perform arithmetic operations. For example, the expanded form of $3456$ is $3000 + 400 + 50 + 6$. These NCERT Exemplar solutions strengthen your understanding of the place value system and numerical operations.
Chapter 2: Geometry
Geometry deals with shapes, sizes, and spatial understanding. Students learn about points, lines, line segments, rays, angles, triangles, quadrilaterals, circles, and polygons. Understand how to identify right angles, acute angles, and obtuse angles using geometric tools. Learn that the sum of the angles on a straight line is $180^\circ$ and around a point is $360^\circ$. The chapter builds the foundation for advanced geometry by introducing basic constructions and properties of shapes.
Chapter 3: Integers
This chapter explains positive and negative numbers and their representation on a number line. Understand addition, subtraction, multiplication, and division of integers using simple rules such as: $(-3) + (+5) = +2$ and $(-4) \times (+2) = -8$. Learn how integers are used in real-world contexts such as temperatures, elevations, and financial transactions. Mastering these NCERT Exemplar solutions helps develop confidence in handling all operations with integers.
Chapter 4: Fractions & Decimals
Explore fractions (like $\frac{1}{2}$, $\frac{3}{4}$) and decimal numbers ($0.25$, $1.5$, $2.75$). Learn different types of fractions — proper, improper, and mixed — and convert between them. Understand operations such as $\frac{1}{2} + \frac{1}{4} = \frac{3}{4}$ and multiplication of decimals like $0.3 \times 0.5 = 0.15$. This chapter builds fluency in fractional and decimal arithmetic, essential for measurement, money, and data interpretation.
Chapter 5: Data Handling
Learn to collect, organize, and represent data in various forms such as tables, bar graphs, pictographs, and tally marks. Understand how to read and interpret data sets to draw meaningful conclusions. For example, you can use a bar graph to compare student attendance or rainfall in different months. This chapter develops analytical thinking and statistical reasoning through hands-on activities using NCERT Exemplar questions.
Chapter 6: Mensuration
Mensuration deals with measuring length, area, and volume of shapes. Learn formulas like perimeter of a rectangle $= 2(l + b)$, area of a square $= s^2$, and volume of a cube $= a^3$. Understand units of measurement and real-life applications such as finding the area of walls, floors, and containers. These Exemplar problems reinforce formula application and help visualize spatial dimensions.
Chapter 7: Algebra
Get introduced to algebraic expressions and simple equations. Learn to use symbols (like $x$, $y$, $z$) to represent numbers and form expressions such as $2x + 3$. Understand how to evaluate and simplify expressions and solve equations like $x + 5 = 9$ (giving $x = 4$). This chapter lays the foundation for algebraic reasoning used in higher classes.
Chapter 8: Ratio & Proportion
Understand the concept of ratios as comparison between quantities, for example, the ratio of $2$ to $3$ is written as $2:3$. Learn how to find proportions and apply them in practical situations like scaling, recipes, and maps. For instance, if $a:b = c:d$, then $\frac{a}{b} = \frac{c}{d}$. This chapter improves reasoning ability and helps in percentage, speed-time, and unitary method problems.
Chapter 9: Symmetry & Practical Geometry
Explore the concept of symmetry in different shapes like triangles, rectangles, and circles. Identify lines of symmetry and learn to perform geometric constructions using a ruler and compass. Practice drawing perpendicular bisectors, circles, and angles using geometric tools. For example, a square has four lines of symmetry, while an equilateral triangle has three. This chapter builds spatial understanding and precision in geometry.