Learning Material Sheets class 6 Ganita prakash

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Learning Material Sheets – Ganita Prakash

Learning Material Sheets: Ganita Prakash Class 6

Chapter 3: Playing with Numbers

Core Concepts

  • Factors: A factor of a number divides that number exactly, without leaving a remainder. (e.g., factors of 12 are 1, 2, 3, 4, 6, 12).
  • Multiples: A multiple of a number is obtained by multiplying it by another whole number. (e.g., multiples of 5 are 5, 10, 15, 20…).
  • Prime Numbers: Numbers that have only two factors: 1 and the number itself. (e.g., 2, 3, 5, 7, 11).
  • Composite Numbers: Numbers that have more than two factors. (e.g., 4, 6, 8, 9, 10).
  • Highest Common Factor (HCF): The largest number that is a factor of two or more given numbers.
  • Lowest Common Multiple (LCM): The smallest number that is a multiple of two or more given numbers.

Solved Example: HCF and LCM

Question: Find the HCF and LCM of 18 and 24.

Solution:

Step 1: Prime Factorisation
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3

Step 2: Find HCF
Find the common prime factors: 2 and 3.
HCF = 2 × 3 = 6

Step 3: Find LCM
Take the highest power of each prime factor present in the numbers: 2³ and 3².
LCM = 2 × 2 × 2 × 3 × 3 = 8 × 9 = 72

Practice Questions

  1. What are the first five multiples of 8?
  2. List all the prime numbers between 20 and 30.
  3. Find all the factors of 48.
  4. Find the HCF of 20 and 50.
  5. Find the LCM of 9 and 15.

Chapter 5: Understanding Elementary Shapes

Core Concepts

  • Angles: Measured in degrees (°).
    • Acute Angle: Less than 90°.
    • Right Angle: Exactly 90°.
    • Obtuse Angle: Greater than 90° but less than 180°.
    • Straight Angle: Exactly 180°.
    • Reflex Angle: Greater than 180° but less than 360°.
  • Triangles (based on sides):
    • Equilateral: All 3 sides are equal.
    • Isosceles: 2 sides are equal.
    • Scalene: No sides are equal.
  • Quadrilaterals: Four-sided polygons. Examples: Square, Rectangle, Rhombus, Parallelogram, Trapezium.

Solved Example: Classifying a Triangle

Question: A triangle has angles 50°, 60°, and 70°. What kind of triangle is it based on its angles and sides?

Solution:

Based on Angles:
All three angles (50°, 60°, 70°) are less than 90°. Therefore, it is an acute-angled triangle.

Based on Sides:
Since all three angles are different, all three sides must also be of different lengths. Therefore, it is a scalene triangle.

Practice Questions

  1. What type of angle is 110°?
  2. A clock’s hands are at 3:00. What angle do they form?
  3. A triangle has two sides of 5 cm and one side of 7 cm. What is it called?
  4. How many right angles are there in a rectangle?
  5. What is the name for a four-sided shape where all sides are equal and all angles are 90°?

Chapter 11: Algebra

Core Concepts

  • Variable: A letter (like x, y, a, b) that can represent any number. Its value is not fixed.
  • Constant: A value that does not change. (e.g., 5, -10, 200).
  • Expression: A combination of variables, constants, and operations (+, -, ×, ÷). (e.g., x + 5, 3y – 7).
  • Equation: A statement that two expressions are equal. It always has an ‘equals’ sign (=). (e.g., x + 5 = 12).
  • Solution of an Equation: The value of the variable that makes the equation true.

Solved Example: Solving an Equation

Question: Find the solution to the equation: p – 7 = 15.

Solution:

We need to find a value for ‘p’ that makes the equation true. We can think: “What number, when you subtract 7 from it, gives you 15?”

Method (Transposition):
To find ‘p’, we can move the ‘-7’ to the other side of the equals sign. When it moves, its sign changes from ‘-‘ to ‘+’.
p = 15 + 7
p = 22

Check: Put p = 22 back into the original equation: 22 – 7 = 15. This is true!

Practice Questions

  1. Write an expression for: “10 added to n”.
  2. Write an expression for: “y multiplied by 5 and then 2 is subtracted”.
  3. Is x = 4 a solution to the equation 3x = 12? (Yes/No)
  4. Find the solution for the equation: m + 9 = 20.
  5. Sarita has 15 more marbles than Ameena. If Ameena has ‘x’ marbles, how many does Sarita have?

Chapter 10: Mensuration

Core Concepts & Formulas

  • Perimeter: The total distance around a closed figure. It is the length of the boundary.
    • Perimeter of a Rectangle = 2 × (length + breadth)
    • Perimeter of a Square = 4 × side
  • Area: The amount of surface enclosed by a closed figure. It is measured in square units (like cm², m²).
    • Area of a Rectangle = length × breadth
    • Area of a Square = side × side

Solved Example: Area and Perimeter

Question: A rectangular garden is 20 metres long and 15 metres wide. Find its perimeter and area.

Solution:

Given: length (l) = 20 m, breadth (b) = 15 m

Perimeter:
Formula: Perimeter = 2 × (l + b)
Perimeter = 2 × (20 + 15)
Perimeter = 2 × 35 = 70 metres

Area:
Formula: Area = l × b
Area = 20 × 15 = 300 square metres (m²)

Practice Questions

  1. Find the perimeter of a square with a side of 12 cm.
  2. Find the area of a square with a side of 10 m.
  3. A rectangular table top is 2 m long and 1.5 m wide. What is its perimeter?
  4. A room is 5 m long and 4 m wide. What is the area of its floor?
  5. The perimeter of a square park is 80 m. What is the length of its side?