Class 6 Mathematics: Algebra

• Introduction to Algebra
  • Meaning of Algebra
    • Branch of mathematics
    • Uses letters and numbers
  • Why Algebra?
    • Generalizes arithmetic rules
    • Helps solve unknown quantities (mysteries)
• Concept of Variables
  • What is a Variable?
    • Quantity that can change (vary)
    • Represented by alphabets ($x$, $y$, $z$, $l$, $m$, etc.)
  • Contrast with Constants
    • Fixed numerical values ($5$, $-7$, $\frac{3}{4}$, etc.)
• Use of Variables in Arithmetic Rules
  • Commutativity of Addition
    • $a + b = b + a$
  • Commutativity of Multiplication
    • $a \times b = b \times a$
  • Distributivity of Multiplication over Addition
    • $a \times (b + c) = (a \times b) + (a \times c)$
• Expressing Geometry with Variables
  • Perimeter of a Square
    • Formula: $P = 4 \times s$ (where $s$ is side length)
  • Perimeter of a Rectangle
    • Formula: $P = 2 \times (l + b)$ (where $l$ is length, $b$ is breadth)
• Matchstick Patterns
  • Finding a Rule
    • Pattern for letter 'T' ($2$ matchsticks): $2n$
    • Pattern for letter 'Z' ($3$ matchsticks): $3n$
    • Pattern for letter 'H' ($5$ matchsticks): $5n$
  • Identifying the Rule using variable $n$ (number of shapes)
• Algebraic Expressions
  • What is an Expression?
    • Combination of numbers, variables, and operations ($+$, $-$, $\times$, $\div$)
  • Formation of Expressions
    • Example: "4 added to $x$" $\rightarrow$ $x + 4$
    • Example: "7 subtracted from $y$" $\rightarrow$ $y - 7$
    • Example: "5 times $m$" $\rightarrow$ $5m$
    • Example: "Divided by 3" $\rightarrow$ $\frac{x}{3}$
• Equations
  • What is an Equation?
    • Condition on a variable
    • Has an equality sign (=)
    • Contains LHS (Left Hand Side) and RHS (Right Hand Side)
  • Solution of an Equation
    • Value of the variable that makes LHS = RHS
  • Methods to Solve Simple Equations
    • Trial and Error Method (plugging in values)