Algebra

1. If n represents the position in the pattern 4, 7, 10, 13, …, which rule gives the number at position n?

   • a) n + 3
   • b) 3n + 1 ✓ (correct answer)
   • c) 4n − 1
   • d) 3n + 4

2. Select all the correct statements about 8y − 3.

   • a) It is an algebraic expression. ✓ (correct answer)
   • b) The variable in it is 3.
   • c) It has two terms: 8y and −3. ✓ (correct answer)
   • d) It is an equation because it has a minus sign.
   • e) The coefficient of y is −3.

3. In the equation x + 6 = 14, subtracting 6 from both sides gives x = 8.

   • a) True ✓ (correct answer)
   • b) False

4. Simplify 3x + 5 + 5x.

   • a) 8x
   • b) 3x + 10
   • c) 13x
   • d) 8x + 5 ✓ (correct answer)

5. If a = 6, calculate 2a + 5.

   • Answer: 17

1. Algebra

Using symbols to describe numbers and patterns

Speaker notes: Algebra uses letters and symbols to represent numbers and relationships. It helps us describe patterns and solve problems.

2. From patterns to algebra

• A pattern adds 3 each time: 4, 7, 10, 13, …
• The next number is found by adding 3 again.
• A rule for the pattern can be written as 3n + 1.
• Here, n represents the position in the pattern.

Speaker notes: For position 1, 3n + 1 gives 4; for position 2, it gives 7. Ask what number the rule gives at position 5.

3. Letters can stand for numbers

• A letter used to represent a number is called a variable.
• The value of a variable may change.
• In 5p, p is the variable and 5 is its multiplier.
• If p = 4, then 5p = 5 × 4 = 20.

Speaker notes: Explain that 5p means 5 multiplied by p; the multiplication sign is often left out. The letter could be any symbol, such as p, x or n.

4. Expression or equation?

• Algebraic expression

• 4x + 7

• Has numbers, variables and operations

• Does not have an equals sign

• Equation

• 4x + 7 = 19

• States that two quantities are equal

• Has an equals sign

Speaker notes: An expression represents a quantity, while an equation says that two quantities have the same value. Ask students to identify which of these has a solution to find: 2a + 3 or 2a + 3 = 11.

5. Terms and coefficients

• Terms are parts separated by + or − signs.
• In 6x + 4, the terms are 6x and 4.
• The coefficient is the number multiplying a variable.
• In 6x, the coefficient is 6; in x, it is 1.

Speaker notes: Point out that the minus sign belongs with the term that follows it: in 8y − 3, the terms are 8y and −3. A variable written without a number has an implied coefficient of 1.

6. Find the value of an expression

• Replace the variable with its given value.
• Then follow the order of operations.
• If a = 3, then 2a + 5 = 2 × 3 + 5.
• So, 2a + 5 = 11.

Speaker notes: Emphasise replacing the variable before calculating and multiplying before adding. For a quick check, ask what 2a + 5 would equal if a = 6.

7. Combine like terms

• Like terms have the same variable part.
• 3x and 5x are like terms; 3x and 5 are not.
• Add or subtract the coefficients of like terms.
• 3x + 5x = 8x; the variable part stays the same.

Speaker notes: Use the idea of combining equal groups: 3x plus 5x makes 8x. A constant such as 4 cannot be combined with an x-term such as 2x.

8. Solve a one-step equation

• An equation is balanced when both sides are equal.
• To solve x + 6 = 14, subtract 6 from both sides.
• This gives x = 8.
• Check: 8 + 6 = 14.

Speaker notes: Explain that doing the same operation to both sides keeps the equation balanced. Encourage checking the value by substituting it into the original equation.

9. Write an algebraic expression

• A notebook costs ₹x.
• The cost of 4 notebooks is 4x rupees.
• If each costs ₹25, then 4x = 4 × 25 = ₹100.
• The letter helps describe the cost before its value is known.

Speaker notes: The expression 4x represents the total cost of four notebooks when each costs ₹x. Ask how the expression would change for six notebooks.

10. Summary: What can algebra describe?

• A variable stands for a number.
• An expression represents a quantity; an equation shows equality.
• Like terms can be combined, and equations can be solved by keeping both sides balanced.
• Reflection: How can you check whether a solution is correct?

Speaker notes: Review the difference between an expression and an equation. Invite students to explain how substitution can check a solution.