Finding the Unknown

From physical two-pan balance scales to Brahmagupta’s ancient Bījagaṇita, unlock the secret of algebraic equations. Master systematic balancing, spot common student pitfalls, unwind multi-step math machines, and crack ancient Indian mathematical puzzles.

4 Sections

7.1 to 7.4

12 Scale Models

Figs 7.1–7.12

9 Student Bugs

Mind the Mistake

40 Practice

Graded Tiers

Two-Pan Balance Metaphor

Balanced (LHS = RHS)

Algebraic Equation

s + 3 = 16

Exact match! Solution: s = 13 kg

Section 7.1

Find the Unknowns

pp. 164–168

An algebraic equation is fundamentally a statement of equality between two expressions, perfectly illustrated by a two-pan balance scale. When both pans hold equal total weights, the beam stays level. To uncover the unknown weight, we simplify by removing or adding equal weights to both pans simultaneously.

Interactive Balance Scale Lab (Figures 7.1 to 7.12)

Select a textbook problem from pages 164–167 to visualize the physical pans and algebraic deduction.

Figure 7.1 (Page 164)Target: x (block weight)

Left Pan Contents:1 unknown block (x) + 3 kg

Right Pan Contents:16 kg weight

Algebraic Equation:x + 3 = 16

Level Pan Balance Scale

Rule: LHS = RHS. Removing equal weights maintains balance.

Matchstick Pattern Sequence: 2n + 1 (pp. 167–168)

Examine the sequence of houses built with matchsticks. Step 1 needs 3 sticks, Step 2 needs 5, Step 3 needs 7...

Formula: S = 2n + 1

Adjust Step Number (n): 5Total Matchsticks: 11

Ganita Prakash Core Question (p. 168):

"Can a figure in this matchstick sequence be made using exactly 200 matchsticks? Explain using algebra."

Equation: 2n + 1 = 200

Subtract 1: 2n = 199

Divide by 2: n = 199 / 2 = 99.5

✗ Impossible! Step number n must be a whole counting number. 2n + 1 is always ODD, but 200 is EVEN.