Ganita Prakash, period by period — fitted to your timetable.
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Balance the Scale, Find the Weight
Find the Unknowns · Discovery
Students often write the unknown on one side only, missing cases where the unknown appears on both plates — watch for this when they frame their own equations. The balance hint (removing equal weights from both sides) is the key intuition the whole chapter builds on, so let students articulate it in their own words before moving to letter notation.
0–10Present the weighing-scale pictures from section 15.1: two plates that balance with known and unknown weights on each side. Students examine each picture and write what must be true for the scales to stay level, using words first, then a letter for the unknown weight.
10–22Introduce the balance hint from the text — removing equal weights from both plates keeps the scale balanced — and guide students to use this to isolate the unknown in each scale picture, writing expressions such as 2e = 6 and 4 + 2y = 16. Students solve each and record the unknown weight they found.
22–33Shift to the matchstick sequence from section 15.1: the arrangement at position n uses 2n + 1 sticks. Students use the same balance reasoning to set up and solve 2n + 1 = 99, discovering that the procedure that kept scales balanced works equally for this new kind of puzzle. Connect this to Example 7, section 15.2 p.174 ("Ranjana's square-tile sequence uses 3k + 1 tiles at Step k....") to show a parallel tile-sequence problem.
33–40Students frame equations of their own for five balance-picture situations from section 15.1, writing each as a statement of equality with an LHS and an RHS, then check their solutions against the weights shown in the pictures.
Example 7, section 15.2 p.174 — Ranjana's square-tile sequence uses 3k + 1 tiles at Step k (shown by two counting methods); to make 100 tiles, solve 3k + 1 = 100 for k.
A matchstick pattern uses 3n + 2 sticks at position n. At which position does the pattern use exactly 65 sticks? Set up the equation and solve it, showing all steps.
Set up: 3n + 2 = 65. Subtract 2 from both sides: 3n = 63. Divide both sides by 3: n = 21. The pattern uses 65 sticks at position 21. Verification: 3 × 21 + 2 = 63 + 2 = 65. ✓
Also saved as 7 periods or 10 periods.
- 2Naming Equations: LHS, RHS, and What They Mean
Find the Unknowns - 3Same Operation on Both Sides: Inverse Operations in Action
Solving Equations Systematically - 4Isolating the Unknown: Solving Linear Equations Step by Step
Solving Equations Systematically - 5Transposition: The Shortcut Rule and Why It Works
Solving Equations Systematically - 6Real Situations, Real Equations: Word Problems as Algebra
Solving Equations Systematically - 7Generating Equations: Working Backwards from a Solution
Solving Equations Systematically - 8Extended Practice: Varied Equations and Puzzles
Solving Equations Systematically - 9Error Detective: Spotting and Correcting Faulty Equation Steps
Mind the Mistake, Mend the Mistake - 10Algebra's Roots: Brahmagupta, Al-Khwarizmi, and Ancient Notation
A Pinch of History - 11Brahmagupta's Formula and a Rich Figure-It-Out Set
A Pinch of History - 12Finding the Unknown: Four Problems, Four Methods
Synthesis
- 1. Large Numbers Around Us
- 2. Arithmetic Expressions
- 3. A Peek Beyond the Point
- 4. Expressions Using Letter-Numbers
- 5. Parallel and Intersecting Lines
- 6. Number Play
- 7. A Tale of Three Intersecting Lines
- 8. Working with Fractions
- 9. Geometric Twins
- 10. Operations with Integers
- 11. Finding Common Ground
- 12. Another Peek Beyond the Point
- 13. Connecting the Dots
- 14. Constructions and Tilings
- 15. Finding the Unknown
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