Ganita Prakash, period by period — fitted to your timetable.
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Tiling the Room: Rediscovering Factors and Common Factors
The Greatest of All · Inductive
Watch for students who confuse factors of a number with multiples; the tiling story helps because a tile side must divide the room dimension exactly. A common error at this stage is listing 6 as a common factor of 12 and 16 — a quick check by division corrects it. For a self-study follow-up, Example 2, section 11.1 p.52 gives a parallel worked case with different prime structures.
0–8Pose the room-tiling situation: a 12 ft × 16 ft floor must be covered by the largest possible whole-number square tile. Students list whole-number common factors of 12 and 16 by inspection, then identify the greatest. The concrete scenario anchors the abstract definition of the Highest Common Factor as the greatest of the common factors of two numbers.
8–20section 11.1 p.48 ("'Jump Jackpot' game: for treasures on (a) 14 and 30....") — pairs play parts (a) and (b) on a number line drawn in their books, writing which jump sizes land on both numbers and circling the longest. Class compares results, naming the pattern observed.
20–32Walk through Example 1, section 11.1 p.52 ("Find the common factors and HCF of 45 and 75...."). Students follow the prime-factorisation steps for 45 and 75, identify the common prime subparts (single 3 and single 5, giving 3, 5, 15), and confirm HCF = 15. They re-express the rule: the HCF is built from each prime shared by both numbers, taken as few times as it appears in either.
32–40Students attempt Jump Jackpot parts (c) and (d) from section 11.1 p.48 ("'Jump Jackpot' game....") independently, writing the prime factorisations of each pair before identifying the common factors. Brief whole-class check of answers.
section 11.1 p.48 — 'Jump Jackpot' game: for treasures on (a) 14 and 30; (b) 7 and 11; (c) 30 and 50; (d) 28 and 42, find the longest jump size from 0 that lands on both numbers, and explain why it equals their HCF.
Which of the following correctly states what the Highest Common Factor (HCF) of two numbers is?
- A The greatest number that is a factor of both numbers.
- B The product of all prime factors of both numbers.
- C The smallest number that is a multiple of both numbers.
- D The sum of all common factors of both numbers.
A. The greatest number that is a factor of both numbers.
What each wrong option reveals
- B The student is mixing up the prime-factorisation procedure (listing all prime factors) with the definition of HCF.
- C The student has confused HCF with LCM, recalling 'smallest common' instead of 'greatest common'.
- D The student has confused the identity of the HCF with a computed sum of common factors, a non-standard operation.
Also saved as 7 periods or 10 periods.
- 2Prime Factorisation as a Tool: Building the Factor Tree
The Greatest of All - 3Computing HCF by Prime Factorisation: Practice and Pitfalls
The Greatest of All - 4Shortest Common Length: Discovering the LCM
Least, but not Last! - 5Computing LCM for Pairs and Triples
Least, but not Last! - 6Making General Statements: When is the HCF the Smaller Number?
Patterns, Properties, and a Pretty Procedure! - 7What Happens When Both Numbers are Doubled? Reasoning About the HCF
Patterns, Properties, and a Pretty Procedure! - 8The Combined Division Procedure: An Efficient Route to HCF and LCM
Patterns, Properties, and a Pretty Procedure! - 9HCF and LCM in Context: Folklore, Cubes, and Divisibility
Patterns, Properties, and a Pretty Procedure! - 10Puzzles, Games, and Mahaviracharya: LCM in Rich Contexts
Patterns, Properties, and a Pretty Procedure! - 11Dog, Rabbit, and Mahaviracharya: Final Contextual Applications
Patterns, Properties, and a Pretty Procedure! - 12Common Ground: Four Problems, Three Methods, One Chapter
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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