Chapter 6 — The Dairy Farm

Chapter 6 of the Class 5 Mathematics NCERT textbook (Maths Mela), "The Dairy Farm", focuses on multiplication strategies — download the PDF to explore how students learn commutativity, doubling and halving, nearest-multiple estimation, and place-value-based long multiplication through real-life dairy and farm contexts.

• Commutativity of Multiplication — The chapter shows through butter-packet arrangements that swapping the number of groups and the group size — for example 8x5 and 5x8 — always gives the same total. Students observe this pattern across multiple examples and connect it to 9x0 and 0x9 to understand multiplication by zero.
• Multiplication by 10s, 100s, and 1,000s — Students revise and extend patterns for multiplying by 10, 100, and 1,000, observing how each digit shifts one, two, or three place values to the left. A place-value table helps them see the pattern of zeros and understand problems like 20x1,000 = 20,000 and 60x50.
• Doubling and Halving Strategy — The chapter introduces a flexible mental strategy: halve one factor and double the other to get an easier product. For example, 3x18 becomes 6x9 = 54. This strategy is especially useful when multiplying by 5, 25, or other half-of-ten multiples.
• Nearest-Multiple Strategy — Students learn to round one factor to the nearest multiple of 10 and then add or subtract the difference. For example, 4x19 is computed as 4x20 minus 4 = 76, and 14x21 as 14x20 plus 14 = 294. This approach makes mental multiplication of numbers near a round figure efficient.
• Expanded (Place-Value) Long Multiplication — For two- and three-digit multiplication, the chapter presents multiple structured methods — Nida's grid expansion, Kanti's partial-products column, John's grouped partial products, and Mili's father's standard algorithm — all grounded in breaking numbers into place-value parts (hundreds, tens, ones) and adding partial products.

1. 01Multiplying a number by 10 shifts every digit one place value to the left; multiplying by 100 shifts it two places, and by 1,000 shifts it three places.
2. 02The order of factors does not change the product — swapping the number of groups and the group size in butter-packet arrangements always gives the same total.
3. 03The doubling-and-halving strategy works especially well with multipliers like 5 and 25, because halving them gives a convenient whole number (10 or 50) to work with.
4. 04The nearest-multiple strategy rounds one factor up or down to the nearest ten, multiplies, then corrects by adding or subtracting the rounded-off difference.
5. 05Daljeet Kaur's dairy context and the dairy cooperative problems provide the real-life settings: 268 villagers with at least 4 cows each give a minimum of 1,072 cows, and 453 Gir cows producing 13 litres each yield 5,889 litres of milk per day.
6. 06A dairy cooperative sells 1 kg of cow ghee for Rs 574 and produces about 125 kg per month, earning Rs 71,750 monthly — solved using expanded place-value multiplication.
7. 07The King's Reward story at the end explores doubling, tripling, and multiplying by 5 over 7 days, connecting multiplication strategies to exponential growth patterns.