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The Dairy Farm – Class 5 Maths Chapter 6 Notes & NCERT PDF

Class 5MathematicsChapter 6NCERT book: Maths Mela - Mathematics Class 5

Notes and a simple summary of Chapter 6 of the NCERT Class 5 Mathematics book, with the official chapter PDF, flashcards, an MCQ quiz and an AI tutor for your doubts.

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Chapter 6: The Dairy Farm

Introduction

This chapter takes us to a dairy farm and a milk cooperative. Daljeet Kaur runs a milk processing unit, butter-milk pouches and butter packets are arranged in rows, and a village cooperative collects milk from hundreds of cows. Through these real situations we learn many different ways to multiply — and why each one works. The big message: there is no single "right" method. Pick the smartest strategy for the numbers in front of you.

Key Ideas

1. Order does not change the product

Daljeet arranges butter packets as 8 rows of 5 and as 5 rows of 8. Both give 40 packets.

The number of groups and the group size can be swapped — the total stays the same. 8 × 5 = 5 × 8, 13 × 6 = 6 × 13. Also, any number × 0 = 0.

2. Multiplying by 10, 100 and 1,000

  • × 10 makes a number 10 times bigger: every digit moves one place to the left (45 → 450).
  • × 100 moves every digit two places left (8 × 100 = 800).
  • × 1,000 moves digits three places left (5 × 1,000 = 5,000).
  • Break tens apart: 30 × 20 = 3 × 10 × 2 × 10 = 6 × 100 = 600.

    • 3. Many ways to find 18 × 5

    The chapter shows five children's methods, and all give 90:

  • Half of 18 is 9; 9 × 5 = 45; 45 + 45 = 90
  • Double 18 → 36, double again → 72, add one more 18 → 90
  • Split 18 = 10 + 8: 50 + 40 = 90
  • 18 × 5 = 9 × 10 = 90
  • 20 × 5 = 100, take away 2 × 5 = 10 → 90

    • 4. Doubling and Halving

    Halve one number and double the other — the product does not change.

    3 × 18 = 6 × 9 = 54 22 × 5 = 11 × 10 = 110

    This works best with 5 and 25, because doubling them makes the friendly numbers 10 and 50.

    5. Nearest Multiple

    Round one number to a nearby ten, then fix the difference.

  • 4 × 19 = 4 × 20 − 4 = 80 − 4 = 76
  • 14 × 21 = 14 × 20 + 14 = 280 + 14 = 294

    • 6. Multiplying larger numbers (place value)

    A family makes 35 kg of kitchen waste every month. In a year: 12 × 35.

  • Nida uses a grid (area model): 300 + 50 + 60 + 10 = 420
  • Kanti writes all four partial products: 10, 60, 50, 300 → 420
  • John multiplies the whole number by each part: 2 × 35 = 70, 10 × 35 = 350 → 420
  • Mili's father uses the column method with carrying (the standard algorithm).

    • Worked Examples

    Example 1 — Dairy Cooperative: 268 villagers each have at least 4 cows. Minimum cows = 268 × 4.

    268 = 200 + 60 + 8 → 800 + 240 + 32 = 1,072 cows.

    Example 2 — Gir cows: 453 Gir cows give 13 litres each daily. 453 × 13:

    3 × 453 = 1,359; 10 × 453 = 4,530; total = 5,889 litres.

    Example 3 — Compost savings: 150 kg compost at ₹24 per kg. 24 × 150:

    4 × 150 = 600; 20 × 150 = 3,000; total = ₹3,600 saved.

    Example 4 — Ghee: 125 kg ghee at ₹574 per kg. 5 × 574 = 2,870; 20 × 574 = 11,480; 100 × 574 = 57,400; total = ₹71,750.

    Example 5 — Use a known fact: If 17 × 23 = 391, then 17 × 24 = 391 + 17 = 408 and 18 × 23 = 391 + 23 = 414.

    Maths Words

  • Multiplication (गुणा), Product (गुणनफल)
  • Multiplier (गुणक), Multiplicand (गुण्य)
  • Doubling (दुगुना करना), Halving (आधा करना)
  • Place value (स्थानीय मान)
  • Estimate (अनुमान), Partial product (आंशिक गुणनफल)
  • Pattern (पैटर्न / प्रतिरूप)

    • Patterns to Enjoy

  • 1 × 1 = 1, 11 × 11 = 121, 111 × 111 = 12,321, 1111 × 1111 = 1,234,321
  • 15 × 15 = 225, 25 × 25 = 625, 35 × 35 = 1,225, 45 × 45 = 2,025
  • 11 × 54 = 594 (5 _ 4 with 5 + 4 = 9 in the middle)
  • 1 × 9 + 1 = 10, 12 × 9 + 2 = 110, 123 × 9 + 3 = 1,110

    • Maths in Daily Life

    Counting seats in an auditorium (35 rows × 42 seats), cloth for kurtas, fodder for cows, bills at an electrical shop, runs in a cricket match — all need multiplication. The King's Reward story shows how fast repeated multiplying grows: 1 coin × 5 each day becomes far more than 5 coins doubled each day.

    Common Mistakes

  • Forgetting place value: in 203 × 54, writing 4 × 203 as 812 but then writing 50 × 203 as 1,015 instead of 10,150 (Pankaj's error in "Check, Check!").
  • Adding the carried digit to the wrong digit (the carry is added to the product, not the digit).
  • Missing zeros when multiplying by tens or hundreds.
  • In nearest multiple, adding when you should subtract (19 is 1 less than 20, so subtract one group).

    • Practice Tips

  • Estimate first: 25 × 31 is about 25 × 30 = 750.
  • Before calculating, ask: Can I double-halve? Can I round to a ten?
  • Check answers by using a different method.
  • Write partial products neatly with place value in mind.

    • 💡 Key Learning Points

    • ✓The order of multiplication does not change the product (8 × 5 = 5 × 8), and any number × 0 = 0.
    • ✓Multiplying by 10, 100 or 1,000 shifts each digit one, two or three places to the left.
    • ✓Doubling one number and halving the other keeps the product the same (22 × 5 = 11 × 10).
    • ✓Nearest-multiple strategy: 4 × 19 = 4 × 20 − 4; 14 × 21 = 14 × 20 + 14.
    • ✓Large numbers are multiplied by breaking them into place-value parts and adding the partial products (268 × 4 = 800 + 240 + 32).

    👨‍🏫 Teaching Tips

    • →Use real or drawn arrays of butter packets so children see that 8 × 5 and 5 × 8 are the same array turned around.
    • →Put 18 × 5 on the board and ask every child to solve it their own way; then compare the five methods from the book.
    • →Use a place-value chart (TTh, Th, H, T, O) to show digits shifting left when multiplying by 10, 100, 1,000.
    • →Draw Nida's grid on chart paper with coloured sections so partial products are visible as areas.
    • →Place Kanti's and John's solutions side by side and ask: which steps are the same? which is shorter?
    • →Play 'Check, Check!': give deliberately wrong solutions and let children find the place-value error.
    • →Act out the King's Reward: three groups calculate each minister's coins day by day and compare the growth.

    📋 Assessment Questions

    1. Can the child find 14 × 21 or 4 × 19 using the nearest multiple strategy and explain why we add or subtract?
    2. Can the child use doubling and halving for problems like 16 × 25 or 12 × 45?
    3. Can the child multiply a 3-digit by a 2-digit number (e.g. 453 × 13) using partial products correctly?
    4. Can the child spot the error in a wrong solution like 203 × 54 = 135 and correct it?
    5. Can the child estimate a product (e.g. 248 × 49 ≈ 12,500) before calculating?

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    Keep learning

    All chapters in Maths Mela - Mathematics Class 5

    1. 1. We the Travellers — I
    2. 2. Fractions
    3. 3. Angles as Turns
    4. 4. We the Travellers — II
    5. 5. Far and Near
    6. 6. The Dairy Farm
    7. 7. Shapes and Patterns
    8. 8. Weight and Capacity
    9. 9. Coconut Farm
    10. 10. Symmetrical Designs
    11. 11. Grandmother’s Quilt
    12. 12. Racing Seconds
    13. 13. Animal Jumps
    14. 14. Maps and Locations
    15. 15. Data Through Pictures