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📖 Mathematics

Std 3
Books Book Guide
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Chapters
1 What's in a Name? 2 Toy Joy 3 Double Century 4 Seeds on Vacation with My Nani Maa 5 Fun with Shapes 6 House of Hundreds - I 7 Raksha Bandhan 8 Fair Share 9 House of Hundreds - II 10 Fun at Class Party! 11 Filling and Lifting 12 Give and Take 13 Time Goes On 14 The Surajkund Fair
7
Chapter 7
Skill: 30%

Raksha Bandhan

Raksha Bandhan

Chapter at a Glance

This chapter introduces students to the core operations of multiplication (repeated addition) and division (equal sharing/repeated subtraction) through the celebratory context of the Raksha Bandhan festival. Children use hands-on materials like threads, beads, flowers, sweets (laddoos, kaju katlis, pedas, and jalebis), and farm animals to understand how groups of equal sizes compose totals and how totals are divided into equal shares. Students also learn to construct times tables up to $10$ using skip-jumping number tracks and stick-intersection grids, study patterns in multiplication tables, and apply division by repeated subtraction to solve larger problems.

Key Definitions & Terminology

  • Multiplication: The process of repeated addition of equal groups, represented by the symbol $\times$ (e.g., $5 \text{ groups of } 2 = 5 \times 2 = 10$).
  • Division: The process of splitting a quantity into equal groups or shares, represented by the symbol $\div$ (e.g., $18 \text{ divided among } 9 = 18 \div 9 = 2$).
  • Repeated Subtraction: A method of dividing a large number by repeatedly taking away the same divisor amount until the remainder is zero or less than the divisor.
  • Skip Jumping: Moving along a number line or track in equal intervals of size $n$, which maps directly to the multiplication table of $n$.
  • Intersection Point: The crossing point of vertical and horizontal sticks used in visual multiplication to determine products.

Formulas, Rules & Properties

  • Commutative Law of Multiplication: The order of the factors does not change the product:
    $$a \times b = b \times a$$
    (e.g., $8 \text{ rows of } 6 \text{ plants} = 6 \text{ rows of } 8 \text{ plants} = 48$).
  • Distributive Composition of Tables: Two smaller multiplication tables can be added together to construct a larger multiplication table (e.g., Table of $2$ + Table of $3$ = Table of $5$):
    $$(a \times n) + (b \times n) = (a + b) \times n$$
  • Pattern of the 5-Times Table: All products in the times-5 table end in either $0$ (for even multipliers) or $5$ (for odd multipliers).

Core Concepts & Topics

  • Repeated Addition as Multiplication:
  • Making $5$ Rakhis where each Rakhi requires $1$ flower, $2$ threads, and $4$ beads (calculated as $5 \times 1$, $5 \times 2$, and $5 \times 4$).
  • Laddoo arrays: Arranging sweets in rectangular grid formations (e.g., $3 \times 3$ or $6 \times 3$).
  • Equal Sharing and Grouping (Division):
  • Distributing kaju katlis or laddoos equally among a set of plates.
  • Determining how many groups of a fixed size can be made from a total (e.g., how many $2$-wheeled cycles can be built from $12$ wheels).
  • Skip-Jumping tracks:
  • Simulating skip jumps on a line to construct tables for $3, 4, 6, 7, 8$.
  • Determining the skip size from a partially recorded sequence (e.g., $32, 40, 48, 56$ represents skip jumps of $8$).
  • Mithu's Stick Method for Tables:
  • Laying down horizontal sticks representing the multiplier, crossing them with vertical sticks representing the multiplicand, and counting the red intersection dots to find the product.
  • Division by Repeated Subtraction (Large Numbers):
  • Solving division problems for numbers beyond standard memorized tables by repeatedly subtracting groups (e.g., dividing $112$ shells into groups of $28$).
  • Currency Exchange Denominations:
  • Dividing a $\text{Rs. } 500$ note into equivalent counts of $\text{Rs. } 50$, $\text{Rs. } 20$, or $\text{Rs. } 10$ notes.

Worked Examples

  • Rakhi Materials Tally:
  • Problem 1: For $5$ Rakhis, how many flowers (1 each), threads (2 each), and beads (4 each) are needed?
    • Solution: $5 \times 1 = 5\text{ flowers}$, $5 \times 2 = 10\text{ threads}$, $5 \times 4 = 20\text{ beads}$.
  • Problem 2: For $10$ Rakhis, how many of each?
    • Solution: $10 \times 1 = 10\text{ flowers}$, $10 \times 2 = 20\text{ threads}$, $10 \times 4 = 40\text{ beads}$.
  • Problem 3: If you have $30$ flowers, $30$ threads, and $30$ beads, how many complete Rakhis can you make?
    • Solution: $30 \text{ beads} \div 4 = 7$ Rakhis (with $2$ beads left over). Flowers ($30 \ge 7$) and threads ($30 \ge 14$) are sufficient. Answer: $7\text{ Rakhis}$.
  • Laddoo & Kaju Katli Division:
  • $18$ laddoos distributed equally to $9$ people $\rightarrow 18 \div 9 = 2$ laddoos each.
  • $20$ kaju katlis shared among $5$ people $\rightarrow 20 \div 5 = 4$ each.
  • $16$ kaju katlis shared among $4$ people $\rightarrow 16 \div 4 = 4$ each.
  • $15$ pedas shared among $5$ people $\rightarrow 15 \div 5 = 3$ each.
  • Jalebi Purchase:
  • Problem: Dhara buys $24$ jalebis. There are $9$ family members. Can they have $4$ each? How many more does she need to buy?
  • Solution: $9$ members $\times 4\text{ each} = 36\text{ jalebis}$. Since $36 > 24$, they cannot. Dhara needs to buy $36 - 24 = 12$ more jalebis.
  • Roro's Jumps:
  • Problem: Roro starts at $0$ and reaches $18$ in $6$ equal jumps. What is his jump size?
  • Solution: $18 \div 6 = 3$ steps per jump.
  • Suma's Savings:
  • Problem: Suma saves $\text{Rs. } 8$ daily. How long to save $\text{Rs. } 56$?
  • Solution: $56 \div 8 = 7\text{ days}$.
  • Mary's Sea-Shells:
  • Problem: Mary has $63$ sea-shells. She gives $7$ shells to each of her $5$ friends. How many left?
  • Solution: Shells given $= 5 \times 7 = 35$. Leftover $= 63 - 35 = 28\text{ shells}$.
  • Bhim's Rath Wheel Spokes:
  • Problem: Each wheel needs $5$ spokes. How many spokes for $20$ wheels?
  • Solution: $20 \times 5 = 100\text{ spokes}$ (calculated as $10 \times 5 = 50$ for first ten wheels, and another $50$ for next ten).
  • Solve: $30 \times 5 = 150$, $40 \times 5 = 200$, $70 \times 5 = 350$, $100 \times 5 = 500$, $50 \times 5 = 250$, $80 \times 5 = 400$, $60 \times 5 = 300$, $90 \times 5 = 450$.
  • Spokes to wheels: With $45$ spokes, Gopal can make $45 \div 5 = 9$ wheels. With $60$ spokes, he can make $60 \div 5 = 12$ wheels.
  • Spider Leg Count:
  • $5$ spiders (8 legs each) $\rightarrow 5 \times 8 = 40\text{ legs}$.
  • $10$ spiders $\rightarrow 10 \times 8 = 80\text{ legs}$.
  • $15$ spiders $\rightarrow 15 \times 8 = 120\text{ legs}$.
  • $23$ spiders $\rightarrow 23 \times 8 = 184\text{ legs}$.
  • Group has $32$ legs $\rightarrow 32 \div 8 = 4\text{ spiders}$.
  • Rickshaw Wheel Count:
  • $18$ rickshaws (3 wheels each) $\rightarrow 18 \times 3 = 54\text{ wheels}$.
  • $34$ rickshaws $\rightarrow 34 \times 3 = 102\text{ wheels}$.
  • Garage has $36$ wheels $\rightarrow 36 \div 3 = 12\text{ rickshaws}$.
  • Shed Animals Count:
  • Total cow legs visible is $48$. How many cows? $\rightarrow 48 \div 4\text{ legs} = 12\text{ cows}$.
  • Total cow horns visible is $24$. How many legs in shed? $\rightarrow 24 \div 2\text{ horns} = 12\text{ cows}$. Total legs $= 12 \times 4 = 48\text{ legs}$.
  • Puri Beach Shopping & Rabdi:
  • Wall hanging: $\text{Rs. } 42$ each $\rightarrow$ Two cost $2 \times 42 = \text{Rs. } 84$.
  • Rabdi cup: $\text{Rs. } 75$ each. $5$ cups cost $5 \times 75 = \text{Rs. } 375$. Preeti pays with $\text{Rs. } 100$ notes. She must give $4$ notes of $\text{Rs. } 100$ ($\text{Rs. } 400$). Change returned $= 400 - 375 = \text{Rs. } 25$.
  • Necklaces Repeated Subtraction:
  • Problem: Dhruv has $112$ shells. Necklace size is $28$ shells. Can he make necklaces for $3$ friends?
  • Solution:
    • $\text{Start} = 112$
    • $112 - 28 = 84\text{ left } (1\text{st necklace})$
    • $84 - 28 = 56\text{ left } (2\text{nd necklace})$
    • $56 - 28 = 28\text{ left } (3\text{rd necklace})$
    • $28 - 28 = 0\text{ left } (4\text{th necklace})$
    • Yes, he can make exactly $4$ necklaces (enough for $3$ friends and himself).
  • Problem 2: Kannu has $100$ shells, necklace size is $17$. How many necklaces?
    • Solution: $100 - 17 = 83 \rightarrow 66 \rightarrow 49 \rightarrow 32 \rightarrow 15$. Answer: $5\text{ necklaces}$ (with $15$ shells left over).
  • Problem 3: Dhruv has $127$ pebbles, shared equally among $3$ friends.
    • Solution: $127 \div 3 = 42\text{ pebbles each}$, with $1\text{ pebble}$ leftover.
  • Rs. 500 Note Exchange:
  • Exchanged for $\text{Rs. } 50$ notes $\rightarrow 500 \div 50 = 10\text{ notes}$.
  • Exchanged for $\text{Rs. } 20$ notes $\rightarrow 500 \div 20 = 25\text{ notes}$.
  • Exchanged for $\text{Rs. } 10$ notes $\rightarrow 500 \div 10 = 50\text{ notes}$.
  • Sealed Envelopes Puzzle:
  • Given card numbers $1-10$ and envelope products:
    • Product $20 \rightarrow {4, 5}$
    • Product $7 \rightarrow {1, 7}$
    • Product $18 \rightarrow {2, 9}$ (since cards are used without repeat: $3 \times 6$ is also possible, but cards $2, 9$ map to others)
    • Product $32 \rightarrow {4, 8}$ (Wait: if cards are $1-10$, ${4, 8}$ is $32$)
    • Product $45 \rightarrow {5, 9}$

Practical Activities & Experiments

  • Rakhi Crafting: Designing custom decorative rakhis using thread, beads, and flowers.
  • Sweet Sharing simulation: Grouping counters or drawing circles on paper to distribute items (like kaju katlis and pedas) equally among plates.
  • Number Track Skip Jumping: Drawing skip tracks on playground dirt and skip-jumping by $3, 4, 6, 7, 8$ to construct multiplication tables.
  • Reach the Flower Game: Placing a token on a target number (e.g. $12$, $24$) and finding which skip-jump size reaches the target in the fewest moves.
  • Mithu's Stick-Grid Method: Assembling matchsticks in grid arrays to solve multiplication queries by counting intersection points.
  • Times-5 Unit Digit Search: Tallying the last digits of times-5 table calculations to identify the repeating ${0, 5}$ pattern.
  • Table Addition Proofs: Using counters to verify that adding matching rows of the times-2 and times-3 tables yields the times-5 table row.
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