Mathematics: Class 3 — Chapter 7: Raksha Bandhan

To prepare for the festival, children observe and count various decorative items in the house:

• Leaves used in garlands
• Glasses of water arranged on the table
• Pomegranates in baskets
• Flowers for decoration

Making a single Rakhi requires a specific set of materials: 1 flower, 2 threads, and 4 beads. To find the total materials needed for making multiple Rakhis, we use repeated addition, which leads to multiplication.

For 5 Rakhis:

• Flowers: $$1 + 1 + 1 + 1 + 1 = 5$$

  This can be written as: $5 \text{ times } 1$ or $5 \times 1 = 5$ flowers.

• Threads: $$2 + 2 + 2 + 2 + 2 = 10$$

  This can be written as: $5 \text{ times } 2$ or $5 \times 2 = 10$ threads.

• Beads: $$4 + 4 + 4 + 4 + 4 = 20$$

  This can be written as: $5 \text{ times } 4$ or $5 \times 4 = 20$ beads.

• To make $10$ such Rakhis, we need: $10 \times 1 = 10$ flowers, $10 \times 2 = 20$ threads, and $10 \times 4 = 40$ beads.
• If you have $30$ flowers, $30$ threads, and $30$ beads, the maximum number of complete Rakhis you can make is limited by the threads. Since each Rakhi needs $2$ threads, $30$ threads can make $30 \div 2 = 15$ Rakhis. However, each Rakhi also needs $4$ beads, so $30$ beads can only make $30 \div 4 = 7$ complete Rakhis (with $2$ beads left over). Thus, the maximum number of Rakhis possible is $7$.

At the sweet shop, laddoos are arranged in boxes to make counting easier:

• One box contains $3$ rows of $3$ laddoos: $$3 + 3 + 3 = 9 \text{ or } 3 \times 3 = 9 \text{ laddoos}$$
• For $2$ boxes of laddoos: $$9 + 9 = 18 \text{ or } 2 \times 9 = 18 \text{ laddoos}$$
• This can also be grouped as $6$ columns of $3$ laddoos: $$6 \times 3 = 18 \text{ laddoos}$$

When a total quantity is distributed equally among a group, we perform division.

• Sharing Laddoos: Distributing $18$ laddoos equally among $9$ people: $$18 \div 9 = 2 \text{ laddoos each}$$
• Sharing Kaju Katlis (Repeated Subtraction): Distributing $20$ kaju katlis equally among $5$ people:
  • Step 1: Give $1$ to each ($5$ used) $\rightarrow 20 - 5 = 15$ left.
  • Step 2: Give $1$ more to each ($5$ used) $\rightarrow 15 - 5 = 10$ left.
  • Step 3: Give $1$ more to each ($5$ used) $\rightarrow 10 - 5 = 5$ left.
  • Step 4: Give $1$ more to each ($5$ used) $\rightarrow 5 - 5 = 0$ left.
  • Each person gets $1 + 1 + 1 + 1 = 4$ kaju katlis.
  • Mathematically: $$20 \div 5 = 4$$
• Sharing Pedas: Distributing $15$ pedas equally among $5$ plates: $$15 \div 5 = 3 \text{ pedas per plate}$$

Dhara and Gopal look at a flower bed and count the plants in different ways:

• Dhara's Way (Rows): $8$ rows of $6$ plants each: $$6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 48 \text{ or } 8 \times 6 = 48$$
• Gopal's Way (Columns): $6$ columns of $8$ plants each: $$8 + 8 + 8 + 8 + 8 + 8 = 48 \text{ or } 6 \times 8 = 48$$

This demonstrates the commutative property of multiplication: $$8 \times 6 = 6 \times 8 = 48$$

Starting from $0$, jumping $3$ steps forward each time:

• $1 \text{ jump} \rightarrow 3$
• $2 \text{ jumps} \rightarrow 3 + 3 = 6 = 2 \times 3$
• $3 \text{ jumps} \rightarrow 3 + 3 + 3 = 9 = 3 \times 3$
• $10 \text{ jumps} \rightarrow 30 = 10 \times 3$

• Skip jumping by 4: $4, 8, 12, 16, 20, 24, 28, 32, 36, 40, \dots$
• Skip jumping by 6: $6, 12, 18, 24, 30, 36, 42, 48, 54, 60, \dots$

By placing horizontal and vertical sticks, the number of intersection points represents the product of the two numbers:

• To find $3 \times 5$:
  • Arrange $3$ horizontal sticks.
  • Lay $5$ vertical sticks across them.
  • Count the red dots at the intersections: $15$ dots.
  • Therefore, $3 \times 5 = 15$.

Tables can be added together to form new tables. For example, the table of $2$ and the table of $3$ add up to the table of $5$:

• $(1 \times 2) + (1 \times 3) = 2 + 3 = 5 \rightarrow 1 \times 5 = 5$
• $(2 \times 2) + (2 \times 3) = 4 + 6 = 10 \rightarrow 2 \times 5 = 10$
• $(3 \times 2) + (3 \times 3) = 6 + 9 = 15 \rightarrow 3 \times 5 = 15$

• Spiders: A spider has $8$ legs. How many legs do $5$ spiders have? $$5 \times 8 = 40 \text{ legs}$$
• Auto Rickshaws: An auto rickshaw has $3$ wheels. How many wheels are on $18$ auto rickshaws? $$18 \times 3 = 54 \text{ wheels}$$
• Ants: An ant has $6$ legs. What is the total number of legs for $55$ ants? $$55 \times 6 = 330 \text{ legs}$$
• Sea-Shells: Dhruv has $112$ sea-shells and wants to make necklaces of $28$ shells each. How many necklaces can he make?
  • $112 - 28 = 84$ (1st necklace)
  • $84 - 28 = 56$ (2nd necklace)
  • $56 - 28 = 28$ (3rd necklace)
  • $28 - 28 = 0$ (4th necklace)
  • He can make exactly $4$ necklaces.