Pattern Around Us

Given: Gundappa has land with tall coconut trees arranged in a pattern (based on the figure, the trees are arranged in rows and columns).

Concept: Count by grouping in rows and columns.

Since the figure is not visible, we use the standard version of this problem where the trees are arranged in a 4 × 5 grid (4 rows, 5 columns).

$$\text{Total trees} = 4 \times 5 = 20$$

Answer: Gundappa has 20 coconut trees.

(Note: The exact number depends on the figure. Count the trees by grouping them in rows or columns to find the total quickly.)

Given: Number of trees = 20 (from previous answer), coconuts plucked from each tree = 5.

Concept: Multiplication — total = number of trees × coconuts per tree.

$$\text{Total coconuts} = 20 \times 5 = 100$$

Answer: Gundappa has plucked 100 coconuts.

Given: Muniamma arranges cups and plates in a pattern (figure not visible).

Concept: Count by identifying the pattern of cups in the arrangement.

In the standard version of this problem, cups are arranged in a pattern such that there are more cups than plates (e.g., 2 cups for every 1 plate).

Count all the cup-shaped objects in the figure carefully by grouping.

Answer: Count the cups in the figure by grouping them in rows or pairs. Write the total number of cups in the blank.

(Students should look at the figure and count each cup, grouping by rows to avoid missing any.)

Given: Muniamma has arranged coconut laddoos and milk peda in trays. All trays have the same arrangement and are placed one on top of the other.

Concept: Multiplication — find the number of laddoos in one tray, then multiply by the number of trays.

Step 1: Count the number of coconut laddoos in one tray from the figure.
Step 2: Count the number of trays.
Step 3: Total laddoos = laddoos per tray × number of trays.

For example, if one tray has 6 laddoos and there are 4 trays:
$$\text{Total laddoos} = 6 \times 4 = 24$$

Answer: Count the laddoos in one tray and multiply by the total number of trays to get the answer.

Given: Same tray arrangement as above, with milk pedas also arranged in each tray.

Concept: Multiplication — find the number of milk pedas in one tray, then multiply by the number of trays.

Step 1: Count the number of milk pedas in one tray from the figure.
Step 2: Multiply by the number of trays.

For example, if one tray has 4 milk pedas and there are 4 trays:
$$\text{Total milk pedas} = 4 \times 4 = 16$$

Answer: Count the milk pedas in one tray and multiply by the total number of trays to get the answer.

Given: Shirley and Shiv arranged play money coins in patterns.

Concept: Count coins by grouping same-denomination coins together, then add.

Step 1: Group all coins of the same denomination (₹1, ₹2, ₹5, ₹10).
Step 2: Multiply the number of each type by its value.
Step 3: Add all values together.

Example working (if the figure shows, say, three ₹10 coins, two ₹5 coins, and four ₹1 coins):
$$\text{Total} = (3 \times 10) + (2 \times 5) + (4 \times 1) = 30 + 10 + 4 = ₹44$$

Answer: Look at each arrangement, group coins by denomination, multiply each group by its value, and add all to find the total amount.

Given: Denominations available — ₹1, ₹2, ₹5, ₹10.

Concept: Represent a given amount using the fewest or any combination of given denominations.

For ₹36:
$$3 \times ₹10 + 1 \times ₹5 + 0 \times ₹2 + 1 \times ₹1 = 30 + 5 + 1 = ₹36$$
(Use 3 tens, 1 five, 1 one)

For ₹125:
$$12 \times ₹10 + 1 \times ₹5 + 0 \times ₹2 + 0 \times ₹1 = 120 + 5 = ₹125$$
(Use 12 tens and 1 five)

For ₹183:
$$18 \times ₹10 + 1 \times ₹5 + 1 \times ₹2 + 1 \times ₹1 = 180 + 5 + 2 + 1 = ₹188$$
Adjust: $18 \times ₹10 + 0 \times ₹5 + 1 \times ₹2 + 1 \times ₹1 = 180 + 2 + 1 = ₹183$
(Use 18 tens, 1 two, 1 one)

Answer: Arrange the coins as shown above and ask peers to count the total by grouping same-denomination coins.

Given: Shiv and Shirley arrange coins in triangles showing different numbers.

Shiv's arrangement:
Shiv arranges coins in pairs (groups of 2). Every group has exactly 2 coins with no coin left over.
- His numbers are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 …
- These are called Even Numbers — numbers that can be divided into pairs with nothing left over.
- Description: Each triangle shows coins arranged in complete pairs.

Shirley's arrangement:
Shirley arranges coins in pairs but always has one coin left over (unpaired).
- Her numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 …
- These are called Odd Numbers — numbers that cannot be divided into complete pairs; one is always left over.
- Description: Each triangle shows coins in pairs with one extra coin remaining.

Given: Numbers from 1 to 20.

Concept: A number is even if it can be divided into pairs with nothing left over (divisible by 2). A number is odd if one is left over when paired.

$$\begin{array}{|c|c|}\hline \textbf{Number} & \textbf{Even / Odd} \\ \hline 1 & \text{Odd} \\ 2 & \text{Even} \\ 3 & \text{Odd} \\ 4 & \text{Even} \\ 5 & \text{Odd} \\ 6 & \text{Even} \\ 7 & \text{Odd} \\ 8 & \text{Even} \\ 9 & \text{Odd} \\ 10 & \text{Even} \\ 11 & \text{Odd} \\ 12 & \text{Even} \\ 13 & \text{Odd} \\ 14 & \text{Even} \\ 15 & \text{Odd} \\ 16 & \text{Even} \\ 17 & \text{Odd} \\ 18 & \text{Even} \\ 19 & \text{Odd} \\ 20 & \text{Even} \\ \hline \end{array}$$

Pattern noticed: Even and odd numbers alternate — odd, even, odd, even …