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📖 Mathematics

Std 4
Books Book Guide
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Chapters
1 Shapes Around Us 2 Hide and Seek 3 Patterns Around Us 4 Thousands Around Us 5 Sharing and Measuring One Quarter 6 Measuring Length 7 The Cleanest Village 8 Fun at Vegetable Market! Weigh It, Pour It 9 Animal Jumps Equal Groups 10 Elephants, Tigers and Leopards 11 Fun with Symmetry 12 Ticking Clocks and Turning Calendar 13 Mystery Matrix The Transport Museum 14 Data Handling Physical Education
7
Chapter 7
Skill: 30%

The Cleanest Village

The Cleanest Village

Chapter at a Glance

This chapter utilizes a school field trip from Shillong to Mawlynnong (Asia's cleanest village) to teach multi-digit addition and subtraction, shopping budget calculations, money balance returns, and logical problem-solving. Students practice regrouping in column algorithms, apply strategic rounding and mental shortcuts, solve mathematical grid puzzles (magic triangles), and work with real-world datasets (like library page tallies and train passenger statistics).

Key Definitions & Terminology

  • Mawlynnong: A village in the East Khasi Hills of Meghalaya, known as "Asia's Cleanest Village" or "God's Own Garden."
  • Living Root Bridge: A natural bridge formed by training and weaving the aerial roots of rubber trees (Ficus elastica) across streams (e.g. Jingmaham Living Root Bridge).
  • Pusaw: A traditional Khasi steamed rice cake snack made from red rice.
  • Regrouping: The mathematical process of carrying over or borrowing values across place value columns (Ones, Tens, Hundreds, Thousands) when performing addition or subtraction.
  • Gombe Habba: A traditional doll festival celebrated during Dussehra in Karnataka.

Formulas, Rules & Properties

  • Arithmetic Regrouping Rules:
  • Addition: $10 \text{ Ones} \rightarrow 1 \text{ Ten}$; $10 \text{ Tens} \rightarrow 1 \text{ Hundred}$; $10 \text{ Hundreds} \rightarrow 1 \text{ Thousand}$.
  • Subtraction: Borrow $1 \text{ Ten} \rightarrow 10 \text{ Ones}$; borrow $1 \text{ Hundred} \rightarrow 10 \text{ Tens}$.
  • Balance Calculation Formula:
    $$\text{Balance Return} = \text{Amount Paid} - \text{Total Cost}$$
  • Magic Triangle Property (for numbers $1-6$):
  • To make side sum $= 9$: place small numbers ${1, 2, 3}$ at the corners.
  • To make side sum $= 10$: place odd numbers ${1, 3, 5}$ at the corners.

Core Concepts & Topics

  • Shopping Combinations:
  • Finding combinations of items from a price list that add up to a target sum (e.g. $\text{Rs. } 163$).
  • Making Change (Paid vs. Balance):
  • Subtracting ticket values from currency notes ($\text{Rs. } 50$, $100$, $200$, $500$).
  • Magic Triangles (Sum Constancy):
  • Positioning digits $1-6$ along the vertices and edges of a triangle so that the sum of the three numbers on each side is equal to $9$ or $10$.
  • Multi-digit Column Addition:
  • Regrouping ones, tens, and hundreds during large additions (e.g., combining teacher and pupil trip tallies).
  • Multi-digit Column Subtraction:
  • Borrowing across columns when values are insufficient (e.g., calculating waiting crowds, spent money, or unsold stock).
  • Logical Estimation and Mental Shortcuts:
  • Using nearby friendly numbers to subtract (e.g., $410 - 12 \rightarrow 410 - 10 = 400$, then $400 - 2 = 398$).
  • Number Pair Hunt:
  • Finding adjacent horizontal or vertical numbers in a grid that give the greatest or smallest sum/difference.

Worked Examples

  • Sapan Dada's Shopping Price List Calculations:
  • Custard apple: $\text{Rs. } 45/\text{kg}$, Beans: $\text{Rs. } 95/\text{kg}$, Radish: $\text{Rs. } 23/\text{kg}$, Onion: $\text{Rs. } 32/\text{kg}$, Potato: $\text{Rs. } 37/\text{kg}$, Yam: $\text{Rs. } 45/\text{kg}$, Sapota: $\text{Rs. } 70/\text{kg}$, Papaya: $\text{Rs. } 65/\text{kg}$, Banana: $\text{Rs. } 55/\text{kg}$.
  • Problem: Identify a combination of items that costs exactly $\text{Rs. } 163$.
    Solution: $1\text{ kg beans } (\text{Rs. } 95) + 1\text{ kg Custard apple } (\text{Rs. } 45) + 1\text{ kg Radish } (\text{Rs. } 23) \rightarrow 95 + 45 + 23 = 163$.
  • Udaya Didi's Balance Return Table:
  • Cost: $\text{Rs. } 113$, Paid: $\text{Rs. } 150 \rightarrow \text{Balance} = 150 - 113 = \text{Rs. } 37$.
  • Cost: $\text{Rs. } 435$, Paid: $\text{Rs. } 500 \rightarrow \text{Balance} = 500 - 435 = \text{Rs. } 65$.
  • Cost: $\text{Rs. } 125$, Paid: $\text{Rs. } 200 \rightarrow \text{Balance} = 200 - 125 = \text{Rs. } 75$.
  • Cost: $\text{Rs. } 185$, Paid: $\text{Rs. } 200 \rightarrow \text{Balance} = 200 - 185 = \text{Rs. } 15$.
  • Cost: $\text{Rs. } 149$, Paid: $\text{Rs. } 500 \rightarrow \text{Balance} = 500 - 149 = \text{Rs. } 351$.
  • Cost: $\text{Rs. } 580$, Paid: $\text{Rs. } 700 \rightarrow \text{Balance} = 700 - 580 = \text{Rs. } 120$.
  • The Orange Crop Puzzle:
  • Four children buy $2$ oranges each at $\text{Rs. } 21$ per orange. Total cost $= 2 \times 21 = \text{Rs. } 42$.
  • Krishna pays $\text{Rs. } 50 \rightarrow \text{Balance} = 50 - 42 = \text{Rs. } 8$.
  • Sudama pays $\text{Rs. } 100 \rightarrow \text{Balance} = 100 - 42 = \text{Rs. } 58$.
  • Mala pays $\text{Rs. } 200 \rightarrow \text{Balance} = 200 - 42 = \text{Rs. } 158$.
  • Neela pays $\text{Rs. } 500 \rightarrow \text{Balance} = 500 - 42 = \text{Rs. } 458$.
  • Triangular Magic Placement (Sum 9 and 10):
  • Sum of 9: Corners are ${1, 2, 3}$. Inside edges are: $5$ (between $1$ and $3$), $6$ (between $1$ and $2$), $4$ (between $2$ and $3$).
  • Sum of 10: Corners are ${1, 3, 5}$. Inside edges are: $6$ (between $1$ and $3$), $4$ (between $1$ and $5$), $2$ (between $3$ and $5$).
  • Tabla/Singer Enrollments (Kalakshitij School):
  • Boys: $78$ Tabla $+ 532$ Singers $= 610\text{ boys}$.
  • Girls: $95$ Tabla $+ 346$ Singers $= 441\text{ girls}$.
  • Total Tabla players: $78 + 95 = 173$. Total Singers: $532 + 346 = 878$.
  • Wakanda Library Reading log:
  • Swami and Friends ($179\text{ pages}$), Panchatantra ($236\text{ pages}$), Karadi ($30\text{ pages}$), Akbar Birbal ($96\text{ pages}$), Blue Umbrella ($90\text{ pages}$), Feluda ($128\text{ pages}$).
  • Question: Rami read Panchatantra ($236\text{ pages}$). Kesu read Akbar Birbal, Karadi, and Blue Umbrella. Who read more and by how much?
    Solution: Kesu read: $96 + 30 + 90 = 216\text{ pages}$. Rami read $236\text{ pages}$. Rami read more: $236 - 216 = 20\text{ pages}$ more.
  • Question: Jaggu read Swami ($179$), Akbar ($96$), and $50$ pages of Feluda. How many pages does he have left to read all books in the library?
    Solution: Total library pages $= 179 + 236 + 30 + 96 + 90 + 128 = 759\text{ pages}$. Jaggu read: $179 + 96 + 50 = 325\text{ pages}$. Pages left $= 759 - 325 = 434\text{ pages}$.
  • Delhi-Aligarh Train Route:
  • The train leaves New Delhi with $894$ passengers. At Dadri, $158$ board and $23$ get off.
  • Passengers on departure from Dadri $= 894 + 158 - 23 = 1029\text{ passengers}$.

Practical Activities & Experiments

  • Classroom Bazaar: Simulating a vegetable and fruit cart where children calculate total purchases and count back change.
  • Magic Triangle Counter Assembly: Arranging counters numbered $1-6$ on a triangular template to find side sum configurations.
  • Library Log Tracking: Keeping a reading journal of books read by counting completed pages and calculating pages left to finish.
  • Token Regrouping Drill: Exchanging ten $10$-tokens for one $100$-token to visualize carrying over in additions.
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