Chapter 7 of 14
Chapter 7: The Cleanest Village
Data Organization, Tally Marks, Environmental Cleanliness Drives & Applied Math | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Using tally marks (groups of 5: ||||) to record counts efficiently.
- Solving multi-step addition and subtraction problems based on community waste collection.
- Calculating recyclable waste weights and earnings from community recycling.
- Promoting civic responsibility through mathematical measurement.
All Textbook Exercises & In-Text Tasks (15 Questions)
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Q1
Tally Chart Interpretation
During a clean-up campaign, children recorded dry leaves baskets using tally marks: Team Red gathered '卌 卌 卌 卌 |', Team Blue gathered '卌 卌 卌 |||', and Team Green gathered '卌 卌 卌 卌 卌'. (a) How many baskets did each team gather? (b) Which team collected the most? (c) What is the total count of baskets?
[3 Marks]
✅ Step-by-Step Solution & Working
(a) Basket counts from tally marks:
• Team Red: 4 bundles of 5 + 1 = (4 × 5) + 1 = 21 baskets.
• Team Blue: 3 bundles of 5 + 3 = (3 × 5) + 3 = 18 baskets.
• Team Green: 5 bundles of 5 = (5 × 5) = 25 baskets.
(b) Maximum collection:
Team Green collected the most with 25 baskets.
(c) Total baskets collected:
Total = 21 + 18 + 25 = 64 baskets.
• Team Red: 4 bundles of 5 + 1 = (4 × 5) + 1 = 21 baskets.
• Team Blue: 3 bundles of 5 + 3 = (3 × 5) + 3 = 18 baskets.
• Team Green: 5 bundles of 5 = (5 × 5) = 25 baskets.
(b) Maximum collection:
Team Green collected the most with 25 baskets.
(c) Total baskets collected:
Total = 21 + 18 + 25 = 64 baskets.
CBSE Step-by-Step Marking Scheme
Correct counts for all three teams
1.5 M
Correct identification of winner and total sum 64
1.5 M
Q2
Weight & Community Cleanliness • Tally Arithmetic
In a village cleanliness drive, four teams collected wet waste: Team A collected 42 kg 500 g, Team B collected 38 kg 250 g, Team C collected 51 kg 750 g, and Team D collected 47 kg. What was the total weight of wet waste collected?
[3 Marks]
✅ Step-by-Step Solution & Working
Column Addition of Weight:
kg g
42 500
+ 38 250
+ 51 750
+ 47 000
-------------------
Sum of grams = 500 + 250 + 750 + 0 = 1,500 g = 1 kg 500 g.
Sum of kg = 42 + 38 + 51 + 47 + 1 (carry) = 179 kg.
Total wet waste collected = 179 kg 500 g.
kg g
42 500
+ 38 250
+ 51 750
+ 47 000
-------------------
Sum of grams = 500 + 250 + 750 + 0 = 1,500 g = 1 kg 500 g.
Sum of kg = 42 + 38 + 51 + 47 + 1 (carry) = 179 kg.
Total wet waste collected = 179 kg 500 g.
CBSE Step-by-Step Marking Scheme
Correct column alignment of kg and g
1.0 M
Gram sum carry-over (1,500 g = 1 kg 500 g)
1.0 M
Final sum: 179 kg 500 g
1.0 M
Q3
Capacity & Conservation • Water Math
A leaky public tap wastes 150 mL of clean drinking water every minute. How many litres of water are wasted if the tap is left leaking for 2 hours?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Calculation:
1. Wastage in 1 hour (60 minutes):
150 mL × 60 = 9,000 mL.
2. Wastage in 2 hours:
9,000 mL × 2 = 18,000 mL.
3. Convert to Litres (1 L = 1,000 mL):
18,000 ÷ 1,000 = 18 Litres.
In 2 hours, 18 litres of precious drinking water are wasted.
1. Wastage in 1 hour (60 minutes):
150 mL × 60 = 9,000 mL.
2. Wastage in 2 hours:
9,000 mL × 2 = 18,000 mL.
3. Convert to Litres (1 L = 1,000 mL):
18,000 ÷ 1,000 = 18 Litres.
In 2 hours, 18 litres of precious drinking water are wasted.
CBSE Step-by-Step Marking Scheme
Calculating minutes in 2 hours (120 mins)
1.0 M
Total mL calculation (18,000 mL)
1.0 M
Conversion to litres (18 L)
1.0 M
Q4
Practical Arithmetic • Garbage Sorting
A school canteen produced 65 kg of garbage in a week. If 3/5 of it was biodegradable food waste and the rest was recyclable plastic and paper, find the weight of recyclable waste.
[2 Marks]
✅ Step-by-Step Solution & Working
Fraction & Weight Solution:
Total garbage = 65 kg
1. Weight of Biodegradable Food Waste:
3/5 of 65 kg = (65 ÷ 5) × 3 = 13 × 3 = 39 kg.
2. Weight of Recyclable Waste:
65 kg - 39 kg = 26 kg.
(Alternatively, 1 - 3/5 = 2/5; 2/5 of 65 = 26 kg).
Total garbage = 65 kg
1. Weight of Biodegradable Food Waste:
3/5 of 65 kg = (65 ÷ 5) × 3 = 13 × 3 = 39 kg.
2. Weight of Recyclable Waste:
65 kg - 39 kg = 26 kg.
(Alternatively, 1 - 3/5 = 2/5; 2/5 of 65 = 26 kg).
CBSE Step-by-Step Marking Scheme
Calculating food waste fraction (39 kg)
1.0 M
Deducting to find recyclable waste (26 kg)
1.0 M
Q5
Textbook Exercise • Real-World Context
In Chapter 7 ('The Cleanest Village'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Practice Time • Measurement & Conversions
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams.
[3 Marks]
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams.
✅ Step-by-Step Solution & Working
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Try These • Geometry and Shapes
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have?
[3 Marks]
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have?
✅ Step-by-Step Solution & Working
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
Money & Accounts • Rate List Calculation
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns?
[3 Marks]
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns?
✅ Step-by-Step Solution & Working
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
Fractions Exploration • Parts of a Whole
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena?
[3 Marks]
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena?
✅ Step-by-Step Solution & Working
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
Time & Clocks • Elapsed Time
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last?
[3 Marks]
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last?
✅ Step-by-Step Solution & Working
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
Perimeter & Area • Fencing a Field
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing.
[3 Marks]
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing.
✅ Step-by-Step Solution & Working
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Mental Math • Division and Multiplication
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ?
[2 Marks]
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ?
✅ Step-by-Step Solution & Working
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Patterns & Symmetries • Rotational Turns
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)?
[2 Marks]
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)?
✅ Step-by-Step Solution & Working
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
Smart Charts • Data Interpretation
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data.
[3 Marks]
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data.
✅ Step-by-Step Solution & Working
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
Chapter Review • True or False
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth).
[3 Marks]
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth).
✅ Step-by-Step Solution & Working
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study
Recycling Waste Funds for Village Library
The village panchayat collected 120 kg of old newspapers and 45 kg of cardboard boxes. The scrap dealer buys newspapers at ₹14 per kg and cardboard at ₹10 per kg.
Analytical Task: How much total money did the village raise for their new reading room?
Evaluation & Model Answer:
Working:
• Money from newspapers = 120 kg × ₹14 = ₹1,680.
• Money from cardboard = 45 kg × ₹10 = ₹450.
• Total funds raised = ₹1,680 + ₹450 = ₹2,130.
• Money from newspapers = 120 kg × ₹14 = ₹1,680.
• Money from cardboard = 45 kg × ₹10 = ₹450.
• Total funds raised = ₹1,680 + ₹450 = ₹2,130.
Rubric: 1 Mark for individual product calculations; 1 Mark for total ₹2,130.