NCERT Class 3 Mathematics • New NEP 2020 / NCF 2023

Chapter 11: Filling and Lifting

Q: State whether you would measure the capacity of the following in 'Litres (L)' or 'Millilitres (mL)': (a) A medicine dropper, (b) Water in a swimming p

Units:• (a) Medicine dropper: Millilitres (mL) (very small liquid volume)• (b) Water in swimming pool: Litres (L) (huge liquid volume)• (c) A cup of tea: Millilitres (mL) (approx 150-200 mL)• (d) Petrol in a car tank: Litres (L) (approx 35-50 L).

Q: A bucket holds 10 litres of water. (a) How many 500 mL mugs of water are needed to fill this bucket completely? (b) How many 1-litre bottles can be fi

Solution:(a) Mugs of 500 mL:• We know that 1 Litre = 2 mugs of 500 mL (500 mL + 500 mL = 1000 mL = 1 L).• For 10 Litres = 10 × 2 = 20 mugs.(b) 1-Litre bottles:• 10 Litres ÷ 1 Litre = 10 bottles.

Q: A vegetable seller has standard weights of 1 kg, 500 g, 200 g, and 100 g. How can she weigh: (a) 1 kg 700 g of potatoes? (b) 800 g of tomatoes using t

Combinations:• (a) 1 kg 700 g potatoes:1 kg + 500 g + 200 g = 1 kg 700 g (3 weights).• (b) 800 g tomatoes:500 g + 200 g + 100 g = 800 g (3 weights).

Q: Arrange the following containers in order of their capacity, from holding the least water to holding the most water:Water tanker, Tea spoon, Bucket, G

Capacity Ordering (Least to Most):1. Tea spoon (~5 mL)2. Glass (~250 mL)3. Water bottle (~1 Litre / 1000 mL)4. Bucket (~15 to 20 Litres)5. Water tanker (~5000 Litres).Order: Tea spoon < Glass < Water bottle < Bucket < Water tanker.

Q: A grocer wants to weigh 1 kg of sugar. He has standard weights of 500 g, 200 g, and 100 g.(a) How many 500 g weights balance 1 kg?(b) How many 200 g w

Step-by-Step Weights:• 1 kg = 1000 grams.(a) 500 g Weights:• 1000 ÷ 500 = 2 weights of 500 g.(b) 200 g Weights:• 1000 ÷ 200 = 5 weights of 200 g.(c) Combined Weights:• One 500 g weight = 500 g• Two 200 g weights = 400 g• One 100 g weight = 100 g• Total = 500 g + 400 g + 100 g = 1000 g = 1 kg.

Q: A family bought a 25 kg sack of wheat flour. In the first week, they used 8 kg 500 g. In the second week, they used 7 kg 250 g.(a) What was the total

Step-by-Step Solution:(a) Total Flour Used:• Week 1: 8 kg 500 g• Week 2: 7 kg 250 g• Sum: (8 + 7) kg + (500 + 250) g = 15 kg 750 g.(b) Remaining Flour:• Total in sack = 25 kg 000 g• Used = 15 kg 750 g• Subtraction: 24 kg 1000 g - 15 kg 750 g = 9 kg 250 g.

Q: A bucket holds 12 litres of water. You only have a 2-litre jug and a 500 mL mug.(a) How many full 2-litre jugs are needed to fill the bucket completel

Step-by-Step Solution:(a) Jugs to fill bucket:• Total bucket capacity = 12 litres.• Jug capacity = 2 litres.• Number of jugs = 12 ÷ 2 = 6 jugs.(b) Mugs per jug:• 1 litre = 1000 mL = two 500 mL mugs.• 2 litres = 2 × 2 = 4 mugs of 500 mL.

Q: In Chapter 11 ('Filling and Lifting'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Expl

Step-by-Step Solution:1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.2. Multiplication fact: 4 × 12 = 48 items.3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.

Q: In 'Filling and Lifting', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.

Verification Method:• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.• Since subtraction brings back the original numbers, the addition is confirmed correct.

Q: Solve mentally:(a) 25 + 75 = ?(b) 150 - 60 = ?(c) Double of 45 = ?(d) Half of 80 = ?

Mental Calculations:• (a) 25 + 75 = 100.• (b) 150 - 60 = 90.• (c) 45 × 2 = 90.• (d) 80 ÷ 2 = 40.

Capacity (Litres & Millilitres), Weight (Kilograms & Grams) & Comparison | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts

Understanding capacity: Litre (L) for large liquids and Millilitre (mL) for small amounts.
1 Litre = 1000 Millilitres (1 L = 1000 mL).
Understanding weight: Kilogram (kg) for heavy items and Gram (g) for light items.
1 Kilogram = 1000 Grams (1 kg = 1000 g).
Using non-standard and standard balance scales to compare weights.

All Textbook Exercises & In-Text Tasks (18 Questions)

100% Complete Ingestion

Q1 Capacity Unit Selection • Real-World Items

State whether you would measure the capacity of the following in 'Litres (L)' or 'Millilitres (mL)': (a) A medicine dropper, (b) Water in a swimming pool, (c) A cup of tea, (d) Petrol in a car tank.

[2 Marks]

✅ Step-by-Step Solution & Working

Units:
• (a) Medicine dropper: Millilitres (mL) (very small liquid volume)
• (b) Water in swimming pool: Litres (L) (huge liquid volume)
• (c) A cup of tea: Millilitres (mL) (approx 150-200 mL)
• (d) Petrol in a car tank: Litres (L) (approx 35-50 L).

CBSE Step-by-Step Marking Scheme

Correct unit for dropper and tea (mL) 1.0 M

Correct unit for pool and car petrol (L) 1.0 M

Q2 Capacity Conversion & Arithmetic

A bucket holds 10 litres of water. (a) How many 500 mL mugs of water are needed to fill this bucket completely? (b) How many 1-litre bottles can be filled from this bucket?

[3 Marks]

✅ Step-by-Step Solution & Working

Solution:
(a) Mugs of 500 mL:
• We know that 1 Litre = 2 mugs of 500 mL (500 mL + 500 mL = 1000 mL = 1 L).
• For 10 Litres = 10 × 2 = 20 mugs.

(b) 1-Litre bottles:
• 10 Litres ÷ 1 Litre = 10 bottles.

CBSE Step-by-Step Marking Scheme

Clear conversion statement (1 L = 2 × 500 mL) 1.5 M

Correct answer for mugs (20) and bottles (10) 1.5 M

Q3 Weight Units & Balancing

A vegetable seller has standard weights of 1 kg, 500 g, 200 g, and 100 g. How can she weigh: (a) 1 kg 700 g of potatoes? (b) 800 g of tomatoes using the least number of weights?

[3 Marks]

✅ Step-by-Step Solution & Working

Combinations:
• (a) 1 kg 700 g potatoes:
1 kg + 500 g + 200 g = 1 kg 700 g (3 weights).

• (b) 800 g tomatoes:
500 g + 200 g + 100 g = 800 g (3 weights).

CBSE Step-by-Step Marking Scheme

Correct weight combination for 1 kg 700 g 1.5 M

Correct weight combination for 800 g 1.5 M

Q4 Capacity Ranking • Everyday Containers

Arrange the following containers in order of their capacity, from holding the least water to holding the most water:
Water tanker, Tea spoon, Bucket, Glass, Water bottle.

[3 Marks]

✅ Step-by-Step Solution & Working

Capacity Ordering (Least to Most):
1. Tea spoon (~5 mL)
2. Glass (~250 mL)
3. Water bottle (~1 Litre / 1000 mL)
4. Bucket (~15 to 20 Litres)
5. Water tanker (~5000 Litres).

Order: Tea spoon < Glass < Water bottle < Bucket < Water tanker.

CBSE Step-by-Step Marking Scheme

Correct ranking from least to most 2.0 M

Reasonable real-life capacity estimates 1.0 M

Q5 Balance Scale • Weights in Grams and Kilograms

A grocer wants to weigh 1 kg of sugar. He has standard weights of 500 g, 200 g, and 100 g.
(a) How many 500 g weights balance 1 kg?
(b) How many 200 g weights balance 1 kg?
(c) Give a combination using all three weights (500 g, 200 g, 100 g) that together equal 1 kg.

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Weights:
• 1 kg = 1000 grams.
(a) 500 g Weights:
• 1000 ÷ 500 = 2 weights of 500 g.

(b) 200 g Weights:
• 1000 ÷ 200 = 5 weights of 200 g.

(c) Combined Weights:
• One 500 g weight = 500 g
• Two 200 g weights = 400 g
• One 100 g weight = 100 g
• Total = 500 g + 400 g + 100 g = 1000 g = 1 kg.

CBSE Step-by-Step Marking Scheme

Correct answers for (a): 2 weights, and (b): 5 weights 1.5 M

Correct mixed combination summing to 1000 g 1.5 M

Q6 Weight Addition & Subtraction • Grocery Sack

A family bought a 25 kg sack of wheat flour. In the first week, they used 8 kg 500 g. In the second week, they used 7 kg 250 g.
(a) What was the total weight of flour used in the two weeks?
(b) How much flour remains in the sack?

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Solution:
(a) Total Flour Used:
• Week 1: 8 kg 500 g
• Week 2: 7 kg 250 g
• Sum: (8 + 7) kg + (500 + 250) g = 15 kg 750 g.

(b) Remaining Flour:
• Total in sack = 25 kg 000 g
• Used = 15 kg 750 g
• Subtraction: 24 kg 1000 g - 15 kg 750 g = 9 kg 250 g.

CBSE Step-by-Step Marking Scheme

Correct addition of compound weights (15 kg 750 g) 1.5 M

Correct subtraction from 25 kg (9 kg 250 g) 1.5 M

Q7 Measuring Jug Puzzle • Liquid Volume

A bucket holds 12 litres of water. You only have a 2-litre jug and a 500 mL mug.
(a) How many full 2-litre jugs are needed to fill the bucket completely?
(b) How many 500 mL mugs are needed to equal one 2-litre jug?

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Solution:
(a) Jugs to fill bucket:
• Total bucket capacity = 12 litres.
• Jug capacity = 2 litres.
• Number of jugs = 12 ÷ 2 = 6 jugs.

(b) Mugs per jug:
• 1 litre = 1000 mL = two 500 mL mugs.
• 2 litres = 2 × 2 = 4 mugs of 500 mL.

CBSE Step-by-Step Marking Scheme

Correct calculation for jugs (6 jugs) 1.5 M

Correct calculation for mugs (4 mugs) 1.5 M

Q8 Textbook Exercise • Practical Problem Solving

In Chapter 11 ('Filling and Lifting'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.

[2 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.

CBSE Step-by-Step Marking Scheme

Repeated addition 12+12+12+12 = 48 1 M

Multiplication 4 × 12 = 48 1 M

Q9 In-Text Activity • Concept Exploration

In 'Filling and Lifting', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.

[2 Marks]

✅ Step-by-Step Solution & Working

Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.

CBSE Step-by-Step Marking Scheme

Addition 65 + 35 = 100 1 M

Inverse check 100 - 35 = 65 1 M

Q10 Practice Time • Mental Math Drills

Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ?

[2 Marks]

✅ Step-by-Step Solution & Working

Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.

CBSE Step-by-Step Marking Scheme

All 4 mental math facts correct 2 M

Q11 Word Problem • Real Life Application

A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.

CBSE Step-by-Step Marking Scheme

Total 3 × 25 = 75 1.5 M

Remainder 75 - 38 = 37 1.5 M

Q12 Critical Thinking • Finding the Pattern

Observe the sequence related to 'Filling and Lifting': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.

[2 Marks]

✅ Step-by-Step Solution & Working

Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.

CBSE Step-by-Step Marking Scheme

Next terms 60, 72 1 M

Rule: multiples of 12 / +12 step 1 M

Q13 Estimation & Measurement • Practical Judgment

Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard.

[2 Marks]

✅ Step-by-Step Solution & Working

Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).

CBSE Step-by-Step Marking Scheme

Correct estimation for all 4 items 2 M

Q14 Data Interpretation • Reading Simple Tables

A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed?

[3 Marks]

✅ Step-by-Step Solution & Working

Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.

CBSE Step-by-Step Marking Scheme

Mango identified 1 M

Difference = 13 1 M

Total = 90 1 M

Q15 Let us Do • Shapes and Symmetry

Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have?

[3 Marks]

✅ Step-by-Step Solution & Working

Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).

CBSE Step-by-Step Marking Scheme

Rectangle = 2 lines 1 M

Triangle = 3 lines 1 M

Circle = infinite lines 1 M

Q16 Puzzle Time • Missing Number Grid

In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?

[2 Marks]

✅ Step-by-Step Solution & Working

Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.

CBSE Step-by-Step Marking Scheme

Opposite corner = 8 with reasoning 2 M

Q17 Money & Shopping • Cash Memo Bill

Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.

[3 Marks]

✅ Step-by-Step Solution & Working

Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.

CBSE Step-by-Step Marking Scheme

Correct item breakdown and total ₹38 2 M

Change = ₹12 1 M

Q18 Chapter Review • Comprehensive Concept Check

True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners.

[3 Marks]

✅ Step-by-Step Solution & Working

Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.

CBSE Step-by-Step Marking Scheme

All 3 statements correctly evaluated as True 3 M

🌟 NEP 2020 Competency-Based Case Study

Community Kitchen Lemonade Preparation

To make lemonade for 50 people at a sports day, students use 8 litres of water, 1 litre of lemon juice, and 500 mL of sugar syrup.

Analytical Task: What is the total volume of lemonade prepared in millilitres? If each glass holds 200 mL, can they serve 45 glasses?

Evaluation & Model Answer:

1. Convert all volumes to millilitres (mL):
• Water = 8 L = 8,000 mL
• Lemon juice = 1 L = 1,000 mL
• Sugar syrup = 500 mL
• Total volume = 8,000 + 1,000 + 500 = 9,500 mL.
2. Volume needed for 45 glasses of 200 mL each = 45 × 200 mL = 9,000 mL.
3. Since 9,500 mL > 9,000 mL, yes, they can easily serve 45 glasses (with 500 mL left over).

Rubric: 1.5M litre to millilitre conversion and summation + 1.5M capacity comparison.