NCERT Class 3 Mathematics • Classic CBSE Track

Chapter 9: How Many Times?

Q: Using the stick crossing method: (a) How many sticks crossing in each direction would you draw for 4 × 5? (b) How many crossing points (dots) will you

Solution:• (a) Sticks: Draw 4 horizontal sticks and 5 vertical sticks crossing them.• (b) Crossing Points: Each of the 4 horizontal sticks crosses all 5 vertical sticks. Total crossing points = 4 × 5 = 20 dots.

Q: A spider has 8 legs. How many legs do 6 spiders have altogether? Write both the repeated addition sentence and the multiplication fact.

Solution:• Legs per spider = 8• Number of spiders = 6• Repeated Addition: 8 + 8 + 8 + 8 + 8 + 8 = 48 legs.• Multiplication Fact: 6 × 8 = 48 legs.

Q: Solve 23 × 4 using the split/box multiplication method. Show the breakdown into tens and ones.

Step-by-step Box Method:1. Split 23 into 20 + 3.2. Multiply each part by 4:• 20 × 4 = 80• 3 × 4 = 123. Add the two partial products:• 80 + 12 = 92.Therefore, 23 × 4 = 92.

Q: There are 5 spiders in a web. Each spider has 8 legs.(a) How many legs are there altogether? Show using repeated addition.(b) Write the multiplication

Step-by-Step Multiplication:(a) Repeated Addition:• 8 + 8 + 8 + 8 + 8 = 40 legs.(b) Multiplication Fact:• 5 × 8 = 40 legs.(c) Octopuses:• 3 octopuses × 8 arms = 24 arms.

Q: Mithu had some matchsticks. She arranged them: 2 vertical sticks crossed by 3 horizontal sticks.(a) How many crossing intersection points are formed?(

Stick Multiplication Method:(a) 2 by 3 Sticks:• 2 vertical sticks crossed by 3 horizontal sticks create 2 × 3 = 6 intersection points.(b) Method for 4 × 5:• Place 4 vertical sticks parallel to each other.• Cross them with 5 horizontal sticks.• Count all the points where the sticks cross each other.(

Q: Tarva the frog jumps 3 steps at a time along a number line.(a) Write the numbers Tarva lands on during his first 6 jumps.(b) Which jump will land Tarv

Multiplication by 3:(a) First 6 jumps:• 1 jump: 1 × 3 = 3• 2 jumps: 2 × 3 = 6• 3 jumps: 3 × 3 = 9• 4 jumps: 4 × 3 = 12• 5 jumps: 5 × 3 = 15• 6 jumps: 6 × 3 = 18.(b) Jump to reach 27:• 27 ÷ 3 = 9th jump.

Q: In Class 3, there are 8 rows of desks. In each row, there are 6 desks.(a) How many desks are in the classroom in total?(b) If 2 children sit at every

Step-by-Step Multiplication:(a) Total Desks:• 8 rows × 6 desks per row = 48 desks.(b) Total Seating Capacity:• 48 desks × 2 children per desk = 96 children.

Q: In Chapter 9 ('How Many Times?'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg

Step-by-Step Solution:1. Cost of 2 kg apples = 2 × ₹60 = ₹120.2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.3. Total cost = ₹120 + ₹120 = ₹240.

Q: In 'How Many Times?', how do you measure and compare quantities accurately? Explain with an example using standard units.

Measurement Explanation:• Standard units provide consistent and reliable measurements across the world.• For length, we use metres (m) and centimetres (cm).• For weight, we use kilograms (kg) and grams (g).• For liquids, we use litres (L) and millilitres (mL).• Unlike non-standard units (such as foo

Q: Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?

Step-by-Step Solution:1. Total money spent = ₹175 + ₹45 = ₹220.2. Amount paid = ₹500.3. Change returned = ₹500 - ₹220 = ₹280.

Repeated Addition, Multiplication Tables, Stick Multiplication & Word Problems | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts

Multiplication as 'times' or repeated addition: 4 times 3 = 3 + 3 + 3 + 3 = 12.
Drawing stick patterns to understand multiplication intersections.
Multiplication properties: multiplying by 0 gives 0, multiplying by 1 gives the same number.
Solving 2-digit by 1-digit multiplication problems.

All Textbook Exercises & In-Text Tasks (17 Questions)

100% Complete Ingestion

Q1 Stick Crossing Multiplication • Concept

Using the stick crossing method: (a) How many sticks crossing in each direction would you draw for 4 × 5? (b) How many crossing points (dots) will you count?

[2 Marks]

✅ Step-by-Step Solution & Working

Solution:
• (a) Sticks: Draw 4 horizontal sticks and 5 vertical sticks crossing them.
• (b) Crossing Points: Each of the 4 horizontal sticks crosses all 5 vertical sticks. Total crossing points = 4 × 5 = 20 dots.

CBSE Step-by-Step Marking Scheme

Correct number of horizontal and vertical sticks 1.0 M

Correct product calculation (20 dots) 1.0 M

Q2 Word Problem • Repeated Grouping

A spider has 8 legs. How many legs do 6 spiders have altogether? Write both the repeated addition sentence and the multiplication fact.

[2 Marks]

✅ Step-by-Step Solution & Working

Solution:
• Legs per spider = 8
• Number of spiders = 6
• Repeated Addition: 8 + 8 + 8 + 8 + 8 + 8 = 48 legs.
• Multiplication Fact: 6 × 8 = 48 legs.

CBSE Step-by-Step Marking Scheme

Correct repeated addition statement 1.0 M

Correct multiplication statement (6 × 8 = 48) 1.0 M

Q3 2-Digit Multiplication • Box Method

Solve 23 × 4 using the split/box multiplication method. Show the breakdown into tens and ones.

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-step Box Method:
1. Split 23 into 20 + 3.
2. Multiply each part by 4:
• 20 × 4 = 80
• 3 × 4 = 12
3. Add the two partial products:
• 80 + 12 = 92.
Therefore, 23 × 4 = 92.

CBSE Step-by-Step Marking Scheme

Correct splitting of 23 into 20 and 3 1.0 M

Correct partial products (80 and 12) 1.0 M

Correct final sum (92) 1.0 M

Q4 Leggy Animals • Multiplication as Repeated Addition

There are 5 spiders in a web. Each spider has 8 legs.
(a) How many legs are there altogether? Show using repeated addition.
(b) Write the multiplication fact.
(c) If 3 octopuses join them (each with 8 arms), how many arms do the octopuses have?

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Multiplication:
(a) Repeated Addition:
• 8 + 8 + 8 + 8 + 8 = 40 legs.

(b) Multiplication Fact:
• 5 × 8 = 40 legs.

(c) Octopuses:
• 3 octopuses × 8 arms = 24 arms.

CBSE Step-by-Step Marking Scheme

Correct repeated addition string (8+8+8+8+8 = 40) 1.0 M

Correct multiplication fact (5 × 8 = 40) 1.0 M

Correct octopus calculation (3 × 8 = 24) 1.0 M

Q5 Multiplication with Sticks • Vedic Method

Mithu had some matchsticks. She arranged them: 2 vertical sticks crossed by 3 horizontal sticks.
(a) How many crossing intersection points are formed?
(b) How can you find 4 × 5 using sticks?
(c) What is 4 × 5?

[3 Marks]

✅ Step-by-Step Solution & Working

Stick Multiplication Method:
(a) 2 by 3 Sticks:
• 2 vertical sticks crossed by 3 horizontal sticks create 2 × 3 = 6 intersection points.

(b) Method for 4 × 5:
• Place 4 vertical sticks parallel to each other.
• Cross them with 5 horizontal sticks.
• Count all the points where the sticks cross each other.

(c) Result:
• 4 × 5 = 20 intersection points.

CBSE Step-by-Step Marking Scheme

Correct intersection points for 2x3 (6 points) 1.0 M

Clear procedural explanation of stick arrangement 1.0 M

Correct product for 4 × 5 = 20 1.0 M

Q6 Tarva Frog Jumps • Step Multiplication

Tarva the frog jumps 3 steps at a time along a number line.
(a) Write the numbers Tarva lands on during his first 6 jumps.
(b) Which jump will land Tarva on number 27?

[3 Marks]

✅ Step-by-Step Solution & Working

Multiplication by 3:
(a) First 6 jumps:
• 1 jump: 1 × 3 = 3
• 2 jumps: 2 × 3 = 6
• 3 jumps: 3 × 3 = 9
• 4 jumps: 4 × 3 = 12
• 5 jumps: 5 × 3 = 15
• 6 jumps: 6 × 3 = 18.

(b) Jump to reach 27:
• 27 ÷ 3 = 9th jump.

CBSE Step-by-Step Marking Scheme

Correct first 6 multiples of 3 (3, 6, 9, 12, 15, 18) 1.5 M

Correct division to find 9th jump 1.5 M

Q7 Word Problem • Classroom Desks

In Class 3, there are 8 rows of desks. In each row, there are 6 desks.
(a) How many desks are in the classroom in total?
(b) If 2 children sit at every desk, how many children can sit in the classroom?

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Multiplication:
(a) Total Desks:
• 8 rows × 6 desks per row = 48 desks.

(b) Total Seating Capacity:
• 48 desks × 2 children per desk = 96 children.

CBSE Step-by-Step Marking Scheme

Correct desks multiplication (8 × 6 = 48) 1.5 M

Correct seating multiplication (48 × 2 = 96) 1.5 M

Q8 Textbook Exercise • Real-Life Math

In Chapter 9 ('How Many Times?'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.

CBSE Step-by-Step Marking Scheme

Apples = ₹120 1 M

Oranges = ₹120 1 M

Total = ₹240 1 M

Q9 In-Text Activity • Hands-on Investigation

In 'How Many Times?', how do you measure and compare quantities accurately? Explain with an example using standard units.

[3 Marks]

✅ Step-by-Step Solution & Working

Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.

CBSE Step-by-Step Marking Scheme

Standard units defined 1.5 M

Examples for length, weight, liquid 1.5 M

Q10 Practice Time • Two-Step Word Problem

Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.

CBSE Step-by-Step Marking Scheme

Total spent = ₹220 1.5 M

Change = ₹280 1.5 M

Q11 Mental Math • Quick Calculations

Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ?

[2 Marks]

✅ Step-by-Step Solution & Working

Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.

CBSE Step-by-Step Marking Scheme

All 4 mental results correct 2 M

Q12 Geometry & Shapes • Edge and Corner Counting

Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners.

[3 Marks]

✅ Step-by-Step Solution & Working

Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.

CBSE Step-by-Step Marking Scheme

Cube 1 M

Cylinder 1 M

Sphere 1 M

Q13 Pattern Time • Sequences and Rules

Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.

[2 Marks]

✅ Step-by-Step Solution & Working

Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.

CBSE Step-by-Step Marking Scheme

Next terms 80, 160 1 M

Rule: multiplying by 2 1 M

Q14 Time & Calendar • Date Calculation

Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).

[3 Marks]

✅ Step-by-Step Solution & Working

Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.

CBSE Step-by-Step Marking Scheme

May days = 17 1.5 M

June days = 30; Total = 47 days 1.5 M

Q15 Equal Sharing • Division Problem

Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.

[2 Marks]

✅ Step-by-Step Solution & Working

Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.

CBSE Step-by-Step Marking Scheme

36 ÷ 4 = 9 cookies 2 M

Q16 Data Handling • Reading a Bar Chart

A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots?

[3 Marks]

✅ Step-by-Step Solution & Working

Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.

CBSE Step-by-Step Marking Scheme

Parrot least 1 M

Total = 38 1 M

Difference = 8 1 M

Q17 Money • Making a Change

A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?

[2 Marks]

✅ Step-by-Step Solution & Working

Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.

CBSE Step-by-Step Marking Scheme

Change = ₹15 1 M

3 coins of ₹5 1 M

🌟 NEP 2020 Competency-Based Case Study

Garden Flowerbed Rows

A municipal botanical garden has 14 flowerbeds. Each flowerbed is planted with 6 marigold plants.

Analytical Task: How many marigold plants are in the garden? If 5 plants dry up, how many healthy plants remain?

Evaluation & Model Answer:

1. Total marigold plants = 14 × 6 = (10 × 6) + (4 × 6) = 60 + 24 = 84 plants.
2. Healthy plants remaining = 84 - 5 = 79 healthy plants.

Rubric: 1.5M multiplication of 14 × 6 + 1.5M subtraction of 5 dried plants.