Chapter 13 of 14
⬅️ Ch 12: Can We Share? Ch 14: Rupees and Paise ➡️
NCERT Class 3 Mathematics • Classic CBSE Track

Chapter 13: Smart Charts!

Tally Marks, Bar Charts, Tables, Traffic Surveys & Drawing Inferences | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts
  • Using tally marks (bundles of 5: four vertical lines crossed by one diagonal line).
  • Constructing and reading frequency tables from real-world surveys.
  • Reading simple bar charts with labeled axes and scales.
  • Interpreting data: finding the most popular, least popular, and total counts.
Smart Bar Chart — Favourite Sports of Class 3 Students 0 10 20 18 Cricket 12 Football 15 Badminton 5 Chess Total = 50

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

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Q1 Bar Chart Interpretation • Sports Survey
Look at the bar chart above: (a) Which is the most popular sport? (b) How many more students prefer cricket over football? (c) How many total students participated in the survey?
[3 Marks]
✅ Step-by-Step Solution & Working
Data Reading:
• (a) Most popular sport: Cricket (18 students, highest bar).
• (b) Difference between Cricket and Football: 18 - 12 = 6 more students.
• (c) Total students: 18 + 12 + 15 + 5 = 50 students.
CBSE Step-by-Step Marking Scheme
Correct most popular sport identified 1.0 M
Correct difference calculation (18 - 12 = 6) 1.0 M
Correct total students sum (50) 1.0 M
Q2 Tally Marks Representation
Draw tally marks for the following frequency counts: (a) 7 cars, (b) 14 bicycles, (c) 19 pedestrians.
[3 Marks]
✅ Step-by-Step Solution & Working
Tally Mark Representations (Bundles of 5):
• (a) 7 cars: |||| || (One bundle of 5 + 2 lines)
• (b) 14 bicycles: |||| |||| |||| (Two bundles of 5 + 4 lines)
• (c) 19 pedestrians: |||| |||| |||| |||| (Three bundles of 5 + 4 lines).
CBSE Step-by-Step Marking Scheme
Correct tally bundle for 7 1.0 M
Correct tally bundles for 14 1.0 M
Correct tally bundles for 19 1.0 M
Q3 Data Table Analysis • Family Helpers
In a class of 30 children, 10 help in setting the dinner table, 12 help in market shopping, and 8 help in cleaning rooms. Represent this data in a clean frequency table with tally marks.
[3 Marks]
✅ Step-by-Step Solution & Working
Frequency Table:
Help ActivityTally MarksNumber of Children
Setting Dinner Table|||| ||||10
Market Shopping|||| |||| ||12
Cleaning Rooms|||| |||8
Total—30
CBSE Step-by-Step Marking Scheme
Correct table layout and categories 1.5 M
Correct tally grouping and frequency total (30) 1.5 M
Q4 Traffic on the Road • Tally Chart
Anu stood at a road crossing for 15 minutes and made tally marks for passing vehicles:
• Bicycles: |||| |||| || (12)
• Cars: |||| ||| (8)
• Auto-rickshaws: |||| |||| (10)
• Buses: |||| (4)
(a) How many vehicles did Anu count in total?
(b) Which vehicle was seen the most, and which the least?
(c) How many more bicycles passed than buses?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Traffic Analysis:
(a) Total Vehicles:
• 12 + 8 + 10 + 4 = 34 vehicles.

(b) Most & Least:
• Most: Bicycles (12).
• Least: Buses (4).

(c) Difference (Bicycles vs Buses):
• 12 - 4 = 8 more bicycles.
CBSE Step-by-Step Marking Scheme
Correct total count (34 vehicles) 1.0 M
Correct most (bicycles) and least (buses) 1.0 M
Correct difference (8) 1.0 M
Q5 Favourite Pets • Bar Chart Reading
A bar chart of children's favorite pets shows:
• Dogs: 10 children
• Cats: 8 children
• Parrots: 6 children
• Rabbits: 4 children
(a) Which is the most popular pet in the class?
(b) How many children like cats or parrots in total?
(c) What is the total number of children surveyed?
[3 Marks]
✅ Step-by-Step Solution & Working
Bar Chart Data:
• (a) Most Popular Pet: Dog (chosen by 10 children).
• (b) Cats or Parrots: 8 (Cats) + 6 (Parrots) = 14 children.
• (c) Total Surveyed: 10 + 8 + 6 + 4 = 28 children.
CBSE Step-by-Step Marking Scheme
Correct most popular pet (Dog) 1.0 M
Correct sum for cats + parrots (14) 1.0 M
Correct total surveyed (28) 1.0 M
Q6 Flowers in the Garden • Smart Chart
In a botanical garden, flowers are counted by color:
• Red roses: 25
• Yellow marigolds: 35
• Blue orchids: 15
• White lilies: 20
(a) Create a frequency table showing the colors and numbers of flowers.
(b) How many yellow marigolds and blue orchids are there combined?
[3 Marks]
✅ Step-by-Step Solution & Working
(a) Frequency Table:
Flower Type & ColorNumber of Flowers
Red Roses25
Yellow Marigolds35
Blue Orchids15
White Lilies20
Total95

(b) Combined Count:
• 35 (Yellow) + 15 (Blue) = 50 flowers.
CBSE Step-by-Step Marking Scheme
Accurate table construction with all 4 flowers 1.5 M
Correct sum of yellow and blue flowers (50) 1.5 M
Q7 Dice Roll Experiment • Data Recording
Rohan rolled a die 20 times and recorded the outcomes:
• Number 1: 3 times
• Number 2: 4 times
• Number 3: 2 times
• Number 4: 5 times
• Number 5: 3 times
• Number 6: 3 times
(a) Which face appeared the maximum number of times?
(b) Which face appeared the minimum number of times?
(c) Did any faces appear the same number of times?
[3 Marks]
✅ Step-by-Step Solution & Working
Data Analysis:
• (a) Maximum Face: Face 4 (appeared 5 times).
• (b) Minimum Face: Face 3 (appeared 2 times).
• (c) Equal Faces: Yes, Faces 1, 5, and 6 each appeared 3 times.
CBSE Step-by-Step Marking Scheme
Correct maximum face (4) 1.0 M
Correct minimum face (3) 1.0 M
Correct identification of tied faces (1, 5, 6) 1.0 M
Q8 Textbook Exercise • Real-Life Math
In Chapter 13 ('Smart Charts!'), 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 'Smart Charts!', 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

School Canteen Fruit Survey

The canteen manager tracked fruit sales on Wednesday: Bananas (45), Apples (30), Oranges (25), and Guavas (20).

Analytical Task: Which fruit was the most demanded? What fraction of the total fruit sales did bananas represent?
Evaluation & Model Answer:
1. Total fruits sold = 45 + 30 + 25 + 20 = 120 fruits.
2. Most demanded fruit: Bananas with 45 sold.
3. Fraction of bananas: 45 out of 120 = 45/120 = 15/40 = 3/8 (three-eighths).
Rubric: 1M total summation + 1M most demanded + 1M simplified fraction.
⬅️ Ch 12: Can We Share? Ch 14: Rupees and Paise ➡️