Chapter 12 of 14
⬅️ Ch 11: Area and its Boundary Ch 13: Ways to Multiply and Divide ➡️
NCERT Class 5 Mathematics • Classic CBSE Track

Chapter 12: Smart Charts

स्मार्ट चार्ट (चपाती चार्ट / पाई चार्ट, टैली चिह्न एवं पेड़ आरेख) | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts
  • Tally marks for rapid counting: 5 is represented by four vertical lines and one cross slash (||||).
  • Chapati Chart (Pie Chart / Circle Graph): Representing portions of a whole as sectors (1/2, 1/4, 1/8).
  • Growth bar graphs: Tracking seed/plant growth over consecutive days.
  • Family trees and generation tracking.
  • Total students: 40.
  • (a) Cricket: $\frac{1}{2} \times 40 = \mathbf{20\text{ students}}$.
  • (b) Football: $\frac{1}{4} \times 40 = \mathbf{10\text{ students}}$.
  • (c) Badminton: $\frac{1}{4} \times 40 = \mathbf{10\text{ students}}$.
Chapati (Pie) Chart: Games Liked by 40 Children Cricket (1/2) Footb. (1/4) Badm. (1/4) Cricket: 20 children (1/2 of 40) Football: 10 children (1/4 of 40) Badminton: 10 children (1/4 of 40) Total Children = 40 | Fraction = Number of children in category ÷ 40

All Textbook Exercises & In-Text Tasks (24 Questions)

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Q1 Textbook Exercise • Tally Marks (Traffic Survey)
Yamini did a project 'Animals and Birds'. She stood on the road for half an hour and noted passing vehicles using tally marks: Cycle (28), Car (12), Auto-rickshaw (18), Bus (15), Cycle-rickshaw (24), Truck (6).
(a) Draw the tally marks for Cycle (28) and Bus (15) using NCERT box notation.
(b) Write the total number of vehicles that passed by in half an hour.
(c) Which vehicle was observed the most?
[4 Marks]
✅ Step-by-Step Solution & Working
Survey Analysis:
• (a) Tally Marks (each complete 5-box is 4 sides + 1 diagonal):
- Cycle (28): 5 complete boxes of five + 3 lines (5 × 5 + 3 = 28).
- Bus (15): 3 complete boxes of five (5 × 3 = 15).
• (b) Total vehicles: 28 + 12 + 18 + 15 + 24 + 6 = 103 vehicles.
• (c) Most observed vehicle: Cycle (28).
CBSE Step-by-Step Marking Scheme
Tally mark representation 1.5 M
Total count: 103 vehicles 1.5 M
Most observed: Cycle 1 M
Q2 Textbook Exercise • Chapati Chart (Pie Chart / Circle Graph)
In a class of 40 students, teacher made a circle chart of their favorite activities after school:
• 1/2 of the children like playing sports.
• 1/4 of the children like watching TV.
• 1/4 of the children like reading books.
(a) How many children like playing sports?
(b) How many children like watching TV?
(c) How many children like reading books?
[3 Marks]
✅ Step-by-Step Solution & Working
Chapati Chart Calculations (Total = 40 students):
• (a) Sports (1/2): 1/2 of 40 = 40 ÷ 2 = 20 students.
• (b) Watching TV (1/4): 1/4 of 40 = 40 ÷ 4 = 10 students.
• (c) Reading books (1/4): 1/4 of 40 = 40 ÷ 4 = 10 students.
CBSE Step-by-Step Marking Scheme
Sports: 20 1 M
TV: 10 1 M
Books: 10 1 M
Q3 Textbook Exercise • Rabbit Population Growth Table
Rabbits were brought to an island. The table shows their numbers each year:
• Year 0: 10 rabbits
• Year 1: 18 rabbits (almost double)
• Year 2: 32 rabbits
• Year 3: 58 rabbits
• Year 4: 108 rabbits
(a) Is the rabbit population growing by adding a fixed number or by multiplying? (b) Predict the approximate number of rabbits in Year 5.
[3 Marks]
✅ Step-by-Step Solution & Working
Population Trend:
• (a) Growth nature: The population is multiplying / almost doubling each year (each year's count is a little less than double the previous year: 10×2-2=18, 18×2-4=32, 32×2-6=58, 58×2-8=108).
• (b) Year 5 prediction: Approximately double of 108 minus 10 ≈ 216 - 10 = around 200 to 210 rabbits.
CBSE Step-by-Step Marking Scheme
Multiplicative / doubling trend identified 1.5 M
Year 5 prediction (approx 200-210) 1.5 M
Q4 Textbook Exercise • Plant Growth Bar Graph
A plant's height was measured every 4 days:
• Day 0: 0 cm
• Day 4: 1.4 cm
• Day 8: 5.3 cm
• Day 12: 9.5 cm
• Day 16: 10.9 cm
• Day 20: 11.1 cm
(a) Between which days did the plant grow the fastest? (b) What was the total growth of the plant in 20 days?
[3 Marks]
✅ Step-by-Step Solution & Working
Growth Intervals:
• Day 0 to 4: 1.4 - 0 = 1.4 cm.
• Day 4 to 8: 5.3 - 1.4 = 3.9 cm.
• Day 8 to 12: 9.5 - 5.3 = 4.2 cm (fastest!).
• Day 12 to 16: 10.9 - 9.5 = 1.4 cm.
• Day 16 to 20: 11.1 - 10.9 = 0.2 cm.
• (a) Fastest growth: Between Day 8 and Day 12 (grew 4.2 cm).
• (b) Total growth: 11.1 - 0 = 11.1 cm.
CBSE Step-by-Step Marking Scheme
Interval analysis 1 M
Fastest: Day 8 to 12 1 M
Total growth: 11.1 cm 1 M
Q5 Textbook Exercise • Helping Hands at Home Survey
Children were asked what work they help most with at home: Going to market (47), Washing utensils (15), Washing clothes (3), Making/serving food (25), Cleaning house (10).
(a) How many children were surveyed in total? (b) Which chore do the most children help with? (c) What fraction of children help with going to the market (approximate)?
[3 Marks]
✅ Step-by-Step Solution & Working
Survey Summary:
• (a) Total children: 47 + 15 + 3 + 25 + 10 = 100 children.
• (b) Most helped chore: Going to market (47 children).
• (c) Market fraction: 47/100 ≈ almost 1/2 of the children (about 47%).
CBSE Step-by-Step Marking Scheme
Total: 100 1 M
Market most helped 1 M
Fraction approx 1/2 (47/100) 1 M
Q6 Textbook Exercise • Attendance Absenteeism Chart
Absentees on Monday across classes: Class 1: 2, Class 2: 1, Class 3: 3, Class 4: 4, Class 5: 2. (a) What was the total number of absent students in the primary school on Monday? (b) Which class had the highest number of absentees?
[2 Marks]
✅ Step-by-Step Solution & Working
Absentee Analysis:
• (a) Total absentees: 2 + 1 + 3 + 4 + 2 = 12 students.
• (b) Highest absentees: Class 4 (4 students absent).
CBSE Step-by-Step Marking Scheme
Total: 12 students 1 M
Class 4 highest 1 M
Q7 Textbook Exercise • Favorite Ice Cream Pictograph
In a pictograph, one ice cream cone symbol 🍦 represents 10 students. The table shows: Vanilla: 3 symbols; Chocolate: 5 symbols; Mango: 4 symbols; Strawberry: 2 symbols.
(a) How many students prefer Chocolate ice cream?
(b) How many more students prefer Mango than Strawberry?
(c) What is the total number of students?
[3 Marks]
✅ Step-by-Step Solution & Working
Pictograph Calculations (1 symbol = 10 students):
• (a) Chocolate: 5 × 10 = 50 students.
• (b) Mango vs Strawberry: (4 - 2) × 10 = 2 × 10 = 20 more students.
• (c) Total students: (3 + 5 + 4 + 2) × 10 = 14 × 10 = 140 students.
CBSE Step-by-Step Marking Scheme
Chocolate: 50 1 M
Mango difference: 20 1 M
Total: 140 1 M
Q8 Textbook Exercise • Temperature Bar Chart
City temperatures on a winter day: Delhi: 15°C, Shimla: 5°C, Chennai: 30°C, Jaipur: 20°C. If a bar graph has 1 cm height = 5°C: (a) What will be the height of the bar for Chennai? (b) What will be the height of the bar for Shimla?
[2 Marks]
✅ Step-by-Step Solution & Working
Bar Chart Heights:
• (a) Chennai (30°C): 30 ÷ 5 = 6 cm.
• (b) Shimla (5°C): 5 ÷ 5 = 1 cm.
CBSE Step-by-Step Marking Scheme
Chennai bar: 6 cm 1 M
Shimla bar: 1 cm 1 M
Q9 Textbook Exercise • Mode in Data
The shoe sizes of 11 boys are: 5, 6, 6, 7, 5, 6, 8, 6, 7, 6, 5. (a) Arrange the data in a frequency table with tally marks. (b) Which shoe size is the most common (mode)?
[3 Marks]
✅ Step-by-Step Solution & Working
Frequency Table:
• Size 5: 3 boys (|||)
• Size 6: 5 boys (🗎 with 5 lines)
• Size 7: 2 boys (||)
• Size 8: 1 boy (|)
• Most common size: Size 6 (occurs 5 times).
CBSE Step-by-Step Marking Scheme
Frequency table with tally 2 M
Mode: Size 6 1 M
Q10 Textbook Exercise • Tree Plantation Data
Five houses planted saplings in 'Van Mahotsav': House 1 (12), House 2 (18), House 3 (15), House 4 (25), House 5 (10). (a) What is the total number of saplings planted? (b) What is the average number of saplings planted per house?
[3 Marks]
✅ Step-by-Step Solution & Working
Calculations:
• (a) Total saplings: 12 + 18 + 15 + 25 + 10 = 80 saplings.
• (b) Average: Total ÷ Number of houses = 80 ÷ 5 = 16 saplings per house.
CBSE Step-by-Step Marking Scheme
Total: 80 saplings 1.5 M
Average: 16 saplings 1.5 M
Q11 Textbook Exercise • Reading Pie Chart Fractions
A circular chart shows: 50% students walk to school, 25% take school bus, 25% ride bicycle. (a) What fraction of students walk? (b) If there are 200 students in the school, how many ride a bicycle?
[2 Marks]
✅ Step-by-Step Solution & Working
Fractions & Counts:
• (a) Walking fraction: 50% = 50/100 = 1/2.
• (b) Bicycle riders: 25% = 1/4 of total. 1/4 of 200 = 200 ÷ 4 = 50 students.
CBSE Step-by-Step Marking Scheme
Walking: 1/2 1 M
Bicycle: 50 students 1 M
Q12 Textbook Exercise • Dice Throw Outcome Bar Chart
A die was rolled 30 times. The outcomes were: 1 (4 times), 2 (6 times), 3 (5 times), 4 (7 times), 5 (3 times), 6 (5 times). (a) Which number turned up the most? (b) Which number turned up the least?
[2 Marks]
✅ Step-by-Step Solution & Working
Dice Analysis:
• (a) Most frequent outcome: Number 4 (turned up 7 times).
• (b) Least frequent outcome: Number 5 (turned up 3 times).
CBSE Step-by-Step Marking Scheme
Most frequent: 4 1 M
Least frequent: 5 1 M
Q13 Textbook Exercise • Rainfall Bar Chart
Monthly rainfall recorded in mm: June (120 mm), July (250 mm), August (300 mm), September (180 mm). (a) Which month had the maximum rainfall? (b) What was the total rainfall during the monsoon season (June to September)?
[2 Marks]
✅ Step-by-Step Solution & Working
Rainfall Data:
• (a) Maximum rainfall: August (300 mm).
• (b) Total rainfall: 120 + 250 + 300 + 180 = 850 mm.
CBSE Step-by-Step Marking Scheme
August (300 mm) 1 M
Total: 850 mm 1 M
Q14 Textbook Exercise • Constructing a Scale for a Bar Graph
The marks obtained by a student are: English 75, Hindi 80, Maths 95, Science 85, Social Science 70. If you draw a bar graph on a paper with maximum height 10 cm, what scale should you choose for the vertical axis?
[2 Marks]
✅ Step-by-Step Solution & Working
Axis Scaling:
• Highest mark = 95 (round up to 100).
• Available height = 10 cm.
• Scale: 100 ÷ 10 = 10 marks per cm. So 1 cm = 10 marks is the ideal scale (the tallest bar for Maths will be 9.5 cm high).
CBSE Step-by-Step Marking Scheme
Proposed scale: 1 cm = 10 marks 1 M
Height verification (9.5 cm for 95) 1 M
Q15 Textbook Exercise • Tally Box Notation
Explain how NCERT Class 5 tally marks are drawn using the 5-line box method.
[3 Marks]
✅ Step-by-Step Solution & Working
NCERT Box Tally Method:
• 1 = 1 vertical line (|)
• 2 = 2 lines forming a right angle (L)
• 3 = 3 sides of a square (U)
• 4 = A complete square (4 sides: 🗆)
• 5 = A square with a diagonal slash crossing it (🗎).
This creates easy-to-read bundles of 5.
CBSE Step-by-Step Marking Scheme
1 to 4 steps explained 1.5 M
5th diagonal slash completing bundle 1.5 M
Q16 Textbook Exercise • Library Books Distribution
A school library has 600 books: Storybooks (250), Science (150), Mathematics (100), History (100). What fraction of total books are Storybooks?
[2 Marks]
✅ Step-by-Step Solution & Working
Fraction Calculation:
• Storybooks = 250.
• Total books = 600.
• Fraction = 250/600 = 25/60 = 5/12 of total books.
CBSE Step-by-Step Marking Scheme
250/600 ratio 1 M
Reduced fraction: 5/12 1 M
Q17 Textbook Exercise • Comparing Double Bar Graph
A double bar graph compares marks of Term 1 and Term 2 for Rohit: Maths (65 → 85), English (70 → 75), Science (60 → 80). In which subject did Rohit show the maximum improvement?
[2 Marks]
✅ Step-by-Step Solution & Working
Improvement Differences:
• Maths: 85 - 65 = 20 marks improvement.
• English: 75 - 70 = 5 marks improvement.
• Science: 80 - 60 = 20 marks improvement.
Rohit showed the maximum improvement of 20 marks equally in Maths and Science.
CBSE Step-by-Step Marking Scheme
Differences calculated 1 M
Maths and Science (20 marks each) 1 M
Q18 Textbook Exercise • Morning Walk Time Line Graph
Rohan recorded time spent on morning walk over 5 days: Monday 20 min, Tuesday 25 min, Wednesday 30 min, Thursday 35 min, Friday 40 min. What is the pattern in time spent, and what is his total walking time in hours?
[3 Marks]
✅ Step-by-Step Solution & Working
Trend & Total Time:
• Pattern: Increases by 5 minutes each day.
• Total time: 20 + 25 + 30 + 35 + 40 = 150 minutes.
• In hours = 150 ÷ 60 = 2 hours and 30 minutes (2.5 hours).
CBSE Step-by-Step Marking Scheme
5-minute increment pattern 1 M
Total 150 minutes 1 M
Converted to 2.5 hours 1 M
Q19 Textbook Exercise • Fruit Seller Inventory
A fruit seller has 80 kg of fruits: Apples 20 kg, Bananas 40 kg, Oranges 20 kg. What fraction of the total fruits are Bananas?
[2 Marks]
✅ Step-by-Step Solution & Working
Fraction:
• Bananas = 40 kg; Total = 80 kg.
• Fraction = 40/80 = 1/2 (half of all fruits).
CBSE Step-by-Step Marking Scheme
40/80 ratio 1 M
Answer: 1/2 1 M
Q20 Textbook Exercise • Newspaper Reading Survey
In an apartment block of 50 families: 30 families read Hindi newspaper, 15 families read English newspaper, and 5 read both. How many families read only Hindi newspaper?
[2 Marks]
✅ Step-by-Step Solution & Working
Venn Subtraction:
• Total Hindi readers = 30 families.
• Read both = 5 families.
• Only Hindi newspaper: 30 - 5 = 25 families.
CBSE Step-by-Step Marking Scheme
Subtraction 30 - 5 1 M
Answer: 25 families 1 M
Q21 Textbook Exercise • Class Strength Comparison
Section A has 35 students and Section B has 45 students. (a) What is the ratio of Section A to Section B in simplest form? (b) How many students should transfer from Section B to Section A to make both sections equal?
[3 Marks]
✅ Step-by-Step Solution & Working
Calculations:
• (a) Ratio: 35 : 45 = (35÷5) : (45÷5) = 7 : 9.
• (b) Equal sections: Total = 35 + 45 = 80 students. Each section needs 80 ÷ 2 = 40 students.
Transfer needed = 45 - 40 = 5 students.
CBSE Step-by-Step Marking Scheme
Ratio 7:9 1.5 M
Transfer 5 students 1.5 M
Q22 Textbook Exercise • Favorite Subject Survey
In a survey of 60 children: 24 voted Maths, 18 voted Science, 12 voted Art, and 6 voted English. Represent this data as percentage of total votes.
[3 Marks]
✅ Step-by-Step Solution & Working
Percentages (Vote ÷ 60 × 100%):
• Maths: (24 ÷ 60) × 100 = 40%.
• Science: (18 ÷ 60) × 100 = 30%.
• Art: (12 ÷ 60) × 100 = 20%.
• English: (6 ÷ 60) × 100 = 10%.
CBSE Step-by-Step Marking Scheme
Maths 40%, Science 30% 1.5 M
Art 20%, English 10% 1.5 M
Q23 Textbook Exercise • Range of a Dataset
Daily maximum temperatures over one week were: 32°C, 35°C, 31°C, 38°C, 34°C, 30°C, 36°C. (a) What was the highest temperature? (b) What was the lowest temperature? (c) What is the 'Range' of the temperature dataset?
[3 Marks]
✅ Step-by-Step Solution & Working
Range Calculation:
• (a) Highest: 38°C.
• (b) Lowest: 30°C.
• (c) Range: Highest - Lowest = 38°C - 30°C = 8°C.
CBSE Step-by-Step Marking Scheme
Highest: 38°C 1 M
Lowest: 30°C 1 M
Range: 8°C 1 M
Q24 Textbook Exercise • Importance of Smart Charts
Why are charts and graphs called 'Smart Charts'? Give two reasons why displaying data in charts is better than raw number lists.
[2 Marks]
✅ Step-by-Step Solution & Working
Advantages of Smart Charts:
1. Instant Visual Understanding: Charts allow readers to grasp trends, comparisons, and peaks at a single glance without reading long tables.
2. Easy Comparison: Tall bars and large pie slices immediately show which category is largest or smallest without performing manual calculations.
CBSE Step-by-Step Marking Scheme
Visual clarity explained 1 M
Immediate comparison benefit explained 1 M
🌟 NEP 2020 Competency-Based Case Study

NEP 2020 Competency Case: Smart Charts

A practical scenario involving Smart Charts in everyday life and community contexts.

Analytical Task: Analyze the quantitative relationships and state the conclusion.
Evaluation & Model Answer:
Apply the step-by-step formulas and concepts mastered in this chapter.
Rubric: 1M formula + 1M working + 1M answer
⬅️ Ch 11: Area and its Boundary Ch 13: Ways to Multiply and Divide ➡️