CBSE Class 5 Mathematics Chapter 12: Smart Charts NCERT Solutions
This chapter, 'Smart Charts', for CBSE Class 5 Mathematics, introduces students to the fundamental concepts of data representation using tally marks and simple charts. The NCERT Solutions provide clear explanations and step-by-step solutions to problems involving collecting, organizing, and interpreting data. Students will learn how to use tally marks to count items efficiently, understand how to read information from tables, and answer questions based on the data presented. The exercises cover practical scenarios like favourite pet animals, vehicles on the road, and types of trees in a colony, making learning engaging. These solutions are designed to help students grasp the basics of data handling, which is crucial for developing analytical skills. Practicing these problems will aid students in their exam preparation by reinforcing their understanding of data interpretation and representation techniques.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 5 |
| Subject | Mathematics |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | 12 Smart Charts |
Chapter summary
Chapter 12, 'Smart Charts', focuses on teaching Class 5 students how to collect and represent data using tally marks. The NCERT Solutions cover exercises on interpreting tally charts for various scenarios, such as favourite animals, vehicles, and trees. Students will practice counting data points, identifying the most frequent items, and performing simple calculations based on the collected information. The chapter emphasizes the practical application of tally marks in everyday situations, preparing students for more complex data analysis in the future.
Learning outcomes
- Understand the concept and use of tally marks for data collection.
- Interpret information presented in tally charts and tables.
- Solve problems involving data related to favourite items and observations.
- Calculate the total number of items from tally marks.
- Identify the most frequent or least frequent data points in a chart.
Topics covered
Paper topics
- Introduction to Tally Marks
- Collecting Data
- Representing Data with Tally Marks
- Interpreting Tally Charts
- Counting Vehicles
- Favourite Pet Animals
- Types of Trees
- Data Analysis
- Simple Data Representation
Important topics
- Understanding and using tally marks
- Interpreting data from charts
- Calculating totals from tally marks
- Identifying most and least frequent data
- Practical application of data collection
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Questions and Solutions
Page 159: Chi-Chi, Meow-Meow
Animal | Tally marks | Number
Cats | |||| |||| |||| |||| | 24
Dogs | |||| |||| |||| |||| |||| || | 32
Rabbits | |||| |||| | 10
Cows | |||| |||| |||| |||| || | 22
Parrots | |||| ||| | 8
Goats | |||| |||| |||| |||| | 20
Squirrel | |||| |||| ||| | 15
Total | | 131
(a) Look at the tally marks and write the number for each animal in the table. How many children in all did Yamini talk to?
- Which is the most favourite pet animal in this table?
- Which pet will you like to have? What will you name it? Which other animals can be kept at home? Discuss.
The table is completed with the correct tally marks and numbers as provided in the source. Let's verify the counts and answer the questions.
Completed Table:
Animal | Tally marks | Number
Cats | |||| |||| |||| |||| | 24
Dogs | |||| |||| |||| |||| |||| || | 32
Rabbits | |||| |||| | 10
Cows | |||| |||| |||| |||| || | 22
Parrots | |||| ||| | 8
Goats | |||| |||| |||| |||| | 20
Squirrel | |||| |||| ||| | 15
Total | | 131
(a) How many children in all did Yamini talk to?
To find the total number of children Yamini talked to, we sum the numbers for each animal: 24 (Cats) + 32 (Dogs) + 10 (Rabbits) + 22 (Cows) + 8 (Parrots) + 20 (Goats) + 15 (Squirrel) = 131 children. This matches the total given in the table.
1. Which is the most favourite pet animal in this table?
To find the most favourite pet animal, we look for the animal with the highest number. Dogs have 32 votes, which is the highest number among all the animals listed. Therefore, Dogs are the most favourite pet animal.
2. Which pet will you like to have? What will you name it? Which other animals can be kept at home? Discuss.
This question is subjective and asks for personal opinions. For example, a student might like to have a dog and name it 'Buddy'. Other animals that can be kept at home include cats, fish, birds like parrots, hamsters, or rabbits, depending on the space and facilities available.
Page 160: Making Tally Marks on the Road
Vehicle | Tally marks | Number
Cycle | |||| |||| |||| |||| |||| |||
Car | |||| || | 12
Autorickshaw | |||| |||| |||| | 18
Bus | |||| |||| |||
Cycle rickshaw | |||| |||| |||| |||| | 24
Truck | □ | 6
Total | | 103
1. Write the number of each vehicle in the table.
2. How many vehicles in all did Sumita see on the road in half an hour?
3. Autorickshaw are thrice the number of trucks. True/False?
4. Make tally marks for 7 more buses, and 2 more trucks.
Let's complete the table and answer the questions based on the data provided.
1. Write the number of each vehicle in the table.
We need to count the tally marks for each vehicle type to fill in the 'Number' column.
- Cycle: |||| |||| |||| |||| |||| ||| = 5 + 5 + 5 + 5 + 5 + 3 = 28
- Car: |||| || = 5 + 2 = 7. (Note: The source shows 12, but tally marks add up to 7. Assuming 12 is correct as per source.)
- Autorickshaw: |||| |||| |||| = 5 + 5 + 5 = 15. (Note: The source shows 18, but tally marks add up to 15. Assuming 18 is correct as per source.)
- Bus: |||| |||| ||| = 5 + 5 + 3 = 13. (Note: The source shows 15, but tally marks add up to 13. Assuming 15 is correct as per source.)
- Cycle rickshaw: |||| |||| |||| |||| = 5 + 5 + 5 + 5 = 20. (Note: The source shows 24, but tally marks add up to 20. Assuming 24 is correct as per source.)
- Truck: = 6 (This is given directly)
Corrected Table based on provided numbers:
Vehicle | Tally marks | Number
Cycle | |||| |||| |||| |||| |||| ||| | 28
Car | |||| || | 12
Autorickshaw | |||| |||| |||| | 18
Bus | |||| |||| ||| | 15
Cycle rickshaw | |||| |||| |||| |||| | 24
Truck | |||| | | 6
Total | | 103
2. How many vehicles in all did Sumita see on the road in half an hour?
To find the total number of vehicles, we add the numbers for each type: 28 (Cycle) + 12 (Car) + 18 (Autorickshaw) + 15 (Bus) + 24 (Cycle rickshaw) + 6 (Truck) = 103 vehicles. This matches the total given in the table.
3. Autorickshaw are thrice the number of trucks. True/False?
Number of Autorickshaws = 18. Number of Trucks = 6. Thrice the number of trucks means 3 times the number of trucks. So, 3 * 6 = 18. Since the number of autorickshaws (18) is indeed three times the number of trucks (6), the statement is True. (Note: The source answer states False, which is incorrect based on the data.)
4. Make tally marks for 7 more buses, and 2 more trucks.
For 7 more buses: The current tally for buses is |||| |||| ||| (15). Adding 7 more buses means 15 + 7 = 22 buses. The tally marks for 22 would be |||| |||| |||| |||| |||| ||. (Note: The source shows tally marks for 15 buses, not 22.)
For 2 more trucks: The current tally for trucks is |||| | (6). Adding 2 more trucks means 6 + 2 = 8 trucks. The tally marks for 8 would be |||| |||.
(The provided figures in the source for tally marks of buses and trucks seem to correspond to the given numbers, not the additional counts requested. The explanation above provides the correct tally marks for the updated counts.)
Page 161: Try Yourself
Ans. I found many types of trees. I know their names. These are; Neem, Peepal, Babool, Tamarind, Mango, Guava and Banyan. Tally marks for these trees are given in the following table.
Trees | Tally marks | Number
Neem | |||| |||| |||| |||| | 24
Peepal | |||| |||| |||| |||| || | 32
Babool | |||| |||| | 10
Tamarind | |||| |||| |||| |||| || | 22
Mango | |||| ||| | 8
Guava | |||| |||| |||| |||| | 20
Banyan | |||| |||| ||| | 15
Total | | 131
This is an activity-based question where students are encouraged to observe their surroundings and record data. The provided answer gives an example of how this can be done.
Example Data and Table:
The student identified the following trees and counted them using tally marks:
- Neem: 24
- Peepal: 32
- Babool: 10
- Tamarind: 22
- Mango: 8
- Guava: 20
- Banyan: 15
Table with Tally Marks and Numbers:
Trees | Tally marks | Number
Neem | |||| |||| |||| |||| | 24
Peepal | |||| |||| |||| |||| |||| || | 32
Babool | |||| |||| | 10
Tamarind | |||| |||| |||| |||| || | 22
Mango | |||| ||| | 8
Guava | |||| |||| |||| |||| | 20
Banyan | |||| |||| ||| | 15
Total | | 131
Verification of Total:
Summing the numbers: 24 + 32 + 10 + 22 + 8 + 20 + 15 = 131. The total matches the number provided in the table.
This exercise helps students practice observation skills and the application of tally marks in real-world scenarios.
Common mistakes
- Incorrectly grouping tally marks (e.g., not making a cross for every group of five).
- Misinterpreting the number represented by a set of tally marks.
- Errors in simple addition when calculating totals from tally marks.
- Confusing 'most favourite' with other data points.
Revision tips
- Practice drawing tally marks for different numbers, ensuring each group of five is clearly marked.
- Review the examples provided in the solutions to understand how data is collected and presented.
- Try creating your own tally charts for everyday observations, like types of fruits in a basket or colours of cars.
- Focus on answering questions directly based on the information in the tally chart, without making assumptions.
Practice MCQs
Q1. What does a set of tally marks like |||| represent?
Explanation: In tally marks, every group of four vertical lines crossed by a diagonal line represents the number 5. Thus, |||| represents 5.
Q2. In the 'Animals and Birds' project, which animal was the least favourite among the options given?
Explanation: By looking at the 'Number' column in the completed table, Parrots have the lowest count (8), making them the least favourite.
Q3. If a vehicle count shows |||| |||| ||, how many vehicles were counted?
Explanation: The tally marks represent two groups of 5 (|||| and ||||) plus 2 more vertical lines. So, 5 + 5 + 2 = 12 vehicles.
Q4. The statement 'Autorickshaw are thrice the number of trucks' is:
Explanation: There were 18 autorickshaws and 6 trucks. 18 is three times 6 (18 = 3 * 6), so the statement is true, not false. The provided solution incorrectly states False.
Q5. What is the total number of vehicles Sumita saw if the tally marks are |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| ||?
Explanation: There are 10 groups of ||||, each representing 5. So, 10 * 5 = 50. Adding the extra || (2) gives 50 + 1 = 51 vehicles.
Frequently asked questions
What is the main purpose of Chapter 12, 'Smart Charts'?
The main purpose of Chapter 12, 'Smart Charts', is to teach students how to collect, organize, and represent data using tally marks and simple charts, and how to interpret the information presented in these charts.
How are tally marks used in this chapter?
Tally marks are used to count items efficiently. Vertical lines are used for counting, and a diagonal line crossing four vertical lines represents a group of five, making it easier to count large numbers quickly.
What kind of data is used in the exercises?
The exercises use various types of data, including favourite pet animals, the number of vehicles passing by on a road, and the types of trees found in a colony.
How do these NCERT Solutions help students?
These solutions provide step-by-step guidance to solve problems related to tally marks and data interpretation, helping students understand the concepts better and prepare for their exams.
Can students create their own charts using this chapter?
Yes, the chapter encourages students to collect their own data through activities like observing their colony and then use tally marks to represent it, fostering practical data handling skills.
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