Smart Charts — Class 5 Mathematics (CBSE)
Based on the NCERT Math Magic Grade 5 textbook. Learn to read and make charts, then solve the practice set without looking at the answers.
1. Why this chapter matters
We see data everywhere — temperature charts in newspapers, election results on TV, cricket scores, and growth charts at the doctor. This chapter teaches students how to collect, organise, and represent data using different types of charts: tally marks, bar graphs, pie charts, and line graphs. Interpreting data is a key life skill that helps in making informed decisions. This prepares students for statistics in higher classes.
2. Collecting and organising data
Data means information. We collect data by observing, counting, or measuring.
Example: A class survey on favourite fruits.
| Fruit | Tally marks | Number of students |
|---|---|---|
| Apple | IIII | 4 |
| Banana | 6 | |
| Mango | 10 | |
| Orange | III | 3 |
| Grapes | 5 |
Total students surveyed = 4 + 6 + 10 + 3 + 5 = 28
Tally marks
Tally marks are a quick way to count. Each mark represents one item. A group of five is shown as IIII (four vertical lines crossed by a horizontal line).
3. Bar graphs
A bar graph uses rectangular bars of different heights to show data. The height of each bar shows the value.
Parts of a bar graph
- Title: Tells what the graph is about.
- X-axis (horizontal): Shows categories.
- Y-axis (vertical): Shows values (numbers).
- Scale: Tells how much each unit on the axis represents.
- Bars: Rectangles of equal width, height showing the value.
Drawing a bar graph
Example: Number of books read by students in a week.
| Student | Books read |
|---|---|
| Amit | 4 |
| Bina | 7 |
| Chetan | 3 |
| Deepa | 5 |
| Esha | 6 |
Steps:
- Draw the X-axis and label it with student names.
- Draw the Y-axis with a scale (1 unit = 1 book) from 0 to 8.
- Draw bars of equal width to the height matching each value.
- Add a title: 'Books Read by Students in a Week'.
Reading a bar graph
From the graph above:
- Who read the most books? Bina (7 books).
- Who read the least? Chetan (3 books).
- How many more books did Bina read than Chetan? 7 — 3 = 4 more books.
4. Pie charts
A pie chart (also called a circle chart) shows data as slices of a circle. Each slice represents a part of the whole.
Example
Favourite colours of 40 students:
| Colour | Number of students | Fraction of total |
|---|---|---|
| Red | 10 | 10/40 = 1/4 |
| Blue | 15 | 15/40 = 3/8 |
| Green | 5 | 5/40 = 1/8 |
| Yellow | 10 | 10/40 = 1/4 |
In a pie chart:
- The whole circle represents 40 students.
- Red takes 1/4 of the circle (90° angle).
- Blue takes 3/8 of the circle (135° angle).
- Green takes 1/8 of the circle (45° angle).
- Yellow takes 1/4 of the circle (90° angle).
Reading a pie chart
From the pie chart above:
- Which colour is most popular? Blue (15 students, 3/8 of the class).
- Which colour is least popular? Green (5 students, 1/8 of the class).
- Which two colours have equal popularity? Red and Yellow (10 students each).
5. Line graphs (introduction)
A line graph shows how something changes over time. Points are plotted and connected with a line.
Example
Temperature in a city over a day:
| Time | Temperature (°C) |
|---|---|
| 6:00 AM | 18 |
| 9:00 AM | 22 |
| 12:00 PM | 28 |
| 3:00 PM | 30 |
| 6:00 PM | 26 |
| 9:00 PM | 22 |
From the line graph:
- When was the temperature highest? At 3:00 PM (30°C).
- When was it lowest? At 6:00 AM (18°C).
- Did the temperature rise or fall between 12 PM and 3 PM? It rose (28°C to 30°C).
- Between 3 PM and 9 PM, the temperature fell steadily.
Parts of a line graph
- Title: Tells what the graph shows.
- X-axis: Usually shows time (hours, days, months).
- Y-axis: Shows the measured quantity (temperature, height, etc.).
- Scale: Both axes need a scale.
- Points: Plotted for each data pair.
- Line: Connects the points in order.
6. Choosing the right chart
| Type of data | Best chart | Example |
|---|---|---|
| Categories to compare | Bar graph | Favourite fruits, marks in subjects |
| Parts of a whole | Pie chart | How you spend your day (hours) |
| Change over time | Line graph | Temperature, plant growth, savings |
| Counting items quickly | Tally chart | Survey results, attendance |
7. Activity corner
Activity 1: Survey 20 classmates on their favourite subject (Maths, English, EVS, Hindi, Art). Record using tally marks. Draw a bar graph.
Activity 2: Track the time you spend on different activities in a day (school, play, study, sleep, eat, other). Show the data as a pie chart.
Activity 3: Measure the height of a plant (or your own height) every week for 4 weeks. Plot the data on a line graph.
8. Common mistakes
- Mistake: Drawing bars of different widths in a bar graph Fix: All bars should have the same width. Only the height should vary.
- Mistake: Not labelling axes Fix: Always label both the X-axis and Y-axis clearly. Write the units.
- Mistake: Choosing the wrong graph type Fix: Use bar graphs for comparing categories, pie charts for parts of a whole, and line graphs for change over time.
- Mistake: Not choosing a proper scale Fix: The scale should fit the data comfortably. If the largest value is 75, use 1 unit = 5 or 10, not 1 unit = 1.
9. Key facts
- Data is collected information. Organise it using tally marks or tables.
- Bar graphs compare quantities across categories.
- Pie charts show how a whole is divided into parts.
- Line graphs show change over time.
- Every graph needs a title, labelled axes, and a scale.
- Choose the chart type based on what you want to show.
- Practise by collecting your own data and making charts.
10. Self-test
- What is a tally mark? How do you show 5 items with tally marks?
- A bar graph shows books read by 5 students. Bina's bar goes up to 7. Deepa's goes up to 5. How many more books did Bina read?
- What chart type is best for showing how you spend 24 hours?
- In a pie chart of favourite colours, blue takes 1/4 of the circle. If 40 students were surveyed, how many chose blue?
- A line graph shows temperature at 9 AM = 20°C and at 12 PM = 26°C. Did it rise or fall? By how much?
11. Answer key
-
What is a tally mark? How do you show 5 items with tally marks? Answer: A tally mark is a quick counting symbol. Five items are shown as four vertical lines crossed by a horizontal line (
IIII). -
A bar graph shows books read by 5 students. Bina's bar goes up to 7. Deepa's goes up to 5. How many more books did Bina read? Answer: Bina read 7 — 5 = 2 more books than Deepa.
-
What chart type is best for showing how you spend 24 hours? Answer: A pie chart, because it shows parts of a whole (24 hours).
-
In a pie chart of favourite colours, blue takes 1/4 of the circle. If 40 students were surveyed, how many chose blue? Answer: 1/4 of 40 = 40 / 4 = 10 students.
-
A line graph shows temperature at 9 AM = 20°C and at 12 PM = 26°C. Did it rise or fall? By how much? Answer: The temperature rose by 26 — 20 = 6°C.
12. Quick revision
- Collect and organise data using tally marks or frequency tables.
- Bar graphs: compare categories with bars of different heights.
- Pie charts: show parts of a whole as slices.
- Line graphs: show change over time.
- Always label the title, axes, and scale.
- Practise by collecting real data from your class or home.
- Choose the right chart for your data type.
