MATHEMATICS SUBJECT ENRICHMENT ACTIVITY Chapter: Proportional Reasoning – II Topic: Representation of Data Using Pie Chart

 

📘 MATHEMATICS SUBJECT ENRICHMENT ACTIVITY

Chapter: Proportional Reasoning – II

Topic: Representation of Data Using Pie Chart (Proportional Reasoning)

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🎯 Aim

To collect data on favourite sports of Class 8 students and represent the data proportionally using a pie chart, and to identify:

• The sport liked by maximum students

• The sport liked by minimum students

• Sports liked by equal number of students

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🧰 Materials Required

• Notebook

• Pen / Pencil

• Scale

• Compass

• Protractor

• Colour pencils / sketch pens

• Graph paper

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📊 Data Collection

A survey was conducted among 40 classmates of Class 8 to find their favourite sport.

Collected Data Table

Sport	Number of Students
Cricket	14
Football	10
Badminton	6
Volleyball	6
Basketball	4
Total	40

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🧮 Calculations (Proportional Reasoning)

Formula used:

$$\text{Angle of sector} = \frac{\text{Number of students}}{40} \times 360^\circ$$

Sport	Students	Fraction	Angle
Cricket	14	14/40	126°
Football	10	10/40	90°
Badminton	6	6/40	54°
Volleyball	6	6/40	54°
Basketball	4	4/40	36°

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🎨 Colourful Pie Chart

(Students should draw this pie chart neatly using the above angles and colour each sector differently.)

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🧑‍🏫 Procedure

1. Conduct a survey among 40 classmates.

2. Record the data in a table.

3. Convert the data into fractions of the total.

4. Calculate angles for each sport using proportional reasoning.

5. Draw a circle using a compass.

6. Mark angles with a protractor.

7. Colour each sector and label it clearly.

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👀 Observations

• Cricket occupies the largest sector.

• Basketball occupies the smallest sector.

• Badminton and Volleyball have equal-sized sectors.

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📝 Conclusion

• Maximum favourite sport: Cricket

• Minimum favourite sport: Basketball

• Same preference: Badminton and Volleyball

• Pie charts help us understand proportional relationships visually.

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💭 Reflection (Student Learning)

• I learned how fractions and ratios are used in real-life data.

• I understood the connection between angles and proportions.

• Drawing a pie chart improved my data handling and reasoning skills.

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🧠 Teacher’s Note (Assessment Link)

✔ Uses proportional reasoning
✔ Integrates data handling
✔ Encourages real-life application
✔ Supports visual learning

Competency-Based Questions (CBQs) perfectly aligned with
Class 8 – Ganita Prakash (Part 2)
Chapter: Proportional Reasoning – II
based on the Favourite Sports Pie Chart Activity.

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🧠 Competency-Based Questions

(Data Handling & Proportional Reasoning)

Case Study

A survey was conducted among 40 Class 8 students to find their favourite sport.
The data collected is shown below:

Sport	Students
Cricket	14
Football	10
Badminton	6
Volleyball	6
Basketball	4

The data is represented using a pie chart.

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🔹 Level 1: Understanding & Interpretation

1. What fraction of the students like Football?
a) 1/4
b) 1/5
c) 1/8
d) 3/10

2. Which sport is liked by the maximum number of students?

3. Name the sports which have equal representation in the pie chart.

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🔹 Level 2: Application of Proportional Reasoning

4. If the total number of students is 40, what angle represents Cricket in the pie chart?

5. The angle representing Basketball is:
a) 36°
b) 54°
c) 72°
d) 90°

6. If 1 student represents 9°, verify whether the angle for Badminton is correct.

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🔹 Level 3: Analysis & Reasoning

7. Compare the sectors of Cricket and Football.
Which is larger and why?

8. If 5 more students start liking Basketball, how will the angle of the Basketball sector change?

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🔹 Level 4: Higher-Order Thinking (HOTS)

9. If the number of students increases to 60 but the ratio of preferences remains the same, find the new angle for Cricket.

10. Why is a pie chart more suitable than a bar graph for showing proportional data in this activity?

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🔹 Assertion–Reason Type

11. Assertion (A): The total angle of all sectors in a pie chart is 360°.
Reason (R): A pie chart represents the whole data set as a circle.

a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is not the correct explanation of A
c) A is true but R is false
d) A is false but R is true

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🔹 Real-Life Application

12. How can this method of data representation help a school decide which sports facilities to improve?

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📝 Teacher Answer Key (Brief)

1. a)

2. Cricket

3. Badminton and Volleyball

4. 126°

5. a)

6. 6 × 9° = 54° ✔

7. Cricket, because it has more students

8. Angle increases proportionally

9. 126° (ratio unchanged)

10. Shows part-to-whole relationship clearly

11. a)

12. Helps in decision-making using data

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🎯 Competencies Assessed

✔ Data Interpretation
✔ Proportional Reasoning
✔ Mathematical Communication
✔ Critical Thinking
✔ Real-life Application