Data Analysis: Finding Equal Values in Student-Ball Number Table

Q: How do I know which operation to try first?

When one number is much larger than the other (like 2 balls vs 100 students), try multiplication or division first. Addition and subtraction work better when numbers are closer in size.

Q: What if I get the wrong operation?

No problem! Just test it with all the data pairs. If 2 + 98 = 100 but 4 + 98 ≠ 200, then addition isn't the right pattern. Keep trying until one operation works for every pair.

Q: Do I need to check all three pairs in the table?

Yes, always! One pair might work by coincidence. Testing all pairs ensures you've found the true pattern that governs the entire relationship.

Q: What if the pattern doesn't work perfectly?

In math problems like this, there should be a perfect pattern. If your operation doesn't work for all pairs, try a different one. Look for patterns like $ \times 2 $, $ \div 3 $, or $ + 10 $.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the pattern between the number of students and the number of balls

00:03 It seems that each time we divide the number of students by 50

00:09 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

The following table shows the number of balls and the number of students in a certain school.

Complete:

The number of balls ______ is equal to the number of students.

2

Step-by-step solution

To solve this problem, we can follow these logical steps:

Step 1: Identify the pattern in the relationships between balls and students.
Step 2: Test a basic arithmetic operation to see which consistently relates the number of balls to the number of students.
Step 3: Verify calculation consistency across all pairs in the table.

Let's begin: From the table, we have the following mappings:

For 2 balls, there are 100 students. Testing $\text{balls} \times 50 = 2 \times 50 = 100$ .
For 4 balls, there are 200 students. Testing $\text{balls} \times 50 = 4 \times 50 = 200$ .
For 6 balls, there are 300 students. Testing $\text{balls} \times 50 = 6 \times 50 = 300$ .

In each case, multiplying the number of balls by 50 gives the number of students, confirming the relationship: The number of balls multiplied by 50 is equal to the number of students.

Thus, the correct operation to fill in the blank is "multiplied by 50."

Therefore, the number of balls multiplied by 50 is equal to the number of students.

3

Final Answer

multiplied by 50

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Look for consistent arithmetic operations between paired values
Testing Method: Try balls × 50: 2 × 50 = 100 students
Verification: Check all pairs: 4 × 50 = 200, 6 × 50 = 300 ✓

Common Mistakes

Avoid these frequent errors

Assuming addition or subtraction patterns first
Don't immediately try adding or subtracting numbers like 2 + 98 = 100! Large differences between small and large numbers usually indicate multiplication or division relationships. Always test multiplication patterns first when one number is much larger than the other.

Practice Quiz

Test your knowledge with interactive questions

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

FAQ

Everything you need to know about this question

How do I know which operation to try first?

+

When one number is much larger than the other (like 2 balls vs 100 students), try multiplication or division first. Addition and subtraction work better when numbers are closer in size.

What if I get the wrong operation?

+

No problem! Just test it with all the data pairs. If 2 + 98 = 100 but 4 + 98 ≠ 200, then addition isn't the right pattern. Keep trying until one operation works for every pair.

Why is it 'balls multiplied by 50' and not 'students divided by 50'?

+

Both are mathematically correct! The question asks for the relationship starting with 'The number of balls...' so we need to describe what happens to the balls to get students: balls × 50 = students.

Do I need to check all three pairs in the table?

+

Yes, always! One pair might work by coincidence. Testing all pairs ensures you've found the true pattern that governs the entire relationship.

What if the pattern doesn't work perfectly?

+

In math problems like this, there should be a perfect pattern. If your operation doesn't work for all pairs, try a different one. Look for patterns like $\times 2$ , $\div 3$ , or $+ 10$ .

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Data Analysis: Finding Equal Values in Student-Ball Number Table

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