Find the Number of Outstanding Students: Solving the Pen Distribution Problem

Q: How do I know each student gets exactly one pen?

The problem says the headteacher 'gives them all out' to outstanding students. In school contexts, awards like pens are typically given one per student to be fair and meaningful.

Q: Could some students get more than one pen?

While mathematically possible, this would be unusual for school awards. The most logical interpretation is that each outstanding student receives exactly one pen as recognition.

Q: What if the problem meant something different?

Always use the most straightforward interpretation unless told otherwise. In word problems, simple one-to-one relationships are the standard assumption.

Q: Is this problem too easy?

Simple problems teach important skills! This builds understanding of one-to-one correspondence and careful reading of word problems - essential foundations for harder math.

One-to-One Distribution with Basic Counting

A headteacher wants to buy pens to give to his most outstanding pupils.

He buys 10 pens and gives them all out to the students.

How many outstanding students are there?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose a number divisible by 10

00:04 A number divisible by 10 is a number that ends with 0

00:07 Let's check each number using this method and choose the number divisible by 10

00:22 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A headteacher wants to buy pens to give to his most outstanding pupils.

He buys 10 pens and gives them all out to the students.

How many outstanding students are there?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information - There are 10 pens in total.
Step 2: Understand the distribution - All pens are given out.
Step 3: Conclude - The number of students is equal to the number of pens.

Let's work through these steps:

Step 1: The problem states clearly that the headteacher bought a total of $10$ pens.

Step 2: As the headteacher gives out all the pens, each student receives exactly one pen.

Step 3: Since there are $10$ pens and each student gets one pen, it follows that there must be exactly $10$ students.

Therefore, the solution to the problem is that there are $10$ outstanding students.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Each item goes to exactly one person
Technique: Count total items: 10 pens = 10 students
Check: Verify each student gets one pen: 10 ÷ 10 = 1 per student ✓

Common Mistakes

Avoid these frequent errors

Assuming students share pens or get multiple pens
Don't assume 10 pens could serve 4 students with sharing = misreading the problem! The problem states each student gets pens (implying one each), not that pens are shared. Always read carefully that 'gives them all out' means one-to-one distribution.

Practice Quiz

Test your knowledge with interactive questions

Is the number 43 divisible by 4?

FAQ

Everything you need to know about this question

How do I know each student gets exactly one pen?

The problem says the headteacher 'gives them all out' to outstanding students. In school contexts, awards like pens are typically given one per student to be fair and meaningful.

Could some students get more than one pen?

While mathematically possible, this would be unusual for school awards. The most logical interpretation is that each outstanding student receives exactly one pen as recognition.

What if the problem meant something different?

Always use the most straightforward interpretation unless told otherwise. In word problems, simple one-to-one relationships are the standard assumption.

Why isn't the answer a smaller number like 4 or 6?

If there were only 4 students, what would happen to the other 6 pens? The problem states all pens are given out, so we need exactly 10 students to use all 10 pens.

Is this problem too easy?

Simple problems teach important skills! This builds understanding of one-to-one correspondence and careful reading of word problems - essential foundations for harder math.

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