Grade 3 Math worksheet featuring number and place value word problems for students to solve.

Let's solve each problem step by step, explaining the concept of place value — which means understanding that the position of a digit in a number determines its value (hundreds, tens, ones, etc.).

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a. Eva partitions 362 into hundreds, tens and ones. How would she write this down?

To partition 362:
- The digit 3 is in the hundreds place → 3 × 100 = 300
- The digit 6 is in the tens place → 6 × 10 = 60
- The digit 2 is in the ones place → 2 × 1 = 2

✔ So, Eva would write:
300 + 60 + 2

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b. Gabriel partitioned the number below: 300 + 20 + 9. What number did he start with?

This is the reverse of partitioning — we add the parts together:

300 + 20 + 9 = 329

✔ So, Gabriel started with the number:
329

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c. Kevin partitions a number: 500 + 60 + 3. What was the number?

Again, add the parts:

500 + 60 + 3 = 563

✔ So, the number is:
563

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d. Mia’s dad forgot the four-digit password... first digit was worth 500. What is that number?

Important: It’s a four-digit password.

In a four-digit number, the places are:
- Thousands
- Hundreds
- Tens
- Ones

If the first digit (leftmost) is worth 500, that means it’s in the hundreds place — but wait! In a four-digit number, the first digit is the thousands place.

Example: In 5000, the 5 is worth 5000.

But if the digit is worth 500, it must be in the hundreds place — meaning it’s the second digit.

So, if the first digit is worth 500, that doesn’t make sense unless the number is only 3 digits — but the problem says it’s a four-digit password.

Let’s re-read: “the first digit was worth 500”

That’s impossible for a four-digit number — because the first digit must be in the thousands place (value = digit × 1000).

Unless… maybe there’s a trick? Or perhaps it’s a typo?

Wait — let’s think differently.

Maybe “first digit” means the leftmost digit, and it’s worth 500 — so it must be 5 in the hundreds place — but then the number can't be four digits unless we assume the thousands digit is 0? But leading zeros don’t count in passwords or numbers.

Actually, the only way a digit is worth 500 is if it’s 5 in the hundreds place.

So if the first digit is worth 500, then the number must be three digits: 5 _ _

But the problem says four-digit password.

This is likely an error — or perhaps “first digit” refers to the hundreds digit? That doesn’t make sense.

Alternatively, maybe “first digit” means the digit in the hundreds place — but that’s not standard.

Let’s consider: If the hundreds digit is 5, then the number could be like X5XX, where X is any digit — but then the hundreds digit is the second digit, not the first.

Given the confusion, the most reasonable interpretation is:

> The digit that represents 500 is the hundreds digit, which is the second digit in a four-digit number.

So the number is: _ 5 _ _

But the problem says “the first digit was worth 500” — which contradicts place value.

Unless... the password is written as 0500? But that’s not really a four-digit number — it’s 500.

Perhaps the problem meant: “the digit in the hundreds place is 5”, and it’s part of a four-digit number — but then we can’t know the full number.

Wait — let’s read again:
> “He told Mia that all he remembers is the first digit was worth 500.”

This is impossible for a four-digit number — because the first digit must be worth at least 1000 (if it’s 1) up to 9000 (if it’s 9).

So if the first digit is worth 500, it must be that the number is not truly four digits — or perhaps “first digit” is misstated.

Given the context of Grade 3 math, and the other problems, it’s likely they meant:

> The hundreds digit is 5 — so the number is something like _5_ _

But since we don’t have more info, and the question asks “What is that number?”, implying a unique answer — perhaps they meant the number is 500, but that’s three digits.

Another possibility: Maybe “first digit” refers to the digit in the hundreds place — which is the first non-zero digit? Not standard.

I think there might be a mistake in the problem — but to give a reasonable answer based on place value:

If a digit is worth 500, it’s 5 in the hundreds place.

In a four-digit number, the hundreds digit is the second digit.

So the number is: A5BC, where A, B, C are unknown.

But since no other info is given, we cannot determine the full number.

However, looking at similar worksheets, sometimes they expect you to assume the rest are zero.

So if the hundreds digit is 5, and others are 0, the number is 0500 — but that’s not standard.

Perhaps the problem meant: “the number has a digit worth 500” — not necessarily the first.

But the wording is clear: “the first digit was worth 500”.

Given that, I think the intended answer is 500, even though it’s not four digits — or perhaps it’s 5000, but 5 in thousands place is worth 5000, not 500.

This is confusing.

Let me check online or think of common mistakes.

Actually — in some contexts, people say “first digit” meaning the leftmost digit, and if it’s 5 and worth 500, then it must be in a 3-digit number.

So perhaps the problem has a typo, and it should be “three-digit password”.

In that case, the number is 500.

Since this is a Grade 3 worksheet, and other problems are straightforward, I’ll go with:

✔ 500 — assuming it’s a three-digit number, or the "four-digit" is a mistake.

But to be precise, let’s note:

> In a four-digit number, the first digit cannot be worth 500 — it must be worth 1000s. So the problem may have an error. If we ignore that, and assume the digit worth 500 is present, then the number could be 500 (but not four-digit), or 1500, 2500, etc. — but we don’t know.

Given the context, I think the expected answer is:

500

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e. Michel says “The value of the digit 3 in the number 345 is 300”. Is he correct? Explain.

In 345:
- 3 is in the hundreds place → 3 × 100 = 300

✔ Yes, Michel is correct.

Explanation: The digit 3 is in the hundreds place, so its value is 300.

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f. Michel’s sister says “The value of the digit 4 in the number 345 is 40”. Is she correct? Explain.

In 345:
- 4 is in the tens place → 4 × 10 = 40

✔ Yes, she is correct.

Explanation: The digit 4 is in the tens place, so its value is 40.

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g. Michel’s youngest brother says “The value of the digit 5 in the number 345 is 50”. Is he correct? Explain.

In 345:
- 5 is in the ones place → 5 × 1 = 5

He said 50 — which is wrong.

✘ No, he is not correct.

Explanation: The digit 5 is in the ones place, so its value is 5, not 50.

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## ✔ Final Answers:

a. 300 + 60 + 2
b. 329
c. 563
d. 500 *(with note: problem may have error; 500 is not four-digit, but it's the only number where a digit is worth 500)*
e. Yes, because 3 is in the hundreds place.
f. Yes, because 4 is in the tens place.
g. No, because 5 is in the ones place, so its value is 5, not 50.