Grade 3 Math Diagnostic Test covering place value, addition, and subtraction with illustrated questions.

Here's the solution to each problem on the worksheet, with a clear explanation for each:

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1. How many boys are behind the second boy?

Look at the row of 6 boys. The “second boy” is the one in red (second from the left). Behind him (to his right) are 4 boys: the one in purple, the one with the backpack, the one with the magnifying glass, and the one running.

✔ Answer: B. Four

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2. Which is the number 548 in expanded form?

Expanded form breaks the number into its place values:
- 5 is in the hundreds place → 500
- 4 is in the tens place → 40
- 8 is in the ones place → 8

So, 548 = 500 + 40 + 8

✔ Answer: C. 500 + 40 + 8

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3. Which is the standard form? 20,000 + 300 + 40 + 8

Add the numbers together:
- 20,000
- + 300 → 20,300
- + 40 → 20,340
- + 8 → 20,348

✔ Answer: B. 20,348

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4. Which statement is true?

Check each option:
- A. 5,678 > 4,321 → TRUE (5,678 is greater than 4,321)
- B. 2,300 > 6,782 → FALSE (2,300 is smaller)
- C. 555 = 5,555 → FALSE (different values)
- D. 6,453 < 3,546 → FALSE (6,453 is larger)

Only A is correct.

✔ Answer: A. 5,678 > 4,321

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5. What is the value of the underlined digit in 457,293?

Assuming the underlined digit is 7 (as it’s commonly underlined in such problems — if not specified, this is the most logical choice based on place value questions).

In 457,293:
- 4 = hundred thousands
- 5 = ten thousands
- 7 = thousands
- 2 = hundreds
- 9 = tens
- 3 = ones

So, 7 is in the thousands place → seven thousand

✔ Answer: D. seven thousand

*(Note: If a different digit was underlined, the answer would change. But since no underline is visible here, we assume 7 is intended.)*

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6. Use mental math to add: 43 + 26 = ___

Break it down:
- 40 + 20 = 60
- 3 + 6 = 9
- 60 + 9 = 69

✔ Answer: C. 69

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7. 40 - 22 = ___

Subtract:
- 40 - 20 = 20
- 20 - 2 = 18

✔ Answer: A. 18

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8. Compare: 20 + 3 ___ 32 - 5

Calculate both sides:
- Left: 20 + 3 = 23
- Right: 32 - 5 = 27

Now compare: 23 < 27

✔ Answer: A. <

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9. A farm has 397 orange trees and 208 apple trees. Which is the best estimate of the total number of trees?

Estimate by rounding:
- 397 ≈ 400
- 208 ≈ 200
- Total ≈ 400 + 200 = 600

Looking at options:
- A. 300 + 200 = 500 → too low
- B. 400 + 300 = 700 → too high
- C. 400 + 200 = 600 → best estimate
- D. 300 + 400 = 700 → too high

✔ Answer: C. 400 + 200

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✔ Final Answers:

1. B
2. C
3. B
4. A
5. D
6. C
7. A
8. A
9. C

Let me know if you’d like a printable version or step-by-step visuals!