Khan 4th Grade Math Diagnostic

Units 1–3 (18 Questions)
Suggested time: 60 minutes
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4th Grade Math Diagnostic — Units 1–3

Suggested time: 60 minutes. Answer every question on your own. No calculator, Khan Academy, hints, or answer checking. Show your work for addition, subtraction, and multiplication.

Unit 1 — Place Value

1. Place-value representations

Saved

a. Use the place value chart to write 406,208.

Hundred thousands
Ten thousands
Thousands
Hundreds
Tens
Ones

b. What is the value of the digit 6 in 406,208?

c. A place-value model has 3 thousand blocks, 5 hundred flats, 0 ten rods, and 7 ones. What number does the model show?

✓ Solution & Answer Key

a. Hundred thousands: 4, Ten thousands: 0, Thousands: 6, Hundreds: 2, Tens: 0, Ones: 8
b. 6,000 (6 thousands)
c. 3,507 (3,000 + 500 + 0 + 7)

2. Number forms

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The number is 508,042.

a. Write 508,042 in expanded form.

b. Write 508,042 in word form.

✓ Solution & Answer Key

a. Expanded form: 500,000 + 8,000 + 40 + 2
b. Word form: five hundred eight thousand, forty-two

3. Regrouping place values

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a. Complete the equation so both sides have the same value.

64,320 = 6 ten thousands + 4 thousands + 3 hundreds + 2 tens
64,320 = 5 ten thousands + thousands + 3 hundreds + 2 tens

b. Regroup the number to express the value in a different way.

7 thousands = hundreds

✓ Solution & Answer Key

a. 14 (Regroup 1 ten thousand into 10 thousands: 4 + 10 = 14 thousands)
b. 70 (1 thousand = 10 hundreds, so 7 thousands = 70 hundreds)

4. Multiply and divide by 10

Saved
a. 470 × 10 =
b. 470 ÷ 10 =
c. 81 ones × 10 = tens
d. 66 hundreds ÷ 10 = tens

✓ Solution & Answer Key

a. 4,700
b. 47
c. 81 (81 ones × 10 = 810 = 81 tens)
d. 66 (66 hundreds = 6,600; 6,600 ÷ 10 = 660 = 66 tens)

5. Compare multi-digit numbers

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Complete each comparison by writing <, >, or =.

a. 407,090 407,900
b. 8,870 eight thousand, seven hundred eighty

✓ Solution & Answer Key

a. < (407,090 < 407,900 because 0 hundreds < 9 hundreds)
b. > (8,870 > 8,780 because 8 hundreds > 7 hundreds)

6. Greatest and smallest numbers

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Use each digit exactly once: 0, 2, 4, 4, 7, 9

a. Write the greatest possible six-digit number.

b. Write the smallest possible six-digit number.

✓ Solution & Answer Key

a. Greatest: 974,420 (ordered largest to smallest)
b. Smallest: 204,479 (first digit nonzero: 2, then 0, then ascending order)

Unit 2 — Addition, Subtraction, and Estimation

7. Round to the nearest hundred

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Round 64,372 to the nearest hundred.

✓ Solution & Answer Key

64,400 (Look at the tens digit 7: since 7 ≥ 5, round hundreds digit 3 up to 4).

8. Round to different place values

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Round 746,154 to each place value.

a. Nearest 100,000

b. Nearest 10,000

c. Nearest 1,000

✓ Solution & Answer Key

a. Nearest 100,000: 700,000 (ten-thousands digit 4 rounds down)
b. Nearest 10,000: 750,000 (thousands digit 6 rounds up)
c. Nearest 1,000: 746,000 (hundreds digit 1 rounds down)

9. Rounding word problem

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A museum had 28,642 visitors last month. Round the number of visitors to the nearest thousand.

✓ Solution & Answer Key

29,000 visitors (Look at the hundreds digit 6: since 6 ≥ 5, round 8 up to 9).

10. Rounding reasoning

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a. Which digit makes the statement true?

53,□72 rounds to 53,500 when rounded to the nearest hundred.

b. A whole number rounds to 28,000 when rounded to the nearest thousand.

Least possible whole number

Greatest possible whole number

✓ Solution & Answer Key

a. 4 (Because tens digit 7 rounds the hundreds digit up by 1: 4 rounds up to 5, giving 53,500)
b. Least possible: 27,500
Greatest possible: 28,499

11. Addition

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a. 468 + 257 =

b. Add. Show your work.

408,736 + 57,894 ───────────

✓ Solution & Answer Key

a. 725 (8+7=15, 6+5+1=12, 4+2+1=7)
b. 466,630
  408,736
+  57,894
─────────
  466,630

12. Subtraction

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a. 704 − 286 =

b. Subtract. Show your work.

500,024 − 268,759 ───────────

✓ Solution & Answer Key

a. 418 (Regroup 700 to 690+14: 14-6=8, 9-8=1, 6-2=4)
b. 231,265
  500,024
− 268,759
─────────
  231,265

Unit 3 — Multiply by 1-Digit Numbers

13. “Times as many”

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a. 24 is times as many as 6.

b. Maya collected 42 shells. She collected 7 times as many shells as Eli. Let E represent the number of shells Eli collected.

Write a multiplication equation.

How many shells did Eli collect?

✓ Solution & Answer Key

a. 4 (24 = 4 × 6)
b. Equation: 7 × E = 42 (or E × 7 = 42)
Eli collected: 6 shells (42 ÷ 7 = 6)

14. Multiply by 10, 100, 1,000, and their multiples

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a. Multiply.

6 × 10 =
6 × 100 =
6 × 1,000 =

b. Multiply.

7 × 80 =
7 × 800 =
7 × 8,000 =

c. Fill in the blanks.

4 × 3,000 = 4 × 3 × 1,000
= × 1,000
=

✓ Solution & Answer Key

a. 60, 600, 6,000
b. 560, 5,600, 56,000
c. 12 × 1,000 = 12,000

15. Area model and break-apart rule: 2-digit × 1-digit

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The area model represents 6 × 47.

40
7
A
B

a. Find each partial area.



b. Find the total product.

c. Complete the break-apart equation.

6 × 47 = 6 × (40 + 7)
= (6 × ) + (6 × )

✓ Solution & Answer Key

a. Partial areas: A = 240 (6 × 40), B = 42 (6 × 7)
b. Total product: 282 (240 + 42 = 282)
c. (6 × 40) + (6 × 7)

16. Area model and break-apart rule: 4-digit × 1-digit

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The area model represents 4 × 1,326.

1,000
300
20
6
A
B
C
D

a. Find each partial area.







b. Write the sum of the partial products.

c. Find the total product.

✓ Solution & Answer Key

a. Partial areas: A = 4,000 (4 × 1,000), B = 1,200 (4 × 300), C = 80 (4 × 20), D = 24 (4 × 6)
b. Sum: 4,000 + 1,200 + 80 + 24
c. Total product: 5,304

17. Estimate a product

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Estimate 5 × 6,482.

a. Round 6,482 to the nearest thousand.

b. Use the rounded number to estimate the product.

✓ Solution & Answer Key

a. 6,000 (hundreds digit 4 rounds down to 6,000)
b. Estimated product: 30,000 (5 × 6,000 = 30,000)

18. Multiplication procedures

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a. Multiply without regrouping.

3 × 2,103 =

b. Complete the partial-products work for 2,104 × 8.

8 × 4 = 32 8 × 0 = 0
8 × 100 =
8 × 2,000 = 16,000
2,104 × 8 =

c. Multiply with regrouping. Show your work.

4,286 × 7 ───────

✓ Solution & Answer Key

a. 6,309 (3 × 2,103)
b. 8 × 100 = 800; 2,104 × 8 = 16,832
c. 30,002
  4,286
×     7
───────
 30,002