Official Grade: 54.5 / 60 (90.8% — Grade A) • Total Time: 1h 04m 28s • Completed September 21, 2026.
Test Submitted & Graded
Official Grade: 54.5 / 60 (90.8% — Grade A) • Autograded: 53 / 60
Total Time Taken: 1h 04m 28s
All answers have been evaluated. See correct answers and step-by-step solutions below.
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
Completed
a. Use the place value chart to write 406,208.
Hundred thousands
Ten thousands
Thousands
Hundreds
Tens
Ones
CorrectCorrectCorrectCorrectCorrectCorrect
b. What is the value of the digit 6 in 406,208?
Half Credit (0.5 / 1 pt)
c. A place-value model has 3 thousand blocks, 5 hundred flats, 0 ten rods, and 7 ones. What number does the model show?
Place Name vs. Digit Value: When a problem asks for the value of the digit, write the number it is worth: 6,000. Writing just the place name ("thousands") identifies the place, but not the digit's total numerical value ($6 \times 1,000 = 6,000$).
2. Number forms
Completed
The number is 508,042.
a. Write 508,042 in expanded form.
Correct
b. Write 508,042 in word form.
Correct
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
Completed
a. Complete the equation so both sides have the same value.
Pay Attention to the Unit Label (Tens): 81 ones × 10 = 810. But notice the box already says tens! 810 is equal to 81 tens because 81 × 10 = 810. Writing 810 tens would mean 8,100.
Similarly in Part d: 66 hundreds = 6,600 ÷ 10 = 660. Because the label is tens, convert 660 into tens: 66 tens.
5. Compare multi-digit numbers
Completed
Complete each comparison by writing <, >, or =.
a. 407,090 Correct 407,900
b. 8,870 Correct 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
Completed
Use each digit exactly once: 0, 2, 4, 4, 7, 9
a. Write the greatest possible six-digit number.
Correct
b. Write the smallest possible six-digit number.
Correct
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
Completed
Round 64,372 to the nearest hundred.
Correct
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
Completed
Round 746,154 to each place value.
a. Nearest 100,000
Correct
b. Nearest 10,000
Correct
c. Nearest 1,000
Correct
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
Completed
A museum had 28,642 visitors last month. Round the number of visitors to the nearest thousand.
Correct
Solution & Answer Key
29,000 visitors (Look at the hundreds digit 6: since 6 ≥ 5, round 8 up to 9).
10. Rounding reasoning
Completed
a. Which digit makes the statement true?
53,□72 rounds to 53,500 when rounded to the nearest hundred.
Correct
b. A whole number rounds to 28,000 when rounded to the nearest thousand.
Least possible whole number
Incorrect (0 / 1 pt)
Greatest possible whole number
Incorrect (0 / 1 pt)
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
Concept & Review Note (Part b)
Finding the Rounding Range for 28,000: When rounding to the nearest thousand:
• The least whole number that rounds up to 28,000 is 27,500 (hundreds digit 5 pushes 27 up to 28).
• The greatest whole number that stays rounded down to 28,000 is 28,499 (because 28,500 would round up to 29,000!). 28,500 and 28,999 both round up to 29,000.
11. Addition
Completed
a. 468 + 257 = Correct
b. Add. Show your work.
408,736
+ 57,894
───────────
Correct
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
Completed
a. 704 − 286 = Correct
b. Subtract. Show your work.
500,024
− 268,759
───────────
Incorrect (0 / 1 pt)
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
Concept & Review Note (Part b)
Regrouping Across Consecutive Zeros: When subtracting $500,024 - 268,759$, you borrow across the zeros from 5 hundred-thousands down to the tens. In the hundreds place, the regrouped 9 minus 7 gives 2 hundreds (giving $231,\mathbf{2}65$). Always check multi-digit subtraction by adding: $231,265 + 268,759 = 500,024$!
Unit 3 — Multiply by 1-Digit Numbers
13. “Times as many”
Completed
a. 24 is Correct 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.
Accepted (Full Credit)
How many shells did Eli collect?
Correct
Solution & Answer Key
a.4 (24 = 4 × 6) b. Equation:7 × E = 42 (or E × 7 = 42) Eli collected:6 shells (42 ÷ 7 = 6)
Concept & Review Note (Part b)
Variables in Comparison Equations: Writing 7 × 6 = 42 proves you know Eli collected 6 shells! When asked to write an equation with a letter variable $E$, write the equation with the letter first: 7 × E = 42, and then solve for Eli: E = 6.
14. Multiply by 10, 100, 1,000, and their multiples