4th Grade Math Test Study Guide — Units 1–3

The examples use different numbers from the test, but the thinking, layouts, and question types are very similar.

Open Study Guide: Free review reference with worked examples and check-yourself problems. Note: Achieving 90% mastery on Khan Academy beforehand is strongly recommended to prepare for test scoring.

Unit 1 — Place Value

1. Place-value charts and models

A digit’s value depends on its place. Moving one place to the left makes its value 10 times as large. Moving one place to the right divides its value by 10.

Hundred thousands | Ten thousands | Thousands | Hundreds | Tens | Ones 5 | 8 | 2 | 4 | 0 | 6

In 582,406, the 8 is worth 80,000 and the 4 is worth 400. The 0 still matters because it holds the tens place.

Thousands: [1000] [1000] [1000] [1000] Hundreds: [100] [100] Tens: [10] [10] [10] Ones: [1]

This model shows 4,231.

Check yourself

In 731,506:

  • a What digit is in the ten-thousands place?
  • b What is the value of the 3?
  • c A model has 6 thousands, 2 hundreds, 0 tens, and 9 ones. What number is shown?
Show check-yourself answer
  • a 3
  • b 30,000
  • c 6,209
Your understanding:

2. Standard, expanded, and word form

Standard form is the usual number. Expanded form shows the value of each nonzero digit. Word form writes the number in words.

472,305
Expanded: 400,000 + 70,000 + 2,000 + 300 + 5
Word form: four hundred seventy-two thousand, three hundred five

Check yourself

For the number 604,219:

  • a Write 604,219 in expanded form.
  • b Write 604,219 in word form.
Show check-yourself answer
  • a 600,000 + 4,000 + 200 + 10 + 9
  • b six hundred four thousand, two hundred nineteen
Your understanding:

3. Regrouping place values

One unit in a place is equal to 10 units in the next place to the right.

1 ten thousand = 10 thousands 1 thousand = 10 hundreds 1 hundred = 10 tens 1 ten = 10 ones

73,240 can be written as 7 ten thousands + 3 thousands + 2 hundreds + 4 tens. Regrouping 1 ten thousand gives 6 ten thousands + 13 thousands + 2 hundreds + 4 tens. The total stays the same.

Check yourself

  • a 52,610 = 4 ten thousands + ___ thousands + 6 hundreds + 1 ten
  • b 8 thousands = ___ hundreds
Show check-yourself answer
  • a 12
  • b 80
Your understanding:

4. Multiplying and dividing by 10

When you multiply a whole number by 10, each digit moves one place left. When you divide by 10, each digit moves one place right.

530 × 10 = 5,300 530 ÷ 10 = 53 43 hundreds × 10 = 43 thousands 72 hundreds ÷ 10 = 72 tens

Check yourself

  • a 680 × 10 = ___
  • b 680 ÷ 10 = ___
  • c 54 hundreds × 10 = ___ thousands
  • d 91 hundreds ÷ 10 = ___ tens
Show check-yourself answer
  • a 6,800
  • b 68
  • c 54
  • d 91
Your understanding:

5. Comparing multi-digit numbers

Compare from left to right. The first place where the digits are different tells which number is larger.

512,407 < 512,470

If one number is written in words, rewrite it in standard form first.

thirty-four thousand, eight hundred = 34,800
34,080 < 34,800

Check yourself

  • a Compare using >, <, or = : 620,401 ___ 620,041
  • b Compare using >, <, or = : 9,204 ___ nine thousand, two hundred forty
Show check-yourself answer
  • a > (620,401 > 620,041)
  • b < (9,204 < 9,240)
Your understanding:

6. Greatest and smallest numbers

For the greatest number, put the largest digit first and continue from greatest to least. For the smallest number, use the smallest nonzero digit first, then 0, then the rest from smallest to largest.

Digits: 0, 1, 3, 6, 6, 8
Greatest = 866,310
Smallest = 103,668

Check yourself

Using the digits 0, 2, 2, 5, 7, 8 exactly once:

  • a Make the greatest six-digit number.
  • b Make the smallest six-digit number.
Show check-yourself answer
  • a 875,220
  • b 202,578
Your understanding:

Unit 2 — Addition, Subtraction, and Estimation

7. Rounding to the nearest hundred

Find the hundreds digit. Look at the tens digit. If the tens digit is 0–4, keep the hundreds digit. If it is 5–9, round up. Change the digits to the right to 0.

28,764 ≈ 28,800

Check yourself

  • Round 43,261 to the nearest hundred.
Show check-yourself answer
  • 43,300
Your understanding:

8. Rounding the same number to different places

583,742 nearest 100,000 → 600,000 nearest 10,000 → 580,000 nearest 1,000 → 584,000

Look exactly one digit to the right of the place you are rounding to.

Check yourself

Round 326,581 to the:

  • a nearest 100,000
  • b nearest 10,000
  • c nearest 1,000
Show check-yourself answer
  • a 300,000
  • b 330,000
  • c 327,000
Your understanding:

9. Rounding in a word problem

The story does not change the rounding rule. Find the number, find the place the problem asks for, then round.

43,687 visitors rounded to the nearest thousand = 44,000 visitors.

Check yourself

  • A library recorded 17,438 visits. Round this number to the nearest thousand.
Show check-yourself answer
  • 17,000
Your understanding:

10. Missing digits and reverse rounding

Missing digit: 61,□84 rounds to 61,700 to the nearest hundred. The tens digit is 8, so the hundreds digit rounds up by 1. The missing digit is 6.

Reverse rounding: Numbers from 34,500 through 35,499 round to 35,000 to the nearest thousand.

34,000 ---- 34,500 ===== 35,000 ===== 35,499 | 35,500 ---- 36,000

Check yourself

  • a 82,□63 rounds to 82,500 to the nearest hundred. What digit is missing in the box?
  • b What is the least whole number that rounds to 64,000 to the nearest thousand?
  • c What is the greatest whole number that rounds to 64,000 to the nearest thousand?
Show check-yourself answer
  • a 4
  • b 63,500
  • c 64,499
Your understanding:

11. Addition with regrouping

Line up place values. Add from right to left. When a place totals 10 or more, regroup 10 of that place as 1 of the next place.

586 + 247 ----- 833 325,708 + 46,936 --------- 372,644

Check yourself

  • a 639 + 184
  • b 217,645 + 58,789
Show check-yourself answer
  • a 823
  • b 276,434
Your understanding:

12. Subtraction with regrouping

Line up place values. Subtract from right to left. If the top digit is too small, regroup 1 from the place to the left. If the next place is 0, keep moving left until you find a digit that is not 0.

812 - 475 ----- 337 500,103 - 247,865 --------- 252,238

Check yourself

  • a 903 − 487
  • b 600,014 − 257,868
Show check-yourself answer
  • a 416
  • b 342,146
Your understanding:

Unit 3 — Multiply by 1-Digit Numbers

13. “Times as many” problems

“Times as many” means multiplication.

35 is 5 times as many as 7.
5 × 7 = 35

If a number is missing, write a multiplication equation and find the missing number.

Nora has 48 beads. She has 6 times as many as Leo.
6 × L = 48
L = 8

Check yourself

  • a 45 is ___ times as many as 9.
  • b Ava has 32 cards, which is 4 times as many as Ben. Write an equation and find Ben’s number of cards.
Show check-yourself answer
  • a 5
  • b 4 × B = 32, so B = 8
Your understanding:

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

8 × 10 = 80 8 × 100 = 800 8 × 1,000 = 8,000 6 × 70 = 420 6 × 700 = 4,200 6 × 7,000 = 42,000

Use the basic fact first, then use place value.

Check yourself

  • a Solve: 9 × 10, 9 × 100, and 9 × 1,000
  • b Solve: 4 × 60, 4 × 600, and 4 × 6,000
Show check-yourself answer
  • a 90, 900, 9,000
  • b 240, 2,400, 24,000
Your understanding:

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

Break the 2-digit number into tens and ones. Multiply each part, then add the smaller products.

7 × 53 53 = 50 + 3 7 × 50 = 350 7 × 3 = 21 350 + 21 = 371
50
3
350
21
7 × 53 = 7 × (50 + 3) = (7 × 50) + (7 × 3) = 371

Check yourself

  • Use an area model and a break-apart equation to solve 5 × 68.
Show check-yourself answer
  • 340  (5 × 60 = 300, 5 × 8 = 40; 300 + 40 = 340)
Your understanding:

16. 3- or 4-digit × 1-digit area model and break-apart rule

Break the larger number into place-value parts. Multiply each part by the 1-digit number, then add.

3 × 2,415 2,415 = 2,000 + 400 + 10 + 5 3 × 2,000 = 6,000 3 × 400 = 1,200 3 × 10 = 30 3 × 5 = 15 Total = 7,245
2,000
400
10
5
6,000
1,200
30
15

Check yourself

  • Use place-value partial products to solve 4 × 3,207.
Show check-yourself answer
  • 12,828  (4 × 3,000 = 12,000; 4 × 200 = 800; 4 × 7 = 28; 12,000 + 800 + 28 = 12,828)
Your understanding:

17. Estimating a product

An estimate is a close answer that is easier to find. Round the large number to the place the problem asks for, then multiply.

4 × 7,621 7,621 ≈ 8,000 4 × 8,000 = 32,000 So 4 × 7,621 ≈ 32,000

Check yourself

  • Estimate 6 × 4,382 by rounding 4,382 to the nearest thousand first.
Show check-yourself answer
  • 24,000  (4,382 ≈ 4,000; 6 × 4,000 = 24,000)
Your understanding:

18. Multiplication procedures

No regrouping

2 × 3,204 = 6,408

Partial products

3 × 1,206 3 × 1,000 = 3,000 3 × 200 = 600 3 × 0 = 0 3 × 6 = 18 Total = 3,618

Regrouping

3,487 × 6 ----------- 20,922

Multiply from right to left and add each regrouped amount at the next place.

Check yourself

  • a Multiply without regrouping: 3 × 2,012
  • b Use partial products: 5 × 1,304
  • c Multiply with regrouping: 2,768 × 7
Show check-yourself answer
  • a 6,036
  • b 6,520
  • c 19,376
Your understanding:

Check-yourself answers

Quick reference answer key for all 18 check-yourself practice problems:

1. Place-value charts and models
  • a 3
  • b 30,000
  • c 6,209
2. Standard, expanded, and word form
  • a 600,000 + 4,000 + 200 + 10 + 9
  • b six hundred four thousand, two hundred nineteen
3. Regrouping place values
  • a 12
  • b 80
4. Multiplying and dividing by 10
  • a 6,800
  • b 68
  • c 54
  • d 91
5. Comparing multi-digit numbers
  • a > (620,401 > 620,041)
  • b < (9,204 < 9,240)
6. Greatest and smallest numbers
  • a 875,220
  • b 202,578
7. Rounding to the nearest hundred
  • 43,300
8. Rounding to different places
  • a 300,000 (nearest 100,000)
  • b 330,000 (nearest 10,000)
  • c 327,000 (nearest 1,000)
9. Rounding in a word problem
  • 17,000
10. Missing digits & reverse rounding
  • a 4
  • b 63,500
  • c 64,499
11. Addition with regrouping
  • a 823
  • b 276,434
12. Subtraction with regrouping
  • a 416
  • b 342,146
13. “Times as many” problems
  • a 5
  • b 4 × B = 32, so B = 8
14. Multiply by 10, 100, 1,000
  • a 90, 900, 9,000
  • b 240, 2,400, 24,000
15. 2-digit × 1-digit area model
  • 340
16. 3- or 4-digit × 1-digit area model
  • 12,828
17. Estimating a product
  • 24,000
18. Multiplication procedures
  • a 6,036
  • b 6,520
  • c 19,376