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

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.

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.

This model shows 4,231.

Check yourself

In 731,506: What digit is in the ten-thousands place? What is the value of the 3? A model has 6 thousands, 2 hundreds, 0 tens, and 9 ones. What number is shown?

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.

Check yourself

Write 604,219 in expanded form and word form.

3. Regrouping place values

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

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

52,610 = 4 ten thousands + ___ thousands + 6 hundreds + 1 ten. Also, 8 thousands = ___ hundreds.

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.

Check yourself

680 × 10; 680 ÷ 10; 54 hundreds × 10 = ___ thousands; 91 hundreds ÷ 10 = ___ tens.

5. Comparing multi-digit numbers

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

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

Check yourself

620,401 ___ 620,041. Then compare 9,204 to nine thousand, two hundred forty.

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.

Check yourself

Using 0, 2, 2, 5, 7, 8 exactly once, make the greatest and smallest six-digit numbers.

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.

Check yourself

Round 43,261 to the nearest hundred.

8. Rounding the same number to different places

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

Check yourself

Round 326,581 to the nearest 100,000, 10,000, and 1,000.

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.

Check yourself

A library recorded 17,438 visits. Round to the nearest thousand.

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.

Check yourself

82,□63 rounds to 82,500 to the nearest hundred. Then find the least and greatest whole numbers that round to 64,000 to the nearest thousand.

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.

Check yourself

639 + 184. Then 217,645 + 58,789.

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.

Check yourself

903 − 487. Then 600,014 − 257,868.

13. “Times as many” problems

“Times as many” means multiplication.

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

Check yourself

45 is ___ times as many as 9. Ava has 32 cards, which is 4 times as many as Ben. Write an equation and find Ben’s number of cards.

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

Use the basic fact first, then use place value.

Check yourself

9 × 10, 9 × 100, 9 × 1,000. Then 4 × 60, 4 × 600, 4 × 6,000.

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.

Check yourself

Use an area model and a break-apart equation to solve 5 × 68.

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.

Check yourself

Use place-value partial products to solve 4 × 3,207.

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.

Check yourself

Estimate 6 × 4,382 by rounding 4,382 to the nearest thousand first.

18. Multiplication procedures

No regrouping

Partial products

Regrouping

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

Check yourself

Multiply without regrouping: 3 × 2,012. Use partial products: 5 × 1,304. Multiply with regrouping: 2,768 × 7.