Part A: Identify the Pattern

I can explain how powers of 10 change a number by using place value.

Success criteria: I can identify the pattern, use exponents, and explain how many places each digit shifts.

Reminder: A power of 10 shows repeated factors of 10. For example, 10^1 = 10, 10^2 = 100, and 10^3 = 1,000. Multiplying by a power of 10 shifts digits to greater place values. Dividing shifts digits to smaller place values.

4, 40, 400, 4,000    Pattern: Each number is multiplied by ______. Power: 10^______.

8,000, 800, 80, 8    Pattern: Each number is divided by ______. Power: 10^______.

0.6, 6, 60, 600

a. What operation changes 0.6 to 60? ____________________

b. How many place-value positions does each digit shift? ____________________

c. Write an equation using a power of 10: ________________________________

Part B: Multiply by 10, 100, and 1,000

I can multiply whole numbers and decimals by powers of 10.

Success criteria: I can find the product, show my work, and check that my answer is reasonable.

a. 37 × 10 = __________

b. 406 × 100 = __________

c. 5.28 × 1,000 = __________

a. 6.4 × 100 = __________

b. __________ × 1,000 = 9,000

c. 72 × __________ = 7,200

Support: Use a place-value chart, draw arrows showing digit shifts, or rehearse your explanation with a partner before writing.

Part C: Divide by Powers of 10

I can divide whole numbers and decimals by 10, 100, and 1,000.

Success criteria: I can find the quotient and explain how division changes the place value of each digit.

a. 5,600 ÷ 10 = __________

b. 48,000 ÷ 100 = __________

c. 7.2 ÷ 10 = __________

d. 36.5 ÷ 100 = __________

3,450 ÷ 1,000 = __________

When dividing by 1,000, each digit shifts ______ place-value positions to the ____________________.

Support: Label a place-value chart from thousands to thousandths. Use color-coded arrows or a sentence frame: “Dividing by ______ moves each digit ______ places to the ______.”

Part D: Explain and Apply

I can explain powers-of-10 patterns and use them to solve real-world problems.

Success criteria: I can write an equation, solve accurately, explain my reasoning, and use estimation to check my answer.

Differentiation: Students may use place-value disks, drawings, enlarged charts, oral rehearsal, or a partner sentence frame. Read directions aloud and complete fewer practice calculations when needed while keeping the explanation task.

Answer Key — Final Page

1. First pattern: multiplied by 10; power 10^1. Second pattern: divided by 10; power 10^1.

2. a. Multiplied by 100. b. Two positions to the left. c. 0.6 × 10^2 = 60.

3. a. 370. b. 40,600. c. 5,280.

4. a. 640. b. 9. c. 100.

5. Answers will vary. Sample: In 5.28 × 1,000, each digit shifts three place-value positions to the left because 1,000 is 10^3. The product is 5,280.

6. a. 560. b. 480. c. 0.72. d. 0.365.

7. 3.45. Each digit shifts three place-value positions to the right, toward smaller place values.

8. Answers will vary. Sample: Multiplying by 10^2 means multiplying by 100, so each digit shifts two places to the left. For example, 6 × 100 = 600.

9. 2.5 × 100 = 250 liters.

10. 4,800 ÷ 1,000 = 4.8. The quotient means 4,800 feet is equal to 4.8 groups of 1,000 feet.

Challenge: Answers will vary. Sample error: 6 × 10^4 = 600. Correction: 6 × 10^4 = 60,000 because 10^4 = 10,000.