Place Value Understanding for Whole Numbers
A digit 7 is in the hundreds place in the number 3,742. How many times as much does this 7 represent as a digit in the tens place?
10 times as much
36 x 5
180
Estimate the quotient: 432 ÷ 8 (then find the exact quotient
54
amie multiplies 45 × 6, then adds 30. What is the result? Write the expression and evaluate. (Order of operations: multiplication before addition.)
45 × 6 = 270; 270 + 30 = 300.
Write 5,000 as a power of 10
5 × 10 to the power of 3
Use place-value reasoning to compute 4,200 × 30
126,000 (4,200 × 30 = 4,200 × (3 × 10) = 12,600 × 10)
Divide 1,296 ÷ 12 using a method based on place value or partial quotients; show any remainder.
108 remainder 0 (1,296 ÷ 12 = 108)
Find the value of 8 × (25 + 15). Show how the grouping symbol changes your steps.
8 × (25 + 15) = 8 × 40 = 320.
If you multiply 8,203 by 10, how does each digit shift and what is the new number?
82,030. (8,203 × 10 = 82,030; each digit shifts one place to the left.)
Multiply 237 × 40 using a place-value method
9,480 (237 × 40 = 237 × 4 × 10 = 948 × 10)
Use a tape diagram or area model to divide 3,504 ÷ 16. Show steps and the remainder
219 remainder 0 (3,504 ÷ 16 = 219)
Convert 3 kilometers to meters
3,000 m. (Multiply by 1,000: 3 × 10 to power of 3 = 3,000
Convert 84 meters to millimeters.
84,000 mm. (Multiply by 1,000: 84 × 10 to the power of 3 = 84,000.)
Use an area model or tape-diagram idea to calculate 1,206 × 8. Show partial products.
9,648 (1,206 × 8 = 1,000×8 + 200×8 + 6×8)
A teacher has 4,875 stickers. She puts them equally into 25 student packs. Use vertical form or partial-quotient reasoning to find how many stickers per pack and any remainder.
195 remainder 0 (4,875 ÷ 25 = 195)
Convert 12,000 meters to kilometers
12 km. (Divide by 1,000: 12,000 ÷ 10 to the power of 3 = 12.)
Explain why dividing 56,400 by 100 results in 564. Use place-value language (how digits shift).
56,400 ÷ 100 = 564 (digits shift two places to the right).
A factory makes 1,245 toys each day. How many toys are made in 360 days? Show multiplication using place-value break-down.
448,200 (1,245 × 360 = 1,245 × (36 × 10) = (1,245 × 36) × 10; compute 1,245×36 = 44,820, then ×10 = 448,200).
Divide 9,743 ÷ 23. First estimate the quotient, then compute using partial quotients or long division. Record any remainder.
423 remainder 14 (9,743 ÷ 23 ≈ 423 R14)
Convert 250 grams to milligrams
250,000 mg. (Multiply by 1,000: 250 × 10 to the power of 3 = 250,000.)