Number and Operations in Base Ten
What you must understand
Grade 4 extends place value to one million: reading, writing, and comparing multi-digit whole numbers in standard, expanded, and word form. You must round whole numbers to any place, and multiply up to four-digit numbers by one-digit numbers and two-digit by two-digit numbers using place-value strategies, partial products, or the standard algorithm. Division involves up to four-digit dividends with one-digit divisors, including remainders, and you should explain the meaning of a remainder in context.
Traps to watch
- Place-value slips. In 407,382 the digit 4 means 400,000, not 4,000. Align digits by place when adding or multiplying.
- Rounding direction. Look only at the digit immediately to the right of the target place. 6,849 rounded to the nearest hundred is 6,800 because the tens digit is 4.
- Partial products. When multiplying 23 x 14, remember the second row shifts one place left (230, not 23).
- Remainders. A remainder must be smaller than the divisor. In a sharing problem the remainder may mean "one more group is needed" or "left over," depending on the question.
Rule of thumb
Estimate first. Round each factor to a friendly number, multiply mentally, and use that estimate to check whether your exact answer is reasonable. If your answer is far from the estimate, look for a place-value error.
Worked example
Round 47,362 to the nearest thousand, then multiply 312 by 4. Rounding: the hundreds digit is 3, so round down to 47,000. Multiplying: 312 x 4 = (300 x 4) + (12 x 4) = 1,200 + 48 = 1,248. Estimate check: 300 x 4 = 1,200, so 1,248 is reasonable.