Number and Operations in Base Ten
Number and Operations in Base Ten in Grade 3 focuses on three big ideas: rounding whole numbers to the nearest 10 or 100, adding and subtracting within 1,000 with fluency, and multiplying one-digit numbers by multiples of 10.
Core rules
- Place value: in 472, the 4 means 400, the 7 means 70, and the 2 means 2.
- Rounding: find the two tens or hundreds the number sits between and choose the closer one (3.NBT.A.1). 472 is between 400 and 500; it is 28 from 500 and 72 from 400, so it rounds to 500.
- When adding or subtracting, line up place values and regroup one place at a time (3.NBT.A.2).
- Multiply a one-digit number by a multiple of 10 by using the basic fact and preserving place value: 4 × 7 = 28, so 4 × 70 = 280, because 70 = 7 × 10 (3.NBT.A.3).
Worked example
503 − 278. Start in the ones place: 3 − 8 cannot be done, so regroup. There is no ten to borrow, so regroup 1 hundred as 10 tens, then 1 ten as 10 ones. Now 503 becomes 4 hundreds, 9 tens, and 13 ones. Subtract: 13 − 8 = 5 ones; 9 − 7 = 2 tens; 4 − 2 = 2 hundreds. The answer is 225. Check by adding: 225 + 278 = 503.
Traps that cost marks
- Subtracting the smaller digit from the larger one instead of regrouping, such as writing 8 − 3 = 5 in the ones place of 503 − 278.
- Forgetting to reduce the hundreds digit after regrouping across a zero.
- Rounding 450 down to 400; by the halfway rule it rounds to 500.
- Writing 4 × 70 = 28. The place value must be preserved: 280.
- Accepting an exact answer without estimating first to see whether it is reasonable.