Number and Operations in Base Ten
What this domain covers
Number and Operations in Base Ten tests place value through 1,000,000, rounding, fluent addition and subtraction, multi-digit multiplication, and division with remainders. You must align place values, regroup accurately, and judge whether an answer is reasonable.
Core rules to know
- Place value: each place is 10 times the place to its right. In 4,582, the 5 means 500; in 45,820, the 5 means 5,000.
- Rounding: find the target place, look at the digit to its right. 5 or more rounds up; 4 or less rounds down. 47,362 rounded to the nearest thousand is 47,000.
- Multiplication: use partial products or the standard algorithm. For two-digit factors, multiply by the ones, then by the tens, and align the second row one place left.
- Division: divide, multiply, subtract, bring down, repeat. The remainder must be less than the divisor.
- Reasonableness: estimate first. If 28 × 145 is about 30 × 150 = 4,500, an answer near 4,060 is plausible.
Worked example
A school orders 28 boxes with 145 pencils in each box. How many pencils? 145 × 28 = 145 × 20 + 145 × 8 = 2,900 + 1,160 = 4,060 pencils. The partial products keep place value visible: 20 × 145 is 2,900, not 290.
Traps that cost marks
- Forgetting the zero placeholder when multiplying by the tens digit.
- Rounding to the wrong place or looking at the wrong digit.
- Misaligning digits by place value during addition or multiplication.
- Writing a remainder equal to or larger than the divisor.
- Accepting an exact answer that is far from a quick estimate.