Number and Operations in Base Ten (Grade 3)
Number and Operations in Base Ten in Grade 3 focuses on whole numbers to 1,000: place value, rounding to the nearest 10 or 100, fluent addition and subtraction within 1,000, and multiplying one-digit numbers by multiples of 10. The NYS test asks students to choose and explain strategies, not just produce answers.
Place value and rounding
- Each digit has a value based on its place: in 472, the 4 means 400, the 7 means 70, and the 2 means 2.
- To round to the nearest 10, find the two tens the number sits between, locate the midpoint, and round up when the digit is 5 or more: 647 is between 640 and 650, past the midpoint 645, so it rounds to 650.
- To round to the nearest 100, use the two hundreds and the midpoint ending in 50. By the usual convention, 650 rounds to 700.
Adding, subtracting, and multiplying by tens
- Use strategies based on place value: partial sums, compensation, or an open number line.
- Addition and subtraction undo each other, so a subtraction can be checked by adding.
- 4 x 60 means 4 x 6 tens = 24 tens = 240.
Worked example
347 + 285. Add hundreds: 300 + 200 = 500. Add tens: 40 + 80 = 120. Add ones: 7 + 5 = 12. Total: 500 + 120 + 12 = 632. Check by rounding: about 350 + 280 = 630, so 632 is reasonable.
Traps
Forgetting to regroup 12 ones as 1 ten and 2 ones. Losing the zero in 4 x 60 and writing 24. Rounding 647 to 640 because the 4 looks small. Subtracting the smaller digit from the larger regardless of place.