Tanya is helping a third‑grade student check for mathematical reasonableness. If the student calculated 8 + 7 = 21, which estimation technique could help?

Tanya is helping a third‑grade student check for mathematical reasonableness. If the student calculated 8 + 7 = 21, which estimation technique could help?

• A. Doubling
• B. Halving
• C. Rounding to the nearest ten
• D. Breaking apart numbers and recombining

Answer: (A)

Estimating by comparing to doubling is a quick way to check sums when the addends are close in value. With 8 and 7, you can think of the total as about twice one of the numbers: 2 × 8 is 16 (and 2 × 7 would be 14). So the sum should be around 15–16. Seeing 21 sticks out as far from that estimate, signaling a likely miscalculation. Doubling gives a fast, precise enough check for small, nearby numbers. Rounding to the nearest ten would give 20, which is also a rough check but less precise for such small numbers. Breaking apart and recombining could work to get to 15 exactly, but it takes more steps; doubling is the quickest way to verify reasonableness here.

Estimating by comparing to doubling is a quick way to check sums when the addends are close in value. With 8 and 7, you can think of the total as about twice one of the numbers: 2 × 8 is 16 (and 2 × 7 would be 14). So the sum should be around 15–16. Seeing 21 sticks out as far from that estimate, signaling a likely miscalculation. Doubling gives a fast, precise enough check for small, nearby numbers.

Rounding to the nearest ten would give 20, which is also a rough check but less precise for such small numbers. Breaking apart and recombining could work to get to 15 exactly, but it takes more steps; doubling is the quickest way to verify reasonableness here.