Rationale
Isabella wrote the estimate that is closest to the actual value.
Isabella's expression, 1,590 × 8, provides an estimation that closely approximates the actual sum of 1,592 + 8, which equals 1,600. This calculation is more accurate than the others because it rounds 1,592 to the nearest hundred and uses the correct multiplier.
A) Isabella
Isabella's estimate of 1,590 × 8 equals 12,720. Although it appears to be a large number, it effectively rounds 1,592 down to 1,590 and maintains the multiplier of 8, yielding a value that serves as a close approximation for the addition problem presented.
B) Jayden
Jayden's estimate of 1,590 × 10 equals 15,900. This estimate is significantly higher than the actual sum of 1,600, as it rounds 1,592 too low while using an inflated multiplier of 10, which leads to an inaccurate approximation of the sum.
C) Michael
Michael's expression of 1,600 × 8 results in 12,800. Although this is a close approximation, it rounds the original value of 1,592 up to 1,600 and, when multiplied by 8, overshoots the actual result of 1,600 from the addition.
D) Sarah
Sarah's estimate of 1,600 × 10 equals 16,000, which is an overestimation compared to the actual sum of 1,600. This choice not only rounds the initial value too high but also uses a multiplier of 10, compounding the discrepancy from the actual value.
Conclusion
In this estimation task, Isabella's response of 1,590 × 8 provides the closest approximation to the actual sum of 1,592 + 8. While other students' estimates involve either incorrect rounding or excessive multipliers, Isabella's method effectively aligns with the intended calculation, demonstrating a clearer understanding of estimation principles.
